Patent Publication Number: US-2023140305-A1

Title: Optical waveguide structure with partially overlapping loops in direction dependent material

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation in part application of U.S. Pat. Application No. 17/450,038 filed Oct. 5, 2021, and entitled “Optical Waveguide Structure With Partially Overlapping Loops In Direction Dependent Material,” attorney docket number 20-3231-US-NP, which is related to and claims the benefit of priority of provisional U.S. Pat. Application Serial No. 63/088,220, entitled “Directional Phase Matching (DPM) Optical Waveguide”, filed on Oct. 6, 2020; provisional U.S. Pat. Application Serial No. 63/201,661, entitled “Directional Phase Matching Optical Waveguide”, filed on May 7, 2021; and provisional U.S. Pat.ent Application Serial No. 63/201,664, entitled “Nonlinear Optical Waveguide Structures for Light Generation and Conversion”, filed on May 7, 2021, all of which are hereby incorporated by reference. 
     This application is related to U.S. Pat. Application No. 17/450,031 filed on Oct. 5, 2021 and entitled “Optical Waveguide Structure With Triple Partially Overlapping Loops”, attorney docket number 20-3178-US-NP, and U.S. Pat. Application No. ______ filed on ______, entitled “Optical Waveguide Structure With Partially Overlapping Loops In Direction Dependent Material,” attorney docket number 20-3178-US-CIP, assigned to the same assignee, and incorporated herein by reference in their entirety. 
    
    
     BACKGROUND INFORMATION 
     1. Field 
     The present disclosure relates generally to optical waveguide structures and, in particular, to phase matching optical waveguide structures with partially overlapping loops to generate light using non-linear optical processes. 
     2. Background 
     Optical waveguides are physical structures that guide electromagnetic waves in an optical spectrum. Optical waveguides can be used as components in integrated optical circuits. With respect to quantum communications and processing, nonlinear optical material structures can be used to create photon transmitters, repeaters, and other quantum devices for communications. Nonlinear optical structures can be used to change the light passing through them depending on factors such as orientation, temperature, wavelength of light, polarization of light, and other factors. For example, a waveguide with light of a blue wavelength passing through the waveguide can generate one or more photons of light that has a longer wavelength, such as green or red, and a correspondingly lower photon energy. This type of conversion can be performed using waveguides that incorporate a material having a second order nonlinear optical susceptibility or a third order nonlinear optical susceptibility. 
     Current waveguides and structures that implement second order nonlinear optical processes are not as efficient as desired. Therefore, it would be desirable to have a method and apparatus that take into account at least some of the issues discussed above, as well as other possible issues. For example, it would be desirable to have a method and apparatus that overcome a technical problem with increasing efficiency in generating light in nonlinear optical waveguide structures. 
     SUMMARY 
     In one illustrative embodiment, an optical waveguide structure comprises a nonlinear optical waveguide, a set of tuning optical waveguides, a set of wavelength selective couplers that couples light between the nonlinear optical waveguide and a tuning optical waveguide based on a wavelength of light, and a set of phase shifters located along one or more tuning optical waveguides in the set of tuning optical waveguides. 
     In another illustrative embodiment, an optical waveguide structure comprises a nonlinear optical waveguide, a tuning optical waveguide, a set of wavelength selective couplers that couples light between the nonlinear optical waveguide and the tuning optical waveguide based on a wavelength of light, and a set of phase shifters located along the set of tuning optical waveguide. 
     In yet another illustrative embodiment, a method facilitates a nonlinear optical interaction process. A wavelength selective coupler couples a first wavelength light from a first segment in a nonlinear optical waveguide into a second segment in the nonlinear optical waveguide. The wavelength selective coupler couples a second wavelength light from the first segment in the nonlinear optical waveguide into a tuning optical waveguide. A phase shifter applies an activation to the tuning optical waveguide to change a phase shift for the second wavelength light in the tuning optical waveguide. 
     The features and functions can be achieved independently in various embodiments of the present disclosure or may be combined in yet other embodiments in which further details can be seen with reference to the following description and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The novel features believed characteristic of the illustrative embodiments are set forth in the appended claims. The illustrative embodiments, however, as well as a preferred mode of use, further objectives and features thereof, will best be understood by reference to the following detailed description of an illustrative embodiment of the present disclosure when read in conjunction with the accompanying drawings, wherein: 
         FIG.  1    is an illustration of a high level block diagram of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG.  2    is another illustration of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG.  3    is an illustration of a block diagram of optical waveguides in accordance with an illustrative example; 
         FIG.  4    is an illustration of loops in optical waveguides in accordance with an illustrative embodiment; 
         FIG.  5    is an illustration of a block diagram of a configuration for nonlinear optical waveguides in accordance with an illustrative embodiment; 
         FIG.  6    is an illustration of phase shifters used to obtain at least one of resonance matching or roundtrip phase matching in accordance with an illustrative embodiment; 
         FIG.  7    is an illustration of a cross-section of an optical waveguide in accordance with an illustrative embodiment; 
         FIG.  8    is an illustration of light coupling by a wavelength-selective coupler in accordance with an illustrative embodiment; 
         FIG.  9    is an illustration of light coupling by a wavelength-selective coupler in accordance with an illustrative embodiment; 
         FIG.  10    is an illustration of light coupling by a wavelength-selective coupler in accordance with an illustrative embodiment; 
         FIG.  11    is an illustration of simulation results of light coupling by a wavelength-selective coupler in accordance with an illustrative embodiment; 
         FIG.  12    is an illustration of simulation results of light coupling by a wavelength-selective coupler is in accordance with an illustrative embodiment; 
         FIG.  13    is an illustration of an optical waveguide structure with five optical waveguides in accordance with an illustrative embodiment; 
         FIG.  14    is an illustration of an optical waveguide structure with five optical waveguides in accordance with an illustrative embodiment; 
         FIG.  15    is an illustration of an optical waveguide structure with five optical waveguides in accordance with an illustrative embodiment; 
         FIG.  16    is an illustration of an optical waveguide structure with five optical waveguides in accordance with an illustrative embodiment 
         FIG.  17    is an illustration of an optical waveguide structure with five optical waveguides in accordance with an illustrative embodiment; 
         FIG.  18    is an illustration of an optical waveguide structure with ten optical waveguides in accordance with an illustrative embodiment; 
         FIG.  19    is an illustration of a flowchart of a process for a non-linear optical process in accordance with an illustrative embodiment; 
         FIG.  20    is an illustration of a flowchart of additional operations for a process for a non-linear optical process in accordance with an illustrative embodiment; 
         FIG.  21    is an illustration of a flowchart of additional operations for a process for a non-linear optical process in accordance with an illustrative embodiment; 
         FIG.  22    is an illustration of a flowchart of an additional operation for a process for a non-linear optical process in accordance with an illustrative embodiment; 
         FIG.  23    is an illustration of a flowchart of additional operation for a process for a non-linear optical process in accordance with an illustrative embodiment; 
         FIG.  24    is an illustration of a flowchart of an additional operation for a process for a non-linear optical process in accordance with an illustrative embodiment; 
         FIG.  25    is an illustration of a flowchart of an additional operation for a process for a non-linear optical process in accordance with an illustrative embodiment; 
         FIG.  26    is an illustration of a flowchart of an additional operation for a process for a non-linear optical process in accordance with an illustrative embodiment; 
         FIG.  27    is an illustration of a block diagram of a product management system in accordance with an illustrative embodiment; 
         FIG.  28    is an illustration of a block diagram of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG.  29    is an illustration of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIGS.  30 A and  30 B  are illustrations of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIGS.  31 A and  31 B  are illustrations of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIGS.  32 A and  32 B  are illustrations of a block diagram of routes for light traveling through an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG.  33    is an illustration of graphs of the effect of waveguide cross-sectional dimensions on the phase walk-off associated with imperfect wave vector matching in accordance with an illustrative embodiment; 
         FIG.  34    is an illustration of an optical waveguide structure with phase shifters for tuning light in separate tuning optical waveguides for signal light and for idler light in accordance with an illustrative example; 
         FIG.  35    is an illustration of an optical waveguide structure with phase shifters for tuning light in accordance with an illustrative example; 
         FIG.  36    is an illustration of a graph of light generation in accordance with an illustrative embodiment; 
         FIGS.  37 A- 37 G  are illustrations of cross-sections for nonlinear optical waveguide structures in accordance with an illustrative embodiment; 
         FIG.  38    is an illustration of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG.  39    is an illustration of an optical waveguide structure with offset tuning optical waveguides in accordance with an illustrative embodiment; 
         FIG.  40    is an illustration of an optical waveguide structure formed on an xy plane in accordance with an illustrative embodiment; 
         FIGS.  41 A and  41 B  are illustrations of phase shifter cross sections in accordance with an illustrative embodiment; 
         FIG.  42    is an illustration of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG.  43    is an illustration of an optical waveguide structure with separate tuning optical waveguides for signal light and for idler light in accordance with an illustrative embodiment; and 
         FIG.  44    is an illustration of an optical waveguide structure with two groups of segments in which one group of the segments is associated with tuning optical waveguides in accordance with an illustrative embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The illustrative embodiments recognize and take into account one or more different considerations. For example, the illustrative embodiments recognize and take into account that a nonlinear optical structure can function as a resonator such that light of a particular wavelength in resonance with the resonator can travel over a longer distance in a nonlinear optical waveguide of the nonlinear optical structure as compared to light of other wavelengths that are not in resonance with the resonator. 
     The illustrative embodiments recognize and take into account that the loss of light from a resonator occurs when some of the light exits the resonator instead of continuing to travel in the resonator. The resonator selects certain wavelengths of light to continue traveling in the resonator. The illustrative embodiments recognize and take into account that different resonators can have different resonances that match to different wavelengths of light. The illustrative embodiments recognize and take into account that the same resonator can have multiple resonances, with different resonances matching to different wavelengths of the light. 
     The illustrative embodiments recognize and take into account that currently used nonlinear optical waveguide structures employ a resonator that implements three-wave mixing and four-wave mixing processes to generate light of one wavelength from light of a different wavelength. In other words, the process changes the wavelength of the light. The illustrative embodiments recognize and take into account that spontaneous parametric down conversion (SPDC) is an example of a three-wave mixing process for generating certain wavelengths of light, such as a signal light and an idler light, in response to the introduction of source light of a different wavelength, such as a pump light, into the nonlinear optical waveguide structure. The illustrative embodiments recognize and take into account that spontaneous parametric down conversion can generate a pair of photons, such as a signal photon and an idler photon, from a pump photon. 
     The illustrative embodiments recognize and take into account that the nonlinear optical waveguide structure, in forming a ring-shaped route for the travel by the light, can employ a nonlinear optical waveguide in which light of three wavelengths involved in spontaneous parametric down conversion and spontaneous four-wave mixing propagates within the nonlinear optical waveguide structure. The illustrative embodiments recognize and take into account that the ring-shaped route formed from the nonlinear optical waveguide structure can be a closed path of a ring resonator. The illustrative embodiments recognize and take into account that for current nonlinear optical waveguides structures, different wavelengths of the light must match resonances of the same resonator. The illustrative embodiments recognize and take into account that this requirement results in severe limitation on allowable wavelengths for the signal light and the idler light that are generated. 
     The illustrative embodiments recognize and take into account that current optical waveguide structures can have optical structures to input and output light from the ring resonator. The illustrative embodiments recognize and take into account that the addition of these input and output optical structures is unhelpful for achieving the resonance match because the three wavelengths for the pump light, the signal light, and the idler light propagate through the ring resonator and are constrained to match the modes of the same ring resonator. 
     The illustrative embodiments recognize and take into account that current nonlinear optical waveguide structures can employ two coupled ring resonators having different values for their circumferences. The illustrative embodiments recognize and take into account that these different values can result in different sets of resonance modes for the two resonators. The illustrative embodiments recognize and take into account that a first resonator can have all three wavelengths for the pump light, the signal light, and the idler light matched to the modes for the first resonator. The illustrative embodiments recognize and take into account that the second resonator can have modes matched to the wavelengths of the signal light and the idler light. The illustrative embodiments recognize and take into account that these two coupled resonators still have the same limitations on resonance matching as a single ring resonator since wavelengths of the signal light and of the idler light must match with resonances of both resonators. The illustrative embodiments recognize and take into account that the use of three coupled ring resonators may provide some improvement, but still have limitations because at least some of the light from all of the three wavelengths travels through all three rings in the current nonlinear optical waveguide structures. 
     The illustrative embodiments recognize and take into account that current nonlinear optical waveguide structures employ multiple resonators that are coupled together directly through common wavelengths and not through a nonlinear optical process. The illustrative embodiments recognize and take into account that at least some light for all of the wavelengths travel through all of these multiple resonators. In other words, the illustrative embodiments recognize and take into account that the light with different wavelengths and traveling through all of the resonators is resonant with each of the individual resonators that are coupled together. 
     With currently used spontaneous parametric down conversion or spontaneous four-wave mixing, all three wavelengths involved in the nonlinear optical process are adjusted to match resonances of the same ring resonator or to match common resonances of multiple coupled rings. However, this type of adjustment of the wavelengths may not be possible if an entangled photon pair, such as entangled pair of idler and signal photons, is used in a quantum photonic circuit that also contains other sources of such photon pairs. The need in quantum photonics to perform optical interference functions involving photons produced by different sources of entangled photons may require those photons to have the same wavelength, so that photons can be indistinguishable. 
     As a result, adjusting the wavelengths associated with a first ring resonator whose output photons are involved in an optical interference function can cause a need to also adjust the wavelengths associated with a second ring resonator whose output photons are interfered with the photons from the first ring resonator. However, if those two ring resonators are not identical, such adjustment may be beyond what is permitted by the spectral width of the resonances of the two ring resonators. 
     For example, a departure of a dimension of the fabricated waveguide, such as the waveguide width, by only 1-2 nm would shift the resonance wavelength beyond the spectral width associated with a quality factor (Q) of 10 3 . Resonators with a higher Q have resonances with narrower spectral width, thereby making them impractical for use in quantum photonic circuits. Thus, if multiple currently available ring resonators are used in a quantum photonic circuit, those resonators would need to have a low Q. 
     As a result, the nonlinear optical interaction distance for producing the entangled photon pairs by spontaneous parametric down conversion or spontaneous four-wave mixing would be much shorter and the photon-pair generation rates would be much lower. 
     The optical waveguide structure in the illustrative examples provides design flexibility to enable three loops through the waveguides to have resonances that correspond to three pre-specified wavelengths. Also, if multiple optical waveguide structures are used together in a quantum photonic circuit, these optical waveguide structures can be adjusted to make the resonances of the optical waveguide structures correspond to specified wavelengths. This type of adjustment is in contrast to having all of the wavelengths adjusted to correspond to one resonator. Thus, the loops in the optical waveguide structures in a quantum photonic circuit can have a higher Q, enabling those optical waveguide structures to generate photon pairs at higher generation rates. 
     In an illustrative example, the optical waveguide structure can be a triple partially overlapping loops for entanglement (TriPOLE) optical waveguide structure that is used in illustrative examples to produce entangled photon pairs by nonlinear optical (NLO) processes. These nonlinear optical processes can be, for example, spontaneous parametric down conversion and spontaneous four-wave mixing. The two entangled photons produced by spontaneous parametric down conversion can be entangled when those photons are produced from the same pump photon. In a similar fashion, the two entangled photons produced by spontaneous four-wave mixing can be entangled when those photons are produced from the same two degenerate pump photons. 
     In this illustrative example, nonlinear optical waveguides in the form of ring resonators can be used to increase the generation rate of these entangled photon pairs, comprising a signal photon and an idler photon. In a high-Q ring resonator, light can travel many times around the circumference of the ring resonator. Thus, the interaction length of a ring resonator can be many times greater than its physical size. In implementing spontaneous parametric down conversion or spontaneous four-wave mixing with three partially overlapping ring resonators as in this example, all three wavelengths of light involved in the nonlinear optical process correspond to resonances of their individual resonators. 
     In an illustrative example, the optical waveguide structure is configured such that light of a particular wavelength can travel on a particular loop through the optical waveguide structure in which the loop is present for that particular wavelength of the light. In the illustrative examples, the loops are partially overlapping such that light of two different wavelengths are not required to travel along the same exact loop. 
     In one illustrative example, an optical waveguide structure comprises a main nonlinear optical waveguide; an extension optical waveguide; a secondary optical waveguide; a first wavelength-selective coupler; and a second wavelength-selective coupler. The first wavelength-selective coupler optically couples a first main location in the main nonlinear optical waveguide and a primary location in the extension optical waveguide to each other. The second wavelength-selective coupler optically couples a second main location in the main nonlinear optical waveguide and a secondary location in the extension optical waveguide to each other. The first wavelength-selective coupler also optically couples a first main location in the main nonlinear optical waveguide and a first location in the secondary optical waveguide to each other. The second wavelength-selective coupler also optically couples a second main location in the main nonlinear optical waveguide and a second location in the secondary optical waveguide to each other. 
     With this example, light of different wavelengths travels on different loops in the optical waveguide structure. A route is a path in which the light travels. In this illustrative example, a loop is a closed route. For example, a first loop can be present in which light of a first wavelength (a first-wavelength light) travels on a first loop having a first length. This first loop can extend through the main nonlinear optical waveguide and a portion of an extension optical waveguide. A second loop can extend through a portion of the main nonlinear optical waveguide and a portion of a secondary optical waveguide. Light of a second wavelength (a second-wavelength light) can travel in the second loop having a second length. The second length can be different from the first length. 
     In this example, the first wavelength-selective coupler and the second wavelength-selective coupler can be selected to cause light of a particular wavelength to travel from one optical waveguide to another optical waveguide. For example, the first wavelength-selective coupler can cause the second-wavelength light to be coupled from the main nonlinear optical waveguide to the secondary optical waveguide. The second wavelength-selective coupler can cause the second-wavelength light to be coupled from the secondary optical waveguide back to the main nonlinear optical waveguide. The second length is determined by the first-main and second-main locations and by the first-secondary and second-secondary locations as well as by the length of the secondary optical waveguide portion (or portions) between these first-secondary and second-secondary locations. The length of the secondary optical waveguide portion (or portions) between the first-secondary and second-secondary locations can be selected to obtain a desired value for the second length. 
     The length of the portions of secondary optical waveguide are selected to achieve a desired value for the second length. This desired value can be selected to achieve a resonance condition for a particular wavelength of light. 
     In this example, the first wavelength-selective coupler also can cause the first-wavelength light to be coupled from the main nonlinear optical waveguide to the extension optical waveguide. The second wavelength-selective coupler can cause the first-wavelength light to be coupled from the extension optical waveguide back to the main nonlinear optical waveguide. The first length is determined by first main location and the second main location in the main nonlinear optical waveguide, the primary-extension location and secondary-extension location in the extension waveguide as well as by the length of the primary optical waveguide portion between these primary-extension and secondary-extension locations. The length of the primary optical waveguide portion between these primary-extension and secondary-extension locations can be selected to obtain a desired value for the first length. 
     In the illustrative example, with this optical waveguide structure, the loops for the different light of different wavelengths in the optical waveguides can have lengths that can be selected such that at least one of resonance or round-trip phase matching is present for the different light of different wavelengths traveling on the different routes. 
     As used herein, the phrase “at least one of,” when used with a list of items, means different combinations of one or more of the listed items can be used, and only one of each item in the list may be needed. In other words, “at least one of” means any combination of items and number of items may be used from the list, but not all of the items in the list are required. The item can be a particular object, a thing, or a category. 
     For example, without limitation, “at least one of item A, item B, or item C” may include item A, item A and item B, or item B. This example also may include item A, item B, and item C or item B and item C. Of course, any combinations of these items can be present. In some illustrative examples, “at least one of” can be, for example, without limitation, two of item A; one of item B; and ten of item C; four of item B and seven of item C; or other suitable combinations. 
     In other words, the length can be selected for a loop such that resonance is achieved for the light traveling in a loop. This type of selection of the length can be made for each loop independently of the lengths for other loops in the optical waveguide structure. In the illustrative example, resonance occurs for each wavelength of the light separately from the other wavelengths of the light. 
     Round-trip phase matching can be achieved for the combination of three loops in which three wavelengths of light travel. Round-trip phase matching involves all three wavelengths of the light. In the illustrative example, the lengths of all three loops are selected jointly such that round-trip phase matching is achieved for the nonlinear optical interaction between the three wavelengths of the light. 
     In some illustrative examples, an optical waveguide structure can be a resonator-enhanced structure for nonlinear optical (NLO) three-wave mixing processes. These nonlinear optical three-wave mixing processes can include difference frequency generation, sum frequency generation, and spontaneous parametric down conversion (SPDC). In other illustrative examples, an optical structure can be a resonator-enhanced structure for degenerately pumped or degenerate output nonlinear optical (NLO) four-wave mixing processes. These degenerate output nonlinear optical four-wave mixing processes can be, for example, difference frequency generation, sum frequency generation, and spontaneous four-wave mixing (SFWM). In these illustrative examples, degenerate means at least two of the waves participating in the nonlinear optical process have the same wavelength. Further, a degenerate three-wave mixing process, such as second harmonic generation, can be used. With second harmonic generation, the two input waves have the same wavelength and produce an output wave of a different wavelength. 
     In the illustrative examples, the nonlinear optical processes can involve three distinct wavelengths of light, a first wavelength, a second wavelength, and a third wavelength. The nonlinear optical waveguide structure in the different illustrative examples comprises triple partially overlapping loops for entanglement (TriPOLE). This optical waveguide structure comprises a main nonlinear optical waveguide, a first extension optical waveguide, a second extension optical waveguide, and a third extension optical waveguide in which light of different wavelengths travels in loops that extend through different combinations of these different optical waveguides. A first loop extends through the main nonlinear optical waveguide and a first extension optical waveguide. This first loop is overlapped by parts of two other loops, which are a second loop and a third loop. A second loop extends through the main nonlinear optical waveguide and a second extension optical waveguide. A third loop extends through the main nonlinear optical waveguide and a third extension optical waveguide. These loops can be closed routes that define optical resonators having resonances at specific sets of wavelengths. 
     The parts of the first loop, the second loop and the third loop that are in common with or that extend through the main nonlinear optical waveguide in the optical waveguide structure are the portions of the optical waveguide structure in which the nonlinear optical three-wave mixing or four-wave mixing processes can occur. In the illustrative examples, the first extension optical waveguide is physically separate from the main nonlinear optical waveguide and is connected to the main nonlinear optical waveguide by a first wavelength-selective coupler that selectively couples only the first-wavelength light into that first extension optical waveguide, but does not couple the second-wavelength light or the third-wavelength light into that first extension optical waveguide. In other words, the first wavelength-selective coupler optically connects the first extension optical waveguide to the main nonlinear optical waveguide only for the first-wavelength light. A second wavelength-selective coupler can couple the first-wavelength light from the first extension optical waveguide back into the main nonlinear optical waveguide. 
     In this illustrative example, the second extension optical waveguide and the third extension optical waveguide are connected to the main nonlinear optical waveguide through a segment of a secondary optical waveguide. In this example, the first wavelength-selective coupler couples the second-wavelength light and the third-wavelength light into a first segment of the secondary optical waveguide. A third wavelength-selective coupler selectively couples the second-wavelength light into the second extension optical waveguide, but the third wavelength-selective coupler does not couple the third-wavelength light into that second extension optical waveguide. 
     In other words, the third wavelength-selective coupler optically connects the second extension optical waveguide to the secondary optical waveguide. The third wavelength-selective coupler also selectively couples the third-wavelength light into the third extension optical waveguide, but the third wavelength-selective coupler does not couple the second-wavelength light into that third extension optical waveguide. In other words, this third wavelength-selective coupler optically connects the third extension optical waveguide to the secondary optical waveguide. As a result, the selection is between the second wavelength and the third wavelength. The first wavelength is assumed to not be present in the secondary optical waveguide in this example. 
     In an illustrative example, the first wavelength-selective coupler couples the second-wavelength light from the main nonlinear optical waveguide to travel in the second extension optical waveguide of the second loop, via a third wavelength-selective coupler, but does not couple light of the first wavelength from the main nonlinear optical waveguide to travel in the second extension optical waveguide. The first wavelength-selective coupler also couples the third-wavelength light from the main nonlinear optical waveguide to travel in the third extension optical waveguide of the third loop, via the third wavelength-selective coupler, but does not couple light of the first wavelength from the main nonlinear optical waveguide to travel in the third extension optical waveguide. 
     The third wavelength-selective coupler couples the light of the second wavelength from the main nonlinear optical waveguide, via the first waveguide-selective coupler, to the second extension optical waveguide of the second loop but does not couple light of the first or third wavelengths into the second extension optical waveguide. The third wavelength-selective coupler also couples the light of the third wavelength from the main nonlinear optical waveguide, via the first wavelength-selective coupler, to travel in the third extension optical waveguide of the third loop but does not couple the light of the first or second wavelengths into the third extension optical waveguide. Thus, only the second-wavelength light travels a second length through the entire second loop. Also, only the third-wavelength light travels a third length through the entire third loop. The first-wavelength light travels only a first length through the first loop that includes the main nonlinear optical waveguide and the first extension optical waveguide, but does not include the second extension optical waveguide or the third extension optical waveguide. 
     The main nonlinear optical waveguide is common to all three loops. The first-wavelength light travels in a first loop that includes the main nonlinear optical waveguide and the first extension optical waveguide. In this example, the first loop also can include the first wavelength-selective coupler and the second wavelength-selective coupler. The second-wavelength light travels in a loop that includes the main nonlinear optical waveguide and the second extension optical waveguide. The third-wavelength light travels in a third loop that includes the main nonlinear optical waveguide and the third extension optical waveguide. Each of the three loops has a length that is designed to be resonant for the light that travels in the loop. The three loops can have different lengths. 
     The length of the first loop for the light of the first wavelength can be selected such that the first-wavelength light is at a resonance of a first resonator comprising the main nonlinear optical waveguide and the first extension optical waveguide. 
     The length of the second loop for the light of the second wavelength can be selected such that the second-wavelength light is at a resonance of a second resonator comprising the main nonlinear optical waveguide and the second extension optical waveguide. The length of the third loop for the light of the third wavelength can be selected so that the third-wavelength light is at a resonance of a third resonator formed by the main nonlinear optical waveguide and the third extension nonlinear optical waveguide. 
     In the illustrative example, a loop may traverse one or more of these optical waveguides. The loops through these optical waveguides can partially overlap with each other. In other words, the different loops are not identical to each other but may have overlaps within the optical waveguide structures. 
     Thus, although the propagation constants or wave vectors for the three wavelengths may be different from each other, the light at the three different wavelengths can still be at resonances when propagating in their respective loops in the optical waveguide structure. The propagation can occur such that the light of the three wavelengths can propagate constructively over many cycles through loops within the optical waveguide structure. This type of propagation can occur because the three loops have different lengths. Furthermore, the relative lengths of the three loops can be selected to meet the phase-matching requirement to sustain the nonlinear optical process over an interaction distance that is greater than the length of the main nonlinear optical waveguide in the optical waveguide structure. 
     The phase matching can be a feature distinct from the resonance that occurs for a resonator in the optical waveguide structure. Thus, five constraints may be applied to the nonlinear optical interaction that occurs in the optical waveguide structure. One constraint is on “energy conservation” which constrains the relationship between the three wavelengths. The other four constraints relate to the propagation constants or wave vectors of the light of the three different wavelengths. 
     The phase-matching condition for the nonlinear optical process occurring in the main nonlinear optical waveguide can be described by a phase walk-off and by a constructive interaction distance. The constructive interaction distance is the distance at which a phase walk-off for the nonlinear optical interaction between the light of the three wavelengths equals 180 degrees or n radians. 
     When the phase walk-off has a value between 0 and n radians, the nonlinear optical interaction is “constructive” and transfers power from the pump into the signal and idler. This transfer of power increases the generation of signal and idler light. However, when the phase walk-off has a value between n and 2n radians, the nonlinear optical interaction is “destructive” and transfers power from the signal and idler back to the pump, thereby reducing the generation of signal and idler light. 
     Constructive generation of signal and idler light occurs for values of the phase walk-off between 0 and n, between 2 n and 3 n, between 4 n and 5 n, etc. Destructive generation of signal and idler occurs for values of the phase walk-off between n and 2 n, between 3 n and 4 n, between 5 n and 6 n, etc. 
     Whether the nonlinear optical generation is constructive or destructive can also depend on the sign of the nonlinear optical coefficient of the nonlinear optical material involved in that nonlinear optical process. For the same value of the phase walk-off, if the sign of the nonlinear optical coefficient changes, the generation can change from being constructive to being destructive, and vice versa. 
     In some illustrative examples, the length of the main nonlinear optical waveguide, in which all three wavelengths of light travel, can be set to be no greater than the constructive interaction distance. This length of the main nonlinear optical waveguide can be the length of multiple separate segments. 
     The length of the first extension optical waveguide, the length of the second extension optical waveguide, and the length of the third extension optical waveguide (when present) can be set such that that the roundtrip phase walk-off for the nonlinear optical interaction between the light of the three wavelengths is a specified value. This round-trip phase walk-off can be set equal to zero or as close to being zero as possible, or can be set as close as possible to being a multiple of 2n radians or 360 degrees. 
     In some examples, tuning electrodes can be located at optical waveguides. For example, the first extension optical waveguide can have a set of tuning electrodes that operates to adjust the roundtrip phase of the light of the first wavelength. The second extension optical waveguide can have a set of tuning electrodes that operate to adjust the roundtrip phase of the light of the second wavelength. The third extension optical waveguide can have a set of tuning electrodes that operate to adjust the roundtrip phase of the light of the third wavelength. The main nonlinear optical waveguide can have a set of phase shifters, such as a set of tuning electrodes, that operate to adjust the roundtrip phase of the light of all three wavelengths, and in particular of the first wavelength. Thus, these tuning electrodes can enable adjusting the resonance conditions to compensate for changes in at least one of the wavelengths of the light, the cross-sectional dimensions of the optical waveguides, and environmental conditions, such as temperature, or other factors. These tuning electrodes can also allow the optical waveguide structure to adjust the phase walk-off for the nonlinear optical interaction occurring in the main nonlinear optical waveguide. 
     For example, a structure for spontaneous parametric down conversion can have the light such as, the pump light, supplied to the main nonlinear optical waveguide through an input optical coupler and travel in the first loop. The optical coupler can be connected to an input optical waveguide that receives the pump light. The signal light and the idler light generated by the spontaneous parametric down conversion process would travel in the second loop and the third loop, respectively. 
     A nonlinear optical generation process such as spontaneous parametric down conversion can result in generation of lower intensity light from higher intensity light. A nonlinear optical generation process also can result in the generation of a higher intensity light from a lower intensity light. However, since the efficiency of a nonlinear optical generation process depends on the intensity of the input or source light for that process, which typically is the pump light, a nonlinear optical process typically results in generation of additional lower intensity light from the higher intensity light. Typically, the pump light has an intensity that is at least twice the intensity of the signal light and at least twice the intensity of the idler light. In some examples, such as many examples as spontaneous parametric down conversion, the intensity of the pump light is at least ten times greater than the intensity of the signal light or of the idler light. Thus, even when a phase-matched condition is present, if the pump light is absent from an optical waveguide comprising nonlinear optical material, and only signal and idler light are present, there is much less generation of pump light from that weaker signal and idler light. 
     In the illustrative examples, an optical waveguide structure can comprise a first nonlinear optical waveguide segment, a second nonlinear optical waveguide segment, an extension optical waveguide, a first wavelength-selective coupler, and a second wavelength-selective coupler. A first-wavelength light and a second-wavelength light travel in the first nonlinear optical waveguide segment. A second-order nonlinear optical process such as spontaneous parametric down conversion can occur in the first and second nonlinear optical waveguide segments. The first nonlinear optical waveguide segment has a nonlinear optical coefficient of a first sign. The second nonlinear optical waveguide segment has a nonlinear optical coefficient of a second sign, which is opposite from the first sign. In this illustrative example, this second nonlinear optical segment is part of the second extension waveguide or the third extension waveguide. It is desirable to divert the pump light away from these extension segments for the signal and idler light. In this example these extension segments comprise electro-optic material to enable them to provide voltage-controlled phase shifts. 
     The first wavelength-selective coupler can optically couple a first location in the first nonlinear optical waveguide segment and a primary extension location in the extension optical waveguide to each other such that the first-wavelength light is coupled from the first nonlinear optical waveguide at the first location to the extension optical waveguide at the primary extension location. The second wavelength-selective coupler can optically couple a second location in the first nonlinear optical waveguide segment and a secondary extension location in the extension optical waveguide to each other such that the first-wavelength light is coupled from the extension optical waveguide at the secondary extension location to the main nonlinear optical waveguide at a location in the first nonlinear optical waveguide segment. Thus, the first-wavelength light bypasses the second nonlinear optical waveguide segment that has a nonlinear optical coefficient of a second sign, which is opposite from the first sign. Instead, the first-wavelength light travels only through the first nonlinear optical waveguide segment that has a nonlinear optical coefficient of the first sign. 
     In the illustrative examples, the wavelength-selective couplers enable selective coupling of light in a manner that directs light of different wavelengths to either travel through or to bypass two different nonlinear optical waveguide segments that have nonlinear optical coefficients of opposite sign. 
     Some examples of the optical waveguide structures can avoid undesired effects of the sign reversal in the nonlinear optical coefficient by removing the pump light or by having an absence of a non-linear optical material in part of the loop traversed by the pump light. Other examples of the optical waveguide structures can take advantage of a sign reversal in the nonlinear optical coefficient by adjusting the phase walk-off to compensate for the sign reversal in the nonlinear optical coefficient for two different segments of nonlinear optical waveguide. 
     With reference now to the figures and, in particular, with reference to  FIG.  1   , an illustration of a high level block diagram of an optical waveguide structure is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  100  comprises optical waveguides  102  in which at least one of optical waveguides  102  is comprised of nonlinear optical material  104 . One or more other optical waveguides in optical waveguides  102  can be comprised of at least one of nonlinear optical material  104  or non-nonlinear optical material  105 . In this example, nonlinear optical material  104  can have first sign  107  and second sign  109  for nonlinear optical coefficient  112  for a nonlinear optical interaction of light with nonlinear optical material  104 . As depicted, first sign  107  is opposite of second sign  109 . Nonlinear optical coefficient  112  is a coefficient that quantifies the strength of the nonlinear optical interaction. Nonlinear optical coefficient  112  can be a second order nonlinear optical coefficient or a third order nonlinear optical coefficient depending on the type of optical process implemented in optical waveguide structure  100 . One or more optical waveguides in optical waveguides  102  also can be comprised of an electro-optic material  103 . The refractive index of an electro-optic material  103  can be changed by applying a DC or low-frequency (as compared to the optical frequency) electric field to the material. In some cases, a material can be both a nonlinear optical material  104  as well as an electro-optic material  103 . 
     In this illustrative example, optical waveguide structure  100  can also include at least one of input optical waveguides  164  or output optical waveguides  166 . In this illustrative example, input optical waveguides  164  and output optical waveguides  166  are connected to one or more of optical waveguides  102  using optical couplers  130 . 
     For example, a set of input optical waveguides  164  can input input-light  168  into one or more of optical waveguides  102 . As another example, a set of output optical waveguides  166  can output output-light  170  from one or more of optical waveguides  102 . The input of input light  168  and output of output light  170  can be facilitated by a set of optical couplers  130  that connect the set of input optical waveguides or the set of output optical waveguides to one or more of optical waveguides  102 . 
     As used herein, a “set of” when used with reference items means one or more items. For example, a set of input optical waveguides  164  is one or more of input optical waveguides  164 . 
     In this illustrative example, light generation can be improved for optical waveguide structure  100  using optical waveguides  102  arranged as loops  116  through optical waveguides  102 . In the illustrative example, loops  116  are defined as the course of travel of light  118  within one or more of optical waveguides  102 . In other words, loops  116  are defined as where light  118  travels within optical waveguides  102 . 
     The manner in which optical waveguides  102  are coupled to each other is through mechanisms such as wavelength-selective couplers  114 , which can be used to define loops  116  along which light  118  can travel within optical waveguides  102 . In the illustrative example, loops  116  can use different portions of optical waveguides  102  and wavelength-selective couplers  114  in optical waveguide structure  100 . 
     As depicted, optical waveguide structure  100  also includes wavelength-selective couplers  114  that can be used to define routes  115  in the form of loops  116  for light  118  traveling within optical waveguide structure  100 . These wavelength-selective couplers can selectively direct light  118  from one optical waveguide to another optical waveguide in optical waveguides  102 . 
     Wavelength-selective couplers  114  can take a number of different forms. For example, wavelength-selective couplers  114  can be selected from at least one of a two-waveguide coupler, a multi-mode interference coupler, a pulley coupler, a Mach-Zehnder interferometer, a 4-port micro-ring resonator coupler, or some other suitable wavelength-selective coupler that can couple light and determine which wavelengths of light are directed through coupling from one optical waveguide to another optical waveguide. 
     As used herein, a “number of” when used with reference items means one or more items. For example, a number of different forms is one or more different forms. 
     In this illustrative example, optical waveguides  102  in optical waveguide structure  100  can support the propagation of light  118  through routes  115  in the form of loops  116 , which are closed routes. Light  118  travels within optical waveguides  102  along routes  115 . In the illustrative example, a closed route is a route for which a starting point and ending point are common or for which no distinct starting point that is separate from an ending point is present. The closed route is also referred to as a loop. 
     In this illustrative example, loops  116  can traverse multiple optical waveguides  102  in optical waveguide structure  100 . Loops  116  also can traverse one or more of wavelength-selective couplers  114  in optical waveguide structure  100 . Loops  116  can comprise multiple loops that overlap each other in portions of some of optical waveguides  102  in optical waveguide structure  100  but do not overlap each other for other optical waveguides  102  traversed by a loop of loops  116 . Different wavelengths of light  118  can travel through different loops. In other words, overlap is present between portions of loops  116  for the different wavelengths of light  118  traveling through optical waveguides  102 . 
     As depicted, wavelength-selective couplers  114  can operate to define different loops in loops  116  for the different wavelengths of light  118 , with these different loops having different lengths. 
     As depicted in this illustrative example, nonlinear optical material  104  has nonlinear optical coefficient  112 . In the illustrative example, nonlinear optical coefficient  112  can be a second order nonlinear optical coefficient or a third order nonlinear optical coefficient depending on the type of optical process implemented in optical waveguide structure  100 . 
     Nonlinear polarization can occur in nonlinear optical material  104  in which the material polarization no longer varies linearly with the electric field amplitude. This nonlinear relationship can be expressed as follows: 
     P = χ (1) E + χ (2) EE + χ (3) EEE + ··· 
     where E is the electric field, χ(1) is the linear optical susceptibility, χ(2) is the second order nonlinear optical susceptibility, etc. The nonlinear susceptibilities, such as χ(2) and χ(3), represent the nonlinear parts of the material dipolar characteristics. 
     In this example, the electric field amplitude is the electric field amplitude of the light wave, which is an electromagnetic field. An electromagnetic field has a traveling (or propagating) electric field and a traveling (or propagating) magnetic field. 
     In this illustrative example, nonlinear optical process  140  can be nonlinear optical mixing processes that can occur within optical waveguide structure  100 . These nonlinear optical mixing processes can be used to generate light  118 . For example, the propagation of first-wavelength light  132  can result in the generation of at least one of second-wavelength light  134  or third-wavelength light  136  using one or more nonlinear optical waveguides employing nonlinear optical mixing processes in optical waveguides  102 . 
     In the illustrative example, nonlinear optical mixing processes can include nonlinear optical three-wave mixing processes and nonlinear optical four-wave mixing processes. In this illustrative example, the nonlinear optical three-wave mixing processes and the nonlinear optical four-wave mixing processes can include difference frequency generation (DFG) and sum frequency generation (SFG). The nonlinear optical three-wave mixing processes can also include spontaneous parametric down conversion (SPDC). The nonlinear optical four-wave mixing can also include spontaneous four-wave mixing (SFWM). 
     In this illustrative example, nonlinear optical wave-mixing processes can include three types of light with three distinct wavelengths such as first-wavelength light  132 , second-wavelength light  134 , and third-wavelength light  136 . 
     For example, nonlinear optical process  140  such as spontaneous three-wave mixing is a second-order nonlinear optical process that can occur in an optical waveguide having nonlinear optical material  104  in optical waveguides  102 . In this process, pair of generated photons  142  are generated from source photons  144  in optical waveguides  102  that have nonlinear optical material  104 . Generated photons  142  of a pair can have different wavelengths from each other, such as of second-wavelength light  134  and third-wavelength light  136  and have wavelengths different from the wavelength, such as first-wavelength light  132 , of source photons  144 . 
     In this illustrative example, “resonance matching” means a given wavelength is matched to a resonance of a resonator. A resonator can have many resonances. Also, a resonator can be designed such that different lengths can still produce resonance matching for a particular wavelength of light. Resonance is achieved every time the round-trip phase is a multiple of 2n. In this illustrative example, lengths for loops  116  can be selected such that at least one of resonance matching or roundtrip phase matching is present for different wavelengths of light  118 . 
     The lengths for loops  116  can be selected based on the locations where wavelength-selective couplers  114  connect to optical waveguides  102 . 
     Thus, optical waveguide structure  100  can have multiple optical waveguides in optical waveguides  102  that are configured or constructed to enable the propagation of light  118  of different wavelengths to travel within optical waveguide structure  100  in a constructive manner. In one illustrative example, the light  118  of the different wavelengths can travel on loops  116  in which each loop is selected to enable light  118  of a particular wavelength to travel in a constructive manner. For example, a loop in loops  116  can traverse through both a main nonlinear optical waveguide and extension optical waveguides in optical waveguides  102  that extend the length of the loop in loops  116  for different wavelengths of light beyond that provided by the main nonlinear optical waveguide. 
     Additionally, some loops in loops  116  can extend through both the main nonlinear optical waveguide and one or more parts of a secondary waveguide in addition to or in place of the extension optical waveguides. As a result, a loop in loops  116  for a light of a particular wavelength can traverse one or more of optical waveguides  102 . 
     Thus, although the propagation constants or wave vectors for the light of three wavelengths may be different from each other, the light at the three different wavelengths can still be at resonances when propagating on their respective loops in optical waveguides  102 . The propagation can occur such that light  118  of the three wavelengths can propagate constructively over many cycles through loops  116  within the optical waveguide structure  100 . This type of propagation can occur because loops  116  have different lengths that are selected to be constructive for light of a particular wavelength. 
     Turning next to  FIG.  2   , another illustration of an optical waveguide structure is depicted in accordance with an illustrative embodiment. In the illustrative examples, the same reference numeral may be used in more than one figure. This reuse of a reference numeral in different figures represents the same element in the different figures. 
     As depicted in this illustrative example, optical waveguide structure  100  comprises optical waveguides  102 . As depicted, optical waveguides  102  include main nonlinear optical waveguide  106 , first extension optical waveguide  108 , secondary optical waveguide  113 , and first wavelength-selective coupler  120 , and second wavelength-selective coupler  122 . In this example, main nonlinear optical waveguide  106  comprises a nonlinear optical material  104 . Main nonlinear optical waveguide  106  also can comprise an electro-optic material  103 . First extension optical waveguide  108  and secondary optical waveguide  113  can comprise a nonlinear optical material  104 , a non-nonlinear optical material  105 , or a combination of a nonlinear optical material and one or more non-nonlinear optical materials. Main nonlinear optical waveguide  106  can comprise a single optical waveguide segment or can comprise multiple optical waveguide segments that are physically separate from each other. Secondary optical waveguide  113  likewise can comprise a single optical waveguide segment or can comprise multiple optical waveguide segments that are physically separate from each other. 
     In this example, first-wavelength light  512  of a first wavelength and second-wavelength light  518  of a second wavelength travel in the main nonlinear optical waveguide  106 . As an example, first-wavelength light  512  can be a pump light with second-wavelength light  518  being at least one of a signal light or an idler light. 
     In this illustrative example, first wavelength-selective coupler  120  optically couples first main location  520  in main nonlinear optical waveguide  106  and primary extension location  522  in first extension optical waveguide  108  to each other. First wavelength-selective coupler  120  optically couples these two optical waveguides such that first-wavelength light  512  is coupled from main nonlinear optical waveguide  106  at first main location  520  to first extension optical waveguide  108  at primary extension location  522 . 
     Second wavelength-selective coupler  122  optically couples second main location  524  in main nonlinear optical waveguide  106  and secondary extension location  526  in first extension optical waveguide  108  to each other. In this example, second wavelength-selective coupler  122  optically couples these two optical waveguides such that first-wavelength light  512  is coupled from first extension optical waveguide  108  at secondary extension location  526  to main nonlinear optical waveguide  106  at second main location  524 . 
     In this example, first-wavelength light  512  travels in first loop  528  that traverses through portions of main nonlinear optical waveguide  106 , portions of first extension optical waveguide  108 , first wavelength-selective coupler  120  and second wavelength-selective coupler  122 . In this example, first loop  528  has first length  530 . 
     In this illustrative example, first wavelength-selective coupler  120  also optically couples first main location  520  in main nonlinear optical waveguide  106  and first secondary location  511  in secondary optical waveguide  113  to each other. First wavelength-selective coupler  120  optically couples these two optical waveguides such that second-wavelength light  518  is coupled from main nonlinear optical waveguide  106  at first main location  520  to secondary optical waveguide  113  at first secondary location  511 . 
     In this example, second wavelength-selective coupler  122  also optically couples second main location  524  in main nonlinear optical waveguide  106  and second secondary location  513  in secondary optical waveguide  113  to each other. In this example, second wavelength-selective coupler  122  optically couples these two optical waveguides such that second-wavelength light  518  is coupled from secondary optical waveguide  113  at second secondary location  513  to main nonlinear optical waveguide  106  at second main location  524 . 
     In this illustrative example, second-wavelength light  518  travels in main nonlinear optical waveguide  106  and is coupled from main nonlinear optical waveguide  106  at first main location  520  to secondary optical waveguide  113  at first secondary location  511  and travels in secondary optical waveguide  113  to second secondary location  513 . Second-wavelength light  518  is coupled from secondary optical waveguide  113  at second secondary location  513  to main nonlinear optical waveguide  106  at second main location  524  by second wavelength-selective coupler  122  such that second-wavelength light  518  travels in second loop  534  having second length  536  for second-wavelength light  518 . Second loop  534  includes portions of main nonlinear optical waveguide  106 , portions of secondary optical waveguide  113 , first wavelength-selective coupler  120  and second wavelength-selective coupler  122 . 
     With reference next to  FIG.  3   , an illustration of a block diagram of optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguides  102  comprise main nonlinear optical waveguide  106 , secondary optical waveguide  113 , first extension optical waveguide  108 , second extension optical waveguide  110 , and third extension optical waveguide  119 . Each of these waveguides, main nonlinear optical waveguide  106 , secondary optical waveguide  113 , first extension optical waveguide  108 , second extension optical waveguide  110 , and third extension optical waveguide  119  can comprise one or more segments. 
     As depicted in this example, main nonlinear optical waveguide  106  is an optical waveguide in the set of optical waveguides  102  and is comprised of nonlinear optical material  104 . Additionally, secondary optical waveguide  113  is another optical waveguide in the set of optical waveguides  102  and can be comprised of nonlinear optical material  104  or non-nonlinear optical material  105 . Secondary optical waveguide  113  can comprise a single optical waveguide segment or can comprise multiple optical waveguide segments that are physically separate from each other. First extension optical waveguide  108  is an example of first extension optical waveguide  108  depicted in  FIG.  2   . 
     In this example, light  118  of three different wavelengths can travel through main nonlinear optical waveguide  106 . For example, first-wavelength light  132 , second-wavelength light  134 , and third-wavelength light  136  can travel in main nonlinear optical waveguide  106 . 
     Light of two different wavelengths can travel through secondary optical waveguide  113 . For example, second-wavelength light  134  and third-wavelength light  136  can travel in secondary optical waveguide  113 . 
     As depicted in this example, light  118  traveling through optical waveguides  102  can comprise at least one of first-wavelength light  132 , second-wavelength light  134 , or third-wavelength light  136 . In this particular example, first-wavelength light  132 , second-wavelength light  134 , and third-wavelength light  136  can refer to a pump light  161 , a signal light  163 , and an idler light  165 , but not necessarily in any particular order. 
     For example, first-wavelength light  132  can also be the signal light  163 , second-wavelength light  134  can be the pump light  161 , and third-wavelength light  136  can be idler light  165 . As another example, first-wavelength light  132  can also be pump light  161 , second-wavelength light  134  can be signal light  163 , and third-wavelength light  136  can be idler light  165 . 
     Typically, pump light  161  has an intensity that is at least twice the intensity of signal light  163  and at least twice the intensity of idler light  165 . In some examples, the intensity of pump light  161  is at least ten times greater than the intensity of signal light  163  or of idler light  165 . Typically, pump light  161  is supplied as an input to optical waveguide structure  100 . In some cases, either of signal light  163  and idler light  165  also can be supplied as a second input to optical waveguide structure  100 . Either or both of signal light  163  and idler light  165  can be generated through nonlinear optical process  140  that occurs in portions of optical waveguide structure  100  that comprise a nonlinear optical material  104 . 
     First extension optical waveguide  108  can be comprised of one at least one of nonlinear optical material  104  or a non-nonlinear optical material  105 . In this example, a light such as a pump light  161  can travel through first extension optical waveguide  108 . 
     Second extension optical waveguide  110  can be comprised of at least one of nonlinear optical material  104  or non-nonlinear optical material  105 . A light such as signal light  163  can travel through second extension optical waveguide  110 . 
     Third extension optical waveguide  119  can also be comprised of one of nonlinear optical material  104  and a non-nonlinear optical material  105 . In this example, a light such as idler light  165  can travel through third extension optical waveguide  119 , which can be a nonlinear optical waveguide. 
     In one illustrative example, first extension optical waveguide  108 , second extension optical waveguide  110 , and third extension optical waveguide  119  are not constructed using nonlinear optical material  104 . In another illustrative example, at least one of first extension optical waveguide  108 , second extension optical waveguide  110  and third extension optical waveguide  119  can be constructed using nonlinear optical material  104 . In yet another illustrative example, at least one of first extension optical waveguide  108 , second extension optical waveguide  110  and third extension optical waveguide  119  can be constructed using electro-optic material  103 . Main nonlinear optical waveguide  106  also can be constructed using electro-optic material  103 . 
     In this illustrative example, wavelength-selective couplers  114  include first wavelength-selective coupler  120 , second wavelength-selective coupler  122 , third wavelength-selective coupler  133 , and fourth wavelength-selective coupler  131 . Wavelength-selective couplers  114  can couple light  118  of different wavelengths to different optical waveguides based on the wavelengths in light  118 . For example, wavelength-selective couplers  114  can be configured to couple first-wavelength light  132 , second-wavelength light  134  and third-wavelength light  136  to selected different routes for travel of light  118  through optical waveguides in optical waveguides  102  based on the wavelengths of the light. For another example, wavelength-selective couplers  114  can be configured to couple at least one of second-wavelength light  134  or third-wavelength light  136  to different selected optical waveguides in optical waveguides  102  based on the wavelengths of the light. 
     For example, first wavelength-selective coupler  120  optically couples first main location  146  in main nonlinear optical waveguide  106  and primary first extension location  148  in first extension optical waveguide  108  to each other such that first-wavelength light  132  is coupled from main nonlinear optical waveguide  106  at the first main location  146  to first extension optical waveguide  108  at primary first extension location  148 . 
     First-wavelength light  132  can travel from primary first extension location  148  to secondary first extension location  150  through first extension segment  141 . In this illustrative example, locations at which first wavelength-selective coupler  120  and second wavelength-selective coupler  122  connect to main nonlinear optical waveguide  106  define the extent of main segment  143  of main nonlinear optical waveguide  106 . Further, main nonlinear optical waveguide  106  also can include additional segments. These additional segments can be defined by additional locations in main nonlinear optical waveguide  106  at which those segments are coupled to wavelength-selective couplers. 
     In this example, second wavelength-selective coupler  122  optically couples second main location  152  in main nonlinear optical waveguide  106  and secondary first extension location  150  in first extension optical waveguide  108  to each other such that first-wavelength light  132  is coupled from first extension optical waveguide  108  at secondary first extension location  150  to main nonlinear optical waveguide  106  at second main location  152 . 
     First-wavelength light  132  can travel from second main location  152  to first main location  146  through main segment  143  in main nonlinear optical waveguide  106 . 
     In this illustrative example, first main location  146  and second main location  152  define main segment  143 , which is the portion of main nonlinear optical waveguide  106  through which first-wavelength light  132 , second-wavelength light  134 , and third-wavelength light  136  can travel. In this example, main segment  143  is comprised of a nonlinear optical material  104  and nonlinear optical processes can occur within main segment  143 . 
     In this example, third wavelength-selective coupler  133  optically couples third secondary location  123  in secondary optical waveguide  113  and primary second extension location  156  in second extension optical waveguide  110  to each other such that second-wavelength light  134  is coupled from secondary optical waveguide  113  at third secondary location  123  to second extension optical waveguide  110  at primary second extension location  156 . 
     In this example, second-wavelength light  134  can travel from primary second extension location  156  to secondary second extension location  158  through second extension segment  145  in second extension optical waveguide  110 . 
     Illustration of waveguide configurations for optical waveguides  102  in  FIG.  1   ,  FIG.  2    and  FIG.  3    are presented as illustrations of some configurations for optical waveguides  102 . These illustrations are not meant to limit the manner in which other illustrative examples can be implemented. For example, one or more waveguide segments can be present in addition to or in place of main segment  143 . As yet another example, additional ones of wavelength-selective couplers  114  can be connected to additional segments of main nonlinear optical waveguide  106 , additional segments of secondary optical waveguide  113  and additional extension optical waveguides in optical waveguide  102 . In other illustrative examples, optical waveguide  102  can omit at least one of second extension optical waveguide  110  or third extension optical waveguide  119 . 
     Turning to  FIG.  4   , fourth wavelength-selective coupler  131  optically couples fourth secondary location  125  in the secondary optical waveguide  113  and secondary second extension location  158  in second extension optical waveguide  110  to each other such that second-wavelength light  134  is coupled from second extension optical waveguide  110  at secondary second extension location  158  to secondary optical waveguide  113  at fourth secondary location  125 . Second-wavelength light  134  can travel from primary second extension location  156  to secondary second extension location  158  through second extension segment  145  in second extension optical waveguide  110 . 
     Second-wavelength light  134  can travel from first secondary location  124  to third secondary location  123  through first secondary segment  147  (in  FIG.  4   ). Second-wavelength light  134  can travel from fourth secondary location  125  to second secondary location  129  through second secondary segment  127  (in  FIG.  4   ). Similarly, third-wavelength light  136  can travel from first secondary location  124  to third secondary location  123  through second secondary segment  127  (in  FIG.  4   ). Third-wavelength light  136  can travel from fourth secondary location  125  to second secondary location  129  through second secondary segment  127  (in  FIG.  4   ). In this illustrative example, first-wavelength light  132  can be pump light  161 , second-wavelength light  134  can be one of signal light  163  and idler light  165 . 
     Additionally, third wavelength-selective coupler  133  can optically couple third secondary location  123  in secondary optical waveguide  113  and primary third extension location  171  in third extension optical waveguide  119  to each other such that third-wavelength light  136  is coupled from secondary optical waveguide  113  at third secondary location  123  to third extension optical waveguide  119  at primary third extension location  171 . 
     Furthermore, fourth wavelength-selective coupler  131  can optically couple fourth secondary location  125  in secondary optical waveguide  113  and secondary third extension location  173  in the third extension optical waveguide  119  to each other such that third-wavelength light  136  is coupled from third extension optical waveguide  119  at secondary third extension location  173  to secondary optical waveguide  113  at fourth secondary location  125 . Third-wavelength light  136  can travel from primary third extension location  171  to secondary third extension location  173  through third extension segment  175  in third extension optical waveguide  119 . Third-wavelength light  136  can travel from third secondary location  123  to fourth secondary location  125  through second secondary segment  127  (in  FIG.  4   ). 
     When second extension optical waveguide  110  and third extension optical waveguide  119  are present and coupled to secondary optical waveguide  113 , both second-wavelength light  134  and third-wavelength light  136  can travel through secondary optical waveguide  113 . In this example, first-wavelength light  132  can be pump light  161 , second-wavelength light  134  can be signal light  163 , and third-wavelength light  136  can be idler light  165 . 
     With reference now to  FIG.  4   , an illustration of loops in optical waveguides is depicted in accordance with an illustrative embodiment. In this example, first loop  200 , second loop  202 , and third loop  204  are examples of loops  116  in  FIG.  1   . 
     In this illustrative example, first-wavelength light  132  travels in first loop  200  through main segment  143  between first main location  146  and second main location  152  within the main nonlinear optical waveguide  106  and first extension segment  141  between primary first extension location  148  and secondary first extension location  150  in the first extension optical waveguide  108 . In this example, first loop  200  has first length  191 . 
     Second-wavelength light  134  travels in second loop  202  through first secondary segment  147  between first secondary location  124  and third secondary location  123  in secondary optical waveguide  113 , second extension segment  145  between primary second extension location  156  and secondary second extension location  158  in second extension optical waveguide  110 , second secondary segment  127  between third secondary location  123  and second secondary location  129  in secondary optical waveguide  113 , and main segment  143  in main nonlinear optical waveguide  106 . In this illustrative example, second loop  202  has second length  193  for second-wavelength light  134 . 
     Third-wavelength light  136  travels in third loop  204  through first secondary segment  147  between first secondary location  124  and third secondary location  123  in secondary optical waveguide  113 , third extension segment  175  between primary third extension location  171  and secondary third extension location  173  in third extension optical waveguide  119 , second secondary segment  127  between fourth secondary location  125  and second secondary location  129  in secondary optical waveguide  113 , and main segment  143  in main nonlinear optical waveguide  106 . In this example, third loop  204  as third length  195 . 
     As depicted, first-wavelength light  132  travels within main segment  143  in main nonlinear optical waveguide  106  and first extension segment  141  in first extension optical waveguide  108  in first loop  200 . In this example, first loop  200  has first length  191 . 
     As depicted, first length  191  can also comprise the length of first wavelength-selective coupler  120  and the length of second wavelength-selective coupler  122 . Second length  193  can also comprise the lengths of third wavelength-selective coupler  133  and fourth wavelength-selective coupler  131  as well as the lengths of first wavelength-selective coupler  120  and second wavelength-selective coupler  122 . Third length  195  of third loop  204  can also comprise the lengths of third wavelength-selective coupler  133  and the length of fourth wavelength-selective coupler  131  as well as the lengths of first wavelength-selective coupler  120  and second wavelength-selective coupler  122 . 
     The lengths of first loop  200 , second loop  202 , and third loop  204  can be selected based on the locations where wavelength-selective couplers  114  connect optical waveguides  102  to each other. First length  191  for first loop  200 , second length  193  for second loop  202 , and third length  195  for third loop  204  can have different lengths from each other. 
     For example, first length  191  of first loop  200  can be selected based on a selection of first main location  146  and primary first extension location  148  for first wavelength-selective coupler  120  connecting main nonlinear optical waveguide  106  to first extension optical waveguide  108  and based on a selection of secondary second extension location  158  and second main location  152  for second wavelength-selective coupler  122  connecting first extension optical waveguide  108  to main nonlinear optical waveguide  106 . 
     As another example, second length  193  of second loop  202  can be selected based on a selection of first secondary location  124  in secondary optical waveguide  113 , and second secondary location  129  and primary second extension location  156  for third wavelength-selective coupler  133  connecting secondary optical waveguide  113  to second extension optical waveguide  110 ; and based on a selection of secondary second extension location  158  and third secondary location  123  for fourth wavelength-selective coupler  131  connecting second extension optical waveguide  110  to secondary optical waveguide  113 , and fourth secondary location  125  in secondary optical waveguide  113 . 
     As yet another example, third length  195  of third loop  204  can be selected based on a selection of first secondary location  124  in secondary optical waveguide  113 , and second secondary location  129  and primary third extension location  171  for third wavelength-selective coupler  133  connecting secondary optical waveguide  113  to third extension optical waveguide  119  and based on a selection of secondary third extension location  173  and third secondary location  123  for fourth wavelength-selective coupler  131  connecting third extension optical waveguide  119  to secondary optical waveguide  113 , and fourth secondary location  125  in secondary optical waveguide  113 . 
     With reference next to  FIG.  5   , an illustration of a block diagram of a configuration for nonlinear optical waveguides is depicted in accordance with an illustrative embodiment. In illustrative example, at least one of resonance matching  300  or roundtrip phase matching  302  for optical waveguides  102  can be achieved through the selection of dimensions  304  for optical waveguides  102 . This selection of dimensions  304  can be made in addition to the selection of lengths, such as first length  191 , second length  193 , and second length  193  for loops  116  optical waveguides  102  to achieve at least one of resonance matching  300  or roundtrip phase matching  302  for optical waveguides  102 . 
     For example, main nonlinear optical waveguide  106  can have main cross-section  308  with a set of dimensions  310  in dimensions  304  selected to achieve resonance condition  306  for first-wavelength light  132  traveling in main nonlinear optical waveguide  106 . In this example, secondary optical waveguide  113  can have secondary cross-section  301  with secondary dimensions  303  selected to achieve resonance condition  306  for one of first-wavelength light  132  and second-wavelength light  134  traveling in secondary optical waveguide  113 . 
     As another example, first extension optical waveguide  108  can have first cross-section  312  with first dimensions  314  selected to achieve resonance condition  306  for first-wavelength light  132  traveling in first extension optical waveguide  108 . Further, second extension optical waveguide  110  can have second cross-section  316  with a set of second dimensions  318  selected to achieve resonance condition  306  for second-wavelength light  134  traveling in second extension optical waveguide  110 . Also, third extension optical waveguide  119  can have third cross-section  317  with a set of third dimensions  319  selected to achieve resonance condition  306  for third-wavelength light  136  traveling in second extension optical waveguide  110 . 
     With reference now to  FIG.  6   , an illustration of phase shifters used to obtain at least one of resonance matching or roundtrip phase matching is depicted in accordance with an illustrative embodiment. At least one of manufacturing deviations from specifications, environmental factors, or other influences can affect whether a resonance condition is present during the operation of optical waveguide structure  100 . 
     When roundtrip phase matching  302  in  FIG.  5    is not present during operation of optical waveguide structure  100 , a set of phase shifters  400  can be used to adjust a set of phases  402  for light  118  propagating within optical waveguides  102 . In one illustrative example, the set of phase shifters  400  can be structures that are located adjacent to one or more of optical waveguides  102 ; connected to one or more of optical waveguides  102 ; include part of one or more of optical waveguides  102 ; or a combination thereof. 
     The set of phase shifters  400  can operate to ensure a desired level of roundtrip phase matching  302  is achieved for light  118  that is generated within optical waveguides  102  in optical waveguide structure  100 . As depicted, light  118  can be generated in an optical waveguide in optical waveguides  102  that is comprised of nonlinear optical material  104 . In the illustrative example, main nonlinear optical waveguide  106  is comprised of nonlinear optical material  104 . Optionally, at least one of first extension optical waveguide  108 , second extension optical waveguide  110  or third extension optical waveguide  119  can be comprised of nonlinear optical material  104 . In an illustrative example, at least one of first extension optical waveguide  108 , second extension optical waveguide  110  or third extension optical waveguide  119  can be comprised of electro-optic material  103 . 
     In one illustrative example, a set of phase shifters  400  can be connected to a set of optical waveguides  102  comprising at least one of main nonlinear optical waveguide  106 , first extension optical waveguide  108  second extension optical waveguide  110 , or third extension optical waveguide  119 . The set of phase shifters  400  can apply a set of activations  404  to achieve a change or shift in the phase of at least one of first-wavelength light  132 , second-wavelength light  134 , or third-wavelength light  136  in light  118  traveling in the set of optical waveguides  102  to which the set of activations  404  is applied. 
     In one illustrative example, the set of phase shifters  400  comprises a set of elements that can be located adjacent to a waveguide. The set of phase shifters  400  can take a number of different forms. For example, the set of phase shifters  400  can be selected from at least one of a tuning electrode, a thermal element, shape memory alloy element, piezo electric element, or some other element that can change the phase of light of a particular wavelength propagating through the optical waveguide. These elements for the set of phase shifters  400  can be at least one of adjacent to part of an optical waveguide, connected to part of an optical waveguide, or include part of an optical waveguide. 
     The set of activations  404  can take a number of different forms. For example, the set of activations  404  can be selected from at least one of a voltage, a current, a thermal energy, an electrically induced strain, or some other type of energy that can be applied to an optical waveguide to affect the manner in which light propagates through the optical waveguide. In particular, the energy can be used to affect the phase of light of a particular wavelength propagating through the optical waveguide. 
     In other words, the set of phase shifters  400  can selectively apply the set of activations  404  to adjust the phase for a particular wavelength of light  118  traveling within loops  116  in optical waveguides  102 . This adjustment can be made by applying the activations  404  using a particular phase shifter located adjacent to an optical waveguide in the set of optical waveguides  102  in a loop in loops  116  for a particular wavelength of light to maintain or reach resonance matching  300  for that particular wavelength of light. 
     For example, a phase shifter, such as main phase shifter  406 , can be located adjacent to a portion of main nonlinear optical waveguide  106 . Main phase shifter  406  can apply an activation in activations  404  such that a phase shifts in first-wavelength light  132  to achieve resonant condition  306  for first-wavelength light  132  for light traveling in first loop  200 . 
     Another phase shifter, such as secondary phase shifter  408  can be located adjacent to a portion of secondary optical waveguide  113 . Secondary phase shifter  408  can apply an activation in activations  404  such that a phase shifts in one or both of second-wavelength light  134  and third-wavelength light  136  to achieve a roundtrip phase matching  302  for the nonlinear optical process. 
     A phase shifter, such as first phase shifter  410 , can be located adjacent to a portion of first extension optical waveguide  108 . First phase shifter  410  can apply an activation in activations  404  such that a phase shifts in first-wavelength light  132  to achieve a resonance condition  306  for first-wavelength light  132  in first loop  200 . First phase shifter  410  also can apply an activation in activations  404  such that a phase shifts in first-wavelength light  132  to achieve a roundtrip phase matching  302  for the nonlinear optical process. 
     In another illustrative example, a phase shifter, such as second phase shifter  412 , can be located adjacent to a portion of second extension optical waveguide  110 . Second phase shifter  412  can apply an activation in activations  404  such that a phase shifts in second-wavelength light  134  to achieve a resonance condition  306  for second-wavelength light  134  in second loop  202 . 
     As another illustrative example, a phase shifter, such as third phase shifter  414 , can be located adjacent to a portion of third extension optical waveguide  119 . Third phase shifter  414  can an activation in activations  404  such that a phase shifts in third-wavelength light  136  to achieve resonance condition  306  for third-wavelength light  136  in third loop  204 . 
     In one illustrative example, the set of phase shifters  400  can be a set of tuning electrodes that apply a set of activations  404  as a set of voltages  418 . With this type of phase shifters in the form of tuning electrodes that apply activations  404  in the form of voltages  418 , the optical waveguides associated with the tuning electrodes can be comprised of an electro-optic material  103 . One example of an electro-optical material  103  is lithium niobate. This material does not have to be use throughout the entire optical waveguide. Lithium niobate can be used in the sections that are associated with or adjacent to the tuning electrodes. 
     Lithium niobate is an electro-optic material for which the material refractive index can be changed by applying an electric field to the lithium niobate material. Lithium niobate has a second order nonlinear optical coefficient that is large enough to result in undesired light generation. As a result, in some illustrative examples the regions in a nonlinear optical waveguide containing the lithium niobate containing regions used for electro-optic tuning from the lithium niobate can be separated from regions containing lithium niobate used for the nonlinear optical generation of signal photons and idler photons. 
     With this example, main phase shifter  406  in the set of phase shifters  400  can be main tuning electrode  420  located adjacent to a portion of main nonlinear optical waveguide  106 . Secondary phase shifter  408  in the set of phase shifters  400  can be secondary tuning electrode  422  located adjacent to a portion of secondary optical waveguide  113 . 
     In this illustrative example, first phase shifter  410  can be first tuning electrode  424  located adjacent to a portion of first extension optical waveguide  108 . Second phase shifter  412  can be second tuning electrode  426  located adjacent to a portion of second extension optical waveguide  110 , and third phase shifter  414  in the set of phase shifters  400  can be third tuning electrode  428  located adjacent to a portion of third extension optical waveguide  119 . 
     First tuning electrode  424 , second tuning electrode  426 , and third tuning electrode  428  can apply the set of activations  404  in the form of a set of voltages  418  to adjust the set of phases  402  in at least one of first-wavelength light  132 , second-wavelength light  134 , or third-wavelength light  136  traveling in a set of loops  116  through optical waveguides  102 . This shift in the set of phases  402  can be made to maintain or reach resonance condition  306  for one or more of the wavelengths of light  118 . These wavelengths of light can be for example, at least one of first-wavelength light  132 , second-wavelength light  134 , or third-wavelength light  136 . This shift in the set of phases  402  also can be made to achieve or maintain roundtrip phase matching  302 . 
     In the illustrative example, when an optical waveguide in the set of optical waveguides  102  comprises an electro-optic material  103 , the activation can take the form of a voltage. When the optical waveguide does not comprise an electro-optic material, other forms of energy such as, for example, thermal energy, such as heat, or strain can be used as the set of activations  404 . In this illustrative example, heat can be generated by applying electrical current to a resistor that forms a phase shifter in the set of phase shifters  400  such that heat is generated. As another example, a voltage can be applied to a piezo electric element for phase shifter in the set of phase shifters  400  to change the dimensions of the tuning electrode to cause strain in the portion of the optical waveguide adjacent to the phase shifter in the set of phase shifters  400 . 
     The illustration of optical waveguide structure  100  and the different components in  FIGS.  1 - 6    is not meant to imply physical or architectural limitations to the manner in which an illustrative embodiment may be implemented. Other components in addition to or in place of the ones illustrated may be used. Some components may be unnecessary. Also, the blocks are presented to illustrate some functional components. One or more of these blocks may be combined, divided, or combined and divided into different blocks when implemented in an illustrative embodiment. 
     For example, additional extension waveguides can be present in optical waveguide structure  100 . For example, another extension waveguide can be optically coupled to second extension optical waveguide  110 . This coupling can be performed using another pair of wavelength-selective couplers to form a third extension segment for third-wavelength light. 
     In another illustrative example, fewer components can be present than depicted in optical waveguide structure  100  in  FIGS.  1 - 6   . In another illustrative example, third extension optical waveguide  119  can be omitted from optical waveguides  111 . In other illustrative examples, phase shifters  400  may be used with some but not all of optical waveguides  102 . In one example, only main phase shifter  406  may be present. 
     With reference now to  FIG.  7   , an illustration of a cross-section of an optical waveguide is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide  700  is shown in a cross-sectional view. This cross-section can be used in the optical waveguides in optical waveguide structure  100  in  FIGS.  1 - 6   . 
     As depicted, optical waveguide  700  comprises core region  702  and cladding region  704 . Core region  702  can be comprised of a material such as silicon nitride (Si 3 N 4 ), silicon (Si) or silicon carbide (SiC) for optical processes based on four wave mixing. Core region  702  can be comprised of a material such as lithium niobate (LiNbO 3 ), gallium phosphide (GaP), aluminum nitride (AlN), aluminum gallium arsenide (AlGaAs), or silicon carbide (SiC) for optical processes based on three-wave mixing. Cladding region  704  can be comprised of silicon dioxide (SiO 2 ) or other material whose refractive index is lower than the refractive index of the material comprising core region  702 . The particular material used in optical waveguide  700  can vary in other illustrative examples depending on the optical process used. 
     In this illustrative example, core region  702  has width w  706  and height tw  708 . Cladding region  704  has height tox  710 . Cladding region  704  can cover any combination of the top, the two sides and the bottom of core region  702 . 
     Optical waveguide  700  can be adjusted to achieve values for the effective refractive indices (neff) of the wavelengths of light  118  traveling through optical waveguide  700 . The effective refractive indices can be adjusted through the selection of the material refractive index at a specific wavelength and varying the waveguide dimensions such as width w  706 , height tw  708 , and top oxide thickness, height tox  710 . 
     The selection of at least one of the material and dimensions for optical waveguide  700  can be based on the conditions for momentum conservation and phase matching. In the illustrative example, momentum conservation is an automatic consequence of the nonlinear optical interaction. Whether the phase matching associated with the particular waveguide structure is consistent with momentum conservation determines the degree of phase walk-off that results as the light travels in the waveguide over some distance. 
     For example, an effective refractive index can be a function of the height and width of core region  702 . The constructive nonlinear generation length is the propagation length at which the phase walk-off equals n radians. The constructive nonlinear generation length is inversely proportional to the phase mismatch. In an illustrative example, the length of the main nonlinear optical waveguide should be no larger than the constructive nonlinear generation length that can be achieved for the main nonlinear optical waveguide. In illustrative examples, the nonlinear optical interaction occurs in all three loops. 
     Additionally, the cross-section shown for optical waveguide  700  is provided as an example and is not meant to limit the manner in which other illustrative examples can implement cross-sections for waveguides. For example, optical waveguide  700  is shown with side  720  and side  722  that are angled for core region  702 . In other illustrative examples, these two sides can be parallel to each other rather than angled. As another example, other components may be present in this cross-section such as side regions that may be located adjacent to side  720  and side  722 . In yet another illustrative example, the cross-section of optical waveguide  700  may also include a phase shifter such as a tuning electrode. As another example, optical waveguide  700  can include a second core region in addition to core region  702  when optical waveguide  700  is used to implement a two-waveguide optical coupler. 
     Turning to  FIG.  8   , an illustration of light coupling by a wavelength-selective coupler is depicted in accordance with an illustrative embodiment. In this illustrative example, pump light  802 , signal light  804 , and idler light  806  travel through optical waveguide  808  and are input into wavelength-selective coupler  810 . Signal light  804  and idler light  806  also travel through optical waveguide  808  and are input into wavelength-selective coupler  810 . As depicted, at the output of wavelength-selective coupler  810 , pump light  802  continues through to optical waveguide  828 . In this example, signal light  804  and idler light  806  cross over from optical waveguide  808  to optical waveguide  822  at the output of wavelength-selective coupler  810 . Signal light  804  and idler light  806  also cross over from optical waveguide  812  at the input of wavelength-selective coupler  810  to optical waveguide  828  at the output of wavelength-selective coupler  810 . Wavelength-selective coupler  810  is an illustration of an implementation for first wavelength-selective coupler  1220  and second wavelength-selective coupler  1222  in optical waveguide structure  1200  in  FIG.  16    and for first wavelength-selective coupler  1320  and second wavelength-selective coupler  1322  in optical waveguide structure  1300  in  FIG.  17   . 
     With reference next to  FIG.  9   , an illustration of light coupling by a wavelength-selective coupler is depicted in accordance with an illustrative embodiment. In this illustrative example, pump light  902 , signal light  904 , and idler light  906  travel through optical waveguide  908  into wavelength-selective coupler  910 . Pump light  912  also travels through optical waveguide  914  and is input into wavelength-selective coupler  910 . 
     As depicted, at the output of wavelength-selective coupler  910 , signal light  904  and idler light  906  continues through into optical waveguide  928 . Pump light  902  traveling into wavelength-selective coupler  910  from optical waveguide  908  crosses over to optical waveguide  924  at the output of wavelength-selective coupler  910 . In a similar fashion, pump light  912  traveling through optical waveguide  914  into wavelength-selective coupler  910  crosses over to optical waveguide  928  at the output of wavelength-selective coupler  910 . Wavelength-selective coupler  910  is illustrative of first wavelength-selective coupler  1120  and second wavelength-selective coupler  1122  in optical waveguide structure  1100  in  FIG.  13   , first wavelength-selective coupler  1020  and second wavelength-selective coupler  1022  in optical waveguide structure  1000  in  FIG.  14   , first wavelength-selective coupler  1420 , second wavelength-selective coupler  1422  in optical waveguide structure  1400  in  FIG.  15   , and first wavelength-selective coupler  1580 , second wavelength-selective coupler  1586 , third wavelength-selective coupler  1584  and fourth wavelength-selective coupler  1582  in optical waveguide structure  1500  in  FIG.  18   , described below. 
     With reference to  FIG.  10   , an illustration of light coupling by a wavelength-selective coupler is depicted in accordance with an illustrative embodiment. In this illustrative example, signal light  4502  and idler light  4504  travel through optical waveguide  4506  and are input into wavelength-selective coupler  4508 . In this depicted example, light is not input into optical waveguide  4510  which is connected to wavelength-selective coupler  4508 . As depicted, at the output of wavelength-selective coupler  4508 , idler light  4504  continues through into optical waveguide  4526  and signal light  4502  crosses over into optical waveguide  4520 . 
     This crossover of signal light  4502  is caused by the design of wavelength-selective coupler  4508 . In illustrative examples, wavelength-selective coupler  4508  can be used for a signal wavelength-selective coupler to selectively couple signal light from a secondary optical waveguide to a signal extension optical waveguide. Wavelength-selective coupler  4508  can also be used to selectively couple signal light from a signal extension optical waveguide to the secondary optical waveguide. Wavelength-selective coupler  4508  is illustrative of wavelength-selective couplers used in optical waveguide structure  1500  in  FIG.  18   . 
     In  FIG.  11   , an illustration of simulation results of light coupling by a wavelength-selective coupler is depicted in accordance with an illustrative embodiment. As depicted, simulation results  4600  comprises plots and. Simulation results  4600  comprise signal extraction plot  4602  for a signal extraction result and idler retention plot  4604  for an idler retention result. These plots are of the optical-field distributions for a signal light and an idler light having different wavelengths from each other. 
     Simulation results  4600  are generated using a wavelength-selective coupler such as wavelength-selective coupler  4508  in  FIG.  10   . This wavelength-selective coupler can be implemented as a two-waveguide optical coupler. In this illustrative example, simulation results  4600  are for a case in which signal light  4502 , that is coupled and exits from the “cross” output of wavelength-selective coupler  4508 , has a larger guided-mode effective index of refraction n eff  and is confined more strongly than the idler light  4504 , that exits from the “through” output of wavelength-selective coupler  4508 . 
     As depicted, signal extraction plot  4602  depicts the electric-field magnitude of the signal light. Plot  4602  has x-axis  4606  that represents the longitudinal direction of the two-guide wavelength-selective coupler structure and y-axis  4608  that represents the transverse direction of the two-guide wavelength-selective coupler structure. Signal extraction plot  4602  in simulation results  4600  shows that signal light is coupled from the lower left waveguide to the upper right waveguide and is illustrative of the cross-state of a coupler. 
     In this illustrative example, idler retention plot  4604  depicts the electric-field magnitude of the idler light. Idler retention plot  4604  has x-axis  4610  that represents the longitudinal direction of the two-guide wavelength-selective coupler structure and y-axis  4612  that represents the transverse direction of the two-guide wavelength-selective coupler structure. As depicted, idler retention plot  4604  shows that the idler light couples from the lower waveguide to the upper waveguide in a few portions of the coupling region but eventually remains in the lower waveguide away from that coupling section and exits from the lower right waveguide, illustrative of the thru-state of a coupler. 
     In this example, these simulation results can be obtained using a wavelength-selective coupler that comprises two curved waveguides that are coupled by a section of a straight waveguide of a length and a gap for wavelength-selective coupler that are selected to result in the coupling of the signal light from a first optical waveguide to a second optical waveguide when passing through the wavelength-selective coupler. 
     Thus, if light of both signal light  4502  and idler light  4504  are supplied to wavelength-selective coupler  4508  through optical waveguide  4506 , signal light  4502  exits wavelength-selective coupler  4508  via optical waveguide  4520  and idler light  4504  exits wavelength-selective coupler  4508  via optical waveguide  4526 . 
     For this example, an example length d s|i  for the coupling section for wavelength-selective coupler  4508  can be described by the following relation: K s|i (λ s ) · d s|i  = π, where K s|i  is the coupling coefficient. To achieve the desired wavelength selectivity, wavelength-selective coupler  4508  can also be constrained by another relation: K s|i (λ I ) · d s|i  = 2 · π · X, where λ I  is the longer wavelength and X is an integer. In the illustrative example, the value of X is 2, such that the photons of signal light wavelength λ s  have approximately  1000  coupling between the two waveguides being coupled, while the photons of idler light wavelength λ I  are coupled back again to the starting waveguide. 
     With reference now to  FIG.  12   , an illustration of simulation results of light coupling by a wavelength-selective coupler is depicted in accordance with an illustrative embodiment. Simulation results  4700  comprise plots that illustrate light coupling using a wavelength-selective coupler such as a two-waveguide optical coupler. 
     As depicted, simulation results  4700  are for pump light in pump plot  4718 , signal light in signal plot  4710 , and idler light in idler plot  4714 . These simulation results are plots of the electric field magnitude distributions of light at the pump, signal, and idler wavelengths. Pump plot  4718  is a plot for field magnitude distribution in linear scale. As depicted, pump plot  4718  has x-axis  4708  that represents the longitudinal direction of the two-guide wavelength-selective coupler structure and y-axis  4702  that represents the transverse direction of the two-guide wavelength-selective coupler structure. 
     In this illustrative example, signal plot  4710  and idler plot  4714  are plots for the signal and idler field magnitude distributions in a logarithmic scale. As depicted, signal plot  4710  has x-axis  4712  that represents the longitudinal direction of the two-guide wavelength-selective coupler structure and y-axis  4705  that represents the transverse direction of the two-guide wavelength-selective coupler structure. Idler plot  4714  has x-axis  4716  that represents the longitudinal direction of the two-guide wavelength-selective coupler structure and y-axis  4707  that represents the transverse direction of the two-guide wavelength-selective coupler structure. 
     In this depicted example, the optical waveguide at the lower portion of the plots for simulation results  4700  has a smaller radius of curvature than the optical waveguide at the upper portion of those plots. The light travels from left to right in these plots for simulation results  4700 . Pump light enters in the upper guide from the upper left of pump plot  4718 . Signal light and idler light enter in the lower, curved guide from the lower left of signal plot  4704  and idler plot  4706 . 
     In this example, the pump light experiences primarily the “cross” state of this coupler and is coupled into the curved, lower guide and exits from the lower right of the plot. The signal and idler light experience the “through” state of this coupler and remain in the curved guide to also exit from the lower right of the plots. For this example, the pump light is carried by a higher-order transverse mode of the lower, curved guide. Thus, the field magnitude distribution of the pump light in that curved guide has several brighter regions. The signal and idler light, however, are carried by the fundamental transverse modes at those wavelengths. Thus, the intensity distributions for the signal and idler light have just one bright region that is brighter near the center of the guide. In this illustrative example, the pump light is carried in the upper guide by the fundamental transverse mode at the pump wavelength. Thus, the intensity distribution for the pump light in the upper waveguide has just one bright region that is brighter near the center of that upper guide. The simulation results  4700  can be examples of the performance of some implementations of wavelength-selective coupler  910  illustrated in  FIG.  9   . 
     The examples of  FIGS.  13 - 18    illustrate different aspects of optical waveguide structure  100  as shown in  FIGS.  1 - 6   . These illustrations are intended to be inclusive rather than exclusive. Thus, although only some features are illustrated in one example and other features are illustrated in another example, this difference in features in different figures is used only for the purpose of clarity and to simplify the description of features in the illustrative examples. 
     With reference to  FIG.  13   , an illustration of an optical waveguide structure with five optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  1100  is an example of an implementation for optical waveguide structure  100  as shown in  FIGS.  1 - 6   . More specifically,  FIG.  13    is an implementation for optical waveguides  102  as depicted in  FIG.  3   . 
     In this illustrative example, optical waveguide structure  1100  can be designed to achieve the concurrent requirements that the three wavelengths are at resonances of their respective resonator loops and also that the phase match condition is met for sustaining the nonlinear optical process over many cycles of travel through the loops. 
     In this illustrative example, optical waveguide structure  1100  comprises optical waveguides in the form of main nonlinear optical waveguide  1110 , segment  1107  in secondary optical waveguide  1108 , segment  1109  in secondary optical waveguide  1108 , pump loop extension  1102 , signal loop extension  1104 , and idler loop extension  1106 . Main nonlinear optical waveguide  1110  is an example of main nonlinear optical waveguide  106  in  FIG.  3    and main nonlinear optical waveguide  106  in  FIG.  2   . Pump loop extension  1102  is an example of an implementation for first extension optical waveguide  108  in  FIG.  3    and first extension optical waveguide  108  in  FIG.  2   . Signal loop extension  1104  and idler loop extension  1106  are optical waveguides that can be coupled to segments of secondary optical waveguide  113  in  FIG.  3    or secondary optical waveguide  113  in  FIG.  2   . Signal loop extension  1104  and idler loop extension  1106  are examples of second extension optical waveguide  110  and third extension optical waveguide  119 , respectively, in  FIGS.  3 - 6   . 
     In these illustrative examples, the individual optical waveguides can be portions or segments from which loops can be established through the use of wavelength selective optical couplers to connect those segments or portions to other segments or portions. 
     In this illustrative example, main nonlinear optical waveguide  1110  of optical waveguide structure  1100  is comprised of a nonlinear optical material  104 . For some second-order nonlinear optical materials, such as x-cut lithium niobate, the nonlinear optical coefficient is much larger for light whose electric-field vector is aligned parallel to one crystallographic axis than for light whose electric-field vector is aligned perpendicular to that crystallographic axis. Thus, for x-cut lithium niobate, a larger second-order nonlinear optical coefficient applies for a nonlinear optical waveguide aligned parallel to the material Y-axis, with the electric-field vector of the propagating transverse-electric (TE) polarized light aligned parallel to the material Z-axis. In this illustrative example, main nonlinear optical waveguide  1110  has a linear shape and is aligned parallel to the lithium niobate material Y-axis. Thus, the propagation direction would be in the +y direction or the -y direction of the lithium niobate crystalline material. 
     In this illustrative example, pump loop extension  1102  is comprised of a non-nonlinear optical material  105 . As depicted, idler loop extension  1106  is comprised of an electro-optic material  103 . As depicted, signal loop extension  1104  is comprised of a nonlinear optical material  104  as well as an electro-optic material  103 . An electro-optic material is a material with a large electro-optic coefficient. Examples of electro-optic materials that can be used are lithium niobate, gallium arsenide, gallium phosphide and silicon carbide. 
     In an illustrative example, the use of an electro-optic material can provide desired propagation properties for light. Electro-optical materials often also are nonlinear optical materials having nonlinear optical coefficient. 
     As depicted, optical waveguide structure  1100  also includes pump input optical waveguide  1132  that inputs pump light  1112 . Optical waveguide structure  1100  also includes signal output optical waveguide  1134  and idler output optical waveguide  1136 . Signal output optical waveguide  1134  can output signal light  1114 . Idler output optical waveguide  1136  can output idler light  1116 . 
     As depicted, first wavelength-selective coupler  1120  and second wavelength-selective coupler  1122  connect pump loop extension  1102  to main nonlinear optical waveguide  1110 . In this illustrative example, third wavelength-selective coupler  1124  and fourth wavelength-selective coupler  1126  connect signal loop extension  1104  and idler loop extension  1106  to segment  1107  and segment  1109  of secondary optical waveguide  1108 . 
     In this illustrative example, pump optical coupler  1131  couples pump input optical waveguide  1132  to pump loop extension  1102 . Signal optical coupler  1135  couples signal output optical waveguide  1134  to signal loop extension  1104 . Idler optical coupler  1137  couples idler output optical waveguide  1136  to idler loop extension  1106 . 
     In this illustrative example, pump light  1112  travels in pump loop  1152  which extends through main nonlinear optical waveguide  1110  and pump loop extension  1102 . Signal light  1114  travels in signal loop  1154  which extends through main nonlinear optical waveguide  1110 , secondary optical waveguide  1108  and signal loop extension  1104 . Idler light  1116  travels in idler loop  1156  which extends through main nonlinear optical waveguide  1110 , secondary optical waveguide  1108  and idler loop extension  1106 . 
     As depicted, optical waveguide structure  1100  also includes phase shifters in the form of tuning electrodes. In this illustrative example, tuning electrode  1160  is located adjacent to a portion of main nonlinear optical waveguide  1110 . Tuning electrode  1164  is located adjacent to a portion of signal loop extension  1104 . Tuning electrode  1166  is located adjacent to a portion of idler loop extension  1106 . 
     In this illustrative example, each wavelength-selective coupler in optical waveguide structure  1100  produces a phase shift for each given wavelength of light at its “thru” state output and a possibly different phase shift for each given wavelength of light at its “cross” state output. For example, first wavelength-selective coupler  1120  extracts pump light  1112  from main nonlinear optical waveguide  1110  into pump loop extension  1102 . First wavelength-selective coupler  1120  also extracts signal light  1114  and idler light  1116  from main nonlinear linear optical waveguide  1110  into segment  1107  of secondary optical waveguide  1108 . 
     In this illustrative example, first wavelength-selective coupler  1120  produces a phase shift of ϕ M1p  for the pump light  1112  coupled from main nonlinear optical waveguide  1110  to pump loop extension  1102  via a “cross” state output of first wavelength-selective coupler  1120 . First wavelength-selective coupler  1120  produces a phase shift of ϕ 1s  for signal light  1114  that is coupled from main nonlinear optical waveguide  1110  into segment  1107  of secondary optical waveguide  1108 , and a phase shift of ϕ 1i  for idler light  1116  that is coupled from main nonlinear optical waveguide  1110  into segment  1107  of secondary optical waveguide  1108  via a “thru” state output of first wavelength-selective coupler  1120 . 
     Furthermore, second wavelength-selective coupler  1122  causes a phase shift of ϕ 1Mp  for pump light  1112  coupled from pump loop extension  1102  back to main nonlinear optical waveguide  1110 . Second wavelength-selective coupler  1122  produces a phase shift of ϕ 1s  for signal light  1114  that is coupled from segment  1109  of secondary optical waveguide  1108  into main nonlinear optical waveguide  1110 , and produces a phase shift of ϕ 1i  for idler light  1116  that is coupled from segment  1109  of secondary optical waveguide  1108  into main nonlinear optical waveguide  1110 . 
     In this illustrative example, third wavelength-selective coupler  1124  and fourth wavelength-selective coupler  1126  between the secondary optical waveguide  1108  and idler loop extension  1106  produce phase shifts of ϕ 2i  and ϕ 2i  for idler light  1116  coupled in their “cross” state output. Third wavelength-selective coupler  1124  and fourth wavelength-selective coupler  1126  between the secondary optical waveguide  1108  and signal loop extension  1104  produce phase shifts of ϕ 2s  and ϕ 2s  for signal light  1114  that exits from their “thru” state outputs. 
     The light propagating in a waveguide can experience a phase shift associated with the length of the waveguide and with the effective refractive index of the wave-guided mode. For transverse-electric (TE) polarized light in x-cut lithium niobate, the material index depends on the direction of propagation. Thus, the phase shift can be estimated by performing a numerical simulation. The phase shifters, such as tuning electrodes, can contribute an additional phase shift that can either advance the phase or retard the phase, depending on the sign of the applied voltage, for an electro-optic phase shifter. 
     For the example in optical waveguide structure  1100  in  FIG.  13   , tuning electrode  1164  for signal loop extension  1104  in signal loop  1154  and tuning electrode  1166  for idler loop extension  1106  in idler loop  1156  can contribute additional phase shifts of Δϕ Es  and Δϕ Ei , respectively. These phase shifts can have a positive or negative value. 
     In this illustrative example, tuning electrode  1160  for main nonlinear optical waveguide  1110  affects pump light  1112 , signal light  1114 , and idler light  1116  and can produce additional phase shifts of Δϕ MEp , Δϕ MEs , and Δϕ MEi  to the pump light  1112 , signal light  1114 , and idler light  1116 , respectively. 
     The resonator for pump light  1112  is comprised of components of optical waveguide structure  1100  in pump loop  1152 . This pump loop comprises main nonlinear optical waveguide  1110 , the cross-state of first wavelength-selective coupler  1120 , the cross-state of second wavelength-selective coupler  1122 , and pump loop extension  1102 . The round-trip phase shift ϕ RTp  for pump light  1112  at the pump wavelength should be equal to a multiple of 2π for pump light  1112  to remain circulating for many round-trips through pump loop  1152  and thus circulate for many passes through main nonlinear optical waveguide  1110 . 
     In this illustrative example, the phase shift of the pump light  1112  due to propagation in the pump loop extension  1102  can be described by the expression: 
     
       
         
           
             
               ϕ 
               
                 1 
                 p 
               
             
             = 
             2 
             π 
             
               n 
               
                 1 
                 p 
               
             
             
               L 
               1 
             
             / 
             
               λ 
               p 
             
             , 
           
         
       
     
      where n 1p  is a net or equivalent effective refractive index of the wave-guided pump light in the pump loop extension  1102 ; L 1  is the length of pump loop extension  1102 ; and λ p  is the wavelength of pump light  1112 . 
     The phase shift of pump light  1112  from propagation through the main nonlinear optical waveguide  1110  can be described as follows: 
     
       
         
           
             
               ϕ 
               
                 M 
                 u 
                 p 
               
             
             = 
             2 
             π 
             
               n 
               
                 M 
                 p 
               
             
             
               L 
               m 
             
             / 
             
               λ 
               p 
             
           
         
       
     
      where n Mp  is the effective refractive index of the wave-guided pump mode in main nonlinear optical waveguide  1110 , L M  is the length of main nonlinear optical waveguide  1110 , which is located between first wavelength-selective coupler  1120  and second wavelength-selective coupler  1122 ; and λ p  is the wavelength of pump light  1112 . 
     Next, the resonance requirement for pump light  1112  can be given by the expression: 
     
       
         
           
             
               ϕ 
               
                 R 
                 T 
                 p 
               
             
             = 
             
               ϕ 
               
                 1 
                 p 
               
             
             + 
             
               ϕ 
               
                 1 
                 M 
                 p 
               
             
             + 
             
               ϕ 
               
                 M 
                 u 
                 p 
               
             
             + 
             
               ϕ 
               
                 M 
                 1 
                 p 
               
             
             + 
             Δ 
             
               ϕ 
               
                 M 
                 E 
                 p 
               
             
             = 
             2 
             π 
             P 
             , 
           
         
       
     
     where P is an integer. In an illustrative example, P can have values that also result in phase matching to maintain constructive generation of signal and idler from pump light. 
     This resonance requirement can be met by designing optical waveguide structure  1100  to have suitable values for the length L 1  and the phase shift ϕ 1p . The phase shift ϕ M1p  is due to the first wavelength-selective coupler and the phase shift ϕ 1Mp  is due to the second wavelength-selective coupler. 
     In this illustrative example, signal loop  1154  extends through main nonlinear optical waveguide  1110 . More specifically signal loop  1154  extends through main nonlinear optical waveguide  1110 , first wavelength-selective coupler  1120  (in its thru state) and second wavelength-selective coupler  1122  (in its thru state); segment  1107  and segment  1109  of secondary optical waveguide  1108 , in which both signal light  1114  and idler light  1116  propagate; third wavelength-selective coupler  1124  (in its thru state) and fourth wavelength-selective coupler  1126  (in its thru state); and signal loop extension  1104 . As depicted, only signal light  1114  propagates through signal loop extension  1104 . 
     In this example, main nonlinear optical waveguide  1110  can have length L Mu . Pump light  1112 , signal light  1114 , and idler light  1116  propagate through main nonlinear optical waveguide  1110 . Segment  1107  and segment  1109  have a total length of L Mc . In this illustrative example, signal loop extension  1104  has a total length of L 2 . 
     Signal loop  1154  is a resonator loop in which the signal light  1114  travels. The round-trip phase shift ϕ RTs  of signal light  1114  traveling in signal loop  1154  can be given by: 
     
       
         
           
             
               ϕ 
               
                 R 
                 T 
                 s 
               
             
             = 
             2 
             
               ϕ 
               
                 1 
                 s 
               
             
             + 
             
               ϕ 
               
                 M 
                 u 
                 s 
               
             
             + 
             Δ 
             
               ϕ 
               
                 M 
                 E 
                 s 
               
             
             + 
             2 
             
               ϕ 
               
                 2 
                 s 
               
             
             + 
             
               ϕ 
               
                 M 
                 c 
                 s 
               
             
             + 
             
               ϕ 
               
                 S 
                 s 
               
             
             + 
             Δ 
             
               ϕ 
               
                 S 
                 E 
                 s 
               
             
             = 
             2 
             π 
             S 
             . 
           
         
       
     
     For signal light  1114  to remain circulating for many round-trips in signal loop  1154  and thus circulate for many passes through main nonlinear optical waveguide  1110 , the round-trip phase shift should be as close as possible to a multiple of 2π, that is, with S being an integer. 
     The phase shift of signal light  1114  propagating in main nonlinear optical waveguide  1110  can be described by the expression: 
     
       
         
           
             
               ϕ 
               
                 M 
                 u 
                 s 
               
             
             = 
             2 
             π 
             
               n 
               
                 M 
                 s 
               
             
             
               L 
               
                 M 
                 u 
               
             
             / 
             
               λ 
               s 
             
           
         
       
     
      where n Ms  is the effective refractive index of signal light  1114  in the main nonlinear optical waveguide  1110 ; L Mu  is the length of main nonlinear optical waveguide  1110 ; and λ s  is the wavelength of signal light  1114 . 
     Each of the two wavelength-selective couplers coupled to main nonlinear optical waveguide  1110 , first wavelength-selective coupler  1120  and second wavelength-selective coupler  1122 , in signal loop  1154  operate in its “cross” state for the signal wavelength and produces a phase shift of ϕ 1s  for the signal wavelength. In a similar fashion, each of the two wavelength-selective couplers coupled to signal loop extension  1104 , third wavelength-selective coupler  1124  and fourth wavelength-selective coupler  1126 , in signal loop  1154  operate in its “thru” state for the signal wavelength and produces a phase shift of ϕ 2s  for the signal light  1114 . The net phase shift from the two corner portions, segment  1107  and segment  1109  of the secondary optical waveguide  1108  in signal loop  1154 , in which both signal light  1114  and idler light  1116  propagate can be given by ϕ Mcs . The phase shift from signal loop extension  1104  in signal loop  1154 , in which only the signal light propagates, can be given by ϕ Ss . 
     In an illustrative example, tuning electrode  1160  used to adjust the phase shift for pump light  1112  in its resonator loop also produces a phase shift for signal light  1114  of Δϕ MEs . However, tuning electrode  1164  in signal loop extension  1104  affects only signal light  1114 . Tuning electrode  1166  produces a phase shift of Δϕ SEs . 
     Idler loop  1156  in which idler light  1116  extends through main nonlinear optical waveguide  1110  and idler loop extension  1106 . In this depicted example, idler loop  1156  comprises segment  1107  in secondary optical waveguide  1108 , first wavelength-selective coupler  1120  and third wavelength-selective coupler  1124 ; segment  1109  in secondary optical waveguide  1108 , fourth wavelength-selective coupler  1126  and second wavelength-selective coupler  1122 ; and idler loop extension  1106 . 
     Each of the two wavelength-selective couplers, first wavelength-selective coupler  1120  and second wavelength-selective coupler  1122 , in idler loop  1156  have a “cross” state for the pump wavelength and a “thru” state for the idler wavelength and produces a phase shift of ϕ 1i  at the “thru” state output of the wavelength-selective coupler. Likewise, each of the two wavelength-selective couplers, third wavelength-selective coupler  1124  and fourth wavelength-selective coupler  1126 , have a “cross” state for the idler wavelength and produces a phase shift of ϕ 2i  at its “cross” state output for idler light  1116 . 
     The total phase shift of idler light  1116  from the two corner portions, segment  1107  and segment  1109 , in which both signal light  1114  and idler light  1116  propagate, can be given by ϕ Mci . The phase shift from idler loop extension  1106 , in which only idler light  1116  propagates, can be given by ϕ lei . 
     In this illustrative example, tuning electrode  1160  for main nonlinear optical waveguide  1110  used to adjust the phase shift for pump light  1112  will also produce a phase shift for idler light  1116  of Δϕ MEi . Tuning electrode  1166  for idler loop extension  1106  affects only idler light  1116 . Tuning electrode  1166  can produce a phase shift of Δϕ IEi . 
     Thus, the round-trip phase shift ϕ RTi  of idler light  1116  can be given by: 
     
       
         
           
             
               ϕ 
               
                 R 
                 T 
                 i 
               
             
             = 
             2 
             
               ϕ 
               
                 1 
                 i 
               
             
             + 
             
               ϕ 
               
                 M 
                 u 
                 i 
               
             
             + 
             Δ 
             
               ϕ 
               
                 M 
                 E 
                 i 
               
             
             + 
             2 
             
               ϕ 
               
                 2 
                 i 
               
             
             + 
             
               ϕ 
               
                 M 
                 c 
                 i 
               
             
             + 
             
               ϕ 
               
                 I 
                 i 
               
             
             + 
             Δ 
             
               ϕ 
               
                 I 
                 E 
                 i 
               
             
             = 
             2 
             π 
             I 
             . 
           
         
       
     
     For idler light  1116  to remain circulating for many roundtrips in idler loop  1156  extending through main nonlinear optical waveguide  1110  and thus making many passes through main nonlinear optical waveguide  1110 , the round-trip phase shift should be a close as possible to a multiple of 2π, that is, with I being an integer. The length and waveguide cross-sectional structure in main nonlinear optical waveguide  1110  can be designed to achieve phase matching for the nonlinear optical interaction. 
     Thus, the value for ϕ Mui  can be determined by the design of the waveguide cross-sectional structure in main nonlinear optical waveguide  1110 . However, the length L 3  of idler loop extension  1106  can be selected to achieve the desired resonance condition for the idler wavelength in its resonator loop, idler loop  1156 . Also, the additional phase shift Δϕ IEi  produced by the tuning electrode  1166  in the idler loop extension  1106  can be used to further adjust that round-trip phase shift for idler light  1116 . 
     In the illustrative example, main nonlinear optical waveguide  1110  is the location where the desired nonlinear optical photon generation occurs in optical waveguide structure  1100 . Main nonlinear optical waveguide  1110  can be designed to achieve a phase matched condition for the nonlinear optical process. This phase matched condition can be achieved through the selection of dimensions of the cross-sectional waveguide structure. 
     The cross-sectional structure of main nonlinear optical waveguide  1110  as well as the propagation direction of the light determines the effective refractive index of the pump light  1112 , signal light  1114  and idler light  1116  in a given portion of main nonlinear optical waveguide  1110 . The propagation direction for light guided in main nonlinear optical waveguide  1110 , in which the desired nonlinear optical interaction occurs, can be chosen to increase the nonlinear optical generation. For example, a waveguide comprising x-cut lithium niobate could be aligned parallel to the material Y-axis. Thus, the propagation direction would be in the +y direction or the -y direction of the lithium niobate crystalline material. 
     For the nonlinear optical process to occur constructively over a long interaction distance so that the generation rate or generation efficiency of the signal photons and idler photons from the pump photons continues to increase as the physical interaction distance is increased, the phase matching condition of the nonlinear optical process also should be maintained. This condition includes the round-trip phase shift of pump light  1112  traveling in the main nonlinear optical waveguide  1110  as well as in pump loop extension  1102 , the round-trip phase shift of signal light  1114  traveling in main nonlinear optical waveguide  1110 , in segment  1107  and segment  1109  of secondary optical waveguide  1108 , as well as in signal loop extension  1104 , and the round-trip phase shift of idler light  1116  traveling in main nonlinear optical waveguide  1110 , in segment  1107  and segment  1109  of secondary optical waveguide  1108 , as well as in idler loop extension  1106 . 
     Thus:  
     
       
         
           
             
               ϕ 
               
                 R 
                 T 
                 p 
               
             
             − 
             
               ϕ 
               
                 R 
                 T 
                 s 
               
             
             − 
             
               ϕ 
               
                 R 
                 T 
                 i 
               
             
             = 
             2 
             π 
             A 
           
         
       
     
      where A is an integer, and can be zero. 
     Furthermore, to increase the nonlinear optical generation of signal and idler light that occurs in a given round-trip, meeting another phase matching condition is desirable for propagation of the three wavelengths of light through main nonlinear optical waveguide  1110 , which is the portion where the nonlinear optical generation occurs. This phase matching condition can be described as follows:  
     
       
         
           
             0 
             ≤ 
             
               ϕ 
               
                 M 
                 u 
                 p 
               
             
             − 
             
               ϕ 
               
                 M 
                 u 
                 s 
               
             
             − 
             
               ϕ 
               
                 M 
                 u 
                 i 
               
             
             ≤ 
             π 
             , 
               
             or 
               
             − 
             π 
             ≤ 
             
               ϕ 
               
                 M 
                 u 
                 p 
               
             
             − 
             
               ϕ 
               
                 M 
                 u 
                 s 
               
             
             − 
             
               ϕ 
               
                 M 
                 u 
                 i 
               
             
             ≤ 
             0 
             , 
           
         
       
     
      and is close to zero. 
     The additional phase shifts that can be achieved by applying bias voltages to the tuning electrodes for optical waveguide structure  1100  can be used to adjust the round-trip phase shifts for pump light  1112  (by adjusting Δϕ MEp ), for the signal light  1114  (by adjusting Δϕ SEs ) and for idler light  1116  (by adjusting Δϕ IEi ). These adjustments can be used to correct or to compensate for departures of the other parameters from their as-designed values in actually fabricated and operating devices. 
     The phase shift that can be obtained for a given electric field in the electro-optic material (due to a voltage applied to a set of tuning electrodes) can be described by the relation: 
     
       
         
           
             Δ 
             
               ϕ 
               
                 K 
                 E 
                 j 
               
             
             = 
             2 
             π 
             
               r 
               j 
             
             
               n 
               j 
             
             
                 
               3 
             
             E 
             
               Γ 
               j 
             
             
               L 
               E 
             
             / 
             
               λ 
               j 
             
           
         
       
     
      where j = p, s, i, and where p indicates pump light  1112 , s indicates signal light  1114 , and i indicates idler light  1116 . Also, K = M, S or P and indicates the optical waveguide with the tuning electrode, such as K=M for main nonlinear optical waveguide  1110 , K═S for signal loop extension  1104  and K═I for idler loop extension  1106 . Other parameters in this expression are: the electric field E, the electro-optic coefficient r j , the refractive index n j , the overlap of the optical field of pump light  1112 , signal light  1114 , or idler light  1116  with the electro-optic material Γ j , the electrode length (or electro-optic interaction distance) L E , and the wavelength λ j  of the pump light  1112 , signal light  1114 , or idler light  1116 . As an example, for an electro-optic material such as lithium niobate and for an electric field applied across the waveguide of 10 6  V/m, the electrode length needed to achieve a phase shift of 2n is about 3-10 mm. 
     Turning to  FIG.  14   , an illustration of an optical waveguide structure with five optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  1000  is an example of an implementation for optical waveguide structure  100  as shown in  FIGS.  1 - 6   . 
     In this illustrative example, optical waveguide structure  1000  comprises optical waveguides. These waveguides include main nonlinear optical waveguide  1010 , secondary optical waveguide  1008  having segment  1007  and segment  1009 , pump loop extension  1002 , signal loop extension  1004 , and idler loop extension  1006 . 
     Main nonlinear optical waveguide  1010  is an example of main nonlinear optical waveguide  106  in  FIG.  3    and main nonlinear optical waveguide  106  in  FIG.  2   . Secondary optical waveguide  1008  is an example of an implementation for secondary optical waveguide  113  in  FIG.  3    and secondary optical waveguide  113  in  FIG.  2   . 
     Pump loop extension  1002  is an example of an implementation for first extension optical waveguide  108  in  FIG.  3    and first extension optical waveguide  108  in  FIG.  2   . Signal loop extension  1004  and idler loop extension  1006  are examples of second extension optical waveguide  110  and third extension optical waveguide  119 , respectively, in  FIGS.  3 - 6   . 
     In this illustrative example, main nonlinear optical waveguide  1010  is comprised of a nonlinear optical material, such as nonlinear optical material  104 . Secondary optical waveguide  1008  can be comprised of a nonlinear optical material, such as nonlinear optical material  104  or a non-nonlinear optical material, such as non-nonlinear optical material  105 . 
     As depicted, pump loop extension  1002  is comprised of a non-nonlinear optical material. Signal loop extension  1004  is comprised of both a nonlinear optical material and an electro-optic material, such as electro-optic material  103 , in this illustrative example. Idler loop extension  1006  has portions comprised of a nonlinear optical material  104  and other portions comprised of a non-nonlinear optical material. In this example, a taper  1049  can join an optical waveguide portion comprising nonlinear optical material and an optical waveguide portion comprising a non-nonlinear optical material. In this illustrative example, section  1043  and section  1045  of idler loop extension  1006  are comprised of a non-nonlinear optical material. Section  1046  of idler loop extension  1006  is comprised of a nonlinear optical material that also is an electro-optic material. Examples of material that have a large second-order nonlinear optical coefficient as well as a large electro-optic coefficient include lithium niobate and gallium arsenide. 
     In this illustrative example, segment  1007  and segment  1009  of secondary optical waveguide  1008  is comprised of a nonlinear optical material that also is an electro-optic material. In this example, signal loop extension  1004  likewise is comprised of a nonlinear optical material that also is an electro-optic material. 
     As depicted, optical waveguide structure  1000  also includes pump input optical waveguide  1032  that inputs pump light  1012 . Optical waveguide structure  1000  also includes signal output optical waveguide  1034  and idler output optical waveguide  1036 . Signal output optical waveguide  1034  can output signal light  1014 . Idler output optical waveguide  1036  can output idler light  1016 . 
     As shown in this figure, first wavelength-selective coupler  1020  and second wavelength-selective coupler  1022  connect pump loop extension  1002  to main nonlinear optical waveguide  1010 . In this illustrative example, third wavelength-selective coupler  1024  and fourth wavelength-selective coupler  1026  connect idler loop extension  1006  to segment  1007  and segment  1009  of secondary optical waveguide  1008 . Third wavelength-selective coupler  1024  and fourth wavelength-selective coupler  1026  also connect signal loop extension  1004  to segment  1007  and segment  1009  of secondary optical waveguide  1008 . 
     In this illustrative example, pump optical coupler  1031  couples pump input optical waveguide  1032  to pump loop extension  1002 . Signal optical coupler  1035  couples signal output optical waveguide  1034  to signal loop extension  1004 . Idler optical coupler  1037  couples idler output optical waveguide  1036  to idler loop extension  1006 . 
     In this illustrative example, pump light  1012  travels in pump loop  1052  which extends through main nonlinear optical waveguide  1010  and pump loop extension  1002 . Signal light  1014  travels in signal loop  1054  which extends through main nonlinear optical waveguide  1010 , segment  1007  and segment  1009  in secondary optical waveguide  1008 , and signal loop extension  1004 . Idler light  1016  travels in idler loop  1056 , which extends through main nonlinear optical waveguide  1010 , segment  1007  and segment  1009  of secondary optical waveguide  1008 , and idler loop extension  1006 . 
     As depicted, optical waveguide structure  1000  also includes phase shifters in the form of tuning electrodes. In this illustrative example, tuning electrode  1060  is located adjacent to a portion of main nonlinear optical waveguide  1010 . In this example, the portion of main nonlinear optical waveguide  1010  is segment  1040 . Tuning electrode  1064  is located adjacent to a portion of signal loop extension  1004 . As depicted, the portion of signal loop extension  1004  is segment  1044 . Tuning electrode  1066  is located adjacent to section  1046  of idler loop extension  1006 . These tuning electrodes can apply voltages to obtain a desired level of resonance to achieve a resonant condition for the three wavelengths of light traveling within optical waveguide structure  1000 . For example, tuning electrode  1060  can adjust the phase for pump light  1012 . Tuning electrode  1064  can adjust the phase of signal light  1014 . Tuning electrode  1066  can adjust the phase of idler light  1016 . 
     A nonlinear optical process for the generation of photons for signal light  1014  and idler light  1016  from photons of pump light  1012  occurs in main nonlinear optical waveguide  1010  in optical waveguide structure  1000 . In this example, the nonlinear optical process does not occur, or negligibly occurs, in other parts of optical waveguide structure  1000 . In this depicted example, pump light  1012  supplied through pump input optical waveguide  1032  travels only through main nonlinear optical waveguide  1010 , first wavelength-selective coupler  1020 , second wavelength-selective coupler  1022  and pump loop extension  1002 . Nonlinear optical generation of signal photons and idler photons from pump photons occurs only where pump light travels and interacts with nonlinear optical material in a waveguide. Thus, both pump light and nonlinear optical material must be present for nonlinear optical generation of signal photons and idler photons from pump photons to occur. 
     In this illustrative example, pump loop extension 1002 is comprised of a material having a negligible second order nonlinear optical coefficient such as Si 3 N 4  and SiO 2 . The other portions of optical waveguide structure  1000  through which pump light  1012  does not propagate can contain a material such as lithium niobate, which has a large electro-optic coefficient and also has a large second-order nonlinear optical coefficient. This material is useful for electro-optic tuning. 
     Additionally, signal light  1014  travels in signal loop  1054  that traverses through main nonlinear optical waveguide  1010 , segment  1007  and segment  1009  of secondary optical waveguide  1008  and signal loop extension  1004 , as well as through first wavelength-selective coupler  1020  and second wavelength-selective coupler  1022  and third wavelength-selective coupler  1024  and fourth wavelength-selective coupler  1026 . In this example, this combination of optical waveguides can also serve as a resonator for signal light  1014 . Tuning electrode  1064  for signal loop extension  1004  is located along signal loop  1054  and can operate to achieve electrically controlled optical phase shifting for signal light  1014 . 
     In this depicted example, idler light  1016  travels in idler loop  1056 . Idler loop  1056  extends through idler loop extension  1006 , and tuning electrode  1066  for idler loop extension  1006  can operate to achieve an electrically controlled optical phase shifting for idler light  1016 . Lithium niobate is an electro-optic material for which the material refractive index can be changed by applying an electrical field. A material such as lithium niobate can be used in the segment  1044  of signal loop extension  1004  adjacent to tuning electrode  1064  and in the section  1046  of idler loop extension  1006  adjacent to tuning electrode  1066 . 
     In this illustrative example, pump loop extension  1002  does not have a tuning electrode. Tuning electrode  1060  can be used adjacent to main nonlinear optical waveguide  1010  and can operate to achieve some electrical control of the optical phase shift for pump light  1012 . However, the use of tuning electrode  1060  can affect the round-trip phase shift of pump light  1012 , as well as the round-trip phase shifts of signal light  1014  and idler light  1016 . 
     These tuning electrodes in optical waveguide structure  1000  can apply voltages to obtain desired levels of phase shifts for the pump light  1012 , signal light  1014  and idler light  1016  to achieve resonance matching  300  in  FIG.  5    for those three wavelengths of light traveling within optical waveguide structure  1000 . These tuning electrodes in optical waveguide structure  1000  also can apply voltages to obtain desired levels of phase shifts for the pump light  1012 , signal light  1014  and idler light  1016  to achieve roundtrip phase matching  302  for the combination of those three wavelengths of light traveling within optical waveguide structure  1000 . 
     With reference now to  FIG.  15   , an illustration of an optical waveguide structure with five optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  1400  is an example of an implementation for optical waveguide structure  100  as shown in  FIGS.  1 - 6   . As depicted, optical waveguide structure  1400  comprises optical waveguides in the form of main nonlinear optical waveguide  1410 , segments of secondary optical waveguide  1408 , pump loop extension  1402 , signal loop extension  1404 , and idler loop extension  1406 . 
     In this illustrative example, main nonlinear optical waveguide  1410  is comprised of a nonlinear optical material  104 . 
     As depicted, pump loop extension  1402  is comprised of a non-nonlinear optical material, such as non-nonlinear optical material  105 . In this example, idler loop extension  1406  is comprised of an electro-optic material  103  that also can have a large second-order nonlinear optical coefficient. In this example, signal loop extension  1404  is comprised of a nonlinear optical material, such as nonlinear optical material  104 , that also has a large electro-optic coefficient. 
     As depicted, optical waveguide structure  1400  includes pump input optical waveguide  1432  that inputs pump light  1412 . Optical waveguide structure  1400  also includes signal output optical waveguide  1434  and idler output optical waveguide  1436 . Signal output optical waveguide  1434  can output signal light  1414 . Idler output optical waveguide  1436  can output idler light  1416 . 
     As depicted, first wavelength-selective coupler  1420  and second wavelength-selective coupler  1422  connect pump loop extension  1402  to main nonlinear optical waveguide  1410 . In this illustrative example, third wavelength-selective coupler  1424  and fourth wavelength-selective coupler  1426  connect idler loop extension  1406  to segment  1407  and segment  1409  of secondary optical waveguide  1408 . In this illustrative example, third wavelength-selective coupler  1424  and fourth wavelength-selective coupler  1426  also connect signal loop extension  1404  to segment  1407  and segment  1409  of secondary optical waveguide  1408 . 
     In this illustrative example, pump input coupler  1431  couples pump input optical waveguide  1432  to pump loop extension  1402 . Signal output coupler  1435  couples signal output optical waveguide  1434  to signal loop extension  1404 . Idler output coupler  1437  couples idler output optical waveguide  1436  to idler loop extension  1406 . 
     In this depicted example, pump loop  1452  is present for pump light  1412 . This pump loop  1452  is a resonator loop in which pump light  1412  travels in pump loop extension  1402  and in main nonlinear optical waveguide  1410 . 
     In this example, signal light  1414  travels in signal loop  1454 . As depicted, signal loop  1454  extends through main nonlinear optical waveguide  1410 , through segments  1407  and  1409  of secondary optical waveguide  1408 , and through signal loop extension  1404 . As shown in the figure, idler light  1416  travels in idler loop  1456 . Further, in this example, idler loop  1456  extends through main nonlinear optical waveguide  1410 , through segments  1407  and segment  1409  of secondary optical waveguide  1408 , and through idler loop extension  1406 . 
     As depicted, optical waveguide structure  1400  also includes phase shifters in the form of tuning electrodes. In this illustrative example, tuning electrode  1460  is located adjacent to main nonlinear optical waveguide  1410 . Tuning electrode  1464  is located adjacent to signal loop extension  1404 . Tuning electrode  1466  is located adjacent to idler loop extension  1406 . 
     In this illustrative example, a nonlinear optical process occurs in main nonlinear optical waveguide  1410  in optical waveguide structure  1400 . Main nonlinear optical waveguide  1410  is constructed using a material such as x-cut lithium niobate, which can have both a large second order nonlinear optical coefficient and a large electro-optic coefficient. 
     As depicted, main nonlinear optical waveguide  1410  has a straight segment  1470  and two corner segments, corner segment  1471  and corner segment  1473 . In this illustrative example, straight segment  1470  is aligned parallel to the y-axis of the x-cut lithium niobate crystal. Segment  1407  and segment  1409  are part of secondary optical waveguide  1408 . In this illustrative example, segment  1407  and segment  1409  are aligned parallel to the z-axis of the x-cut lithium niobate crystal. 
     In this depicted example, transverse-electric (TE) polarized light propagating in main nonlinear optical waveguide  1410  can encounter the largest electro-optic coefficient r 33  when the light travels in straight segment  1470  in main nonlinear optical waveguide  1410 . TE polarized light also encounters the largest electro-optic coefficient r 33  of x-cut lithium niobate when the light travels in segment  1474  of signal loop extension  1404  adjacent to tuning electrode  1464  and when the light travels in the portion of idler loop extension  1406  adjacent to tuning electrode  1466 . 
     As depicted, light travels in a clockwise direction through main nonlinear optical waveguide  1410 , pump loop extension  1402 , signal loop extension  1404 , and idler loop extension  1406 . This direction is selected by the configuration of the input and output couplers, such as pump input coupler  1431 , signal output coupler  1435 , and idler output coupler  1437 . However, these three input and output couplers could be configured to have the light travel in a counter-clockwise direction through main nonlinear optical waveguide  1410 , pump loop extension  1402 , signal loop extension  1404 , and idler loop extension  1406 , and by where pump light  1412  is supplied to pump input optical waveguide  1432 . Counter-clockwise travel is established by supplying pump light into the opposite end of pump input coupler  1431 , extracting signal light out from the opposite end of signal output coupler  1435 , and extracting idler light out from the opposite end of idler output coupler  1437 . 
     As depicted, first wavelength-selective coupler  1420  connects corner segment  1471  of main nonlinear optical waveguide  1410  to segment  1407  of secondary optical waveguide  1408 . Second wavelength-selective coupler  1422  connects segment  1409  of secondary optical waveguide  1408  to corner segment  1473  of main nonlinear optical waveguide  1410 . 
     As depicted, third wavelength-selective coupler  1424  and fourth wavelength-selective coupler  1426  operate to establish a resonator loop, idler loop  1456 , for idler light  1416  and also to establish a resonator loop, signal loop  1454 , for signal light  1414 . In this illustrative example, third wavelength-selective coupler  1424  extracts idler light  1416  away from segment  1407  of secondary optical waveguide  1408  and into the idler loop extension  1406 . Fourth wavelength-selective coupler  1426  returns idler light  1416  back into segment  1409  of secondary optical waveguide  1408  after idler light  1416  has propagated through idler loop extension  1406  while traveling in idler loop  1456 . 
     In this illustrative example, third wavelength-selective coupler  1424  also extracts signal light  1414  away from segment  1407  of secondary optical waveguide  1408  and into the signal loop extension  1404 . Fourth wavelength-selective coupler  1426  also returns signal light  1414  back into segment  1409  of secondary optical waveguide  1408  after signal light  1414  has propagated through signal loop extension  1404  while traveling in idler loop  1456 . Signal light  1414  travels to a thru-state output of third wavelength-selective coupler  1424  and travels to a thru-state output of fourth wavelength-selective coupler  1426 . Idler light  1416  travels to a cross-state output of third wavelength-selective coupler  1424  and travels to a cross-state output of fourth wavelength-selective coupler  1426 , as discussed before with reference to  FIG.  10   . 
     In this illustrative example, first wavelength-selective coupler  1420  and second wavelength-selective coupler  1422  operate to establish a resonator loop, pump loop  1452  for pump light  1412 . As depicted, first wavelength-selective coupler  1420  extracts pump light  1412  away from main nonlinear optical waveguide  1410  and into pump loop extension  1402  to travel in pump loop  1452 . Second wavelength-selective coupler  1422  returns pump light  1412  to main nonlinear optical waveguide  1410  after pump light  1412  has propagated through pump loop extension  1402  while traveling in pump loop  1452 . 
     In this illustrative example, the material for idler loop extension  1406  and the material for signal loop extension  1404  can be a material such as lithium niobate for which the electro-optic coefficient is large. The large electro-optic coefficient allows the phase shifters in the signal loop extension and the idler loop extension to be more efficient, producing a larger phase shift for a given applied voltage. But for lithium niobate, the second order nonlinear optical coefficient also is large. However, pump light  1412  is not supplied to these portions of optical waveguide structure  1400 , resulting in an absence of undesired nonlinear optical generation of additional signal or idler photons in these portions. In this illustrative example, pump loop extension  1402  is comprised of a non-nonlinear optical material. 
     As depicted, pump light  1412  propagates primarily only in main nonlinear optical waveguide  1410  and pump loop extension  1402 . The second order nonlinear optical coefficient is largest d 33  for light propagating in straight segment  1470  of main nonlinear optical waveguide  1410  and is smaller for light propagating in corner segment  1471  and corner segment  1473 . Also, the sign of a component d 22  of the second order nonlinear optical coefficient in corner segment  1471  is opposite from the sign of that component of the second order nonlinear optical coefficient in corner segment  1473 . As a result, the generation of signal light  1414  and idler light  1416  occurs mainly in straight segment  1470  and occurs much less in other portions of optical waveguide structure  1400  because of the manner in which pump light  1412  is introduced and removed from main nonlinear optical waveguide  1410 . 
     In this illustrative example, pump light  1412  can be extracted from main nonlinear optical waveguide  1410  before idler light  1416  is extracted from main nonlinear optical waveguide  1410  through secondary optical waveguide  1408  into idler loop extension  1406 . Also in this example, pump light  1412  is re-supplied to main nonlinear optical waveguide  1410  from pump loop extension  1402  after idler light  1416  is re-supplied to main nonlinear optical waveguide  1410  from idler loop extension  1406  through secondary optical waveguide  1408 . A similar arrangement applies for the pump light  1412  in relation to the signal light  1414 . 
     As a result, although the nonlinear optical material is present along the entire length of the signal loop  1054  for signal light  1414  and idler loop  1456  for idler light  1416 , the nonlinear optical generation of photons for signal light  1414  and idler light  1416  from photons for pump light  1412  occurs only in main nonlinear optical waveguide  1410 . Nonlinear optical generation of signal light  1414  and idler light  1416  is absent in secondary optical waveguide  1408 , idler loop extension  1406  and signal loop extension  1404 . The absence of nonlinear optical generation is because pump light  1412  is supplied only to main nonlinear optical waveguide  1410 . 
     A nonlinear optical generation process can result in generation of lower intensity light from higher intensity light. A nonlinear optical generation process also can operate in reverse and result in the generation of a higher intensity light from a lower intensity light. The efficiency of the nonlinear optical generation process depends on the intensity of the source light involved in that generation process, or the intensities of the source light of several different wavelengths if source light of multiple wavelengths is involved in that process. For spontaneous parametric down conversion as an illustrative example of a nonlinear optical generation process, the pump light, which is the input or source light, has an intensity that is at least twice the intensity of the generated signal light and at least twice the intensity of the generated idler light. 
     In many examples of spontaneous parametric down conversion, the intensity of the pump light is at least ten times greater than the intensity of the signal light or of the idler light. Thus, even when a phase-matched condition is present, if the pump light is absent from an optical waveguide comprising nonlinear optical material and only signal and idler light are present, the reverse process in which pump light, or light at the pump wavelength, is generated from the weaker source light at the signal and idler wavelengths is much less efficient and may produce very little or possibly even negligible light at the pump wavelength. 
     With reference next to  FIG.  16   , an illustration of an optical waveguide structure with five optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  1200  is an example of an implementation for optical waveguide structure  100  as shown in  FIGS.  1 - 6   . 
     As depicted, optical waveguide structure  1200  comprises optical waveguides in the form of main nonlinear optical waveguide  1210 , pump loop extension  1202 , secondary optical waveguide  1208 , signal loop extension  1204 , and idler loop extension  1206 . Main nonlinear optical waveguide  1210  is an example of main nonlinear optical waveguide  106  in  FIG.  3    and main nonlinear optical waveguide  106  in  FIG.  2   . Pump loop extension  1202  is an example of an implementation for first extension optical waveguide  108  in  FIG.  3    and first extension optical waveguide  108  in  FIG.  2   . Idler loop extension  1206  and signal loop extension  1204  are optical waveguides that can be coupled to secondary optical waveguide  113  in  FIG.  3    or coupled to secondary optical waveguide  113  in  FIG.  2   . 
     In this illustrative example, first loop  1252  through main nonlinear optical waveguide  1210  and pump loop extension  1202  has a rectangular shape with curved corners and may also be referred to as a racetrack shape. First loop  1252  for the pump light is a closed path route. 
     As depicted in this example, first loop  1252  for pump light  1212  through main nonlinear optical waveguide  1210  and through pump loop extension  1202  traverses segments of waveguide comprised of nonlinear optical material  104  and segments of waveguide comprised of non-nonlinear optical material  105 . The nonlinear optical material is present in main nonlinear optical waveguide  1210 , which includes straight segment  1270  corner segment  1271 , and corner segments  1273 . The nonlinear optical material also is present in portions of corner segment  1275  and corner segment  1277  of pump loop extension  1202 . A non-nonlinear optical material  105  is present in segment  1272  of pump loop extension  1202 . 
     A non-nonlinear optical material also can be present in corner segment  1275  and corner segment  1277  of pump loop extension  1202  instead of the nonlinear optical material. As depicted in this figure, a tapered transition  1247  can be present between the portion of corner segment  1275  and corner segment  1277  that contains a nonlinear optical material and the portion of corner segment  1275  and corner segment  1277  that does not contain a nonlinear optical material but rather comprises only non-nonlinear optical material. 
     In this illustrative example, both signal loop extension  1204  and idler loop extension  1206  have portions that comprise an electro-optic material  103  that also is a nonlinear optical material  104  and other portions that comprise a non-nonlinear optical material  105 . The electro-optic material is located in section  1244  of signal loop extension  1204  and in section  1246  of idler loop extension  1206 . To reduce optical losses and reflections, there can be a tapered transition  1249  between a waveguide portion comprising an electro-optic material and a waveguide portion comprising a non-nonlinear optical material. 
     As depicted, optical waveguide structure  1200  also includes pump input optical waveguide  1232  that inputs pump light  1212 . Optical waveguide structure  1200  also includes signal output optical waveguide  1234  and idler output optical waveguide  1236 . Signal output optical waveguide  1234  can output signal light  1214 . Idler output optical waveguide  1236  can output idler light  1216 . 
     In this illustrative example, pump optical coupler  1231  couples pump input optical waveguide  1232  to pump loop extension  1202 . Signal optical coupler  1235  couples signal output optical waveguide  1234  to signal loop extension  1204 . Idler optical coupler  1237  couples idler output optical waveguide  1236  to idler loop extension  1206 . 
     In this illustrative example, first wavelength-selective coupler  1220  and second wavelength-selective coupler  1222  connect pump loop extension  1202  to main nonlinear optical waveguide  1210 . Pump light  1212  is coupled via the thru-state outputs of first wavelength-selective coupler  1220  and second wavelength-selective coupler  1222 . As depicted, first wavelength-selective coupler  1220  and second wavelength-selective coupler  1222  also connect signal light  1214  and idler light  1216  between main nonlinear optical waveguide  1210  and segments of secondary optical waveguide  1208 . Signal light  1214  and idler light  1216  are coupled via the cross-state outputs of first wavelength-selective coupler  1220  and second wavelength-selective coupler  1222 . In this illustrative example, third wavelength-selective coupler  1224  and fourth wavelength-selective coupler  1226  connect idler loop extension  1206  to segment  1207  and segment  1209  of secondary optical waveguide  1208 . Third wavelength-selective coupler  1224  and fourth wavelength-selective coupler  1226  also connect signal loop extension  1204  to segment  1207  and segment  1209  of secondary optical waveguide  1208 . Signal light  1214  is coupled via the thru-state outputs of third wavelength-selective coupler  1224  and fourth wavelength-selective coupler  1226 . Idler light  1216  is coupled via the cross-state outputs of third wavelength-selective coupler  1224  and fourth wavelength-selective coupler  1226 . 
     In this illustrative example, first loop  1252  is present for pump light  1212 . This first loop is a resonator loop in which pump light  1212  travels in main nonlinear optical waveguide  1210  and in pump loop extension  1202 . Signal light  1214  travels in second loop  1254 . As depicted, second loop  1254  extends through main nonlinear optical waveguide  1210 , through segment  1207  and segment  1209  of secondary optical waveguide  1208  and through signal loop extension  1204 . In this illustrative example, idler light  1216  travels in third loop  1256 . As depicted, third loop  1256  extends through main nonlinear optical waveguide  1210 , through segment  1207  and segment  1209  of secondary optical waveguide  1208 , and through idler loop extension  1206 . 
     As depicted, optical waveguide structure  1200  also includes phase shifters in the form of tuning electrodes. In this illustrative example, tuning electrode  1260  is located adjacent to section  1240  in main nonlinear optical waveguide  1210 . Tuning electrode  1264  is located adjacent to section  1244  in signal loop extension  1204  and tuning electrode  1266  is located adjacent to section  1246  in idler loop extension  1203 . These tuning electrodes can apply voltages to obtain a desired level of resonance to achieve a resonant condition for light traveling within optical waveguide structure  1200 . 
     In this illustrative example of optical waveguide structure  1200  having triple partially overlapping loop resonators for entanglement with direction dependent material, pump light  1212 , signal light  1214 , and idler light  1216  travel in different resonator loops, first loop  1252 , second loop  1254 , and third loop  1256 , respectively. First loop  1252  is a resonator loop for the pump light  1212  and extends through main nonlinear optical waveguide  1210 , first wavelength-selective coupler  1220  (via its thru-state output), second wavelength-selective coupler  1222  (via its thru-state output), pump loop extension  1202 , and pump optical coupler  1231  (via its thru-state output). 
     In this illustrative example, second loop  1254  is a resonator loop for signal light  1214 . Second loop  1254  extends through main nonlinear optical waveguide  1210 , first wavelength-selective coupler  1220  (via its cross-state output), segment  1207  of secondary optical waveguide  1208 , third wavelength-selective coupler  1224  (via its thru-state output), signal loop extension  1204 , and signal optical coupler  1235  (via its thru-state output) fourth wavelength-selective coupler  1226  (via its thru-state output), segment  1209  of secondary optical waveguide  1208 , and second wavelength-selective coupler  1222  (via its cross-state output), looping again to main nonlinear optical waveguide  1210 . 
     As depicted, third loop  1256  is a resonator loop for idler light  1216 . This third loop  1256  extends through main nonlinear optical waveguide  1210 , first wavelength-selective coupler  1220  (via its cross-state output); segment  1207  of secondary optical waveguide  1208  located between first wavelength-selective coupler  1220  and third wavelength-selective coupler  1224 ; third wavelength-selective coupler  1224  (via its cross-state output); idler loop extension  1206 ; idler optical coupler  1237  (via its thru-state output); fourth wavelength-selective coupler  1226  (via its cross-state output); segment  1209  of secondary optical waveguide  1208  located between fourth wavelength-selective coupler  1226  and second wavelength-selective coupler  1222 ; and second wavelength-selective coupler  1222  (via its cross-state output); looping back to main nonlinear optical waveguide  1210 . 
     In this illustrative example of optical waveguide structure  1200  having triple partially overlapping loop resonators for entanglement constructed from a direction dependent material, main nonlinear optical waveguide  1210  is common to and overlaps all three loop resonators. Also, first wavelength-selective coupler  1220  and second wavelength-selective coupler  1222  are encountered by the light in all three loops. However, first loop  1252  for pump light  1212  encounters the thru-state of these couplers. In this example, second loop  1254  and third loop  1256  for signal light  1214  and idler light  1216 , respectively, encounter the cross-state of these couplers. 
     In this illustrative example, a second-order nonlinear optical process such as spontaneous parametric down conversion occurs in optical waveguide structure  1200 . Nonlinear optical generation of signal photons and idler photons from pump photons, which is a result of spontaneous parametric down conversion, occurs when pump light propagates in an optical waveguide comprising nonlinear optical material such as lithium niobate which has a large second-order nonlinear optical coefficient. Optical waveguide structure  1200  includes main nonlinear optical waveguide  1210 . Main nonlinear optical waveguide  1210  is the primary part of optical waveguide structure  1200  for which pump light  1212  is present and propagates in a waveguide comprising nonlinear optical material. As result, most of the generation of signal photons and idler photons from pump photons occurs in main nonlinear optical waveguide  1210 . Essentially, negligible generation of signal photons and idler photons occurs in other portions of optical waveguide structure  1200 . As depicted, main nonlinear optical waveguide  1210  comprises a nonlinear optical material. Most of the pump loop extension  1202 , such as portion or segment  1272  of pump loop extension  1202  does not comprise a nonlinear optical material. 
     The various optical waveguides in optical waveguide structure  1200  can be fabricated using x-cut lithium niobate and in particular, from x-cut thin-film lithium niobate. In this illustrative example, straight segment  1270  in main nonlinear optical waveguide  1210  and segment  1272  in pump loop extension  1202  can be considered long legs of a rectangular-shaped path with curved corners or of a racetrack shaped path. These two segments are oriented to be aligned parallel to the y-axis of the x-cut lithium niobate crystal. As depicted, corner segments  1271  and  1273  of main nonlinear optical waveguide  1210  together with corner segment  1275  and corner segment  1277  of pump loop extension  1202  are the short legs of this rectangular-shaped or racetrack shaped path. The straight portions of corner segment  1271  and corner segment  1275  closest to first wavelength-selective coupler  1220  and the straight portions of corner segment  1273  and corner segment  1277  closest to second wavelength-selective coupler  1222  are aligned parallel to the z-axis of the x-cut lithium niobate crystal. In this example, transverse-electric (TE) polarized light propagating in main nonlinear optical waveguide  1210  encounters the largest second order nonlinear optical coefficient d 33  when the light travels in straight segment  1270  in main nonlinear optical waveguide  1210 . 
     In this example, when phase matching is achieved, most of the nonlinear optical generation of signal light  1214  and idler light  1216  occurs in straight segment  1270  of main nonlinear optical waveguide  1210 . Some nonlinear optical generation of signal and idler photons also occurs in corner segments  1271  and  1273  of main nonlinear optical waveguide  1210 . Some generation of signal light  1214  and idler light  1216  also can occur in portions of corner segment  1275  and corner segment  1277  of pump loop extension  1202  because these portions comprise nonlinear optical material, as depicted in  FIG.  16   . However, the second order nonlinear optical coefficient d 22  for transverse-electric (TE) polarized light in these portions is more than one order of magnitude smaller than the second order nonlinear optical coefficient d 33  for transverse-electric (TE) polarized light in straight segment  1270  in this illustrative example. Moreover, the nonlinear optical generation of signal and idler photons that occurs in corner segment  1275  is partially counter-acted by the nonlinear optical generation of signal and idler photons that occurs in corner segment  1277 . This is because the second order nonlinear optical coefficient d 22  in these two segments have opposite sign. Segment  1272  in pump loop extension  1202  comprises a non-nonlinear optical material. Thus, no generation of signal and idler photons occurs in that segment. 
     Turning next to  FIG.  17   , an illustration of an optical waveguide structure with five optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  1300  is an example of an implementation for optical waveguide structure  100  as shown in  FIGS.  1 - 6   . As depicted, optical waveguide structure  1300  comprises optical waveguides in the form of main nonlinear optical waveguide  1310 , secondary optical waveguide  1308  having segment  1307  and segment  1309 , pump loop extension  1302 , signal loop extension  1304 , and idler loop extension  1306 . 
     In this illustrative example, main nonlinear optical waveguide  1310  and pump loop extension  1302  form a path that has a rectangular shape with curved corners and may also be referred to as a racetrack shape. Main nonlinear optical waveguide  1310  is comprised of a nonlinear optical material  104 . Pump loop extension  1302  also is comprised of a nonlinear optical material  104 . Optical waveguide structure  1300  is similar to optical waveguide structure  1200  in  FIG.  16    but with the entire length of pump loop extension  1302  being comprised of nonlinear optical material  104  rather than having a portion of its length being comprised of a non-nonlinear optical material  105 . In this example, main nonlinear optical waveguide  1310  has at least portion  1340  that comprises an electro-optic material  103 . Also, pump loop extension  1302  has at least portion  1342  that comprises an electro-optic material. 
     As depicted in this illustrative example, both signal loop extension  1304  and idler loop extension  1306  have a portion of their length comprising a nonlinear optical material  104  and another portion of their length comprising a non-nonlinear optical material  105 . Nonlinear optical material  104  is included in these waveguides because nonlinear optical material  104  is electro-optic material  103  that is efficient with a large electro-optic coefficient. The portion of waveguide with the electro-optic (and nonlinear optical) material is located in section  1344  of signal loop extension  1304  and in section  1346  of idler loop extension  1306 . 
     As depicted, optical waveguide structure  1300  includes pump input optical waveguide  1332  that inputs pump light  1312 . Optical waveguide structure  1300  also includes signal output optical waveguide  1334  and idler output optical waveguide  1336 . Signal output optical waveguide  1334  can output signal light  1314 . Idler output optical waveguide  1336  can output idler light  1316 . 
     In this illustrative example, pump optical coupler  1331  couples pump input optical waveguide  1332  to pump loop extension  1302 . Signal optical coupler  1335  couples signal output optical waveguide  1334  to signal loop extension  1304 . Idler optical coupler  1337  couples idler output optical waveguide  1336  to idler loop extension  1306 . 
     As depicted, first wavelength-selective coupler  1320  and second wavelength-selective coupler  1322 , operated in their thru-state, connect pump loop extension  1302  to main nonlinear optical waveguide  1310 . In this illustrative example, first wavelength-selective coupler  1320  and second wavelength-selective coupler  1322  operated in their cross-state connect the segments of secondary optical waveguide  1308  to main nonlinear optical waveguide  1310 . In this illustrative example, third wavelength-selective coupler  1324  and fourth wavelength-selective coupler  1326  operated in their thru-state connect signal loop extension  1304  to segments of secondary optical waveguide  1308 . In this illustrative example, third wavelength-selective coupler  1324  and fourth wavelength-selective coupler  1326  operated in their cross-state connect idler loop extension  1306  to segments of secondary optical waveguide  1308 . 
     In this illustrative example, first loop  1352  is present for pump light  1312 . This first loop is a resonator loop in which pump light  1312  travels in a route that extends through main nonlinear optical waveguide  1310  and pump loop extension  1302 . Signal light  1314  travels in second loop  1354 . As depicted, second loop  1354  extends through main nonlinear optical waveguide  1310 , through segments of secondary optical waveguide  1308  and through signal loop extension  1304 . In this illustrative example, idler light  1316  travels in third loop  1356 . As depicted, third loop  1356  extends through main nonlinear optical waveguide  1310 , through segments of secondary optical waveguide  1308 , and through idler loop extension  1306 . 
     In this illustrative example, first wavelength-selective coupler  1320  operating in its thru-state connects segment  1371  of main nonlinear optical waveguide  1310  and segment  1375  of pump loop extension  1302 , and second wavelength-selective coupler  1322  connects segment  1377  of pump loop extension  1302  and segment  1373  of main nonlinear optical waveguide  1310 . As depicted, first wavelength-selective coupler  1320 , operating in its thru-state, couples pump light  1312  away from main nonlinear optical waveguide  1310  and into pump loop extension  1302  and second wavelength-selective coupler  1322 , operating in its thru-state, couples pump light  1312  away from pump loop extension  1302  and into main nonlinear optical waveguide  1310  such that pump light  1312  travels in first loop  1352 . 
     In this illustrative example, first wavelength-selective coupler  1320 , operating in its cross-state, extracts signal light  1314  and idler light  1318  away from main nonlinear optical waveguide  1310  and into segment  1307  of secondary optical waveguide  1308  such that signal light  1314  generated in main nonlinear optical waveguide  1310  does not travel in first loop  1352  but instead travels in second loop  1354  and idler light  1316  generated in main nonlinear optical waveguide  1310  does not travel in first loop  1352  but instead travels in third loop  1356 . In this illustrative example, second wavelength-selective coupler  1322 , operating in its cross-state, returns signal light  1314  traveling in second loop  1354  and idler light  1316  traveling in third loop  1356  back through main nonlinear optical waveguide  1310 . 
     In this illustrative example, signal light  1314  reaches signal loop extension  1304  by passing through a segment  1307  of secondary optical waveguide  1308  before being coupled by third wavelength-selective coupler  1324 , operating in its thru-state, into signal loop extension  1304 . Additionally, signal light  1314  is returned from signal loop extension  1304  into a segment  1309  of secondary optical waveguide  1308  by fourth wavelength-selective coupler  1326 , operating in its thru-state. In this example, signal light  1314  passes through another portion, segment  1309 , of secondary optical waveguide  1308  before being coupled back into main nonlinear optical waveguide  1310  by second wavelength-selective coupler  1322 , operating in its cross-state. 
     In this illustrative example, idler light  1316  reaches idler loop extension  1306  by passing through a segment  1307  of secondary optical waveguide  1308  before being coupled by third wavelength-selective coupler  1324 , operating in its cross-state, into the idler loop extension  1306 . Additionally, idler light  1316  is returned from idler loop extension  1306  into another segment  1309  of secondary optical waveguide  1308  by fourth wavelength-selective coupler  1326 , operating in its cross-state. In this example, idler light  1316  passes through another portion of secondary optical waveguide  1308  before being coupled back into main nonlinear optical waveguide  1310  by second wavelength-selective coupler  1322 , operating in its cross-state. 
     In this illustrative example, pump light  1312 , signal light  1314 , and idler light  3016  travel in different resonator loops. In this illustrative example, first loop  1352  is a resonator loop for pump light  1312 . First loop  1352  extends through main nonlinear optical waveguide  1310 , pump loop extension  1302 , first wavelength-selective coupler  1320 , and second wavelength-selective coupler  1322 . 
     Second loop  1354  is resonator loop for signal light  1314 . This second loop extends through main nonlinear optical waveguide  1310 , first wavelength-selective coupler  1320  and second wavelength-selective coupler  1322 ; segments  1307 ,  1309  of secondary optical waveguide  1308 , third wavelength-selective coupler  1324 ; fourth wavelength-selective coupler  1326 ; and signal loop extension  1304 . 
     Third loop  1356  is a resonator loop for idler light  1316 . Third loop  1356  comprises main nonlinear optical waveguide  1310 ; first wavelength-selective coupler  1320 ; a segment  1307  of secondary optical waveguide  1308  between first wavelength-selective coupler  1320  and third wavelength-selective coupler  1324 ; third wavelength-selective coupler  1324 ; idler loop extension  1306 ; fourth wavelength-selective coupler  1326 ; a segment  1309  of secondary optical waveguide  1308  between fourth wavelength-selective coupler  1326  and second wavelength-selective coupler  1322 . 
     As depicted, optical waveguide structure  1300  also includes phase shifters in the form of tuning electrodes. In this illustrative example, tuning electrode  1360  is located adjacent to a portion  1340  of main nonlinear optical waveguide  1310 . Tuning electrode  1362  is located adjacent to a portion  1342  of pump loop extension  1302 . Tuning electrode  1364  is located adjacent to section  1344  of signal loop extension  1304  and tuning electrode  1366  is located adjacent to section  1346  of idler loop extension  1306 . These tuning electrodes can apply voltages to obtain desired level of resonance to achieve a resonant condition for light traveling within optical waveguide structure  1300 . These tuning electrodes also can apply voltages to obtain a desired round-trip phase matching condition for the nonlinear optical generation process that occurs in optical waveguide structure  1300 . 
     Compared to optical waveguide structure  1200  of  FIG.  16   , optical waveguide structure  1300  has four tuning electrodes rather than three tuning electrodes. The additional tuning electrode (or set of tuning electrodes) provides greater flexibility for simultaneously achieving resonance conditions for all three wavelengths of light - pump light  1312 , signal light  1314 , and idler light  1316  in their respective resonator loops, first loop  1352 , second loop  1354  and third loop  1356  as well as to achieve round-trip phase matching. For example, tuning electrode  1360  can be used to adjust the round-trip phase Φ RTp  of pump light  1312  in first loop  1352 . Tuning electrode  1364  can be used to adjust the round-trip phase Φ RTs  of signal light  1314  in second loop  1354 , which is a signal loop. Tuning electrode  1366  can be used to adjust the round-trip phase Φ RTi  of idler light  1316  in third loop  1356 , which is an idler loop. Tuning electrode  1362  can be used to further adjust the round-trip phase Φ RTp  of pump light  1312  in order to achieve round-trip phase matching for the nonlinear optical process that occurs in main nonlinear optical waveguide  1310 . Using the terminology defined with reference to optical waveguide structure  1100  shown in  FIG.  13   , the round-trip phase matching condition is achieved when: 
     Φ RTp  - Φ RTs  - Φ RTi  = 2πA 
     where A is an integer, and can be zero. This means: P - S - I = A with the integers P, S and I defined earlier with reference to optical waveguide structure  1100  shown in  FIG.  13   . Thus, for the example of optical waveguide structure  1300 , the four conditions for achieving integer values for the parameters P, S, I and A can be satisfied by adjusting the four tuning electrodes, tuning electrode  1360 , tuning electrode  1364 , tuning electrode  1366  and tuning electrode  1362 . 
     In this illustrative example, electrically controlled phase shifts are provided in optical waveguide structure  1300 . In this illustrative example, portions of optical waveguide structure  1300  can be fabricated in x-cut lithium niobate. As depicted, the main nonlinear optical waveguide  1310  and pump loop extension  1302  through which the first loop  1352  extends form a rectangular shape with rounded corners. The orientation of optical waveguide structure  1300  can be such that segment  1370  in main nonlinear optical waveguide  1310  and segment  1372  in pump loop extension  1302  are aligned parallel to the y-axis of the lithium niobate crystal in the x-cut lithium niobate. These two segments —segment  1370  of main nonlinear optical waveguide  1310  and segment  1372  of pump loop extension  1302  - can be referred to as the long legs of the rectangular shape. 
     The other portions of optical waveguides in the rectangular shaped waveguide structure defined by first loop  1352  include segment  1371  and segment  1373  of main nonlinear optical waveguide  1310  as well as segment  1375  and segment  1377  of pump loop extension  1302 . These segments are part of what can be referred to as the corners and short legs of the rectangular shaped or race-track shaped path traversed by first loop  1352 . In this illustrative example, segment  1371 , segment  1373 , segment  1375  and segment  1377  together with first wavelength-selective coupler  1320  and second wavelength-selective coupler  1322  are aligned mainly parallel with the z-axis of the x-cut lithium niobate crystal. 
     In this illustrative example, orientation for optical waveguide structure  1300 , transverse-electric (TE) polarized light propagating in the optical waveguides traversed by first loop  1352  encounters the largest electro-optic coefficient of x-cut lithium niobate when the light travels in portion  1340  and portion  1342  of main nonlinear optical waveguide  1310  and pump loop extension  1302 , respectively. Portion  1340  and portion  1342  portions in which tunable phase shifts can occur. As depicted, the light travels in a clockwise direction around first loop  1352 . Furthermore, TE polarized signal light traversing portion in section  1344  of signal loop extension  1304  and TE polarized idler light traversing portion in section  1346  of idler loop extension  1306  also encounter the largest electro-optic coefficient of x-cut lithium niobate. Thus, the orientation depicted in  FIG.  17    for optical waveguide structure  1300  can achieve efficient voltage-controlled electro-optic phase shifting. 
     In this illustrative example, a nonlinear optical light generation process occurs in main nonlinear optical waveguide  1310 . Furthermore, to increase the nonlinear optical generation of signal and idler light that occurs in a given round-trip, it is desirable to meet another phase matching condition for propagation of the three wavelengths of light through segment  1370  of main nonlinear optical waveguide  1310 , which is the portion where most of the desired nonlinear optical generation occurs. This phase matching can be as follows:  
     
       
         
           
             0 
             ≤ 
             
               ϕ 
               
                 M 
                 u 
                 p 
               
             
             − 
             
               ϕ 
               
                 M 
                 u 
                 s 
               
             
             − 
             
               ϕ 
               
                 M 
                 u 
                 i 
               
             
             ≤ 
             π 
             , 
               
             or 
               
             − 
             π 
               
             ≤ 
             
               ϕ 
               
                 M 
                 u 
                 p 
               
             
             − 
             
               ϕ 
               
                 M 
                 u 
                 s 
               
             
             − 
             
               ϕ 
               
                 M 
                 u 
                 i 
               
             
             ≤ 
             0 
             , 
           
         
       
     
      and is close to zero. 
     Many materials such as lithium niobate that have a large electro-optic coefficient for a certain orientation also have a large second-order nonlinear optical coefficient. In this illustrative example, transverse-electric (TE) polarized light propagating in the optical waveguides traversed by first loop  1352 , which is a pump loop, encounters the largest second order nonlinear optical coefficient when the light travels in segment  1370  of main nonlinear optical waveguide  1310  and in segment  1372  of pump loop extension  1302 . In this illustrative example, the entire length of the optical waveguides traversed by the light in first loop  1352 , which includes main nonlinear optical waveguide  1310  and pump loop extension  1302 , comprises a nonlinear optical material. As a result, photons for signal light  1314  and idler light  1316  can be generated both in segment  1370  of main nonlinear optical waveguide  1310  and in segment  1372  of pump loop extension  1302 . Some, albeit typically less, generation of signal and idler light also occurs in the corner segments, segment  1371 , segment  1373 , segment  1375  and segment  1377 . 
     In this illustrative example, the optical fields of signal light  1314  and idler light  1316  generated in an optical waveguide segment that comprises nonlinear optical material can be described by expressions such as: 
     
       
         
           
             
               A 
               i 
             
             
               L 
             
             = 
             
               
                 
                   ω 
                   i 
                   2 
                 
               
               
                 
                   k 
                   i 
                 
                 
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                     A 
                     B 
                   
                 
               
             
             
               
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                   A 
                   p 
                 
                 
                   A 
                   s 
                 
               
               1 
             
             
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                 k 
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             d 
             z 
             ~ 
             
               
                 2 
                 i 
                 
                   d 
                   
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                     f 
                     f 
                   
                 
                 
                   ω 
                   i 
                   2 
                 
                 
                   A 
                   p 
                 
                 
                   A 
                   s 
                 
                 L 
               
               
                 
                   k 
                   i 
                 
                 
                   c 
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                       e 
                       
                         i 
                         
                           
                             
                               ϕ 
                               
                                 M 
                                 u 
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                             − 
                             
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                                 M 
                                 u 
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                             − 
                             
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                                 M 
                                 u 
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                         − 
                         1 
                       
                     
                   
                   
                     i 
                     
                       
                         
                           ϕ 
                           
                             M 
                             u 
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                         − 
                         
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                             M 
                             u 
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                         − 
                         
                           ϕ 
                           
                             M 
                             u 
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      and 
     
       
         
           
             
               A 
               s 
             
             
               L 
             
             = 
             
               
                 
                   ω 
                   s 
                   2 
                 
               
               
                 
                   k 
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                 ∫ 
                 
                   
                       
                     A 
                     B 
                   
                   
                     
                       2 
                       i 
                       
                         d 
                         
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                           f 
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                         A 
                         p 
                       
                       
                         A 
                         i 
                       
                     
                     1 
                   
                   
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                       2 
                       i 
                       
                         d 
                         
                           e 
                           f 
                           f 
                         
                       
                       
                         ω 
                         s 
                         2 
                       
                       
                         A 
                         p 
                       
                       
                         A 
                         i 
                       
                       L 
                     
                     
                       
                         k 
                         s 
                       
                       
                         c 
                         2 
                       
                     
                   
                 
               
             
             
               
                 
                   
                     
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                         i 
                         
                           
                             
                               ϕ 
                               
                                 M 
                                 u 
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                             − 
                             
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                                 M 
                                 u 
                                 s 
                               
                             
                             − 
                             
                               ϕ 
                               
                                 M 
                                 u 
                                 i 
                               
                             
                           
                         
                       
                     
                     − 
                     1 
                   
                   
                     i 
                     
                       
                         
                           ϕ 
                           
                             M 
                             u 
                             p 
                           
                         
                         − 
                         
                           ϕ 
                           
                             M 
                             u 
                             s 
                           
                         
                         − 
                         
                           ϕ 
                           
                             M 
                             u 
                             i 
                           
                         
                       
                     
                   
                 
               
             
             . 
           
         
       
     
     In these expression, A and B are the starting and ending points of a segment, such as segment  1370  of main nonlinear optical waveguide  1310  or segment  1372  of pump loop extension  1302 , with L being the length of that segment. The subscripts i, s, and p indicate pump, signal, and idler, respectively. The second order nonlinear optical coefficient d eff  in segment  1370  has the opposite sign from the second order nonlinear optical coefficient d eff  in segment  1372 . As a result, the contributions to the signal and idler optical fields from segment  1370  of main nonlinear optical waveguide  1310  and segment  1372  of pump loop extension  1302  can counteract each other, or the optical fields can interfere in a destructive manner, if the optical fields from these two segments are combined together, assuming the phase matching is perfect. 
     Optical waveguide structure  1300  avoids the interaction of signal and idler light generated in segment  1370  with signal and idler light generated in segment  1372 . First wavelength-selective coupler  1320  functions to couple signal light  1314  and idler light  1316  generated in segment  1370  away from pump loop extension  1302  and thus away from segment  1372  by diverting that light into segment  1307  of secondary optical waveguide  1308 . Similarly, second wavelength-selective coupler  1322  functions to couple signal light  1314  and idler light  1316  generated in segment  1372  away from main nonlinear optical waveguide  1310  and thus away from segment  1370 , as shown by arrow  1380  into output optical waveguide  1305 . This coupling function done by second wavelength-selective coupler  1322  is performed in addition to coupling signal light  1314  in second loop  1354  and idler light  1316  in third loop  1356  from segment  1309  of secondary optical waveguide  1308  into main nonlinear optical waveguide  1310 . Thus, the signal light  1314  and idler light  1316  coupled back into main nonlinear optical waveguide  1310  through second wavelength-selective coupler  1322  is generated in a prior pass through main nonlinear optical waveguide  1310  and is not generated in the pump loop extension  1302 . 
     As a result, any destructive interaction between signal light  1314  and idler light  1316  generated in segment  1370  and generated in segment  1372  is absent. Thus, signal light  1314  and idler light  1316  that result from circulation through many round-trips in the optical waveguide structure  1300  are those photons for signal light  1314  and idler light  1316  generated primarily in segment  1370  in main nonlinear optical waveguide  1310 . 
     Next,  FIG.  18    is an illustration of an optical waveguide structure with ten optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  1500  is an example of an implementation for optical waveguide structure  100  as shown in  FIGS.  1 - 6   . More specifically,  FIG.  18    is an implementation for optical waveguides  102  as depicted in  FIG.  2   . 
     As depicted, optical waveguide structure  1500  comprises optical waveguides in the form of first main nonlinear optical waveguide segment  1510 A, second main nonlinear optical waveguide segment  1510 B, first pump bypass optical waveguide  1502 A, second pump bypass optical waveguide  1502 B, first secondary optical waveguide portion  1508 A, second secondary optical waveguide portion  1508 B, first signal loop extension  1504 A, second signal loop extension  1504 B, first idler loop extension  1506 A, and second idler loop extension  1506 B. First main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B of main nonlinear optical waveguide  1510  are examples of main nonlinear optical waveguide  106  in  FIG.  2   . First pump bypass optical waveguide  1502 A and second pump bypass optical waveguide  1502 B are examples of an implementation for first extension optical waveguide  108  in  FIG.  2   . First secondary optical waveguide portion  1508 A and second secondary optical waveguide portion  1508 B are examples of an implementation of secondary optical waveguide  113  in  FIG.  2   . 
     As depicted in the detailed illustrative example of  FIG.  18   , main nonlinear optical waveguide  1510  comprises two separate segments, first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B. Secondary optical waveguide  1508  comprises multiple segments that are part of first secondary optical waveguide portion  1508 A and second secondary optical waveguide portion  1508 B. In this example, extension optical waveguide  1502  has two distinct portions, called pump bypass waveguides. In this illustrative example, first pump bypass optical waveguide  1502 A and second pump bypass optical waveguide  1502 B are connected to optical couplers at each of the two ends of each of those optical waveguides. These optical waveguides are comprised of a non-nonlinear optical material  105  in this example. 
     First secondary optical waveguide portion  1508 A is connected to first signal loop extension  1504 A and first idler loop extension  1506 A. Second secondary optical waveguide portion  1508 B is connected to second signal loop extension  1504 B and second idler loop extension  1506 B. These connections from the secondary optical waveguide portions to the various signal loop extensions and idler loop extensions are made through wavelength-selective couplers such as first signal loop coupler  1594 A, first idler loop coupler  1596 A, second signal loop coupler  1594 B, and second idler loop coupler  1596 B. Connections between first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B of the main nonlinear optical waveguide and first secondary optical waveguide portion  1508 A and second secondary optical waveguide portion  1508 B of the secondary optical waveguide are made through wavelength selective optical couplers, such as first wavelength-selective coupler  1580 , second wavelength-selective coupler  1586 , third wavelength-selective coupler  1584 , and fourth wavelength-selective coupler  1582 . 
     In this illustrative example, optical waveguide structure  1500  also includes pump input optical waveguide  1532 , signal output optical waveguide  1534 , and idler output optical waveguide  1536 . Pump input optical waveguide  1532  can input pump light  1512  into second pump bypass optical waveguide  1502 B. Signal output optical waveguide  1534  can output signal light  1514  from second signal loop extension  1504 B. Idler output optical waveguide  1536  can output idler light  1516  from second idler loop extension  1506 B. 
     In this illustrative example, pump optical coupler  1531  couples pump input optical waveguide  1532  to second pump bypass optical waveguide  1502 B. Signal optical coupler  1535  couples second signal loop extension  1504 B to signal output optical waveguide  1534 . Idler optical coupler  1537  couples second idler loop extension  1506 B to idler output optical waveguide  1536 . 
     As depicted, first wavelength-selective coupler  1580  and second wavelength-selective coupler  1586  connect pump bypass optical waveguide  1502 A to two different segments, first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B, of main nonlinear optical waveguide  1510 . In this illustrative example, third wavelength-selective coupler  1584  and fourth wavelength-selective coupler  1582  connect second pump bypass optical waveguide  1502 B to the opposite ends of those two segments, first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B, of main nonlinear optical waveguide  1510 . 
     In this illustrative example, pump light  1512  travels in pump loop  1552 . Pump loop  1552  is a resonator loop that extends through first main nonlinear optical waveguide segment  1510 A of main nonlinear optical waveguide; first wavelength-selective coupler  1580 ; first pump bypass optical waveguide  1502 A; second wavelength-selective coupler  1586 ; second main nonlinear optical waveguide segment  1510 B of main nonlinear optical waveguide; third wavelength-selective coupler  1584 ; second pump bypass optical waveguide  1502 B; and fourth wavelength-selective coupler  1582 ; and continues again through first main nonlinear optical waveguide segment  1510 A of main nonlinear optical waveguide  1510 . The lengths of the various waveguides through which pump light  1512  of pump wavelength travels in pump loop  1552  can be selected so that pump wavelength matches a resonance condition for pump loop  1552 . 
     Pump light  1512 , signal light  1514  and idler light  1516  all travel through first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B of main nonlinear optical waveguide  1510 . As depicted, first wavelength-selective coupler  1580  couples pump light  1512  into first pump bypass optical waveguide  1502 A. First wavelength-selective coupler  1580  also couples signal light  1514  and idler light  1516  into first secondary optical waveguide portion  1508 A. Thus, only signal light  1514  and idler light  1516  travel through second secondary optical waveguide portion  1508 B. First signal loop coupler  1594 A couples signal light from segment  1571  of first secondary optical waveguide portion  1508 A into first signal loop extension  1504 A. First signal loop coupler  1594 A also couples signal light that has propagated through first signal loop extension  1504 A into segment  1573  of first secondary optical waveguide portion  1508 A. Signal light  1514  then continues to propagate through first secondary optical waveguide portion  1508 A, being coupled by first idler loop coupler  1596 A from segment  1573  to segment  1575  of first secondary optical waveguide portion  1508 A. Second wavelength-selective coupler  1586  couples signal light  1514  from first secondary optical waveguide portion  1508 A into second main nonlinear optical waveguide segment  1510 B. Second wavelength-selective coupler  1586  also couples pump light from first pump bypass optical waveguide  1502 A into second main nonlinear optical waveguide segment  1510 B. 
     As with first main nonlinear optical waveguide segment  1510 A of main nonlinear optical waveguide  1510 , pump light  1512 , signal light  1514  and idler light  1516  all travel through second main nonlinear optical waveguide segment  1510 B of main nonlinear optical waveguide  1510 . As depicted, third wavelength-selective coupler  1584  couples pump light  1512  into second pump bypass optical waveguide  1502 B. Third wavelength-selective coupler  1584  also couples signal light  1514  and idler light  1516  into second secondary optical waveguide portion  1508 B. Thus, only signal light  1514  and idler light  1516  travel through second secondary optical waveguide portion  1508 B. 
     Second signal loop coupler  1594 B couples signal light from segment  1576  of second secondary optical waveguide portion  1508 B into second signal loop extension  1504 B. Second signal loop coupler  1594 B also couples signal light that has propagated through second signal loop extension  1504 B into segment  1574  of second secondary optical waveguide portion  1508 B. Signal light  1514  then continues to propagate through second secondary optical waveguide portion  1508 B, being coupled by second idler loop coupler  1596 B from segment  1574  to segment  1572  of second secondary optical waveguide portion  1508 B. Fourth wavelength-selective coupler  1582  couples signal light  1514  from second secondary optical waveguide portion  1508 B again into first main nonlinear optical waveguide segment  1510 A. Fourth wavelength-selective coupler  1582  also couples pump light  1512  from first pump bypass optical waveguide  1502 A into first main nonlinear optical waveguide segment  1510 A. 
     In this illustrative example, signal light  1514  travels in signal loop  1554 . Signal loop  1554  is a resonator loop that can be thought of as comprising two halves. One half of signal loop  1554  extends through first main nonlinear optical waveguide segment  1510 A of main nonlinear optical waveguide  106 ; first wavelength-selective coupler  1580  (in its thru state); segment  1571  of first secondary optical waveguide portion  1508 A; first signal loop coupler  1594 A (in its cross state); first signal loop extension  1504 A; a second pass through first signal loop coupler  1594 A (again in its cross state); segment  1573  of first secondary optical waveguide portion  1508 A; first idler loop coupler  1596 A (in its thru state); segment  1575  of first secondary optical waveguide portion  1508 A; and second wavelength-selective coupler  1586  (in its thru state). A second half of signal loop  1554  extends through second main nonlinear optical waveguide segment  1510 B of main nonlinear optical waveguide  1510 ; third wavelength-selective coupler  1584  (in its thru state); segment  1576  of second secondary optical waveguide portion  1508 B; second signal loop coupler  1594 B (in its cross state); second signal loop extension  1504 B; a second pass through second signal loop coupler  1594 B (again in its cross state); segment  1574  of second secondary optical waveguide portion  1508 B; second idler loop coupler  1596 B (in its thru state); segment  1572  of second secondary optical waveguide portion  1508 B; and fourth wavelength-selective coupler  1582  (in its thru state). The lengths of the various waveguides through which signal light  1514  of a signal wavelength travels in signal loop  1554  can be selected so that signal wavelength matches a resonance condition for signal loop  1554 . 
     Additionally, besides coupling signal light  1514 , first wavelength-selective coupler  1580  also couples idler light  1516  into first secondary optical waveguide portion  1508 A. Thus, only signal light  1514  and idler light  1516  travel through first secondary optical waveguide portion  1508 A. Idler light  1516  then continues to propagate through first secondary optical waveguide portion  1508 A, being coupled by first signal loop coupler  1594 A from segment  1571  to segment  1573  of first secondary optical waveguide portion  1508 A. 
     In this illustrative example, first idler loop coupler  1596 A couples idler light  1516  from segment  1573  of first secondary optical waveguide portion  1508 A into first idler loop extension  1506 A. First idler loop coupler  1596 A also couples idler light that has propagated through first idler loop extension  1506 A into segment  1575  of first secondary optical waveguide portion  1508 A. Second wavelength-selective coupler  1586  couples idler light  1516  from first secondary optical waveguide portion  1508 A into second main nonlinear optical waveguide segment  1510 B. Pump light  1512 , signal light  1514  and idler light  1516  all travel through second main nonlinear optical waveguide segment  1510 B of main nonlinear optical waveguide  1510 . Besides coupling pump light  1512  into second pump bypass optical waveguide  1502 B, third wavelength-selective coupler  1584  also couples idler light  1516  and signal light  1514  into second secondary optical waveguide portion  1508 B. Thus, only idler light  1516  and signal light  1514  travel through second secondary optical waveguide portion  1508 B. Idler light  1516  then continues to propagate through second secondary optical waveguide portion  1508 B, being coupled by second signal loop coupler  1594 B from segment  1576  to segment  1574  of second secondary optical waveguide portion  1508 B. 
     As depicted, second idler loop coupler  1596 B couples idler light  1516  from segment  1574  of second secondary optical waveguide portion  1508 B into second idler loop extension  1506 B. Second idler loop coupler  1596 B also couples idler light that has propagated through second idler loop extension  1506 B into segment  1572  of second secondary optical waveguide portion  1508 B. Fourth wavelength-selective coupler  1582  couples idler light  1516  from second secondary optical waveguide portion  1508 B into first main nonlinear optical waveguide segment  1510 A. 
     In this illustrative example, idler light  1516  travels in idler loop  1556 . Idler loop  1556  is a resonator loop that can be thought of as comprising two halves. One half of idler loop  1556  extends through first main nonlinear optical waveguide segment  1510 A of main nonlinear optical waveguide  1510 ; first wavelength-selective coupler  1580  (in its thru state); segment  1571  of first secondary optical waveguide portion  1508 A; first signal loop coupler  1594 A (in its thru state); segment  1573  of first secondary optical waveguide portion  1508 A; first idler loop coupler  1596 A (in its cross state); first idler loop extension  1506 A; a second pass through first idler loop coupler  1596 A (again in its cross state); segment  1575  of first secondary optical waveguide portion  1508 A; and second wavelength-selective coupler  1586  (in its thru state). A second half of idler loop  1556  extends through second main nonlinear optical waveguide segment  1510 B of main nonlinear optical waveguide  1510 ; third wavelength-selective coupler  1584  (in its thru state); segment  1576  of second secondary optical waveguide portion  1508 B; second signal loop coupler  1594 B (in its thru state); segment  1574  of second secondary optical waveguide portion  1508 B; second idler loop coupler  1596 B (in its cross state); second idler loop extension  1506 B; a second pass through second idler loop coupler  1596 B (again in its cross state); segment  1572  of second secondary optical waveguide portion  1508 B; and fourth wavelength-selective coupler  1582  (in its thru state). The lengths of the various waveguides through which idler light  1516  of idler wavelength travels in idler loop  1556  can be selected so that the idler wavelength matches a resonance condition for idler loop  1556 . 
     As depicted, the resonator loops, pump loop  1552 , signal loop  1554 , and idler loop  1556 , have portions that overlap each other and portions that do not overlap each other. All three loops include nonlinear optical waveguide segments, such as first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B. Signal loop  1554  and idler loop  1556  further overlap each other through portions, such as first secondary optical waveguide portion  1508 A and second secondary optical waveguide portion  1508 B. Phase shifters can be placed at the non-overlapping portions of pump loop  1552 , signal loop  1554 , and idler loop  1556  to produce phase shifts for pump light  1512 , idler light  1516 , and signal light  1514  that can be adjusted separately from each other. 
     The signal loop  1554 , idler loop  1556 , and pump loop  1552  can each be considered as having two halves. These halves can be distinguished in the illustration of  FIG.  18    by their location relative to the reference line  1595 . A first half includes the components to the right of reference line  1595 . A second half includes the components to the left of reference line  1595 . 
     As depicted, optical waveguide structure  1500  includes phase shifters in the form of tuning electrodes. In this example, tuning electrode  1564 A and tuning electrode  1565 A are located adjacent to first signal loop extension  1504 A. These tuning electrodes enable adjustment of the phase of signal light  1514  in the first half of signal loop  1554 . Tuning electrode  1566 A and tuning electrode  1567 A are located adjacent to first idler loop extension  1506 A. These tuning electrodes enable adjustment of the phase of idler light  1516  in the first half of idler loop  1556 . Tuning electrode  1564 B and tuning electrode  1565 B are located adjacent to second signal loop extension  1504 B. These tuning electrodes enable adjustment of the phase of signal light  1514  in the second half of signal loop  1554 . Tuning electrode  1566 B and tuning electrode  1567 B are located adjacent to second idler loop extension  1506 B. These tuning electrodes enable adjustment of the phase of idler light  1516  in the second half of idler loop  1556 . 
     Tuning electrode  1560 A is located adjacent to first main nonlinear optical waveguide segment  1510 A. Tuning electrode  1560 A can be used to adjust the phase of pump light  1512  in the first half of pump loop  1552 . Tuning electrode  1560 B is located adjacent to second main nonlinear optical waveguide segment  1510 B. Tuning electrode  1560 B can be used to adjust the phase of pump light  1512  in the second half of pump loop  1552 . Since signal light  1514  and idler light  1516  also propagate through first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B for main nonlinear optical waveguide  1510 , tuning electrode  1560 A and tuning electrode  1560 B also affect the phase of signal light  1514  and idler light  1516 . The use of tuning electrodes to accomplish resonance matching and round-trip phase matching was described with reference to  FIG.  13   , as an example. 
     In optical waveguide structure  1500 , nonlinear optical generation of signal light  1514  and idler light  1516  from pump light  1512  occurs only in first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B of main nonlinear optical waveguide  1510 . First main nonlinear optical waveguide segment  1510 A can be considered as part of the first half of optical waveguide structure  1500 . Second main nonlinear optical waveguide segment  1510 B can be considered as part of the second half of optical waveguide structure  1500 . 
     In this example, signal light  1514  and idler light  1516  propagate in first secondary optical waveguide portion  1508 A and second secondary optical waveguide portion  1508 B of secondary optical wavelength and in first signal loop extension  1504 A and second signal loop extension  1504 B as well as in first idler loop extension  1506 A and second idler loop extension  1506 B without further nonlinear optical generation of signal photons or idler photons. Pump light  1512 , from which the signal light  1514  and idler light  1516  are generated, is absent from those waveguides. 
     In this illustrative example, the phases of the pump light  1512 , signal light  1514  and idler light  1516  in the two halves of optical waveguide structure  1500  can be adjusted to achieve a constructive interaction between the signal light and idler light generated in the first half of optical waveguide structure  1500  and the signal light and idler light generated in the second half of optical waveguide structure  1500 . This constructive interaction can be achieved even though the nonlinear optical coefficient can have a first sign in first main nonlinear optical waveguide segment  1510 A of the first half and a second sign, opposite to the first sign, in second main nonlinear optical waveguide segment  1510 B of the second half. 
     In this illustrative example, the nonlinear optical coefficient for light propagating in the first main nonlinear optical waveguide segment  1510 A of the upper-right half-structure  1591  of optical waveguide structure  1500  has one sign for the nonlinear optical coefficient  112 . The light propagating in second main nonlinear optical waveguide segment  1510 B in lower-left half-structure  1592  of optical waveguide structure  1500  has an opposite sign for the nonlinear optical coefficient. 
     In other words, the two segments, first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B, of main nonlinear optical waveguide  1510  can be considered as part of two half-structures, upper-right half-structure  1591  and lower-left half-structure  1592 . As depicted, these two half-structures are separated by reference line  1595  extending from the upper left corner of optical waveguide structure  1500  to the lower right corner of optical waveguide structure  1500 . As shown, reference line  1595  intersects optical waveguide structure  1500  at a location A between second wavelength-selective coupler  1586  for reinserting pump light  1512  in second main nonlinear optical waveguide segment  1510 B of main nonlinear optical waveguide  1510  and the tuning electrode  1560 B in second main nonlinear optical waveguide segment  1510 B and at another location B between fourth wavelength-selective coupler  1582  for reinserting pump light  1512  into first main nonlinear optical waveguide segment  1510 A of main nonlinear optical waveguide  1510  and tuning electrode  1560 A in first main nonlinear optical waveguide segment  1510 A. 
     For the upper-right half-structure  1591 , the relative phase walk-off for travel from upper left to lower right (i.e., from location A to location B) of upper-right half-structure  1591  should preferably be an odd multiple of n radians. Also, the relative phase walk-off from travel through first main nonlinear optical waveguide segment  1510 A of main nonlinear optical waveguide  1510 , where the nonlinear optical generation occurs, is preferably less than n radians and as close to zero as possible. The cross-sectional structure of first main nonlinear optical waveguide segment  1510 A can be designed to achieve the desired phase match (and minimal relative phase walk-off) for travel through first main nonlinear optical waveguide segment  1510 A. Similarly, for lower-left half-structure  1592 , the relative phase walk-off for travel from lower right to upper left (i.e., from location B to location A) of lower-left half-structure  1592  should be an odd multiple of n radians. Also, the relative phase walk-off from travel through the second main nonlinear optical waveguide segment  1510 B, where the nonlinear optical generation occurs, is less than n radians and as close to zero as possible. The cross-sectional structure of second main nonlinear optical waveguide segment  1510 B can be designed to achieve the desired phase match (and minimal relative phase walk-off) for travel through second main nonlinear optical waveguide segment  1510 B. 
     Thus, the lengths of the pump loop  1552 , the signal loop  1554 , and idler loop  1556  in each of the upper-right half-structure  1591  and the lower-left half-structure  1592 , as well as the cross-sectional structures of the waveguides in each of those two half-structures can be designed to achieve the desired relative phase walk-off that is preferably an odd multiple of n radians. Also, the relative phase walk-off from travel through first main nonlinear optical waveguide segment  1510 A for main nonlinear optical waveguide  1510 , where additional nonlinear optical generation occurs, is preferably less than n radians and ideally is zero. Similarly, the relative phase walk-off from travel through second main nonlinear optical waveguide segment  1510 B, where additional nonlinear optical generation again occurs, is preferably less than n radians and ideally is zero. Furthermore, the lengths and the cross-sectional structure of the waveguides traversed in both upper-right half-structure  1591  and the lower-left half-structure  1592  can be selected to also achieve round-trip phase matching for the nonlinear optical generation that occurs in the combination of two halves of optical waveguide structure  1500 . Thus, the round-trip phase for the nonlinear optical interaction of the pump, signal and idler light is preferably a multiple of 360° or 2n radians. 
     Making the phase walk-off for each half-structure, such as upper-right half-structure  1591  and lower-left half-structure  1592 , have a value that is an odd multiple of 180° or n radians compensates for the reversal in sign of the nonlinear optical coefficient of the nonlinear optical material in the nonlinear optical waveguide segments, such as first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B, of those two half-structures. First main nonlinear optical waveguide segment  1510 A is in upper-right half-structure  1591  and second main nonlinear optical waveguide segment  1510 B is in lower-left half-structure  1592 . The nonlinear optical coefficient  112  in first main nonlinear optical waveguide segment  1510 A has a first sign  107  and the nonlinear optical coefficient  112  in second main nonlinear optical waveguide segment  1510 B has a second sign  109  that is opposite from the first sign. The configuration of two half-structures is especially useful for optical waveguide structures  1500  that comprise second-order nonlinear optical material. An example of such material is x-cut lithium niobate. This configuration of two half-structures is especially useful when the nonlinear optical waveguide segments, such as first main nonlinear optical waveguide segment  1510 A and second main nonlinear optical waveguide segment  1510 B containing x-cut lithium niobate are oriented parallel to the material Y-axis, with the propagating optical fields of the pump light  1512 , signal light  1514  and idler light  1516  having transverse electric (TE) components that are aligned parallel to the material X-axis. 
     Besides meeting the phase matching conditions for the two half-structures, upper-right half-structure  1591  and lower-left half-structure  1592  that form optical waveguide structure  1500 , the other optical waveguides in optical waveguide structure  1500  can be designed to enable the pump light  1512 , signal light  1514 , and idler light  1516  to match resonances of their respective resonator loops, pump loop  1552 , signal loop  1554 , and idler loop  1556 . 
     Turning next to  FIG.  19   , an illustration of a flowchart of a process for a non-linear optical process is depicted in accordance with an illustrative embodiment. The process in this flowchart can be implemented in optical waveguide structure  100  in  FIG.  1    as well the other optical waveguide structures depicted in other figures. 
     The process begins by routing a first-wavelength light in a main nonlinear optical waveguide having a first length (operation  1900 ). The process optically couples, by a first wavelength-selective coupler, a first main location in the main nonlinear optical waveguide and a first extension location in the extension optical waveguide to each other such that the first-wavelength light is coupled from the main nonlinear optical waveguide at the first main location to the extension optical waveguide at the first extension location (operation  1902 ). The process does not optically couple a second-wavelength light from the main nonlinear optical waveguide at the first main location to the extension optical waveguide at the first extension location (operation  1903 ). The process does not optically couple a third-wavelength light from the main nonlinear optical waveguide at the first main location to the extension optical waveguide at the first extension location (operation  1904 ). 
     The process optically couples, by a second wavelength-selective coupler, a second main location in the main nonlinear optical waveguide and a second extension location in the extension optical waveguide to each other such that the first wavelength-light is coupled from the extension optical waveguide at the second extension location to the main nonlinear optical waveguide at the second main location (operation  1905 ). The process does not optically couple the second-wavelength light from the extension optical waveguide at the second extension location to the main nonlinear optical waveguide at the second main location (operation  1906 ). The process does not optically couple the third-wavelength light from the extension optical waveguide at the second extension location to the main nonlinear optical waveguide at the second main location (operation  1908 ). The process terminates thereafter. 
     With reference to  FIG.  20   , an illustration of a flowchart of additional operations for a process for a non-linear optical process is depicted in accordance with an illustrative embodiment. The process in this flowchart depicts additional operations that can be performed in addition to the operations in  FIG.  19   . 
     The process optically couples, by the first wavelength-selective coupler the first main location in the main nonlinear optical waveguide and a first secondary location in the secondary optical waveguide to each other such that the second-wavelength light is coupled from the main nonlinear optical waveguide at the first main location to the secondary optical waveguide at the first secondary location (operation  2000 ). The process optical couples, by a third wavelength-selective coupler, a third secondary location in the secondary optical waveguide and a primary second extension location in the second extension optical waveguide to each other such that the second-wavelength light is coupled from the secondary optical waveguide at the third secondary location to the second extension optical waveguide at the primary second extension location (operation  2001 ). The process does not optically couple a third-wavelength light from the secondary optical waveguide at the third secondary location to the second extension optical waveguide at the primary second extension location (operation  2003 ). The process optically couples, by a fourth wavelength-selective coupler, a fourth secondary location in the secondary optical waveguide and a secondary second extension location in the second extension optical waveguide to each other such that the second-wavelength light is coupled from the second extension optical waveguide at the secondary second extension location to the secondary optical waveguide at the fourth secondary location (operation  2004 ). The process does not optically couple the third-wavelength light from the second extension optical waveguide at the secondary second extension location to the secondary optical waveguide at the fourth secondary location (operation  2006 ). The process optically couples, by the second wavelength-selective coupler, a second secondary location in the secondary optical waveguide and the second main location in the main nonlinear optical waveguide to each other such that the second-wavelength light is coupled from the secondary optical waveguide at the second secondary location to the main nonlinear optical waveguide at the second main location (operation  2008 ). The process terminates thereafter. 
     Turning to  FIG.  21   , an illustration of a flowchart of additional operations for a process for a non-linear optical process is depicted in accordance with an illustrative embodiment. The process in this flowchart depicts additional operations that can be performed in addition to the operations in  FIG.  19   . 
     The process optically couples, by the first wavelength-selective coupler, the first main location in the main nonlinear optical waveguide and a first secondary location in the secondary optical waveguide to each other such that the third-wavelength light is coupled from the main nonlinear optical waveguide at the first main location to the secondary optical waveguide at the first secondary location (operation  2100 ). Also, the process optical couples, by the third wavelength-selective coupler, a third secondary location in the secondary optical waveguide and a primary third extension location in the third extension optical waveguide to each other such that the third-wavelength light is coupled from the secondary optical waveguide at the third secondary location to the third extension optical waveguide at the primary third extension location (operation  2101 ). The process does not optically couple the second-wavelength light from the secondary optical waveguide at the third secondary location to the third extension optical waveguide at the primary third extension location (operation  2102 ). The process optically couples, by the fourth wavelength-selective coupler, a fourth secondary location in the secondary optical waveguide and a secondary third extension location in the third extension optical waveguide to each other such that the third-wavelength light is coupled from the third extension optical waveguide at the secondary third extension location to the secondary optical waveguide at the fourth secondary location (operation  2103 ). The process does not optically couple the second-wavelength light from the third extension optical waveguide at the secondary third extension location to the secondary optical waveguide at the fourth secondary location (operation  2104 ). The process optically couples, by the second wavelength-selective coupler, the second secondary location in the secondary optical waveguide and the second main location in the main nonlinear optical waveguide to each other such that the third-wavelength light is coupled from the secondary optical waveguide at the second secondary location to the main nonlinear optical waveguide at the second main location (operation  2106 ). The process terminates thereafter. 
     Turning to  FIG.  22   , an illustration of a flowchart of an additional operation for a process for a non-linear optical process is depicted in accordance with an illustrative embodiment. The process in this flowchart depicts additional operations that can be performed in addition to the operations in  FIGS.  19 - 21   . 
     The process applies an activation to a portion of the main nonlinear optical waveguide such that a phase shifts in the first-wavelength light to achieve a resonance condition for the first-wavelength light (operation  2200 ). The process terminates thereafter. 
     With reference next to  FIG.  23   , an illustration of a flowchart of an additional operation for a process for a non-linear optical process is depicted in accordance with an illustrative embodiment. The process in this flowchart depicts additional operations that can be performed in addition to the operations in  FIG.  21    and  FIG.  22   . 
     The process applies an activation to a portion of the second extension waveguide such that a phase shifts in the second-wavelength light to achieve a resonance condition for the second-wavelength light (operation  2300 ). The process terminates thereafter. 
     Turning now to  FIG.  24   , an illustration of a flowchart of an additional operation for a process for a non-linear optical process is depicted in accordance with an illustrative embodiment. The process in this flowchart depicts additional operations that can be performed in addition to the operations in  FIG.  21    and  FIG.  23   . 
     The process applies an activation to a portion of the third extension optical waveguide such that a phase shifts in the third-wavelength light to achieve a resonance condition for the third-wavelength light (operation  2400 ). The process terminates thereafter. 
     Turning now to  FIG.  25   , an illustration of a flowchart of an additional operation for a process for a non-linear optical process is depicted in accordance with an illustrative embodiment. The process in this flowchart depicts additional operations that can be performed in addition to the operations in  FIGS.  22 - 24   . 
     The process applies at least one of an activation to a portion of the main nonlinear optical waveguide such that a phase shifts in the first-wavelength light, an activation to a portion of the second extension waveguide such that a phase shifts in the second-wavelength light, and an activation to a portion of the third extension optical waveguide such that a phase shifts in the third-wavelength light to achieve a round-trip phase matching condition for the nonlinear optical process involving the first-wavelength light, the second-wavelength light, and the third-wavelength light (operation  2500 ). The process terminates thereafter. 
     To achieve phase matching, the activation does not necessarily need to be applied to all three of the main nonlinear optical waveguide, the second extension waveguide, and the third extension waveguide. The activation can be applied to one of some combination of the three waveguides or waveguide portions. 
     Turning now to  FIG.  26   , an illustration of a flowchart of an additional operation for a process for a non-linear optical process is depicted in accordance with an illustrative embodiment. The process in this flowchart depicts additional operations that can be performed in addition to the operations in  FIGS.  22 - 25   . 
     The process applies an activation to a portion of the first extension optical waveguide such that a phase shifts in the first-wavelength light to achieve a resonance condition for the first-wavelength light and to achieve a round-trip phase matching condition for the nonlinear optical process involving the first-wavelength light, the second-wavelength light, and the third-wavelength light (operation  2600 ). The process terminates thereafter. In operation  2600 , this activation can be accomplished by tuning electrode  1362  in  FIG.  17   . 
     The flowcharts and block diagrams in the different depicted embodiments illustrate the architecture, functionality, and operation of some possible implementations of apparatuses and methods in an illustrative embodiment. In this regard, each block in the flowcharts or block diagrams can represent at least one of a module, a segment, a function, or a portion of an operation or step. For example, one or more of the blocks can be implemented as program code, hardware, or a combination of the program code and hardware. When implemented in hardware, the hardware can, for example, take the form of integrated circuits that are manufactured or configured to perform one or more operations in the flowcharts or block diagrams. When implemented as a combination of program code and hardware, the implementation may take the form of firmware. Each block in the flowcharts or the block diagrams can be implemented using special purpose hardware systems that perform the different operations or combinations of special purpose hardware and program code run by the special purpose hardware. 
     In some alternative implementations of an illustrative embodiment, the function or functions noted in the blocks may occur out of the order noted in the figures. For example, in some cases, two blocks shown in succession may be performed substantially concurrently, or the blocks may sometimes be performed in the reverse order, depending upon the functionality involved. Also, other blocks may be added in addition to the illustrated blocks in a flowchart or block diagram. 
     Turning now to  FIG.  27   , an illustration of a block diagram of a product management system is depicted in accordance with an illustrative embodiment. Product management system  2700  is a physical hardware system. In this illustrative example, product management system  2700  includes at least one of manufacturing system  2702  or maintenance system  2704 . 
     Manufacturing system  2702  is configured to manufacture products. As depicted, manufacturing system  2702  includes manufacturing equipment  2706 . Manufacturing equipment  2706  includes at least one of fabrication equipment  2708  or assembly equipment  2710 . 
     Fabrication equipment  2708  is equipment that used to fabricate the nonlinear optical waveguide structure. Multiple copies or multiple versions of nonlinear optical waveguide structures can be fabricated on a substrate wafer. 
     The substrate wafer can comprise a material such as silicon, lithium niobate, quartz, sapphire, silicon carbide, or some other suitable substrate. Fabrication equipment  2708  can be used to fabricate at least one of optical waveguide structures, nonlinear optical waveguides, optical couplers, optical waveguide segments, laser transmitters, ultraviolet transmission systems, point-to-point communication devices, laser infrared countermeasure sources, through water optical communication devices, or other suitable devices, antennas, or other suitable types of parts. For example, fabrication equipment  2708  can include machines and tools. 
     With respect to fabricating semiconductor components and optical waveguide components, fabrication equipment  2708  can comprise at least one of an epitaxial reactor, an oxidation system, a diffusion system, an etching system, a cleaning system, a bonding machine, a dicing machine, a wafer saw, an ion implantation system, a physical vapor deposition system, a chemical vapor deposition system, a photolithography system, an electron-beam lithography system, a plasma etcher, a die attachment machine, a wire bonder, a die overcoat system, molding equipment, a hermetic sealer, an electrical tester, a burn-in oven, a retention bake oven, a UV erase system, or other suitable types of equipment that can be used to manufacture semiconductor structures. 
     Assembly equipment  2710  is equipment used to assemble parts to form a product such as a chip, an integrated circuit, a multi-chip module, a computer, a signal processor, an aircraft, or some other product. Assembly equipment  2710  also can include machines and tools. These machines and tools may be at least one of a robotic arm, a spinner system, a sprayer system, and elevator system, a rail-based system, or a robot. 
     In this illustrative example, maintenance system  2704  includes maintenance equipment  2712 . Maintenance equipment  2712  can include any equipment needed to perform maintenance on and evaluation of a product. Maintenance equipment  2712  may include tools for performing different operations on parts on a product. These operations can include at least one of disassembling parts, refurbishing parts, inspecting parts, reworking parts, manufacturing replacement parts, or other operations for performing maintenance on the product. These operations can be for routine maintenance, inspections, upgrades, refurbishment, or other types of maintenance operations. 
     In the illustrative example, maintenance equipment  2712  may include optical inspection devices, electron-beam imaging systems, x-ray imaging systems, surface-profile measurement systems, drills, vacuum leak checkers, and other suitable devices. In some cases, maintenance equipment  2712  can include fabrication equipment  2708 , assembly equipment  2710 , or both to produce and assemble parts that needed for maintenance. 
     Product management system  2700  also includes control system  2714 . Control system  2714  is a hardware system and may also include software or other types of components. Control system  2714  is configured to control the operation of at least one of manufacturing system  2702  or maintenance system  2704 . In particular, control system  2714  can control the operation of at least one of fabrication equipment  2708 , assembly equipment  2710 , or maintenance equipment  2712 . 
     The hardware in control system  2714  can be implemented using hardware that may include computers, circuits, networks, and other types of equipment. The control may take the form of direct control of manufacturing equipment  2706 . For example, robots, computer-controlled machines, and other equipment can be controlled by control system  2714 . In other illustrative examples, control system  2714  can manage operations performed by human operators  2716  in manufacturing or performing maintenance on a product. For example, control system  2714  can assign tasks, provide instructions, display models, or perform other operations to manage operations performed by human operators  2716 . In these illustrative examples, the different processes for fabricating semiconductor structures, optical structures, nonlinear optical waveguides, laser transmitters, photon generators, photon transmitters, photon detectors, ultraviolet transmission systems, point-to-point communication devices, laser infrared countermeasure sources, through water optical communication devices, or other suitable devices can be manufactured using processes implemented in control system  2714 . 
     In the different illustrative examples, human operators  2716  can operate or interact with at least one of manufacturing equipment  2706 , maintenance equipment  2712 , or control system  2714 . 
     This interaction can occur to manufacture semiconductor structures and other components for products such as semiconductor devices or components for use in products such as aircraft, spacecraft, communications systems, computation systems, and sensor systems. 
     Further, control system  2714  can be used to adjust manufacturing of nonlinear optical waveguides, optical waveguides, optical couplers, phase shifters, and other components dynamically in or by the waveguides during the manufacturing process. For example, many points in the process of fabricating the optical waveguide structure including the nonlinear optical waveguide as well as other components are present at which adjustments can be made to control characteristics of components in an optical waveguide structure. 
     Some features of the illustrative examples are described in the following clauses. These clauses are examples of features not intended to limit other illustrative examples. 
     Clause 1 
     An optical waveguide structure comprising: 
     a main nonlinear optical waveguide, wherein a first-wavelength light and a second-wavelength light travel in the main nonlinear optical waveguide;   a first extension optical waveguide;   a secondary optical waveguide;   a first wavelength-selective coupler that optically couples the main nonlinear optical waveguide and the first extension optical waveguide to each other such that the first-wavelength light is coupled from the main nonlinear optical waveguide to the first extension optical waveguide,   and that optically couples the main nonlinear optical waveguide and the secondary optical waveguide to each other such that the second-wavelength light is coupled from the main nonlinear optical waveguide to the secondary optical waveguide; and   a second wavelength-selective coupler that optically couples the main nonlinear optical waveguide and the first extension optical waveguide to each other such that the first-wavelength light is coupled from the first extension optical waveguide to the main nonlinear optical waveguide,   and that optically couples the main nonlinear optical waveguide and the secondary optical waveguide to each other such that the second-wavelength light is coupled from the secondary optical waveguide to the main nonlinear optical waveguide.   

     Clause 2 
     The optical waveguide structure according to clause 1 further comprising: 
     a second extension optical waveguide;   a third wavelength-selective coupler that optically couples the secondary optical waveguide and the second extension optical waveguide to each other such that the second-wavelength light is coupled from the secondary optical waveguide to the second extension optical waveguide; and   a fourth wavelength-selective coupler that optically couples the secondary optical waveguide and the second extension optical waveguide to each other such that the second-wavelength light is coupled from the second extension optical waveguide to the secondary optical waveguide.   

     Clause 3 
     The optical waveguide structure according to clause 2 further comprising: 
     a third extension optical waveguide;   wherein the third wavelength-selective coupler optically couples the secondary optical waveguide and the third extension optical waveguide to each other such that a third-wavelength light is coupled from the secondary optical waveguide to the third extension optical waveguide and the second-wavelength light is not coupled into the third extension optical waveguide; and   wherein the fourth wavelength-selective coupler optically couples the secondary optical waveguide and the third extension optical waveguide to each other such that the third-wavelength light is coupled from the third extension optical waveguide to the secondary optical waveguide.   

     Clause 4 
     The optical waveguide structure according to any of clauses 2-4, wherein the first-wavelength light travels in a first loop through a main segment between a first main location and a second main location within the main nonlinear optical waveguide, through the first extension optical waveguide, and through the first wavelength-selective coupler and the second wavelength-selective coupler, in which the first loop has a first length, and 
     wherein the second-wavelength light travels in a second loop through the main segment between the first main location and the second main location within the main nonlinear optical waveguide, through a secondary segment in the secondary optical waveguide, through the second extension optical waveguide, and through the first wavelength-selective coupler and the second wavelength-selective coupler, in which the second loop has a second length for the second-wavelength light.   

     Clause 5 
     The optical waveguide structure according to clause 3, wherein the first-wavelength light travels in a first loop through a main segment within the main nonlinear optical waveguide, through and a first extension segment, through the first wavelength-selective coupler and the second wavelength-selective coupler, in which the first loop has a first length; 
     wherein the second-wavelength light travels in a second loop through a secondary segment in the secondary optical waveguide, through the second extension optical waveguide, through the first wavelength-selective coupler and the second wavelength-selective coupler, through the third wavelength-selective coupler and the fourth wavelength-selective coupler, and through the main segment in the nonlinear optical waveguide, in which the second loop has a second length for the second-wavelength light; and   wherein the third-wavelength light travels in a third loop through the secondary segment in the secondary optical waveguide, through the third extension optical waveguide, through the first wavelength-selective coupler and the second wavelength-selective coupler, through the third wavelength-selective coupler and the fourth wavelength-selective coupler, and through the main segment in the nonlinear optical waveguide, in which the third loop has a third length for the third-wavelength light.   

     Clause 6 
     The optical waveguide structure according to any of clauses 2-6, wherein the first-wavelength light is a pump light and the second-wavelength light is one of a signal light and an idler light, and wherein an intensity of the first-wavelength light is greater than an intensity of the second-wavelength light. 
     Clause 7 
     The optical waveguide structure according to any of clauses 3 or 5 wherein the first-wavelength light is a pump light, the second-wavelength light is a signal light, and the third-wavelength light is an idler light; and wherein an intensity of the firs-wavelength t light is greater than an intensity of the second-wavelength light and is greater than an intensity of the third-wavelength light. 
     Clause 8 
     The optical waveguide structure according to any of clauses 1-7, wherein the main nonlinear optical waveguide is comprised of an electro-optic material. 
     Clause 9 
     The optical waveguide structure according to any of clauses 2-8, wherein the second extension optical waveguide is comprised of at least one of an electro-optic material, a nonlinear optical material or a non-nonlinear optical material 
     Clause 10 
     The optical waveguide structure according to any of clauses 3, 5, or 7, wherein the third extension optical waveguide is comprised of at least one of an electro-optic material, a nonlinear optical material or a non-nonlinear optical material 
     Clause 11 
     The optical waveguide structure according to any of clauses 1-10, wherein the main nonlinear optical waveguide is comprised of a nonlinear optical material. 
     Clause 12 
     The optical waveguide structure according to any of clauses 2-11, wherein the second extension optical waveguide is comprised of an electro-optic material. 
     Clause 13 
     The optical waveguide structure according to any of clauses 3, 5, 7, or 10, wherein the third extension optical waveguide is comprised of an electro-optic material. 
     Clause 14 
     The optical waveguide structure according to any of clauses 2-13, wherein the first wavelength-selective coupler, the second wavelength-selective coupler, the third wavelength-selective coupler, and the fourth wavelength-selective coupler are selected from at least one of a two-waveguide coupler, a multi-mode interference coupler, a pulley coupler, a Mach-Zehnder interferometer, or a 4-port micro-optical waveguide resonator coupler. 
     Clause 15 
     The optical waveguide structure according to any of clauses 3, 5, 7, 10, or 13 further comprising: 
     a set of output optical waveguides that outputs output light out of at least one of the first extension optical waveguide, the second extension optical waveguide, or the third extension optical waveguide.   

     Clause 16 
     The optical waveguide structure according to any of clauses 3, 5, 7, 10, 13, or 15 further comprising: 
     a set of input optical waveguides that inputs input light into at least one of the first extension optical waveguide, the second extension optical waveguide, or the third extension optical waveguide.   

     Clause 17 
     The optical waveguide structure according to clause 4 further comprising: 
     a phase shifter located adjacent to a portion of the main nonlinear optical waveguide, wherein the phase shifter applies an activation such that a phase shifts in the first-wavelength light to achieve a resonance condition for the first-wavelength light.   

     Clause 18 
     The optical waveguide structure according to any of clauses 4 or 17 further comprising: 
     a phase shifter located adjacent to a portion of the second extension optical waveguide, wherein the phase shifter applies an activation such that a phase shifts in the second-wavelength light to achieve a resonance condition for the second-wavelength light.   

     Clause 19 
     The optical waveguide structure according to clause 5 further comprising: 
     a phase shifter located adjacent to a portion of the third extension optical waveguide, wherein the phase shifter applies an activation such that a phase shifts in the third-wavelength light to achieve the resonance condition for the third-wavelength light.   

     Clause 20 
     The optical waveguide structure according to any of clauses 1-19 further comprising: 
     a phase shifter located adjacent to a portion of the main nonlinear optical waveguide, wherein the phase shifter applies an activation such that a phase shifts in the first-wavelength light to achieve a round-trip phase matching condition for a nonlinear optical process involving the first-wavelength light.   

     Clause 21 
     The optical waveguide structure according to any of clauses 2-20 further comprising: 
     a phase shifter located adjacent to a portion of the second extension optical waveguide, wherein the phase shifter applies an activation such that a phase shifts in the second-wavelength light to achieve a round-trip phase matching condition for a nonlinear optical process involving the second-wavelength light.   

     Clause 22 
     The optical waveguide structure according to any of clauses 3, 5, 7, 10, 13, 15, or 16 further comprising: 
     a phase shifter located adjacent to a portion of the third extension optical waveguide, wherein the phase shifter applies an activation such that a phase shifts in the third-wavelength light to achieve a round-trip phase matching condition for a nonlinear optical process involving the third-wavelength light.   

     Clause 23 
     The optical waveguide structure according to any of clauses 1-24 further comprising: 
     a phase shifter located adjacent to a portion of the main nonlinear optical waveguide, wherein the phase shifter applies an activation such that a phase shifts in the first-wavelength light to achieve a phase walk-off that is an odd multiple of 180 degrees.   

     Clause 24 
     The optical waveguide structure according to any of clauses 2-23 further comprising: 
     a phase shifter located adjacent to a portion of the second extension optical waveguide, wherein the phase shifter applies an activation such that a phase shifts in the second-wavelength light to achieve a phase walk-off that is an odd multiple of 180 degrees.   

     Clause 25 
     The optical waveguide structure according to any of clauses 35, 7, 10, 13, 15, 16, or 22 further comprising: 
     a phase shifter located adjacent to a portion of the third extension optical waveguide, wherein the phase shifter applies an activation such that a phase shifts in the third-wavelength light to achieve a phase walk-off that is an odd multiple of 180 degrees.   

     Clause 26 
     A method for facilitating a non-linear optical process comprising: 
     routing a first-wavelength light and a second-wavelength light in a main nonlinear optical waveguide;   optically coupling, by a first wavelength-selective coupler, the main nonlinear optical waveguide and an extension optical waveguide to each other such that the first-wavelength light is coupled from the main nonlinear optical waveguide to the extension optical waveguide and the second-wavelength light is not coupled from the main nonlinear optical waveguide to the extension optical waveguide but rather is coupled to a secondary optical waveguide; and   optically coupling, by a second wavelength-selective coupler, the main nonlinear optical waveguide and the extension optical waveguide to each other such that the first-wavelength light is coupled from the extension optical waveguide to the main nonlinear optical waveguide.   

     Clause 27 
     The method of according to clause 26 further comprising: 
     optically coupling, by a third wavelength-selective coupler, the secondary optical waveguide and a second extension optical waveguide to each other such that the second-wavelength light is coupled from the secondary optical waveguide to the second extension optical waveguide, and such that a third-wavelength light is not coupled from the secondary optical waveguide to the second extension optical waveguide; and   optically coupling, by a fourth wavelength-selective coupler, the secondary optical waveguide and the second extension optical waveguide to each other such that the second-wavelength light is coupled from the second extension optical waveguide to the secondary optical waveguide.   

     Clause 28 
     The method of according to clause 27 comprising: 
     routing the third-wavelength light in the main nonlinear optical waveguide;   optically coupling, by the third wavelength-selective coupler, the secondary optical waveguide and a third extension optical waveguide to each other such that the third-wavelength light is coupled from the secondary optical waveguide to the third extension optical waveguide and the second-wavelength light is not coupled from the secondary optical waveguide to the third extension optical waveguide; and optically coupling, by the fourth wavelength-selective coupler, the secondary optical waveguide and the third extension optical waveguide to each other such that the third-wavelength light is coupled from the third extension optical waveguide to the secondary optical waveguide.   

     Clause 29 
     The method according to clause 27, wherein the first-wavelength light travels in a first loop through a main segment between a first main location and a second main location within the main nonlinear optical waveguide and through a first extension segment, in which the first loop has a first length selected to achieve a resonance condition for the first-wavelength light; and 
     wherein the second-wavelength light travels in a second loop through a secondary segment in the secondary optical waveguide, through the second extension optical waveguide, and through the main segment in the main nonlinear optical waveguide, in which the second loop has a second length for the second-wavelength light selected to achieve the resonance condition for the second-wavelength light.   

     Clause 30 
     The method according to clause 27, wherein the first-wavelength light travels in a first loop through a main segment between a first main location and a second main location within the main nonlinear optical waveguide and through a first extension optical waveguide, in which the first loop has a first length selected to achieve a resonance condition for the first-wavelength light; 
     wherein the second-wavelength light travels in a second loop through a segment in the secondary optical waveguide, through the second extension optical waveguide, and through the main segment in the nonlinear optical waveguide, in which the second loop has a second length for the second-wavelength light selected to achieve the resonance condition for the second-wavelength light; and   wherein the third-wavelength light travels in a third loop through the segment in the secondary optical waveguide, through the third extension optical waveguide, and through the main segment in the nonlinear optical waveguide, in which the third loop as a third length selected to achieve a resonance condition for the third-wavelength light.   

     Clause 31 
     The method according to any of clauses 27-30, wherein the first-wavelength light is a pump light, the second-wavelength light is one of a signal light and an idler light. 
     Clause 32 
     The method according to any of clauses 27-30, wherein the first-wavelength light is one of a signal light and an idler light and the second-wavelength light is a pump light. 
     Clause 33 
     The method according to any of clauses 27-30, wherein the first-wavelength light is a pump light, the second-wavelength light is a signal light, and the third-wavelength light is an idler light. 
     Clause 34 
     The method according to any of clauses 26-33 further comprising: 
     applying an activation to a portion of the main nonlinear optical waveguide such that a phase shifts in the first-wavelength light to achieve a resonance condition for the first-wavelength light.   

     Clause 35 
     The method according to any of clauses 27-34 further comprising: 
     applying an activation such to a portion of the second extension optical waveguide such that a phase shifts in the second-wavelength light to achieve a resonance condition for the second-wavelength light.   

     Clause 36 
     The method according to clause 30 further comprising: 
     applying an activation to a portion of the third extension optical waveguide such that such that a phase shifts in the third-wavelength light to achieve a resonance condition for the third-wavelength light.   

     Clause 37 
     The method according to any of clauses 27-36 further comprising: 
     applying an activation to a portion of the second extension optical waveguide such that a phase shifts in the second-wavelength light.   

     Clause 38 
     The method according to any of clauses 27-37 further comprising: 
     applying an activation to a portion of the main nonlinear optical waveguide such that a phase shifts in the first-wavelength light to achieve a round trip phase matching condition for a nonlinear optical process involving the first-wavelength light, the second-wavelength light, and the third-wavelength light.   

     Thus, the illustrative examples include the wavelength-selective couplers that enable selective coupling of light in a manner that establishes loops in which light of different wavelengths can travel. Additionally, optical waveguides in the illustrative examples are designed to manage a reversal in the sign of the nonlinear optical coefficient that occurs for the two halves of an optical waveguide structure for which the light travels in opposite directions in portions of those two halves. The optical waveguide structures in this optical waveguide structure can avoid undesired effects of the sign reversal in the nonlinear optical coefficient by removing the pump light or by having an absence of a non-linear optical material in part of the structure. 
     In another illustrative embodiment, loops formed from optical waveguides is unnecessary. For example, the nonlinear optical waveguide structure in the different illustrative examples described above in  FIGS.  1 - 27    can comprise triple partially overlapping loops for entanglement (TriPOLE). In this illustrative example, these partially overlapping loops for entanglement are unnecessary to obtain a desired level of performance. 
     In this illustrative example, phase adjustment is provided to control the phases of different wavelengths of light traveling through optical waveguide structures that do not include closed loops. The illustrative embodiments recognize and take into account a number of different considerations. Some of these considerations are recognized and taken into account as described below. 
     For example, maintenance of phase matching is important for achieving nonlinear optical processes that are efficient in terms of usage of input source power and that can produce high power of the light generated by the nonlinear optical process. Higher efficiency and higher generated power can be achieved by using a longer nonlinear optical waveguide. However, imperfect phase matching can limit the length of nonlinear optical waveguide for which the nonlinear optical generation process continues to be effective in producing additional light. 
     Further, in a nonlinear optical process, such as parametric down conversion (PDC) or difference frequency generation (DFG) and parametric up conversion (PUC) or sum frequency generation (SFG), the phase of the idler light generated at a given location in the nonlinear optical waveguide is determined by the phases of the source pump wave and signal wave at that location. With perfect phase matching, the wave-vector of the generated idler light continues to be matched with the wave-vectors of the source pump light and signal light so that the phase of the idler light generated at a first location and then propagated to a second location match the phase of the idler light generated at the second location. 
     As a result, a constructive nonlinear optical interaction occurs at the second location between the previously generated idler light and the pump and signal waves at that second location to produce additional generation of idler light at the second location. Thus, the intensity of the idler light can increase for longer nonlinear optical waveguides. 
     Alternatively, the efficiency of nonlinear optical generation, such as by spontaneous parametric down conversion (SPDC), can increase as the nonlinear optical waveguide becomes longer. However, when the phases for the light are not matched, the phase walk-off between the signal and idler light generated at different locations can result in destructive nonlinear optical interaction at the second location between those components of the signal light and the idler light and the pump light. 
     As a result, the additional generation of signal and idler light at the second location can be reduced or, for some values of the phase walk-off, the signal and idler light at the second location can even be consumed to produce pump light. This situation reverses the nonlinear optical generation process. Thus, increasing the length of the nonlinear optical waveguide does not continue to increase the nonlinear optical generation efficiency or the intensity of the generated signal and idler light. 
     The illustrative embodiments recognize and take into account that in a nonlinear optical (NLO) generation process, the phase(s) of the generated light is determined by the phase(s) of the source light(s). A nonlinear optical waveguide structure can be designed to achieve a condition of matching of the phases for the source light and the previously generated light. This type of matching enables the nonlinear optical generation process to become more efficient and to produce more power in the generated light for longer nonlinear optical waveguides. However, current nonlinear optical waveguide structures are not fabricated with perfect matching of the wave vectors needed to sustain efficient nonlinear optical generation over a long nonlinear optical waveguide. When a nonlinear optical waveguide does not have the wave-vector match to achieve perfect phase matching for sustaining a nonlinear optical process, the phase walk-off of the light generated can result in destructive interference. The generated light can be, for example, signal and idler light generated in spontaneous parametric down conversion (SPDC) from different locations in the nonlinear optical waveguide. Thus, the nonlinear optical interaction between source and generated light can be constructive for producing more generated light at some locations and destructive at other locations 
     Some approaches to compensate for imperfect phase matching are based on quasi-phase-matching (QPM). Quasi-phase-matching involves a periodic change in the structure of a nonlinear optical waveguide. Some examples of quasi-phase-matching involve changing a transverse dimension of the nonlinear optical waveguide, such as the waveguide width. Other examples of quasi-phase-matching involve changing the polarization direction of the nonlinear optical material in the nonlinear optical waveguide. With quasi-phase-matching the longitudinal period of the structural or material change in the nonlinear optical waveguide must exactly the longitudinal distance over which the imperfect phase match results in a phase walk-off of 2n radians or 360 degrees. 
     Yet other examples involve using a nonlinear optical waveguide structure that comprises two parallel and optically coupled nonlinear optical waveguides. For these two-coupled-waveguide structures, either the generated light or the source light, but not both, is gradually and continuously coupled from a first waveguide of the two parallel waveguides to the second waveguide and then back from the second waveguide to the first waveguide. The length over which the round-trip coupling from first waveguide to second waveguide and back to first waveguide occurs is matched to the length over which phase walk-off of the generated light reaches 2n radians or 360 degrees. 
     For one example with a two-coupled-waveguide structure, the light generated in a first location in the first waveguide does not propagate to a second location in the first waveguide at which the light generated in the first location and the light generated in the second location would have a phase walk-off of n radians (180 degrees) and would otherwise result in a fully destructive interaction. Instead, the light generated in the first location becomes fully coupled into the second waveguide by that point and does not interfere with the light generated at that second location in the first waveguide. The light generated in the first location becomes fully coupled back from the second waveguide to the first waveguide at a third location in the first waveguide for which the light generated in the first location would have a phase walk-off of 2n radians (360 degrees) and would result in a fully constructive interaction. This gradual and continuous coupling of the generated light from the first waveguide into the second waveguide and then back again from the second waveguide into the first waveguide can be designed, by designing the coupling coefficient of the two-guide coupling structure, to occur in a periodic manner with the longitudinal period selected to avoid a periodically destructive interaction in the nonlinear optical generation process and to reinforce a periodically constructive interaction in the nonlinear optical generation process. In practice, it is difficult to achieve accurate control of the coupling coefficient for a two-guide coupling structure that exactly matches the phase walk-off, especially when the actual values obtained for the various wave vectors and for the two-guide coupling coefficient can change depending on fabrication-related tolerances and variations in the operational environment. 
     In the following examples of the illustrative embodiments, a nonlinear optical waveguide structure includes tuning optical waveguides that can operate to adjust the phase of light traveling through these tuning optical waveguides. In these illustrative examples, phase shifters are associated with the tuning optical waveguides. These phase shifters can adjust the phases of the light and the resulting phase match to enable the full length of the fabricated nonlinear optical waveguide to be useful for increasing the nonlinear optical generation efficiency and increasing the power in the light generated by the nonlinear optical process. 
     In the illustrative examples of these illustrative embodiments, a nonlinear optical waveguide structure provides one or more benefits that are not present with nonlinear optical waveguide structures that do not use phase tuning optical waveguides. For example, without phase tuning optical waveguides, an ability to have controlled adjustment of the light and thus of the phase matching to compensate for fabrication or operational tolerances is not present. 
     Further, when phase tuning optical waveguides are present for adjusting the phases of the generated light, the use of closed-loop nonlinear optical waveguide structures results in the source light cycling repeatedly through the closed-loop nonlinear optical waveguide. Also, the generated light propagates in other closed loop waveguides. These types of nonlinear optical waveguides can have challenges in using the phase shifters to both adjust the source and generated light to achieve phase matching of the nonlinear optical process as well as adjust the source and generated light to achieve a match to a spectral resonance of a closed-loop path. The need to match two constraints limits the flexibility of these types of nonlinear optical waveguide structures to compensate for different tolerances. 
     Thus, this example of these illustrative embodiments, provides phase adjustments to control the phases of different wavelengths of light traveling through optical waveguide structures without a need for closed loops. 
     With reference now to the figures describing this illustrative example and in particular with reference to  FIG.  28   , an illustration of a block diagram of an optical waveguide structure is depicted in accordance with an illustrative embodiment. In this example, optical waveguide structure  2800  comprises a number of different components. As depicted, optical waveguide structure  2800  comprises nonlinear optical waveguide  2809 , a set of tuning optical waveguides  2840 , a set of wavelength selective couplers  2820 , and a set of phase shifters  2860 . 
     Nonlinear optical waveguide  2809  and the set of tuning optical waveguides  2840  are optical waveguides in optical waveguide structure  2800 . Nonlinear optical waveguide  2809  is comprised of nonlinear optical material  2897  and can include other types of materials. In some illustrative examples, a tuning optical waveguide, a portion of the tuning optical waveguide, or multiple tuning optical waveguides can be comprised of nonlinear optical material  2897 . With nonlinear optical material  2897  present, light generation can occur while light  2810  travels through nonlinear optical waveguide  2809 . 
     In this illustrative example, light  2810  has a set of wavelengths  2899  and comprises first wavelength light  2811 . Further, light  2810  can also include at least one of second wavelength light  2813  or third wavelength light  2815 . One or both of second wavelength light  2813  and third wavelength light  2815  can have a different wavelength in wavelengths  2899  from the wavelength of first wavelength light  2811 . Further, second wavelength light  2813  and third wavelength light  2815  can have values for their wavelengths in wavelengths  2899  that are different from each other or second wavelength light  2813  and third wavelength light  2815  can the same value for their wavelength in wavelengths  2899 . This condition of second wavelength light  2813  and third wavelength light  2815  having the same wavelength occurs when degenerate down conversion is the nonlinear optical process. Further, first wavelength light  2811  and second wavelength light  2813  can have the same wavelength, or first wavelength light  2811  and third wavelength light  2815  can have the same wavelength in another example. This condition occurs in up-conversion processes such as second harmonic generation. 
     At least one of second wavelength light  2813  or third wavelength light  2815  can be produced from first wavelength light  2811  through nonlinear optical interaction  2898  within nonlinear optical waveguide  2809  caused by nonlinear optical material  2897  in nonlinear optical waveguide  2809 . In one example, first wavelength light  2811  is pump light  2812  and second wavelength light  2813  can be signal light  2814  or idler light  2816 . In another example, first wavelength light  2811  is pump light  2812  and second wavelength light  2813  is signal light  2814 , and third wavelength light  2815  is idler light  2816 . 
     A nonlinear optical process involves a nonlinear optical interaction  2898  between source light  2817  and nonlinear optical material  2897  in a portion of nonlinear optical waveguide  2809  that can produce generated light  2819 . 
     In these examples, source light  2817  includes first wavelength light  2811 . When source light comprises only first wavelength light  2811 , such as in a spontaneous parametric down conversion (SPDC) process, generated light  2819  could include second wavelength light  2813  as well as third wavelength light  2815 . In some nonlinear optical processes such as parametric up-conversion or parametric down-conversion, source light could further include second wavelength light  2813  or third wavelength light  2815 . When source light further comprises second wavelength light  2813 , such as in a parametric frequency-conversion (up-conversion or down-conversion) process, generated light  2819  would comprise third wavelength light  2815 . Similarly, when source light  2817  further comprises third wavelength light  2815 , generated light  2819  would comprise second wavelength light  2813 . 
     The set of wavelength selective couplers  2820  couples light  2810  between nonlinear optical waveguide  2809  and the set of tuning optical waveguides  2840  based on wavelengths  2899  of light  2810 . The set of wavelength selective couplers  2820  route first wavelength light  2811 , second wavelength light  2813 , and third wavelength light  2815  in light  2810  between segments of nonlinear optical waveguide  2809  and the set of tuning optical waveguides  2840  based on wavelengths  2899  of first wavelength light  2811 , second wavelength light  2813 , and third wavelength light  2815 . 
     As a result, some components of light  2810  can be routed to one or more of the set of tuning optical waveguides  2840  while routing other components of light  2810  to continue to traverse through nonlinear optical waveguide  2809 . In the illustrative example, a component of light  2810  light  2810  having a particular wavelength. For example, first wavelength light  2811  and second wavelength light  2813  are two components in light  2810 . 
     In this example, first wavelength light  2811  can continue to travel in nonlinear optical waveguide  2809  while at least one of second wavelength light  2813  or third wavelength light  2815  can be routed between nonlinear optical waveguide  2809  and the set of tuning optical waveguides  2840 . 
     The set of phase shifters  2860  can be located along the set of tuning optical waveguides  2840 . In other words, a single phase shifter or multiple phase shifters in the set of phase shifters  2860  can be associated with a tuning optical waveguide in the set of tuning optical waveguides  2840  or multiple phase shifters can be associated with one or more of tuning optical waveguides  2840 . 
     The set of phase shifters  2860  can be located along nonlinear optical waveguide  2809  or the set of tuning optical waveguides  2840  by being at least one of adjacent to part of nonlinear optical waveguide  2809  or the set of tuning optical waveguides  2840 , connected to part of the nonlinear optical waveguide  2809  or the set of tuning optical waveguides  2840 , or integrated as part of the nonlinear optical waveguide  2809  or the set of tuning optical waveguides  2840 . 
     The set of phase shifters  2860  can apply a set of activations  2890  to the nonlinear optical waveguide  2809  or to the set of tuning optical waveguides  2840  to change phase shift  2895  for different wavelengths of light  2810  in the nonlinear optical waveguide  2809  or the set of tuning optical waveguides  2840 . In the illustrative examples, activations  2890  as applied to tuning optical waveguide  2840  can change the refractive index of tuning optical waveguides  2840 . This change in the refractive index can changes the phase shift of light traveling in tuning optical waveguides  2840 . Activations  2890  that change the refractive index can be for example, heat or an electric field. 
     The particular wavelength of light  2810  for which phase shift occurs can be selected based on the set of activations  2890  applied to light  2810  traveling through the set of tuning optical waveguides  2840 . The set of activations  2890  can be applied to cause phase shift  2895  to light  2810  propagating in the set of the set of tuning optical waveguides  2840  that results in phase walk-off  2896  for nonlinear optical interaction  2898  having a desired value. In these illustrative examples, a phase shift is a change in the phase of the light, such as the phase of one component of the light wave. This component, such as first wavelength light  2811  or second wavelength light  2813 , can have a single wavelength. 
     For example, the set of activations  2890  can be applied such that particular wavelengths of light  2810  have phase shift  2895  that result in the nonlinear optical interaction  2898  having values for the phase walk-off  2896  of zero or an even multiple of n radians. In other examples, phase walk-off  2896  can be close to zero or close to an even multiple of n radians. For example, the phase walk-off can be within 0.25 n radians or 0.5 n radians. The desired value of phase walk-off  2896  achieved using the set of activations  2890  can depend on the amount of light generation desired. 
     For example, one or more phase shifters can also be associated with nonlinear optical waveguide  2809  in addition to being associated with the set of tuning optical waveguides  2840  or in place of being associated with the set of tuning optical waveguides  2840 . 
     With reference to  FIG.  29   , an illustration of an optical waveguide structure is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  2900  comprises nonlinear optical waveguide  2909 , tuning optical waveguide  2948 , a set of wavelength selective couplers  2920 , and a set of phase shifters  2960 . 
     In this illustrative example, light  2910  can comprise first wavelength light  2911  and second wavelength light  2913 . Second wavelength light  2913  is produced from first wavelength light  2911  through nonlinear optical interaction  2998  occurring within nonlinear optical waveguide  2909 . In other words, second wavelength light  2913  is produced within nonlinear optical waveguide  2909  through nonlinear optical interaction  2998  of first wavelength light  2911  and second wavelength light  2913  with nonlinear optical material  2997  in nonlinear optical waveguide  2909 . The light generated in a preceding segment of a nonlinear optical waveguide can participate in the nonlinear optical interaction that produces additional generated light in a subsequent segment of the nonlinear optical waveguide. Thus, the phase of the previously generated second wavelength light should be considered in order to have constructive light generation when second wavelength light generated in different segments are included. 
     In this example, the set of wavelength selective couplers  2920  couples light  2910  between nonlinear optical waveguide  2909  and a set of tuning optical waveguides  2940  based on wavelengths  2999  of light  2910  and in particular for wavelengths  2999  of first wavelength light  2911 , second wavelength light  2913 , and third wavelength light  2915  in light  2910 . In this example, the set of tuning optical waveguides  2940  includes first set of tuning optical waveguides  2941  and second set of tuning optical waveguides  2942 . A set of phase shifters  2960  is located along the set of tuning optical waveguides  2940 . For example, one or more phase shifters  2960 , such a phase shifter  2968 , in the set of phase shifters  2960  is located along tuning optical waveguide  2948  in the set of tuning optical waveguides  2940 . 
     In this example, wavelength selective coupler  2928  in the set of wavelength selective couplers  2920  couples second wavelength light  2913  from exit location  2971  in nonlinear optical waveguide  2909  to starting point  2978  in tuning optical waveguide  2948 . Wavelength selective coupler  2928  also couples second wavelength light  2913  from ending point  2979  in tuning optical waveguide  2948  back into nonlinear optical waveguide  2909  at entry location  2930 . Wavelength selective coupler  2928  does not couple first wavelength light  2911  from the nonlinear optical waveguide  2909  into tuning optical waveguide  2948 . Instead, first wavelength light  2911  is coupled from exit location  2971  in nonlinear optical waveguide  2909  to a different location in nonlinear optical waveguide  2909 . 
     Phase shifter  2968  in the set of phase shifters  2960  is located between starting point  2978  and ending point  2979  in the tuning optical waveguide  2948 . In this example, phase shifter  2968  applies activation  2994  to tuning optical waveguide  2948  to change phase shift  2995  of second wavelength light  2913  in tuning optical waveguide  2948 . 
     In another illustrative example, optical waveguide structure  2900  can have another configuration that includes first wavelength selective coupler  2921 , second wavelength selective coupler  2922  in the set of wavelength selective couplers  2920 , tuning optical waveguide  2948  in the set of tuning optical waveguides  2940 , and phase shifter  2968  in the set of phase shifters  2960 . 
     In yet another illustrative example, optical waveguide structure  2900  can have another configuration that includes a combination of wavelength selective coupler  2928  with a pair of first wavelength selective coupler  2921  and second wavelength selective coupler  2922 . 
     In this example, first wavelength selective coupler  2921  in the set of wavelength selective couplers  2920  couples second wavelength light  2913  from exit location  2971  in the nonlinear optical waveguide to starting point  2978  in tuning optical waveguide  2948 . Second wavelength selective coupler  2922  in the set of wavelength selective couplers  2920  couples second wavelength light  2913  from ending point  2979  in tuning optical waveguide  2948  to entry location  2930  in nonlinear optical waveguide  2909 . 
     Further, phase shifter  2968  in the set of phase shifters  2960  is located between starting point  2978  and ending point  2979  in tuning optical waveguide  2948 . In this example, phase shifter  2968  applies activation  2994  to tuning optical waveguide  2948  to change phase shift  2995  of second wavelength light  2913  in tuning optical waveguide  2948 . Thus, optical waveguide structure  2800  in  FIG.  28    and optical waveguide structure  2900  illustrated in  FIG.  29    enable adjusting light traveling through optical waveguides such as tuning optical waveguides to obtain a desired level of light generation within the optical waveguide structures. The set of phase shifters  2960  provides the ability to adjust parameters such as phase shift  2995  of one or more components of light  2910 . As are result, adjusting phase walk-off  2996  for nonlinear optical interaction  2998  can enable the manufacture of devices such as optical sources that are more compact and can be produced at a lower cost as compared to current devices because these devices comprise nonlinear optical waveguides. In other words, the use of optical waveguides comprising nonlinear optical materials instead of propagating “unguided” light through nonlinear optical material enables the devices in the illustrative examples to be more compact and also to be produced at lower cost as compared to currently available devices. These devices can be designed without partially overlapping loops for entanglement when those loops are unnecessary to obtain a desired level of performance and physical size. 
     With reference to  FIGS.  30 A and  30 B , illustrations of an optical waveguide structure are depicted in accordance with an illustrative embodiment. This figure illustrates cascading of many segments in nonlinear optical waveguide  3009  that increases the physical length of nonlinear optical waveguide  3009 . 
     In this depicted example, optical waveguide structure  3000  is comprised as first segment  3001  in nonlinear optical waveguide  3009 , second segment  3002  in nonlinear optical waveguide  3009 , third segment  3003  in nonlinear optical waveguide  3009 , first tuning optical waveguide  3041  in the set of tuning optical waveguides  3040 , first wavelength selective coupler  3021  in the set of wavelength selective couplers  3020 , and first phase shifter  3061  in a set of phase shifters  3060 . First phase shifter  3061  is located along first tuning optical waveguide  3041 . 
     In this example, first segment  3001  and second segment  3002  in nonlinear optical waveguide  3009  are physically separated from each other by first wavelength selective coupler  3021 . In this example, second segment  3002  and third segment  3003  in nonlinear optical waveguide  3009  are physically separated from each other by second wavelength selective coupler  3022  and by third wavelength selective coupler  3023 . In the illustrative example, first wavelength light  3011  can be supplied to first segment  3001  at first entry location  3030   
     With this example, first wavelength selective coupler  3021  couples first wavelength light  3011  from first segment  3001  in nonlinear optical waveguide  3009  into second segment  3002  in nonlinear optical waveguide  3009  at entry location  3032 . First wavelength selective coupler  3021  couples second wavelength light  3017 , which is generated in first segment  3001 , from first segment  3001  into first tuning optical waveguide  3041 . Further, second wavelength light  3017  in first tuning optical waveguide  3041  is coupled from first tuning optical waveguide  3041  to third segment  3003  by second wavelength selective coupler  3022 . In this example, second wavelength light  3017  is coupled away from third segment  3003  in nonlinear optical waveguide  3009  by second wavelength selective coupler  3022 . 
     In this example, second wavelength light  3017  generated in first segment  3001  goes through first tuning optical waveguide  3041  and then to third segment  3003  after having its phase shift adjusted to again re-establish a phase-matching condition. Additionally, second wavelength light  3018  generated in second segment  3002  is intentionally not coupled into third segment  3003  but rather is diverted into second tuning optical waveguide  3042 . 
     In this example, second wavelength light  3017  generated in first segment  3001  is coupled by second wavelength selective coupler  3022  into entry location  3034  of third segment  3003 . 
     In this depicted example, second wavelength selective coupler  3022  in the set of wavelength selective couplers  3020  couples first wavelength light  3011  from the second segment  3002  into the third segment  3003 . Second wavelength light  3017  in first tuning optical waveguide  3041  is coupled from first tuning optical waveguide  3041  to third segment  3003  by second wavelength selective coupler  3022 . 
     In the illustrative example, optical waveguide structure  3000  further comprises second tuning optical waveguide  3042  in the set of tuning optical waveguides  3040 ; second phase shifter  3062  in the set of phase shifters  3060 , and third wavelength selective coupler  3023  in the set of wavelength selective couplers  3020 . Second phase shifter  3062  is located along second tuning optical waveguide  3042 . 
     Second wavelength light  3018  generated in second segment  3002  in nonlinear optical waveguide  3009  is not coupled into third segment  3003  in nonlinear optical waveguide  3009  by second wavelength selective coupler  3022 . Instead, second wavelength light  3018  generated in second segment  3002  is coupled by third wavelength selective coupler  3023  into second tuning optical waveguide  3042 . Second wavelength light  3018  generated in second segment  3002  is coupled by third wavelength selective coupler  3023  from second segment  3002  into second tuning optical waveguide  3042 , and thus does not even enter second wavelength selective coupler  3022 . 
     Second wavelength light  3017  is generated in first segment  3001  and second wavelength light  3018  is generated in second segment  3002 . Second wavelength light  3017  and second wavelength light  3018  can have different phases relative to each other. Second wavelength light  3017  and second wavelength light  3018  will experience an interference if they are combined into the same optical waveguide. This interference can result in an increase or a decrease in the intensity or power of the combined second wavelength light, depending, respectively, on whether the interference is constructive or destructive. In this example, second wavelength light  3017  and second wavelength light  3018  are intentionally kept separate until they both reach combiner  3188  in  FIG.  31 B  as described below. In the examples, different tuning optical waveguides and different phase shifters can be used to adjust the phases of these two components of second wavelength light  3017  and  3018  to reduce their destructive interference and enhance their constructive interference when second wavelength light  3017  and second wavelength light  3018  are combined at combiner  3188  in  FIG.  31 B  as described below. 
     In this example, third wavelength selective coupler  3023  couples second wavelength light  3018 , generated in second segment  3002 , from second segment  3002  into second tuning optical waveguide  3042 . Third wavelength selective coupler  3023  also couples first wavelength light  3011  from second segment  3002  into third segment  3003  through second wavelength selective coupler  3022 . 
     In this illustrative example, optical waveguide structure  3000  can further comprise fourth segment  3004  in nonlinear optical waveguide  3009  and fourth wavelength selective coupler  3024  in the set of wavelength selective couplers  3020 . With this example, fourth wavelength selective coupler  3024  couples second wavelength light  3018 , generated in second segment  3002 , from second tuning optical waveguide  3042  into fourth segment  3004 . Additionally, fourth wavelength selective coupler  3024  couples the first wavelength light  3011  from third segment  3003  into fourth segment  3004 . 
     In this illustrative example, optical waveguide structure  3000  can further comprise third tuning optical waveguide  3043  in the set of tuning optical waveguides  3040  and fifth wavelength selective coupler  3025  in the set of wavelength selective couplers  3020 . In this example, fifth wavelength selective coupler  3025  in the set of wavelength selective couplers  3020  couples second wavelength light  3017  from third segment  3003  into third tuning optical waveguide  3043  and couples first wavelength light  3011  from third segment  3003  into fourth segment  3004  through fourth wavelength selective coupler  3024 . In this illustrative example, third phase shifter  3063  in the set of phase shifters  3060  can be located along third tuning optical waveguide  3043  and can apply activation  3093  to second wavelength light  3017  in third tuning optical waveguide  3043 . 
     In this example, additional second wavelength light can be produced as a result of the nonlinear optical interaction that occurs in third segment  3003 . Thus, the second wavelength light  3017  that is coupled from third segment  3003  by fifth wavelength selective coupler  3025  could comprise a combination of second wavelength light generated in first segment  3001  and additional second wavelength light generated in third segment  3003 . First phase shifter  3061  in first tuning optical waveguide  3041  adjusts the phase of the second wavelength light  3017  coupled into entry location  3034  of third segment  3003  in order to achieve a phase walk-off  3096  with a value of zero or a multiple of 2n radians for the nonlinear optical interaction  3098  occurring up through entry location  3034  in the third segment  3003 . As a result, the second wavelength light  3017  exiting the third segment and coupled through fifth wavelength selective coupler  3025  can be greater than the second wavelength light  3017  exiting the first segment  3001  and coupled into third segment  3003 . 
     Further, optical waveguide structure  3000  can include other optical components. For example, optical waveguide structure  3000  can include source input coupler  3031  that supplies first wavelength light  3011 , such as pump light  3012 , from a location external to optical waveguide structure  3000  into first segment  3001  of nonlinear optical waveguide  3009 . The first wavelength light  3011  can be supplied, via source input coupler  3031 , to first entry location  3030  in first segment  3001 . 
     The phase walk-off of interest at entry location  3034  in third segment  3003  is the phase walk-off for the cumulative nonlinear optical interaction that occurs through nonlinear optical waveguide  3009  from first entry location  3030  in first segment  3001  to entry location  3034  in third segment  3003 . The additional generation of second wavelength light  3017  that occurs in third segment  3003  depends on this phase walk-off, which is affected by the first phase shifter  3061  that adjusts the phase of the second wavelength light  3017  generated in first segment  3001 , as discussed above. However, second wavelength light  3018  generated in second segment  3002  is diverted away from third segment  3003  by third wavelength selective coupler  3023 . Thus, the phase of second wavelength light  3018  is not a factor in determining the phase walk-off of interest at entry location  3034  in third segment  3003 . 
     In this illustrative example, optical waveguide structure  3000  can further comprise fifth segment  3005  in nonlinear optical waveguide  3009 , fourth tuning optical waveguide  3044  in the set of tuning optical waveguides  3040  and seventh wavelength selective coupler  3027  as well as sixth wavelength selective coupler  3026  in the set of wavelength selective couplers  3020 . In this example, seventh wavelength selective coupler  3027  in the set of wavelength selective couplers  3020  couples second wavelength light  3018  from fourth segment  3004  into fourth tuning optical waveguide  3044  and also couples first wavelength light  3011  from fourth segment  3004  into fifth segment  3005  through seventh wavelength selective coupler  3027  and then through sixth wavelength selective coupler  3026 . In this illustrative example, fourth phase shifter  3064  in the set of phase shifters  3060  can be located along fourth tuning optical waveguide  3044  and can apply activation  3094  to second wavelength light  3018  in fourth tuning optical waveguide  3044 . 
     In this example, additional second wavelength light can be produced as a result of the nonlinear optical interaction that occurs in fourth segment  3004 . Thus, the second wavelength light  3018  that is coupled by seventh wavelength selective coupler  3027  could comprise a combination of second wavelength light generated in second segment  3002  and additional second wavelength light generated in fourth segment  3004 . Second phase shifter  3062  in second tuning optical waveguide  3042  adjusts the phase of the second wavelength light  3018  coupled into entry location  3036  of fourth segment  3004  in order to achieve a phase walk-off  3096  with a value of zero or a multiple of 2n radians for the nonlinear optical interaction  3098  occurring up through entry location  3036  in the fourth segment  3004 . As a result, the second wavelength light  3018  exiting the fourth segment and coupled through seventh wavelength selective coupler  3027  can be greater than the second wavelength light  3018  exiting the second segment  3002  and coupled into fourth segment  3004 . 
     In this illustrative example, different phase shifters can apply different activations depending on the phase adjustment desired. In this depicted example, first phase shifter  3061  in set of phase shifters  3060  applies activation  3091  to second wavelength light  3017  in first tuning optical waveguide  3041  to change the phase shift for second wavelength light  3017  in first tuning optical waveguide  3041  such that the phase walk-off  3096  for the nonlinear optical interaction  3098  in nonlinear optical waveguide  3009  from first entry location  3030  in first segment  3001  where first wavelength light  3011  is supplied to first segment  3001  to entry location  3034  in third segment  3003  has a value of zero or an even multiple of n radians. In other examples, the phase walk-off  3096  can have a value close to zero or close to an even multiple of n radians. For example, the value for the phase walk-off can be within 0.25 n radians or 0.5 n radians. Entry location  3034  is where second wavelength selective coupler  3022  and third segment  3003  connect to each other. 
     Further in this example, second phase shifter  3062  can apply activation  3092  to second wavelength light  3018  in second tuning optical waveguide  3042 . The second wavelength light  3018  in second tuning optical waveguide  3042  was generated in second segment  3002 . Activation  3092  is applied to this second wavelength light  3018  in second tuning optical waveguide  3042  such that the phase walk-off  3096  for nonlinear optical interaction  3098  in nonlinear optical waveguide  3009  from entry location  3032 , at which first wavelength selective coupler  3021  connects to second segment  3002 , to entry location  3036 , at which fourth wavelength selective coupler  3024  connects to fourth segment  3004  has a value that is zero or is an even multiple of n radians. 
     In other examples, the phase walk-off  3096  can have a value close to zero or close to an even multiple of n radians. For example, the value for the phase walk-off can be within 0.25 n radians or 0.5 n radians. Entry location  3036  is where fourth wavelength selective coupler  3024  and fourth segment  3004  connect to each other. 
     In this example, the order of components in optical waveguide structure  3000  can be first segment  3001 , first wavelength selective coupler  3021 , second segment  3002 , third wavelength selective coupler  3023 , second wavelength selective coupler  3022 , and third segment  3003 . To continue with this order of components, additional components can be fifth wavelength selective coupler  3025 , fourth wavelength selective coupler  3024 , fourth segment  3004 , seventh wavelength selective coupler  3027 , sixth wavelength selective coupler  3026  and fifth segment  3005 . 
     In this illustrative example, additional phase shifters can apply additional activations depending on the phase adjustment desired to achieve effective nonlinear optical interactions in segments of the nonlinear optical waveguide  3009  beyond the first segment  3001  and the second segment  3002 . In this depicted example, third phase shifter  3063  in set of phase shifters  3060  applies activation  3093  to second wavelength light  3017  in third tuning optical waveguide  3043  to change the phase shift for second wavelength light  3017  in third tuning optical waveguide  3043  such that the phase walk-off  3096  for the nonlinear optical interaction  3098  in nonlinear optical waveguide  3009  from first entry location  3030  in first segment  3001  where first wavelength light  3011  is supplied to first segment  3001  to entry location  3038  in fifth segment  3005  has a value of zero or an even multiple of n radians. The second wavelength light  3017  in the third tuning optical waveguide  3043  can be generated in the first segment  3001  and in the third segment  3003 . In other examples, the phase walk-off  3096  can have a value close to zero or close to an even multiple of n radians. For example, the value for the phase walk-off can be within 0.25 n radians or 0.5 n radians. Entry location  3038  is where sixth wavelength selective coupler  3026  and fifth segment  3005  connect to each other. 
     Likewise, as depicted in  FIGS.  30 A and  30 B , fourth phase shifter  3064  can apply activation  3094  to second wavelength light  3018  in fourth tuning optical waveguide  3044 . The second wavelength light  3018  in fourth tuning optical waveguide  3044  was generated in second segment  3002  and in fourth segment  3004 . Activation  3094  is applied to this second wavelength light  3018  in fourth tuning optical waveguide  3044  such that the phase walk-off  3096  for nonlinear optical interaction  3098  in nonlinear optical waveguide  3009  from entry location  3032 , at which first wavelength selective coupler  3021  connects to second segment  3002 , to an entry location (not shown), at which fourth wavelength selective coupler  3024  connects to a sixth segment  3006  through eighth wavelength selective coupler  3028  of nonlinear optical waveguide  3009  has a value that is zero or is an even multiple of n radians. 
     In this example, first segment  3001  and second segment  3002  in nonlinear optical waveguide  3009  are physically separated from each other by first wavelength selective coupler  3021 . In this example, second segment  3002  and third segment  3003  in nonlinear optical waveguide  3009  are physically separated from each other by second wavelength selective coupler  3022  and by third wavelength selective coupler  3023 . In this example, third segment  3003  and fourth segment  3004  are physically separated from each other by fourth wavelength selective coupler  3024  and by fifth wavelength selective coupler  3025 . In the illustrative example, first wavelength light  3011  can be supplied to first segment  3001  at first entry location  3030 . In this example, first wavelength light  3011  can be pump light  3012 . 
     With reference to  FIGS.  31 A and  31 B , illustrations of an optical waveguide structure is depicted in accordance with an illustrative embodiment. This figure illustrates how the two components for generated light, such as second wavelength light  3117  and second wavelength light  3118  can be combined such that constructive interference of second wavelength light  3117  and second wavelength light  3118  occurs. 
     In this illustrative example, optical waveguide structure  3100  comprises nonlinear optical waveguide  3109 , a set of wavelength selective couplers  3120 , a set of phase shifters  3160 , and a set of tuning optical waveguides  3140 . Like the example in  FIGS.  30 A and  30 B , the example illustrated in  FIGS.  31 A and  31 B  has a first segment  3101  of nonlinear optical waveguide  3109  into which first wavelength light  3111  is supplied and in which second wavelength light  3117  can be generated by a nonlinear optical interaction occurring in the first segment  3101 . The example illustrated in  FIGS.  31 A and  31 B  further has a second segment  3102  of nonlinear optical waveguide  3109  into which first wavelength light is supplied, through first wavelength selective coupler  3121 , and in which second wavelength light  3118  can be generated by a nonlinear optical interaction occurring in the second segment  3102 . 
     In this example, the nonlinear optical interaction can be extended to more and more segments of nonlinear optical waveguide  3109 . Second wavelength light  3117  generated in first segment  3101  is coupled through first wavelength selective coupler  3121  to first tuning optical waveguide  3141  and then through second wavelength selective coupler  3122  to third segment  3103 . In third segment  3103 , additional second wavelength light  3117  can be generated by nonlinear optical interaction of the first wavelength light  3111  and the second wavelength light present in the third segment  3103 , which can include the second wavelength light generated in the first segment. 
     In this example, second wavelength light  3118  generated in second segment  3102  is coupled through third wavelength selective coupler  3123  to second tuning optical waveguide  3142  and then through fourth wavelength selective coupler  3124  to fourth segment  3104 . In fourth segment  3104 , additional second wavelength light  3118  can be generated by nonlinear optical interaction of the first wavelength light  3111  and the second wavelength light present in the fourth segment  3104 , which can include the second wavelength light generated in the second segment  3102 . 
     The example illustrated in  FIGS.  31 A and  31 B  shows that more and more segments of nonlinear optical waveguide can be cascaded in this manner. Second wavelength light  3117  can be coupled from Nth segment  3107  through (2N-1) th wavelength selective coupler  3127  and Nth tuning optical waveguide  3147 . (2N-1) th wavelength selective coupler  3127  couples second wavelength light  3117  from Nth segment  3107  to Nth tuning optical waveguide  3147  and couples first wavelength light  3111  from Nth segment  3107  to (2N-2)th wavelength selective coupler  3126 , which then couples first wavelength light  3111  to (N+1) th segment  3108 . Second wavelength light  3118  can be coupled from (N-1) th tuning optical waveguide (not shown) through (2N-2)th tuning optical waveguide  3126  to (N+1) th segment  3108 . Second wavelength light  3118  can be coupled through (N+1) th segment  3108  of nonlinear optical waveguide  3109  and (N+1) th tuning optical waveguide  3148 . (2N+1) th wavelength selective coupler  3129  couples second wavelength light  3118  from (N+1) th segment  3108  into (N+1) th tuning optical waveguide  3148 . (2N+1) th wavelength selective coupler  3129  also couples first wavelength light  3111  from (N+1) th segment  3108  through 2Nth wavelength selective coupler  3128  to final segment  3189 . 
     The example illustrated in  FIGS.  31 A and  31 B  also shows a way in which the two cascades can be terminated. 2Nth wavelength selective coupler  3128  couples second wavelength light  3117  from Nth tuning optical waveguide  3147  into final segment  3189  of optical waveguide structure  3100 . Second wavelength light  3117  travels through final segment  3189  is connected to combiner junction  3187  of combiner  3188 . As depicted, (2N+1) th wavelength selective coupler  3129  couples second wavelength light  3118  from (N+1) th segment  3108  into (N+1) th tuning optical waveguide  3148  in tuning optical waveguides  3140 . Second wavelength light  3118  travels through (N+1) th tuning optical waveguide  3148  to combiner junction  3187  of combiner  3188 . 
     In a simplified example of optical waveguide structure  3100 , Nth tuning optical waveguide  3147  can be a third tuning optical waveguide and (N+1) th tuning optical waveguide  3148  can be a fourth tuning optical waveguide. For this example, Nth segment would be third segment  3103 . For this example, (N-1) th segment would be second segment  3102  and (N+1) th segment would be fourth segment  3104 . For this example, (2N-1) th wavelength selective coupler  3127  would be fifth wavelength selective coupler  3125  and (2N-2)th wavelength selective coupler  3126  would be fourth wavelength selective coupler  3124 . 
     In one example of optical waveguide structure  3100 , as illustrated in  FIGS.  31 A and  31 B , source output coupler  3133  is connected to final segment  3189 . For this example, final segment  3189  does not comprise a substantial amount of nonlinear optical material  3197 , so that no nonlinear optical interaction would occur. Source output coupler  3133  removes first wavelength light  3111 , which could be pump light  2812  to a source out port or waveguide of the structure. Source output coupler  3133  also couples second wavelength light  3117  to combiner junction  3187  of combiner  3188 . 
     In other examples (not depicted), final segment  3189  could comprise nonlinear optical material  3197 . For these other examples, source output coupler  3133  is located between 2Nth wavelength selective coupler  3128  and final segment  3189 . In these cases, source output coupler  3133  couples first wavelength light  3111  from Nth tuning optical waveguide  3147  away from final segment  3189 . Thus, first wavelength light  3111  is removed and does not propagate through final segment  3189  of optical waveguide structure  3100  when final segment  3189  comprises nonlinear optical material  3197 . As a result, no additional generation of second wavelength light occurs in final segment  3189  even if that final segment comprises nonlinear optical material, since the first wavelength light  3111 , which serves as the pump light for the nonlinear optical interactions that occur in the nonlinear optical waveguide  3109 , is absent. 
     In these examples, no first wavelength light  3111  is supplied to optical waveguide structure  3100  besides first wavelength light  3111  supplied to first segment  3101  through source input coupler  3131 . First wavelength light  3111  in second segment  3102  is supplied through first segment  3101 . First wavelength light  3111  in third segment  3103  is supplied through first segment  3101 , and travels through second segment  3102  to third segment  3103 . 
     In the illustrated example, optical waveguide structure  3100  further comprises combiner  3188 . Second wavelength light  3117  is supplied through final segment  3189  to a combiner junction  3187  of combiner  3188 . In addition, second wavelength light  3118  is supplied through (N+1) th tuning optical waveguide  3148  to the combiner junction  3187  of combiner  3188 . The phase of second wavelength light  3117  at the combiner junction  3187  and the phase of second wavelength light  3118  at the combiner junction  3187  are adjusted to produce a constructive interference condition for these two components of second wavelength light  3117  and second wavelength light  3118 . The combining of second wavelength light  3117  from the route through first segment  3101  and other odd-numbered segments and second wavelength light  3118  from the route through second segment  3102  and other even-numbered segments form combined second wavelength light  3113 . In this example, combined second wavelength light  3113  is an idler light. 
     In the example of  FIGS.  31 A and  31 B , an optional final phase shifter  3169  can be located along final segment  3189 . This final phase shifter  3169  of the set of phase shifters  3160  applies activation  3190  to adjust the phase of second wavelength light  3117  traveling in final segment  3189 . 
     In the illustrated example, the optical waveguide structure  3100  also can comprise an optional auxiliary input segment  3176  into which third wavelength light  3115  is supplied. This third wavelength light  3115  serves as an auxiliary source light for nonlinear optical processes such as parametric up-conversion and parametric down-conversion that occur in nonlinear optical waveguide  3109 . The third wavelength light  3115  can be signal light or can be idler light, depending on whether second wavelength light is signal light or idler light. If second wavelength light is idler light, then third wavelength light would be signal light. Conversely, if second wavelength light is signal light, then third wavelength light would be idler light. When supplied as a source light, third wavelength light  3115  is coupled via source input coupler  3131  into nonlinear optical waveguide  3109 . In this example, third wavelength light  3115  is directed through the segments of nonlinear optical waveguide  3109  in the same route followed by first wavelength light  3111 . Optical waveguide structure  3100  can further comprise optional auxiliary output coupler  3135 . In this example, source output coupler  3133  couples third wavelength light  3115  from final segment  3189  to auxiliary output coupler  3135 . Auxiliary output coupler  3135  then couples third wavelength light  3115  away to an output waveguide or port of the structure. In some variations of this example, auxiliary output coupler  3135  can be located between source output coupler  3133  and combiner  3188 . In those variations, auxiliary output coupler also couples second wavelength light  3117  from source output coupler  3133  to combiner  3188 . As a result, only second wavelength light  3117  and second wavelength light  3118 , which would be components of combined second wavelength light  3113 , are supplied to combiner  3188 . 
     In this illustrative example, different phase shifters can apply different activations depending on the phase adjustment desired. In this depicted example, first phase shifter  3161  in set of phase shifters  3160  applies activation  3191  to first tuning optical waveguide  3141  to change the phase shift for second wavelength light  3117  in first tuning optical waveguide  3141  such that the phase walk-off  3196  for the nonlinear optical interaction  3198  in nonlinear optical waveguide  3109  from first entry location  3130  in first segment  3101  where first wavelength light  3111  is supplied to first segment  3101  to entry location  3134  in third segment  3103  has a value of zero or an even multiple of n radians. In other examples, phase walk-off  3196  can have a value close to zero or close to an even multiple of n radians. For example, the value for the phase walk-off can be within 0.25 n radians or 0.5 n radians. Entry location  3134  is where second wavelength selective coupler  3122  and third segment  3103  connect to each other. 
     Further in this example, second phase shifter  3162  can apply activation  3192  to second tuning optical waveguide  3142  to change the phase shift for second wavelength light  3118  in second tuning optical waveguide  3142 . The second wavelength light  3118  in second tuning optical waveguide  3142  was generated in second segment  3102 . Activation  3192  is applied to second tuning optical waveguide  3142  such that the phase walk-off  3196  for nonlinear optical interaction  3198  in nonlinear optical waveguide  3109  from entry location  3132 , at which first wavelength selective coupler  3121  connects to second segment  3102 , to entry location  3136 , at which fourth wavelength selective coupler  3124  connects to fourth segment  3104  has a value that is zero or is an even multiple of n radians. In other examples, the phase walk-off  3196  can have a value close to zero or close to an even multiple of n radians. For example, the value for the phase walk-off can be within 0.25 n radians or 0.5 n radians. 
       FIGS.  31 A and  31 B  illustrates additional functions of the embodiment of optical waveguide structure  3100  depicted in  FIG.  31 A . With reference to  FIGS.  31 A and  31 B , optical waveguide structure  3100  further comprises combiner  3188 . First component of combined second wavelength light  3113  is second wavelength light  3117 . This component is supplied through Nth tuning optical waveguide  3147  and final segment  3189  to the combiner junction  3187  of combiner  3188 . In addition, second component of combined second wavelength light  3113  is second wavelength light  3118 , which is supplied through (N+1) th tuning optical waveguide  3148  to the combiner junction  3187  of combiner  3188 . The phase of second wavelength light  3117  of combined second wavelength light  3113  at the combiner junction  3187  and the phase of the second wavelength light  3118  of combined second wavelength light  3113  at the combiner junction  3187  are adjusted to produce a constructive interference condition for second wavelength light  3117  and second wavelength light  3118 . 
     In this example, Nth phase shifter  3167  applies activation  3193  to second wavelength light  3117  in Nth tuning optical waveguide  3147  to change the phase shift for second wavelength light  3117  in Nth tuning optical waveguide  3147 . Second wavelength light  3117  further traverses through final segment  3189 . Optional final phase shifter  3169  in final segment  3189  can apply activation  3190  to second wavelength light  3117  to further change the phase of second wavelength light  3117  presented at combiner junction  3187  of combiner  3188 . 
     Further in this example, (N+1) th phase shifter  3168  can apply activation  3194  to second wavelength light  3118  in (N+1) th tuning optical waveguide  3148 . Second wavelength light  3118  is generated in the even-numbered segments of nonlinear optical waveguide  3109 . Activation  3194  is applied to second wavelength light  3118  in (N+1) th tuning optical waveguide  3148  to change the phase of second wavelength light  3118  presented at combiner junction  3187  of combiner  3188 . 
     In this depicted example, combiner junction  3187  of combiner  3188  functions as an optical interferometer. Combined second wavelength light  3113 , the combined output from combiner  3188 , has the greatest intensity when the relative phases of second wavelength light  3117  and second wavelength light  3118  are the same or are an even multiple of n radians. Thus, for this example, Nth phase shifter  3167  and optional final phase shifter  3169  apply activation  3193  and activation  3190  to second wavelength light  3117  and (N+1) th phase shifter  3168  applies activation  3194  to second wavelength light  3118  such that, ideally, the relative phases of second wavelength light  3117  and second wavelength light  3118  are the same or are different by an even multiple of n radians when second wavelength light  3117  and second wavelength light  3118  are presented at combiner junction  3187  of combiner  3188 . In other examples, the relative phases of second wavelength light  3117  and second wavelength light  3118  presented at the combiner junction  3187  can be within 0.25 n radians or 0.5 n radians. In other words, the phase difference between second wavelength light  3117  and second wavelength light  3118  can be as large as 0.25 n radians or even as large as 0.5 n radians. 
     With reference to  FIGS.  30 A,  30 B,  31 A, and  31 B , optical waveguide structure  3000  and optical waveguide structure  3100  can have as few as only two segments of nonlinear optical waveguide  3009  and nonlinear optical waveguide  3109 . These two segments would be first segment  3001  and first segment  3101  and second segment  3002  and second segment  3102 . Second wavelength light  3017  and second wavelength light  3117  is generated by nonlinear optical interaction of first wavelength light  3011  and first wavelength light  3111  in first segment  3001  and first segment  3101  and second wavelength light  3018  and second wavelength light  3118  is generated by nonlinear optical interaction of first wavelength light  3011  and first wavelength light  3111  in second segment  3002  and second segment  3102 . 
     In one example, N=1. Thus, Nth tuning optical waveguide  3147  is first tuning optical waveguide  3041 , (2N-1) th wavelength selective coupler  3127  is first wavelength selective coupler  3021 , and 2Nth wavelength selective coupler  3128  is second wavelength selective coupler  3022  in  FIG.  30 A . Also, (N+1) th tuning optical waveguide  3148  is second tuning optical waveguide  3042  in  FIG.  30 A , (2N+1) th wavelength selective coupler  3129  is third wavelength selective coupler  3023  in  FIG.  30 A . Second wavelength light  3017  and second wavelength light  3117  from first tuning optical waveguide  3041  are coupled through final segment  3189  to combiner  3188 ; and second wavelength light  3018  and second wavelength light  3118  from second tuning optical waveguide  3042  in  FIGS.  30 A and  30 B  also would be coupled to combiner  3188 . 
     In another illustrative example, again with reference to  FIGS.  30 A and  30 B  and  FIGS.  31 A and  31 B , optical waveguide structure  3000  and optical waveguide structure  3100  can have just four segments of nonlinear optical waveguide  3009  and nonlinear optical waveguide  3109 . These four segments would be first segment  3001 , second segment  3002 , third segment  3003  and fourth segment  3004 . Second wavelength light  3017  and second wavelength light  3117  are generated by nonlinear optical interaction of first wavelength light  3011  and first wavelength light  3111  in first segment  3001  and first segment  3101  and in third segment  3003  and third segment  3103 . Second wavelength light  3018  and second wavelength light  3118  is generated by nonlinear optical interaction of first wavelength light  3011  and first wavelength light  3111  in second segment  3002  and second segment  3102  and in fourth segment  3004  and fourth segment  3104 . 
     In this example in  FIGS.  31 A and  31 B , N is equal to 3. Thus, Nth tuning optical waveguide  3147  is third tuning optical waveguide  3043  in  FIG.  30 B , (2N-1) th wavelength selective coupler  3127  can be a fifth wavelength selective coupler  3025  in  FIG.  30 A , and 2Nth wavelength selective coupler  3128  is a sixth wavelength selective coupler  3026 . Also, (N+1) th tuning optical waveguide  3148  is fourth tuning optical waveguide  3044  in  FIG.  30 B , (2N+1) th wavelength selective coupler  3129  is seventh wavelength selective coupler  3027  in  FIG.  30 B . Second wavelength light  3017  from third tuning optical waveguide  3043  and second wavelength light  3018  from fourth tuning optical waveguide  3044  are coupled to combiner  3188 . 
     With reference to  FIGS.  32 A and  32 B , illustrations of a block diagram of routes for light traveling through an optical waveguide structure is depicted in accordance with an illustrative embodiment. In this example, routes  3250  are depicted for light traveling through optical waveguide structure  3000  in  FIG.  30 A  and for light traveling through optical waveguide structure  3100  in  FIG.  31 A . 
     First wavelength light  3011  travels in route  3251  that traverses, in sequence, source input coupler  3031 , first segment  3001 , first wavelength selective coupler  3021 , second segment  3002 , third wavelength selective coupler  3023 , second wavelength selective coupler  3022 , third segment  3003 , fifth wavelength selective coupler  3025 , fourth wavelength selective coupler  3024 , and fourth segment  3004 . Route  3251  for first wavelength light  3011  can be extended to pass through additional segments of nonlinear optical waveguide  3109  and additional wavelength selective couplers of the set of wavelength selective couplers  3120  as illustrated in  FIG.  31 A . These additional segments and couplers include, in sequence, Nth segment  3107 , (2N-1) th wavelength selective coupler  3127 , (2N-2)th wavelength selective coupler  3126 , (N+1) th segment  3108 , (2N+1) th wavelength selective coupler  3129 , 2Nth wavelength selective coupler  3128 , final segment  3189 , and source output coupler  3133 . 
     In this illustrative example, odd index route  3257  and even index route  3258  are present in optical waveguide structure  3100 . Odd index route  3257  comprises odd numbered segments and their associated components. Even index route  3258  comprises even numbered segments and their associated components. 
     Two different components of second wavelength light traverse these two different routes through optical waveguide structure  3000 . For example, second wavelength light  3017  can be generated in first segment  3001  as well in third segment  3003 . Odd index route  3257  for second wavelength light  3017  traverses, in sequence, first segment  3001 , first wavelength selective coupler  3021 , first tuning optical waveguide  3041 , second wavelength selective coupler  3022 , third segment  3003 , and fifth wavelength selective coupler  3025 . 
     Odd index route  3257  for second wavelength light  3017  can be further extended, as illustrated in  FIGS.  31 A and  31 B , to traverse through additional segments of nonlinear optical waveguide  3109 , additional wavelength selective couplers of the set of wavelength selective couplers  3120 , and additional tuning optical waveguides of the set of tuning optical waveguides  3140  as illustrated in  FIG.  31 A . These additional segments and couplers can include, in sequence, Nth segment  3107 , (2N-1) th wavelength selective coupler  3127 , Nth tuning optical waveguide  3147 , 2Nth wavelength selective coupler  3128 , final segment  3189 , source output coupler  3133 , auxiliary output coupler  3135 , and combiner  3188 . As depicted, second wavelength light  3117  is generated in the odd-indexed segments of nonlinear optical waveguide  3109 . 
     As depicted, second wavelength light  3018  is generated in second segment  3002 . Second wavelength light  3018  travels in even index route  3258  that is different from odd index route  3257  traveled by second wavelength light  3017 . In even index route  3258 , second wavelength light  3018  traverses, in sequence, second segment  3002 , third wavelength selective coupler  3023 , second tuning optical waveguide  3042 , fourth wavelength selective coupler  3024 , and fourth segment  3004 . 
     In the illustrative example, even index route  3258  for second wavelength light  3018  can be further extended, as illustrated in  FIGS.  31 A and  31 B , to traverse through additional segments of nonlinear optical waveguide  3109 , additional wavelength selective couplers of the set of wavelength selective couplers  3120 , and additional tuning optical waveguides of the set of tuning optical waveguides  3140  as illustrated in  FIGS.  31 A and  31 B . These additional segments and couplers can include, in sequence, (N+1) th segment  3108 , (2N+1) th wavelength selective coupler  3129 , (N+1) th tuning optical waveguide  3148 , and combiner  3188 . The second wavelength light  3018  of second wavelength light is generated in the even-numbered segments of nonlinear optical waveguide  3109 . 
     Turning next to  FIG.  33   , an illustration of graphs of the effect of waveguide cross-sectional dimensions on the phase walk-off associated with imperfect wave vector matching is depicted in accordance with an illustrative embodiment. Graphs  3300  are for a nonlinear optical waveguide structure comprising a nonlinear optical waveguide using cross-sections  3700  shown in  FIGS.  37 A- 37 G  and described below. As depicted, graphs  3300  show the dependence of the n phase walk-off distance on the values for different features in a waveguide. Graphs  3300  illustrate tolerances for variations in different dimensions in nonlinear optical waveguides. These dimensions shown in graphs  3300  have ranges in which normal operating regions are present that have a desired level of performance. Although the designs can have dimensions within these normal operating ranges, the environment during operation of the waveguides and deviations in fabrication can result in the values of these dimensions being out of tolerance for the desired level of performance within an operating region. 
     The length selected for a nonlinear optical waveguide segment can depend on the desired fabrication and operational variations that can be tolerated by the nonlinear optical waveguide structure. Graphs  3300  give some examples of expected values for the nonlinear optical interaction distance at which a phase walk-off of n radians is obtained and the dependence of this n phase walk-off distance on variations in some examples of different types of waveguide dimensions. 
     Line  3301  in graph  3302  and line  3305  in graph  3306  show the distance for a nonlinear optical interaction at which the phase walk-off reaches n radians. Line  3301  in graph  3302  shows this phase walk-off distance for different values of the strip width. Line  3305  in graph  3306  shows this phase walk-off distance for different values of the strip height. 
     In this example, the portion of line  3301  within desired fabrication tolerance  3307  of strip widths in graph  3302  is desired operating region  3309 . Likewise, the portion of line  3305  within desired operating region  3312  of strip heights in graph  3306  is desired operating region  3313 . This desired operating region constrains the tolerable variation in strip width or strip height that provides the desired operation for a waveguide in which the cross section is implemented. For example, if a nonlinear optical waveguide is 1 mm long, this degree of variation can be tolerated in the strip width or strip height. But, if greater nonlinear optical interaction distance than 1 mm is desired, phase shifters can be used to provide desired levels of constructive nonlinear optical interaction the result in an increased amount of the generated light. 
     In other words, the portion of line  3305  within desired operating region  3312  constrains a desired operating region  3312  for the strip height. Likewise, the portion of line  3301  within desired operating region  3309  constrains desired fabrication tolerance  3307  for the strip width. In desired operating region  3309  and  3312 , the distance for nonlinear optical interaction can be 1 mm or greater before the phase walk-off of that nonlinear optical interaction reaches or exceeds n radians. As discussed above, when the phase walk-off has a value smaller than n radians, the nonlinear optical generation process continues to be constructive and produces more and more generated light from the source light. However, when the phase walk-off has a value greater than n radians and up to a value of 2n radians, the nonlinear optical generation process becomes destructive and reduces the amount of generated light, converting some previously generated light back to source light. Thus, it is desirable to keep the phase walk-off between zero and n radians, and as close to zero as possible. 
     In these illustrative examples, fabrication tolerances of approximately ±1 nm (or ±0.001 um) in waveguide dimensions such as the strip width and the strip height reduce the distance at which the phase walk-off reaches n radians from being infinite (for perfect wave vector matching) to being on the order of 1 mm. If the departure of the fabricated waveguide dimensions such as the strip width and the strip height from the specified values is greater than ±1 nm, the maximum distance at which the phase walk-off reaches n radians can be much smaller than 1 mm. 
     To achieve longer nonlinear optical interaction distances, the examples in  FIGS.  29 - 31    as well as the following examples couple the generated light into a phase tuning path that contains a phase shifter. An activation applied by the phase shifter can change the phase of the light propagating through the phase tuning path. This change in the phase of the generated light that is diverted to propagate through the phase tuning path and then is coupled back into the nonlinear optical waveguide can be used to adjust the phase walk-off observed at the point where the generated light is coupled back into the nonlinear optical waveguide so that the phase walk-off has a value that is zero or an even multiple of n radians. 
     To produce the desired amount of adjustable phase change, the length of a phase tuning path formed by a tuning optical waveguide can be selected to have a length to accommodate the desired applicable length of the phase shifter associated with that phase tuning path. For example, with phase shifters that are based on electro-optic (EO) control of the wave vector, the change in the effective index achieved by an electro-optic phase shifter for light such as idler light can be described by an expression such as Δn I  = n I   3 r eff ΔE applied . The change in phase for the idler light can be described by an expression such as  
     
       
         
           
             Δ 
             
               ϑ 
               i 
             
             = 
             
               
                 
                   
                     2 
                     π 
                   
                   
                     
                       λ 
                       I 
                     
                   
                 
               
             
             Δ 
             
               n 
               I 
             
             
               D 
               i 
             
             ⋅ 
           
         
       
     
     In these expressions, applied, is the applied electric field, r eff  is the value of the relevant electro-optic coefficient, n I  is the refractive of the electro-optic material for the idler light, λ I  is the wavelength of the idler light, and D i  is the applicable length of the phase shifter, with i being an index that indicates a specific phase shifter and tuning optical waveguide. 
     In this illustrative example, the “activation” applied by the phase shifter upon the tuning optical waveguide is the electric field. This applied electric field results in a change of the effective index of that waveguide that changes the phase of the light traveling through that waveguide. 
     For practical widths of the electro-optic material in the phase shifter, the maximum E-field that can be applied before risking breakdown can be on the order of 10 V/um. For an electro-optic material such as x-cut lithium niobate and TE polarized light in the phase shifter, the value for n I   3 r eff  is on the order of 3×10 -4  µm/V. To achieve a maximum electrically controlled phase shift of ±n radians, the applicable length of the phase shifter should be at least  
     
       
         
           
             
               
                 
                   
                     
                       D 
                       i 
                     
                   
                   
                     
                       λ 
                       I 
                     
                   
                 
               
             
             ~ 
             1.5 
             × 
             
               
                 10 
               
               3 
             
             . 
           
         
       
     
     As an example, if the idler wavelength is 1.5 µm, the applicable length of the phase shifter should be approximately 3 mm. 
     A phase shifter can comprise multiple sections. For appropriate supply of the electrical control signals to these multiple phase shifter sections, the applicable length of the phase shift adjustment can be as long as the total length of the multiple phase shifter sections. If the phase shifter comprises a material that has a large thermo-optic coefficient, such a thermo-optic phase shifter can have a shorter length than an electro-optic phase shifter. 
     The phase shifters in the final tuning optical waveguide and the phase shifters in the next-to-final tuning optical waveguide are used to control the phases of the two components of generated light that are combined together. These two phase shifters can be operated in a push-pull manner, with one tuning optical waveguide producing a positive phase shift and the other tuning optical waveguide producing a negative phase shift. Thus, the resulting net phase shift between the outputs from these two tuning optical waveguides can be two times as large as the phase shift applied in tuning optical waveguide. As a result, the phase shifters of the final and the next-to-final tuning optical waveguide can have a smaller applicable length than the phase shifters in the preceding tuning optical waveguide of the nonlinear optical waveguide structure and still achieve a maximum electrically adjustable phase shift of ±n radians. 
     Turning now to  FIG.  34   , an illustration of an optical waveguide structure is depicted in accordance with an illustrative example. In this example, optical waveguide structure  3400  is an open-ended nonlinear optical waveguide structure. In other words, loops for recirculating light are not used. 
     As depicted, optical waveguide structure  3400  comprises nonlinear optical waveguide  3409 , first idler tuning optical waveguide  3441 A, first signal tuning optical waveguide  3441 B, second idler tuning optical waveguide  3442 A, second signal tuning optical waveguide  3442 B, first idler wavelength selective coupler  3421 A, first signal wavelength selective coupler  3421 B, second idler wavelength selective coupler  3422 A, second signal wavelength selective coupler  3422 B, pump input waveguide  3472 , signal input waveguide  3474 , pump output waveguide  3473 , signal output waveguide  3475 , idler output waveguide  3479 , pump input coupler  3432 , signal input coupler  3434 , pump output coupler  3433 , signal output coupler  3435 , idler output coupler  3439 , first idler phase shifter  3461 A, first signal phase shifter  3461 B, second idler phase shifter  3462 A, second signal phase shifter  3462 B. 
     In this illustrative example, nonlinear optical waveguide  3409 , has nonlinear optical waveguide segments. As depicted, these nonlinear optical waveguide segments are first segment  3401 , second segment  3402 , and third segment  3403 . 
     As depicted, pump input coupler  3432  couples pump light  3412  introduced through pump input waveguide  3472  to first segment  3401 . Optional signal input coupler  3434  couples signal light  3414  introduced in signal input waveguide  3474  to first segment  3401 . Pump output coupler  3433  couples pump light  3412  from third segment  3403  to pump output waveguide  3473 . Signal output coupler  3435  couples signal light  3414  from third segment  3403  to signal output waveguide  3475 . Idler output coupler  3439  couples idler light  3416  from third segment  3403  to idler output waveguide  3479 . 
     As depicted, nonlinear optical waveguide  3409  and other components are formed on a yz plane defined by z-axis  3493  and y-axis  3492  in which an x-axis  3491  is perpendicular to the plane. In an illustrative example, nonlinear optical waveguides can be fabricated from a nonlinear optical material such as x-cut lithium niobate. In this example, the x-axis of the nonlinear optical material is perpendicular to the yz plane of the structure of nonlinear optical waveguide  3409  and the other components. 
     In this illustrative example, first idler wavelength selective coupler  3421 A couples idler light  3416  by extracting idler light  3416  from first segment  3401  into first idler tuning optical waveguide  3441 A and reinserting idler light  3416  into second segment  3402  after activations have been applied using first idler phase shifter  3461 A associated with first idler tuning optical waveguide  3441 A. Each phase shifter is comprised of three pairs of electrodes in this example. First signal wavelength selective coupler  3421 B couples signal light  3414  by extracting signal light  3414  from first segment  3401  into first signal tuning optical waveguide  3441 B and reinserting signal light  3414  into second segment  3402  after activations have been applied using first signal phase shifter  3461 B associated with first signal tuning optical waveguide  3441 B. 
     In this illustrative example, second idler wavelength selective coupler  3422 A couples idler light  3416  by extracting idler light  3416  from second segment  3402  into second idler tuning optical waveguide  3442 A and reinserting idler light  3416  into third segment  3403  after activations have been applied using second idler phase shifter  3462 A associated with second idler tuning optical waveguide  3442 A. Second signal wavelength selective coupler  3422 B couples signal light  3414  by extracting signal light  3414  from second segment  3402  into second signal tuning optical waveguide  3442 B and reinserting signal light  3414  into third segment  3403  after activations have been applied using second signal phase shifter  3462 B associated with second signal tuning optical waveguide  3442 B. 
     In this example, the phase shifters for the different tuning optical waveguides can apply activations to the light traveling through the tuning optical waveguides. The application of the activations can adjust the phase of the light to obtain a desired phase walk-off when at least one of the environment or fabrication inconsistencies result in a dimension of the nonlinear optical waveguide being out of tolerance for design level performance. In other words, the phase shifters can be used when the length of the tuning optical waveguides do not provide a desired phase walk-off for a nonlinear optical interaction involving light that has traveled through the tuning optical waveguides. In this example, both the length of a tuning optical waveguide and a phase shifter associated with the tuning optical waveguide can be used to obtain a desired phase walk-off. The phase shifter essentially adjusts the effective length of the tuning waveguide by applying an activation to change the tuning optical waveguide in a manner that changes the phase shift of light traveling through the tuning optical waveguide. 
     Consider an illustrative implementation of optical waveguide structure  3400 , nonlinear optical waveguide  3409  that has strip width and strip height designed to achieve perfect phase matching, so that the n phase walk-off distance for nonlinear optical waveguide  3409  is essentially infinite. Realistic fabrication tolerances may cause the achieved n phase walk-off distance to be at least 1 mm. Thus, this implementation has the lengths of first segment  3401 , second segment  3402  and third segment  3403  no larger than 1 mm. This implementation also sets the length of first idler tuning optical waveguide  3441 A and the length of first signal tuning optical waveguide  3441 B so that the phase walk-off for the nonlinear optical interaction occurring in nonlinear optical waveguide  3409  from a starting point of first segment  3401  to a starting point of second segment  3402  has a value of zero or an even multiple of n radians. The starting point of first segment  3401  is where pump input coupler  3432  connects with first segment  3401 . The starting point of second segment  3402  is where first signal wavelength selective coupler  3421 B connects with second segment  3402 . For this illustrative implementation, first segment  3401  connects with first idler wavelength selective coupler  3421 A, which connects with first signal wavelength selective coupler  3421 B, which then connects with second segment  3402 . 
     This implementation also sets the length of second idler tuning optical waveguide  3442 A and the length of second signal tuning optical waveguide  3442 B so that the phase walk-off for the nonlinear optical interaction occurring in nonlinear optical waveguide  3409  from the starting point of second segment  3402  to a starting point of third segment  3403  has a value of zero or an even multiple of n radians. The starting point of third segment  3403  is where second signal wavelength selective coupler  3422 B connects with third segment  3403 . For this illustrative implementation, second segment  3402  connects with second idler wavelength selective coupler  3422 A, which connects with second signal wavelength selective coupler  3422 B, which then connects with third segment  3403 . 
     This illustrative implementation also has first idler phase shifter  3461 A designed to apply activations to first idler tuning optical waveguide  3441 A and has first signal phase shifter  3461 B designed to apply activations to first signal tuning optical waveguide  3441 B so that the phase walk-off for the nonlinear optical interaction occurring in nonlinear optical waveguide  3409  from the starting point of first segment  3401  to the starting point of second segment  3402  has a value of zero or an even multiple of n radians even when the strip width and strip height of first idler tuning optical waveguide  3441 A, first signal tuning optical waveguide  3441 B and first segment  3401  depart from their as-designed values as a result of fabrication tolerances or of a variation in an operating condition such as temperature. 
     This implementation also has second idler phase shifter  3462 A designed to apply activations to second idler tuning optical waveguide  3442 A and has second signal phase shifter  3462 B designed to apply activations to second signal tuning optical waveguide  3442 B so that the phase walk-off for the nonlinear optical interaction occurring in nonlinear optical waveguide  3409  from the starting point of second segment  3402  to the starting point of third segment  3403  has a value of zero or an even multiple of n radians even when the strip width and strip height of second idler tuning optical waveguide  3442 A, second signal tuning optical waveguide  3442 B and second segment  3402  depart from their as-designed values as a result of fabrication tolerances or of a variation in an operating condition. 
     Each segment in nonlinear optical waveguide  3409  except the last segment is associated with a tuning optical waveguide for the generated idler light and a different tuning optical waveguide for the generated signal light. In some examples of optical structures, the two wavelength selective couplers, for the signal light and for the idler light, are located near the end of a given segment and just before the start of the next segment. As depicted, pump removing coupler is located at the end of the last segment. Pump input coupler  3432  and the pump output coupler  3433  establish the overall length of the nonlinear optical interaction that produces the generated light. 
     Optical waveguide structure  3400  can be used for nonlinear optical processes such as spontaneous parametric down conversion (SPDC) by omitting the optional signal input coupler  3434  and by using both the idler-phase tuning paths and the signal-phase tuning paths. The structure of  FIG.  34    also can be used for dual-source nonlinear optical processes such as difference frequency generation (DFG) with signal light  3414  as an auxiliary source or input light that is supplied to optical waveguide structure  3400  in addition to the pump light. In this case, optical waveguide structure can include optional signal input coupler  3434  and signal light can be supplied to the structure through signal input waveguide  3474 . The overall length of a segment and including the lengths of the two wavelength-selective couplers (for the idler light and for the signal light) associated with that segment is selected to be sufficiently small that the magnitude of the phase walk-off resulting from anticipated fabrication and operational tolerances is no greater than n radians. 
     The phase shifters in a phase tuning path are configured to have a length sufficiently large to achieve an electrically controlled phase shift as much as ±n radians or greater. The overall length of a phase tuning path is selected to achieve a relative phase shift that is 0 or a multiple of 2n radians between the previously generated light reinserted from the phase tuning path into the subsequent segment and the newly generated light in the subsequent segment. 
     In this example, the generation of light by a nonlinear optical process in optical waveguide structure can include difference-frequency generation (DFG) and spontaneous parametric down conversion (SPDC). However, the elements of optical waveguide structure  3400  described in this example can apply to generation of light by other nonlinear optical processes such as sum-frequency generation and four-wave mixing. These nonlinear optical processes in optical waveguide structure  3400  can involve second-order nonlinearity, such as for the examples discussed, as well as third order nonlinearity. 
     Further in  FIG.  34   , in optical waveguide structure  3400 , first route  3452  includes first segment  3401 , second segment  3402  and third segment  3403 . First route  3452  is traversed by the pump light  3412 . Second route  3456  includes first segment  3401 , first idler tuning optical waveguide  3441 A, second segment  3402 , second idler tuning optical waveguide  3442 A, and third segment  3403 . Second route  3456  is traversed by the idler light  3416 . Third route  3454  includes first segment  3401 , first signal tuning optical waveguide  3441 B, second segment  3402 , second signal tuning optical waveguide  3442 B, and third segment  3403 . Third route  3454  is traversed by signal light  3414 . In this example, the generated light is idler light  3416 . 
     For the example depicted in  FIG.  34   , the same wavelength selective coupler functions as both an extracting out-coupler from a nonlinear optical waveguide segment and an inserting in-coupler to a different nonlinear optical waveguide segment. For some examples of optical waveguide structure  3400 , the idler coupler is located as close as feasible to the signal coupler for the same index value. This proximity of the two couplers reduces the length of nonlinear optical waveguide  3409  between them so that the additional phase shifts applied to the idler light and the signal light are done at essentially the same point on the nonlinear optical waveguide. 
     As depicted, nonlinear optical waveguide  3409  in waveguide structure  3400  has a series of nonlinear optical waveguide segments coupled to a series of tuning optical waveguides. As depicted, nonlinear optical waveguide  3409  has only one group of nonlinear optical waveguide segments and tuning optical waveguides. Optical waveguide structure  3400  is suitable for nonlinear optical processes such as ones involving TE polarized light in x-cut lithium niobate. As depicted in  FIG.  34   , optical waveguide structure  3400  has a single wavelength-selective coupler for each tuning optical waveguide. In this example, each of these wavelength selective couplers functions both as an out-coupler to couple a generated idler or signal light from nonlinear optical waveguide  3409  into a tuning optical waveguide and also as an in-coupler to couple phase-shifted idler or signal light from the tuning optical waveguide back into nonlinear optical waveguide  3409 . In other examples, discussed below, the optical waveguide structure has two wavelength-selective couplers for each phase tuning path. In this example, a first wavelength selective coupler functions as an out-coupler to couple generated idler light or signal light into a tuning optical waveguide and a second wavelength selective coupler functions as an in-coupler to couple phase-shifted idler or phase shifted signal light from the tuning optical waveguide back into nonlinear optical waveguide  3409 . 
     Turning to  FIG.  35   , an illustration of an optical waveguide structure with phase shifters for tuning light is depicted in accordance with an illustrative example. In this illustrative example, optical waveguide structure  3500  comprises a number of different components. As depicted, optical waveguide structure  3500  comprises nonlinear optical waveguide  3509  first tuning optical waveguide  3541 , second tuning optical waveguide  3542 , third tuning optical waveguide  3543 , fourth tuning optical waveguide  3544 , first idler out wavelength selective coupler  3521 , second idler in wavelength selective coupler  3522 , third idler out wavelength selective coupler  3523 , fourth idler in wavelength selective coupler  3524 , fifth idler out wavelength selective coupler  3525 , sixth idler in wavelength selective coupler  3526 , seventh idler out wavelength selective coupler  3527 , and idler combiner  3528 , pump input waveguide  3572 , signal input waveguide  3574 , pump output waveguide  3573 , signal output waveguide  3575 , idler output waveguide  3579 , pump input coupler  3532 , signal input coupler  3534 , pump output coupler  3533 , signal output coupler  3535 , idler output coupler  3539 , first phase shifter  3561 , second phase shifter  3562 , third phase shifter  3563 , fourth phase shifter  3564 , and fifth phase shifter  3565 . 
     In this illustrative example, nonlinear optical waveguide  3509 , has nonlinear optical waveguide segments. As depicted, these nonlinear optical waveguide segments are first segment  3501 , second segment  3502 , third segment  3503 , fourth segment  3504 , and fifth segment  3505 . In this example, fifth segment  3505  can be considered a “final segment” having a nonlinear optical material. 
     In this example, pump input coupler  3532  couples pump light  3512  introduced through pump input waveguide  3572  to first segment  3501 . Signal input coupler  3534  couples signal light  3514  introduced in signal input waveguide  3574  to first segment  3501 . Pump output coupler  3533  couples pump light  3512  from fifth segment  3505  to pump output waveguide  3573 . As a result, pump light  3512  does not travel through fifth segment  3505 . Idler output coupler  3539  couples a combination of idler light  3517  from fifth segment  3505  and idler light  3518  from fourth tuning optical waveguide  3544  to form idler light  3516 . Idler output coupler  3539  couples idler light  3516  from fifth segment  3505  to idler output waveguide  3579 . Optional signal output coupler  3535  couples signal light  3514  to signal output waveguide  3575 . 
     In this example, signal output coupler  3535  can be an optional component because idler output coupler  3539  typically can be designed to separate signal light  3514  from idler light  3516 . Thus, the two outputs for idler output coupler  3539  can be connected to idler output waveguide  3579  and signal output waveguide  3575 . 
     As depicted, nonlinear optical waveguide  3509  and other components are formed on a yz plane defined by z-axis  3593  and y-axis  3592  in which x-axis  3591  for the nonlinear optical material is perpendicular to the yz plane. In an illustrative example, nonlinear optical waveguide  3509  can be fabricated from a nonlinear optical material such as x-cut lithium niobate. In this example, nonlinear optical waveguide  3509  is aligned parallel to the y-axis  3592  of the nonlinear optical material and is aligned perpendicular to the z-axis  3593  of the nonlinear optical material, with the light propagating in nonlinear optical waveguide  3509  being in a TE mode of nonlinear optical waveguide  3509 . 
     For this example, both pump light  3512  and signal light  3514  can be supplied at the input end of the nonlinear optical waveguide  3509  in optical waveguide structure  3500 . The generated idler light is obtained from the output end of nonlinear optical waveguide  3509  in optical waveguide structure  3500 . The portion of nonlinear optical waveguide  3509  between the pump input coupler  3532  and first idler out wavelength selective coupler  3521  is considered first segment  3501 . Idler light  3517  generated in first segment  3501  is diverted into first tuning optical waveguide  3541  by the first idler out wavelength selective coupler  3521 . This wavelength selective coupler diverts idler light  3517  into first tuning optical waveguide  3541  but couples pump light  3512  and signal light  3514  to travel through second segment  3502  in nonlinear optical waveguide  3509 . 
     As depicted in this example, optical waveguide structure  3500  can be used in a difference-frequency generation (DFG) process or a sum-frequency generation (SFG) process, such as second harmonic generation, in which source light in the form of both pump light  3512  and signal light  3514  are used to produce generated light in the form of idler light  3516 . In this example, idler light  3516  results from combining idler light  3517  and idler light  3518 , which travel through the two different routes for the generated light. 
     Pump light  3512  and signal light  3514  continue to propagate in the nonlinear optical waveguide  3509  and are not diverted into the tuning optical waveguides. In this example, only the generated idler light is diverted into the tuning optical waveguides. 
     In this example, idler light  3517  propagates through first tuning optical waveguide  3541  and is inserted back into the third segment  3503  in nonlinear optical waveguide  3509  by second idler in wavelength selective coupler  3522 . This idler in wavelength selective coupler, like the other idler in wavelength selective couplers in the nonlinear optical waveguide  3509 , is a wavelength-selective coupler, and is similar to the idler out wavelength selective couplers. In this example second idler in wavelength selective coupler  3522  is located at the beginning of third segment  3503 . 
     The portion of nonlinear optical waveguide  3509  between first idler out wavelength selective coupler  3521 , second idler in wavelength selective coupler  3522  is second segment  3502 . Since pump light  3512 , as well as signal light  3514 , still travels in the nonlinear optical waveguide  3509 , additional idler light can be generated in second segment  3502 . 
     In this example, idler light  3518  generated in second segment  3502  is diverted into second tuning optical waveguide  3542  by third idler out wavelength selective coupler  3523 . This wavelength selective coupler keeps the generated idler light  3518  from interacting with the nonlinear optical process that occurs in third segment  3503 . The diverted idler light  3518  propagates through the second tuning optical waveguide  3542  and is inserted back into nonlinear optical waveguide  3509  by fourth idler in wavelength selective coupler  3524 . This fourth idler in wavelength selective coupler is located at the beginning of fourth segment  3504 . As depicted, fourth idler in wavelength selective coupler  3524  functions as an idler in coupler and is connected to the beginning of fourth segment  3504  and couples idler light  3518  from second tuning optical waveguide  3542  into fourth segment  3504  at the beginning of fourth segment  3504 . 
     In this illustrative example, third segment  3503  and fifth idler out wavelength selective coupler  3525  are similar to first segment  3501  and the first idler out wavelength selective coupler  3521 . Likewise, fourth segment  3504  and seventh idler out wavelength selective coupler  3527  are similar to second segment  3502  and third idler out wavelength selective coupler  3522 . In this illustrative example, first segment  3501  and third segment  3503  form part of a first, odd index, group of segments. Second segment  3502  and fourth segment  3504  form part of a second, even index, group of segments. 
     The final portion of the nonlinear optical waveguide  3509  is used to combine constructively the generated light of the odd indexed segments with the generated light of the even indexed segments. In this illustrative example, this final portion includes fifth segment  3505 , fourth tuning optical waveguide  3544 , and third tuning optical waveguide  3543 . In this example, sixth idler in wavelength selective coupler  3526  re-inserts idler light  3517  from third tuning optical waveguide  3543  into nonlinear optical waveguide  3509  at the starting point of fifth segment  3505 . Just prior to sixth idler in wavelength selective coupler  3526 , seventh idler out wavelength selective coupler  3527  extracts idler light  3518  from fourth segment  3504 , coupling idler light  3518  into fourth tuning optical waveguide  3544 . 
     Shortly following sixth idler in wavelength selective coupler  3526 , pump output coupler  3533  removes pump light  3512  into pump output waveguide  3573 . Thus, since pump light  3512  is absent, nonlinear optical generation of additional idler light in fifth segment  3505  does not occur. Idler light  3517  inserted into and propagating through the fifth segment  3505  was generated in third segment  3503  and in first segment  3501 . Both third tuning optical waveguide  3543  and fifth segment  3505  conduct idler light  3517  generated in third segment  3503  and first segment  3501  with no additional generation of idler light  3517 . Since no additional idler light is generated, fifth segment  3505  functions like an extension of the third tuning optical waveguide  3543 . 
     Light from the final segment, which in this case is fifth segment  3505 , and light from the final tuning optical waveguide, which in this case is fourth tuning optical waveguide  3544 , are combined together at the final in-coupling point. Idler combiner  3528  at the final in-coupling point couples together light that has been generated from two different routes. In optical waveguide structure  3500 , first route  3557  includes first segment  3501 , first tuning optical waveguide  3541 , third segment  3503 , the third tuning optical waveguide  3543 , and fifth segment  3505 . Second route  3558  includes second segment  3502 , second tuning optical waveguide  3542 , fourth segment  3504 , and fourth tuning optical waveguide  3544 . 
     In the illustrative example, two differences are present between the generated idler light  3517  from first route  3557  and the generated idler light  3518  from second route  3558 . The first difference is that the two routes have different values for the phases of the source light contributing to the generation of idler light  3517  and idler light  3518 . Thus, the phase of idler light  3517  supplied from fifth segment  3505  into idler combiner  3528  is different from the phase of idler light  3518  supplied from fourth tuning optical waveguide  3544  into idler combiner  3528 . Idler light  3517  is supplied through fifth idler out wavelength selective coupler  3525  and through third tuning optical waveguide  3543 . Idler light  3518  is supplied through seventh idler out wavelength selective coupler  3527  and through fourth tuning optical waveguide  3544 . The difference between the phase of idler light  3517  inserted by the sixth idler in wavelength selective coupler  3526  to idler combiner  3528  and idler light  3518  inserted from fourth tuning optical waveguide  3544  to idler combiner  3528  is approximately the difference between the phase of the source light at the end of first segment  3501  and the source light at the end of second segment  3502 . The magnitude of this difference, modulo 2n, can be as large as n radians. 
     The second difference is that first route  3557  has one segment more than second route  3558 . In optical waveguide structure  3500 , first route  3557  has three segments, but second route  3558  has only two segments. Thus, first route  3557  is longer than second route  3558 , assuming the corresponding segments and phase tuning paths of the two routes are matched in their lengths. The additional length of first route  3557  is designed to at least partially compensate for the difference between the phases of the source light for the two routes, and thus the difference between the phases of the generated light. 
     In this example, the length of the final segment, fifth segment  3505 , and the lengths of the final tuning optical waveguide, fourth tuning optical waveguide  3544 , and the next-to-final tuning optical waveguide, third tuning optical waveguide  3543  can be selected such that constructive interference is present between the light from the final segment, fifth segment  3505 , and the light from the final tuning optical waveguide, fourth tuning optical waveguide  3544  when they are combined together at the final in-coupling point at coupler, also called idler combiner  3528 , which couples together the light that has been generate in these two different routes. 
     In optical waveguide structure  3500 , The final in-coupling point in nonlinear optical waveguide  3509  is unlike any of the other coupling points in nonlinear optical waveguide  3509 . As depicted, the fourth tuning optical waveguide  3544  terminates at idler combiner  3528 . Fifth segment  3505  also terminates at idler combiner  3528 . A wavelength selective coupler, like the idler out wavelength selective couplers, such as first idler out wavelength selective coupler  3521 , third idler out wavelength selective coupler  3523 , fifth idler out wavelength selective coupler  3525  and seventh idler out wavelength selective coupler  3527  and the idler in wavelength selective couplers, such as second idler in wavelength selective coupler  3522 , fourth idler in wavelength selective coupler  3524 , and sixth idler in wavelength selective coupler  3526 , is designed to be in a “cross” state for the wavelength of idler light  3517  or idler light  3518  but to be in a “thru” state for the wavelength of pump light  3512  and for the wavelength of signal light  3514 . The idler combiner  3528  in the final portion, following fifth segment  3505  of nonlinear optical waveguide  3509 , is designed to combine equally the idler light supplied to that combiner from the fourth tuning optical waveguide  3544  and from fifth segment  3505 . This idler combiner  3528  functions more like a 50-50 coupler that couples “in phase” light into one output of that coupler and couples “out of phase” light into another output of that coupler. The “in phase” idler light is coupled to an output segment of nonlinear optical waveguide  3509 . Idler output coupler  3539  can extract the combined idler light to idler output waveguide  3579  of optical waveguide structure  3500 , leaving residual signal light in nonlinear optical waveguide  3509 . In an alternative implementation, optional signal output coupler  3535  can extract signal light  3514  from nonlinear optical waveguide  3509  before the signal light  3514  reaches idler combiner  3528 . 
     In the illustrative example of optical waveguide structure  3400  in  FIG.  34    and optical waveguide structure  3500  in  FIG.  35   , optical waveguide structure  3400  has a single route, second route  3456  for idler light  3416  that is generated. As depicted second route  3456  extends through all of the successive segments and idler tuning waveguides. In contrast, optical waveguide structure  3500  in  FIG.  35    has two routes for idler light  3517  and  3518  that are generated and then combined to comprise idler light  3516 . These routes are first route  3557  and second route  3558 . Each of these two routes extends through every other segment and tuning waveguide in optical waveguide structure  3500 . In this example, idler light  3516  is present in optical waveguide structure  3500  only after idler combiner  3528 . Before idler combiner  3528 , idler light  3517  and idler light  3518  are present. 
     Turning now to  FIG.  36   , an illustration of a graph of light generation is depicted in accordance with an illustrative embodiment. In graph  3600 , an illustration of normalized light generation rates based on distances of nonlinear optical interactions are shown. This light generation can be for a light such as idler light or signal light traveling through an optical waveguide structure having a nonlinear optical waveguide with segments and tuning optical waveguides coupled to segments of nonlinear optical waveguide. In this example, the light generation depicted occurs in an optical waveguide structure such as optical waveguide structure  3500  in  FIG.  35   . 
     As depicted in graph  3600 , x-axis  3602  illustrates the nonlinear optical interaction distance for light and nonlinear optical waveguide while y-axis  3604  illustrates the normalized generation rate of light as a result of that nonlinear optical interaction. As depicted, line  3607  and line  3608  illustrates light generation for light traveling through different routes within the optical waveguide structure. In this illustrative example, line  3607  illustrates the light generation rates for light traveling through first route  3557  through odd indexed segments of optical waveguide structure  3500 . Line  3608  illustrates light generation rates for light traveling through second route  3558  using even index segments in optical waveguide structure  3500  in  FIG.  35   . As can be seen, line  3607  and line  3608  have a stair stepped shape in which light generation rates increase as the light travels though segments and tuning optical waveguides in optical waveguide structure  3500 . 
     Line  3607  and line  3608  both have sections that corresponding to structures in optical waveguide structure  3500 . These sections include horizontal sections and angled sections relative to x-axis  3602 . As depicted, line  3607  has angled section  3611 , horizontal section  3621 , angled section  3613 , horizontal section  3623 , and horizontal section  3615 . For line  3607 , angled section  3611  corresponds to light generation that occurs in first segment  3501 ; horizontal section  3621  corresponds to light generation that occurs in first tuning optical waveguide  3541 , angled section  3613  corresponds to light generation that occurs in third segment  3503 , horizontal section  3623  corresponds to light generation that occurs in third tuning optical waveguide  3543 , and horizontal section  3615  corresponds to light generation that occurs in fifth segment  3505 , fifth segment  3505  can be a final segment. For line  3608 , angled section  3632  corresponds to light generation that occurs in second segment  3502 , horizontal section  3642  corresponds to light generation that occurs in second tuning optical waveguide  3542 , angled section  3634  corresponds to light generation that occurs in fourth segment  3504 , and horizontal section  3644  corresponds to light generation that occurs in fourth tuning optical waveguide  3544 . As indicated by the sections of lines  3607  and  3608 , light generation occurs only in the nonlinear optical waveguide segments, such as first segment  3501 , second segment  3502 , third segment  3503 , and fourth segment  3504 . These are segments comprised of nonlinear optical material and through which pump light  3512  also travels. Light generation does not occur in tuning optical waveguides, such as first tuning optical waveguide  3541 , second tuning optical waveguide  3542 , third tuning optical waveguide  3543 , and fourth tuning optical waveguide  3544 . Pump light  3512  does not travel through these tuning optical waveguides. Light generation also does not occur in fifth segment  3505  because pump light is removed at the start of fifth segment  3505  and thus does not travel through fifth segment  3505 . 
     As depicted a jump occurs from horizontal section  3615  and horizontal section  3644  to horizontal section  3619  because of the idler light  3517  from first, odd index, first route  3557  being combined with the idler light  3518  from second, even index, second route  3558  by idler combiner  3528 , which is located after fifth segment  3505  and prior to idler output waveguide  3579 . 
     With reference to  FIGS.  37 A- 37 G , illustrations of cross-sections for nonlinear optical waveguide structures are depicted in accordance with an illustrative embodiment. As depicted, cross-sections  3700  can be used to implement optical waveguide structures such as nonlinear optical waveguides, tuning optical waveguides, optical couplers such as wavelength selective couplers and input or output couplers as well as combiners, and phase shifters. 
     As depicted, cross-section  3701  ( FIG.  37 A ) can be used to implement a nonlinear optical waveguide. Cross-section  3701  comprises core region  3702  within cladding  3703  formed from silicon oxide (SiO 2 ) and cladding  3703  is located on silicon substrate  3704 . Core region  3702  comprises lithium niobate center section  3705  and side sections  3706  formed from silicon nitride. As depicted, center width  3708  is the width of lithium niobate center section  3705 . Strip width  3712  is the width of core region  3702 . The height of core region  3702  is strip height  3714 . 
     As depicted, cross-section  3715  ( FIG.  37 B ) has core region  3716  comprised of silicon nitride located within cladding  3717  formed from silicon oxide. Cladding  3717  is located on silicon substrate  3718 . In this illustrative example, core region  3716  has strip width  3719  and strip height  3720 . Cross-section  3721  ( FIG.  37 D ) has core region  3722  comprised of lithium niobate (LiNbO 3 ) located within cladding  3723  formed from on silicon oxide. Cladding  3723  is located on silicon substrate  3724 . As depicted, core region  3721  has strip width  3725  and strip height  3726 . 
     These two cross-sections can be used to implement tuning optical waveguides. For example, tuning optical waveguides using cross-section  3715  and cross-section  3721  can have tapers that transition gradually between waveguide portions with the silicon nitride core and with the lithium niobate core in these cross-sections. 
     In this illustrative example, cross-section  3727  ( FIG.  37 C ) is a cross-section for an optical coupler between a nonlinear optical waveguide and another waveguide such as a tuning optical waveguide or an input waveguide or an output waveguide. As depicted, core region  3728  can be for the nonlinear optical waveguide while core region  3729  is for another optical waveguide. Core region  3728  is comprised of lithium niobate center section  3730  with silicon nitride sides  3731 . Core region  3729  is comprised of silicon nitride. 
     As depicted, core region  3728  has strip width  3732  and lithium niobate center section  3730  has center width  3733 . Core region  3729  has strip width  3734 . In this illustrative example, both core regions have strip height  3735 . Gap  3736  is present between core region  3728  and core region  3729 . These components are within cladding  3737  formed using silicon oxide, which is located on silicon substrate  3738 . 
     The coupler using cross-section  3727  can be, for example, a wavelength selective out-coupler, a wavelength selective in-coupler, or a combiner. This coupler also can be a pump input coupler, signal input coupler or idler input coupler, a pump removal coupler, a signal output coupler, or an idler output coupler. Further, lithium niobate can be present in core region  3728  when core region  3728  is for a nonlinear optical waveguide. 
     In this example, cross-section  3739  ( FIG.  37 E ) is an example of the cross-section that can be used for a phase shifter. In this illustrative example, cross-section  3739  comprises electrodes  3740  for the phase shifter located on each side of core region  3741 . Core region  3741  is comprised of lithium niobate, which is an electro-optic material for an electro-optically activated optical waveguide phase shifter. In this example, silicon nitride structure  3742  is located on core region  3741 . These components are located within cladding  3744  which is comprised of silicon oxide. Cladding  3744  is located on silicon substrate  3745 . The phase shifter using cross-section  3739  is an electro-optic phase shifter. 
     Cross-section  3747  ( FIG.  37 F ) is an example of a cross section that can be used in a phase shifter for phase tuning for a nonlinear optical waveguide. Core region  3748  is for a nonlinear optical waveguide. 
     In this example, core region  3748  is comprised of lithium niobate center section  3749  and silicon nitride sides  3750 . These components are located within cladding  3753 . Cladding  3753  is comprised of silicon oxide and is located on silicon substrate  3754 . 
     Cross-section  3756  ( FIG.  37 G ) is a cross-section for an optical coupler between a nonlinear optical waveguide and a tuning optical waveguide. As depicted, core region  3728  can be for the nonlinear optical waveguide while core region  3729  is for another optical waveguide. 
     As depicted, cross section  3756  is a cross-section for an optical coupler between a nonlinear optical waveguide and another waveguide. As depicted, core region  3757  can be for the nonlinear optical waveguide while core region  3758  is for a tuning optical waveguide. Core region  3757  is comprised of lithium niobate center section  3761  with silicon nitride sides  3762 . Core region  3758  is comprised of lithium niobate. 
     As depicted, core region  3757  has strip width  3764  and lithium niobate center section  3761  has center width  3765 . Core region  3758  has strip width  3766 . In this illustrative example, both core regions have strip height  3767 . Gap  3768  is present between core region  3757  and core region  3758 . These components are within cladding  3759  formed using silicon oxide, which is located on silicon substrate  3760  in cross-section  3756 . Whether a wavelength selective coupler is implemented with cross-section  3756  or cross-section  3727  is dependent on the specific values for the wavelengths of the pump light, signal light and idler light as well as on whether the wavelength selective coupler couples only idler light (which typically has the longest wavelength) between a nonlinear optical waveguide segment and a tuning optical waveguide or couples both idler light and signal light, of differing wavelengths, between the nonlinear optical waveguide and the tuning optical waveguide. The wavelength selective coupler of these exemplary cross-sections would couple pump light from one nonlinear optical waveguide segment to another nonlinear optical waveguide segment. 
     Although cross-sections  3700  depicted in  FIGS.  37 A- 37 G  are for waveguides with core regions comprising lithium niobate and silicon nitride and cladding regions comprising silicon dioxide, other materials and combinations of materials could be used for the core regions and the cladding regions. For example, other materials can include at least one of gallium arsenide, aluminum gallium arsenide, silicon carbide, titanium dioxide, aluminum nitride, or gallium nitride. 
     In the illustrative examples, the different examples of optical waveguide structures can be scaled to a large number of segments and tuning optical waveguides. The particular configurations used can depend on the desired length of components such as phase shifters used with the tuning optical waveguides. Design specifications can limit the length of a single pair of electrodes of a phase shifter associated with a tuning optical waveguide. As a result, tuning optical waveguide can have folds with phase shifters having electrodes on the folds. In some examples, folds are used in the tuning optical waveguides to provide the amount of activation desired from phase shifters associated with tuning optical waveguides. 
     With reference to  FIG.  38   , an illustration of an optical waveguide structure is depicted in accordance with an illustrative embodiment. As depicted, optical waveguide structure  3800  comprises nonlinear optical waveguide  3809 , first tuning optical waveguide  3841 , second tuning optical waveguide  3842 , third tuning optical waveguide  3843 , fourth tuning optical waveguide  3844 , first idler out wavelength selective coupler  3821 , second idler in wave selective coupler  3822 , third idler out wavelength selective coupler  3823 , fourth idler in wavelength selective coupler  3824 , fifth idler out wavelength selective coupler  3825 , sixth idler in wavelength selective coupler  3826 , seventh idler out wavelength selective coupler  3827 , combiner  3828 , pump input waveguide  3872 , signal input waveguide  3874 , pump output waveguide  3873 , signal output waveguide  3875 , idler output waveguide  3879 , pump input coupler  3832 , signal input coupler  3834 , pump output coupler  3833 , signal output coupler  3835 , idler output coupler  3839 , first phase shifter  3861 , second phase shifter  3862 , third phase shifter  3863 , and fourth phase shifter  3864 . 
     In this illustrative example, nonlinear optical waveguide  3809  has nonlinear optical waveguide segments. As depicted, these nonlinear optical waveguide segments are first segment  3801 , second segment  3802 , third segment  3803 , fourth segment  3804 , and fifth segment  3805   
     In this example, pump input coupler  3832  couples pump light  3812  introduced through pump input waveguide  3872  to first segment  3801 . Signal input coupler  3834  couples signal light  3814  introduced in signal input waveguide  3874  to first segment  3801 . Pump output coupler  3833  couples pump light  3812  from fifth segment  3805  to pump output waveguide  3873 . Signal output coupler  3835  couples signal light  3814  from fifth segment  3805  to signal output waveguide  3875 . Combiner  3828  combines idler light  3817  from fifth segment  3805  and idler light  3818  from fourth tuning optical waveguide  3844  to form idler light  3816 . Idler output coupler  3839  couples idler light  3816  from fifth segment  3805  to idler output waveguide  3879 . 
     As depicted, nonlinear optical waveguide  3809  and other components are formed on a yz plane defined by z-axis  3893  and y-axis  3892 , with x-axis  3891  perpendicular to the yz plane. In an illustrative example, nonlinear optical waveguides can be fabricated from a nonlinear optical material such as x-cut lithium niobate. In this example, y-axis  3892  of the nonlinear optical material is parallel to the direction in which the nonlinear optical waveguide segments are oriented and z-axis  3893  of the nonlinear optical material is perpendicular to the propagation direction of the light in the nonlinear optical waveguide segments. For nonlinear optical materials such as x-cut lithium niobate, this orientation of the nonlinear optical waveguides allows a nonlinear optical interaction such as spontaneous parametric down conversion, or parametric down conversion or up conversion, or second harmonic generation to make use of the largest second order nonlinear optical coefficient d 33  of the lithium niobate material when the light is in a TE mode of the waveguide. For an accompanying phase shifter formed in a tuning optical waveguide comprising an electro-optic material such as x-cut lithium niobate, orienting the phase shifter parallel to the material’s y-axis and perpendicular to the material’s z-axis also allows an electro-optic phase shifter to make use of the largest electro-optic coefficient r 33  of the lithium niobate material when the light is in a TE mode of the waveguide. 
     In this illustrative example, the phase shifters have more electrodes than used in optical waveguide structure  3500  in  FIG.  35   . The additional electrodes can be placed on the folds of the tuning optical waveguides. 
     In this example, a phase shifter has a pair of electrodes on the portion of tuning optical waveguide following a fold of the tuning optical waveguide. These folds allow for a longer length on the combined electrodes in each phase shifter while reducing the length needed for nonlinear optical waveguide  3809  along y-axis  3892 . 
     As depicted, first tuning optical waveguide  3841  has eight folds, second tuning optical waveguide  3842  has eight folds, third tuning optical waveguide  3843  has four folds, and fourth tuning optical waveguide  3844  has four folds. For example, the eight folds of first tuning optical waveguide  3841  are first fold  3850 , second fold  3851 , third fold  3852 , fourth fold  3853 , fifth fold  3854 , sixth fold  3855 , seventh fold  3856  and eighth fold  3848 . In this example, first phase shifter  3861  comprises electrode pair  3880  located between first fold  3850  and second fold  3851 ; electrode pair  3881  located between second fold  3851  and third fold  3852 ; electrode pair  3882  located between third fold  3852  and fourth fold  3853 ; electrode pair  3883  located between fourth fold  3853  and fifth fold  3854 ; electrode pair  3884  located between fifth fold  3854  and sixth fold  3855 ; electrode pair  3885  located between sixth fold  3855  and seventh fold  3856 ; and electrode pair  3886  located between seventh fold  3856  and eighth fold  3848  of the first tuning optical waveguide  3841 . In this example, the four folds of third tuning optical waveguide  3843  are first fold  3857 , second fold  3858 , third fold  3859  and fourth fold  3849 . Third phase shifter  3863  comprises electrode pair  3887  located between first fold  3857  and second fold  3858 ; electrode pair  3888  located between second fold  3858  and third fold  3859 ; and electrode pair  3889  located between third fold  3859  and fourth fold  3849  of the third tuning optical waveguide  3843 . 
     Thus, the phase shifters in optical waveguide structure  3800  can have a larger applicable length for a given segment length in a segment in nonlinear optical waveguide  3809 . The number of folds can be increased from those shown in optical waveguide structure  3800  as needed to provide an over length of a phase shifter with multiple electrode pairs placed in the folds of the tuning optical waveguide. 
     The number of segments in a nonlinear optical waveguide in an optical waveguide structure can affect the configuration of tuning optical waveguides used in the optical waveguide structure. For example, if the number of segments is relatively small number, such as 11 or fewer segments, optical waveguide structure can have a configuration that comprises an offset arrangement of tuning optical waveguides that each have 4 folds. 
     With reference to  FIG.  39   , an illustration of an optical waveguide structure with offset tuning optical waveguides is depicted in accordance with an illustrative embodiment. As depicted, optical waveguide structure  3900  comprises nonlinear optical waveguide  3909 , first tuning optical waveguide  3941 , second tuning optical waveguide  3942 , third tuning optical waveguide  3943 , fourth tuning optical waveguide  3944 , fifth tuning optical waveguide  3945 , sixth tuning optical waveguide  3946 , first idler out wavelength selective coupler  3921 , second idler in wave selective coupler  3922 , third idler out wavelength selective coupler  3923 , fourth idler in wavelength selective coupler  3924 , fifth idler out wavelength selective coupler  3925 , sixth idler in wavelength selective coupler  3926 , seventh idler out wavelength selective coupler  3927 , eighth idler in wavelength selective coupler  3928 , ninth idler out wavelength selective coupler  3987 , tenth idler in wavelength selective coupler  3988 , eleventh idler out wavelength selective coupler  3989 , combiner  3980 , pump input waveguide  3972 , signal input waveguide  3974 , pump output waveguide  3973 , signal output waveguide  3975 , idler output waveguide  3979 , pump input coupler  3932 , signal input coupler  3934 , pump output coupler  3933 , signal output coupler  3935 , idler output coupler  3939 , first phase shifter  3961 , second phase shifter  3962 , third phase shifter  3963 , fourth phase shifter  3964 , fifth phase shifter  3965 , and sixth phase shifter  3966 . 
     In this illustrative example, nonlinear optical waveguide  3909 , has nonlinear optical waveguide segments. As depicted, these nonlinear optical waveguide segments are first segment  3901 , second segment  3902 , third segment  3903 , fourth segment  3904 , fifth segment  3905 , sixth segment  3906 , and seventh segment  3907 . 
     In this example, pump input coupler  3932  couples pump light  3912  introduced through pump input waveguide  3972  to first segment  3901 . Signal input coupler  3934  couples signal light  3914  introduced in signal input waveguide  3974  to first segment  3901 . Pump output coupler  3933  couples pump light  3912  from sixth segment  3906  to pump output waveguide  3973  so that pump light  3912  does not travel in seventh segment  3907 . Signal output coupler  3935  couples signal light  3914  from seventh segment  3907  to signal output waveguide  3975  prior to combiner  3980 . Combiner  3980  combines idler light  3917  from seventh segment  3907  and idler light  3918  from sixth tuning optical waveguide  3946  to form idler light  3916 . Optional idler output coupler  3939  couples idler light  3916  from seventh segment  3907  to idler output waveguide  3979 . 
     As depicted, nonlinear optical waveguide  3909  and other components are formed on a yz plane defined by z-axis  3993  and y-axis  3992  in which x-axis  3991  is perpendicular to the plane. In an illustrative example, nonlinear optical waveguides can be fabricated from a nonlinear optical material such as x-cut lithium niobate. In this example, x-axis  3991  of the nonlinear optical material is perpendicular to the yz plane of the structure of nonlinear optical waveguide  3909  and the other components 
     In this example, each tuning optical waveguide in optical waveguide structure  3900  can extend over more than two segments. Furthermore, each tuning optical waveguide has four folds with an electrode pair placed in the portion of the tuning optical waveguide after three of the four folds of the tuning optical waveguide. In this example, first tuning optical waveguide  3941  has first fold  3951 , second fold  3952 , third fold  3953  and fourth fold  3954 . First phase shifter  3961  comprises first electrode pair  3981  located between first fold  3951  and second fold  3952 , second electrode pair  3982  located between second fold  3952  and third fold  3953 , and third electrode pair  3983  located between third fold  3953  and fourth fold  3954 . Thus, the phase shifters in optical waveguide structure  3900  can have a larger applicable length for a given segment length in a segment in nonlinear optical waveguide  3909 . The length of the second electrode pair  3982  and the portion of first tuning optical waveguide  3941  between second fold  3952  and third fold  3953  can be increased as shown in optical waveguide structure  3900  as needed to provide a desired overall length for first phase shifter  3961 . For example, second electrode pair  3982  extends over first segment  3901 , second segment  3902 , third segment  3903 , fourth segment  3904 , and fifth segment  3905 . 
     Likewise, third tuning optical waveguide  3943  has first fold  3956 , second fold  3957 , third fold  3958  and fourth fold  3959 . Third phase shifter  3963  comprises first electrode pair  3984  located between first fold  3956  and second fold  3957 , second electrode pair  3985  located between second fold  3957  and third fold  3958 , and third electrode pair  3986  located between third fold  3958  and fourth fold  3959 . The length of the second electrode pair  3985  of third phase shifter  3963  and the portion of third tuning optical waveguide  3943  between second fold  3957  and third fold  3958  can be increased as needed to provide a desired overall length for third phase shifter  3963 . For example, second electrode pair  3985  extends over third segment  3903 , fourth segment  3904 , fifth segment  3905 , sixth segment  3906 , and seventh segment  3907 . 
     In this example a first group of odd index segments comprises first segment  3901 , third segment  3903 , fifth segment  3905 , and seventh segment  3907 . A second group of even index segments comprises second segment  3902 , fourth segment  3904 , and sixth segment  3906 . 
     Each of these groups of segments and tuning optical waveguides forms a route. As a result, 2 routes are present through which idler light  3917  and idler light  3918  travel within optical waveguide structure  3900 . For example, first route is traveled by idler light  3917  and is formed by the odd index segments and the associated tuning optical waveguides. In this example first route is comprised of first segment  3901 , third segment  3903 , fifth segment  3905 , first tuning optical waveguide  3941 , third tuning optical waveguide  3943 , and fifth tuning optical waveguide  3945 . Second route is traveled by idler light  3918  and is formed by even index segments and the associated tuning optical waveguides. In this example, second route comprises second segment  3902 , fourth segment  3904 , sixth segment  3906 , second tuning optical waveguide  3942 , fourth tuning optical waveguide  3944 , and sixth tuning optical waveguide  3946 . 
     In this example, the tuning optical waveguides in same group can have configurations that are different from each other. For example, in the first group of the odd index segments, first tuning optical waveguide  3941  and third tuning optical waveguide  3943  each have a longer length than fifth tuning optical waveguide  3945 . In the second group of even index segments, second tuning optical waveguide  3942  and fourth tuning optical waveguide  3944  each have a longer length than sixth tuning optical waveguide  3946 . The phase shifters associated with the different tuning optical waveguides can be located at different offset distances from nonlinear optical waveguide  3909 . Each tuning optical waveguide can have a length that is selected to achieve a value that is some multiple of 2n radians for the phase walk-off of the nonlinear optical generation process that occurs between the beginning portion of the nonlinear optical waveguide segment that immediately precedes the tuning optical waveguide and the beginning portion of the subsequent segment in nonlinear optical waveguide  3909  into which that phase shifted idler light is coupled via the idler in wavelength selective coupler. For example, for third tuning optical waveguide  3943 , the immediately preceding nonlinear optical waveguide segment is third segment  3903  and the subsequent nonlinear optical waveguide segment is fifth segment  3905 . 
     As depicted for optical waveguide structure  3900  in  FIG.  39   , the phase shift associated with the tuning optical waveguides is modulo 2n. For example, first tuning optical waveguide  3941  can have a phase shift of 100 n; third tuning optical waveguide  3943  can have a phase shift of 98 n. As a result, latitude is present on the length of optical waveguides in optical waveguide structure  3900 . 
     Additionally, as depicted in  FIG.  39   , the placement of phase shifters can be staggered. For example, first phase shifter  3961  and third phase shifter  3963  can have a “staggered” placement along z-axis  3993 . Thus, a portion of first phase shifter  3961  can overlap a portion of third phase shifter  3963  along y-axis  3992 . 
     With reference now to  FIG.  40   , an illustration of an optical waveguide structure formed on a xy plane is depicted in accordance with an illustrative embodiment. As depicted, nonlinear optical waveguide  4009  is form on a xy plane defined by x-axis  4091  and y-axis  4092 , in which a z-axis  4093  is perpendicular to the xy plane. In an illustrative example, nonlinear optical waveguides can be fabricated from a nonlinear optical material such as z-cut lithium niobate, c-axis aligned, and c-axis aligned 4H-SiC. In this example, z-axis  4093  of the nonlinear optical material such as z-cut lithium niobate, is perpendicular to the xy plane. 
     In this example, optical waveguide structure  4000  comprises nonlinear optical waveguide  4009 , first tuning optical waveguide  4041 , second tuning optical waveguide  4042 , third tuning optical waveguide  4043 , fourth tuning optical waveguide  4044 , fifth tuning optical waveguide  4045 , sixth tuning optical waveguide  4046 , first idler out wavelength selective coupler  4021 , second idler in wave selective coupler  4022 , third idler out wavelength selective coupler  4023 , fourth idler in wavelength selective coupler  4024 , fifth idler out wavelength selective coupler  4025 , sixth idler in wavelength selective coupler  4026 , seventh idler out wavelength selective coupler  4027 , eighth idler in wavelength selective coupler  4028 , ninth idler out wavelength selective coupler  4087 , tenth idler in wavelength selective coupler  4088 , eleventh idler out wavelength selective coupler  4089 , combiner  4080 , pump input waveguide  4072 , signal input waveguide  4074 , pump output waveguide  4073 , signal output waveguide  4075 , idler output waveguide  4079 , pump input coupler  4032 , signal input coupler  4034 , pump output coupler  4033 , signal output coupler  4035 , first phase shifter  4061 , second phase shifter  4062 , third phase shifter  4063 , fourth phase shifter  4064 , fifth phase shifter  4065 , and sixth phase shifter  4066 . 
     In this illustrative example, nonlinear optical waveguide  4009  has nonlinear optical waveguide segments. As depicted, these nonlinear optical waveguide segments are first segment  4001 , second segment  4002 , third segment  4003 , fourth segment  4004 , fifth segment  4005 , sixth segment  4006 , and seventh segment  4007 , with seventh segment  4007  also serving as a final segment. 
     In this example, pump input coupler  4032  couples pump light  4012  introduced through pump input waveguide  4072  to first segment  4001 . Signal input coupler  4034  couples signal light  4014  introduced in signal input waveguide  4074  to first segment  4001 . Pump output coupler  4033  couples pump light  4012  from sixth segment  4006  to pump output waveguide  4073  so that pump light  4012  is not coupled into seventh segment  4007 . Signal output coupler  4035  couples signal light  4014  from seventh segment  4007  to signal output waveguide  4075 . Pump output coupler  4033  and signal output coupler  4035  are both located prior to combiner  4080  which is located at the end of seventh segment  4007 . Combiner  4080  combines idler light  4017  from seventh segment  4007  and idler light  4018  from sixth tuning optical waveguide  4046  to form idler light  4016 . Combiner  4080  can couple idler light  4016  to idler output waveguide  4079 . 
     In the illustrative example, materials such as z-cut lithium niobate and c-axis aligned 4H-SiC used for nonlinear optical generation involving TM polarized light in optical waveguide structure  4000  do not have the geometric constraints imposed by x-cut lithium niobate. With these types of materials, the phase shifters in optical waveguide structure  4000  can be aligned in any direction along the xy plane, which is perpendicular to the z-axis  4093 . 
     Thus, the length of the segments in nonlinear optical waveguide  4009  do not limit the length of the phase shifters associated with the tuning optical waveguides as depicted for optical waveguide structure  4000 . Also, a phase shifter in a tuning optical waveguide does not need to have a straight path that is aligned along a particular crystallographic direction, unlike the phase shifters used in the optical waveguide structures depicted in  FIG.  35   ,  FIG.  38   , and  FIG.  39   . Instead, a circular path as depicted in  FIG.  40    for the phase shifters in optical waveguide structure  4000  can be used. The multiple phase tuning paths and phase shifters in such a nonlinear optical waveguide structure each could have a shape resembling the Greek letter capital omega, with the “feet” of the omega being the out wavelength selective coupler and in wavelength selective coupler for that tuning optical waveguide. In this example, the length of a segment is shorter than the length of a tuning optical waveguide and even is shorter than the length of a phase shifter. 
     Thus, the configuration of optical waveguide structure  4000  can potentially provide compensation for a greater tolerance in the waveguide cross-sectional dimensions. This configuration also can be scaled readily to increasingly larger numbers of segments. 
     Further, other shapes can be used in addition to or in place of the omega shape shown for the tuning optical waveguides in optical waveguide structure  4000 . For example, even a meandering or irregular shape can be used for the tuning optical waveguides in addition to the omega. Additionally, the tuning optical waveguides in optical waveguide structure  4000  can have different shapes from each other. 
     With reference next to  FIGS.  41 A and  41 B , illustrations of phase shifter cross sections is depicted in accordance with an illustrative embodiment. Cross-sections  4100  can be used for shifting the phase of light traveling or propagating in optical waveguide structures using z-cut lithium niobate or c-axis aligned 4H-SiC, such as optical waveguide structure  4000  in  FIG.  40   . For TM polarized light in z-cut lithium niobate or c-axis aligned 4H-SiC, one of the electrodes for an electro-optic phase shifter should be located above the core region of the optical waveguide such as shown in cross-section  4102  and cross-section  4104 . 
     Cross-section  4102  ( FIG.  41 A ) is for an electro-optic (EO) phase shifter  4105  that is representative of phase shifters such as first phase shifter  4061 , second phase shifter  4062 , third phase shifter  4063 , fourth phase shifter  4064 , fifth phase shifter  4065 , and sixth phase shifter  4066 , that can be associated with tuning optical waveguides such as first tuning optical waveguide  4041 , second tuning optical waveguide  4042 , third tuning optical waveguide  4043 , fourth tuning optical waveguide  4044 , fifth tuning optical waveguide  4045 , and sixth tuning optical waveguide  4046 , respectively. As depicted, first tuning optical waveguide  4041 , second tuning optical waveguide  4042 , third tuning optical waveguide  4043 , fourth tuning optical waveguide  4044 , fifth tuning optical waveguide  4045  or sixth tuning optical waveguide  4046  comprises lithium niobate core region  4108  with silicon nitride rib structure  4110 . Electro-optic phase shifter  4105  also comprises side electrode  4112 , side electrode  4114 , and top electrode  4116 . These components are located within cladding  4118  which is located on silicon substrate  4120 . 
     In this example, cross-section  4104  ( FIG.  41 B ) is for an electro-optic (EO) phase shifter  4125  that can be associated with a segment in a nonlinear optical waveguide. As depicted, the nonlinear optical waveguide comprises core region  4128  that is comprised of lithium niobate center section  4130  with silicon nitride sides  4131 . In this cross section, electro-optic phase shifter  4125  comprises side electrode  4132 , side electrode  4134 , and top electrode  4136 . These components are located within cladding  4138  which is located on silicon substrate  4140 . 
     In this illustrative example, cross-section  4102  and cross-section  4104  have electrode arrangements that provide increased values for the electro-optic (EO) coefficient of the material to be used as compared to other arrangements of electrodes. An example of an electro-optic coefficient is the r33 coefficient of lithium niobate. 
     With reference to  FIG.  42   , an illustration of an optical waveguide structure is depicted in accordance with an illustrative embodiment. As depicted, optical waveguide structure  4200  comprises a number of different components. As depicted, optical waveguide structure  4200  comprises nonlinear optical waveguide  4209 , first tuning optical waveguide  4241 , second tuning optical waveguide  4242 , third tuning optical waveguide  4243 , fourth tuning optical waveguide  4244 , first wavelength selective coupler  4221 , second wavelength selective coupler  4222 , third wavelength selective coupler  4223 , fourth wavelength selective coupler  4224 , fifth wavelength selective coupler  4225 , sixth wavelength selective coupler  4226 , seventh wavelength selective coupler  4227 , combiner  4280 , pump input waveguide  4272 , optional signal input waveguide, optional idler input waveguide, pump output waveguide  4273 , signal output waveguide  4275 , idler output waveguide  4279 , pump input coupler  4232 , optional signal input coupler  4234 , optional idler input coupler, pump output coupler  4233 , signal output coupler  4235 , idler output coupler  4239 , first phase shifter  4261 , second phase shifter  4262 , third phase shifter  4263 , fourth phase shifter  4264 , and fifth phase shifter  4265 . For spontaneous parametric down conversion, only pump light  4212  is supplied as the source light. Both signal light  4214  and idler light  4216  are generated by the nonlinear process occurring in optical waveguide structure  4200 . For a parametric difference frequency generation or sum frequency generation process, signal light  4214  is supplied as an auxiliary source light with idler light  4216  generated by the nonlinear optical process or, alternatively, idler light  4216  is supplied as an auxiliary source light with signal light  4214  generated by the nonlinear optical process. 
     In this illustrative example, nonlinear optical waveguide  4209  has nonlinear optical waveguide segments. As depicted, these nonlinear optical waveguide segments are first segment  4201 , second segment  4202 , third segment  4203 , fourth segment  4204 , and fifth segment  4205 . 
     In this example, pump input coupler  4232  couples pump light  4212  introduced through pump input waveguide  4272  to first segment  4201 . Optional signal input coupler  4234  couples signal light  4214  introduced in optional signal input waveguide to first segment  4201 . Optional idler input coupler couples idler light  4217  introduced in optional idler input waveguide to first segment  4201 . Pump output coupler  4233  couples pump light  4212  from fourth segment  4204  to pump output waveguide  4273  so that pump light  4212  is not coupled into fifth segment  4205 . Signal output coupler  4235  couples signal light  4214  from fifth segment  4205  to signal output waveguide  4275 . Idler output coupler  4239  couples idler light  4216  from fifth segment  4205  to idler output waveguide  4279 . 
     As depicted, nonlinear optical waveguide  4209  and other components are formed on a yz plane defined by z-axis  4293  and y-axis  4292  in which an x-axis  4291  is perpendicular to the plane. In an illustrative example, nonlinear optical waveguides can be fabricated from a nonlinear optical material such as x-cut lithium niobate. In this example, x-axis  4291  of the nonlinear optical material is perpendicular to the yz plane of nonlinear optical waveguide  4209  and the other components. 
     In optical waveguide structure  4200 , a first group of odd index segments comprises first segment  4201 , third segment  4203 , and fifth segment  4205 . A second group of even index segments comprises second segment  4202 , and fourth segment  4204 . As depicted, first tuning optical waveguide  4241 , second tuning optical waveguide  4242  are tuning optical waveguides for signal light  4215  and idler light  4217  traveling through the odd index segments. Second tuning optical waveguide  4242  and fourth tuning optical waveguide  4244  are tuning optical waveguides for signal light  4213  and idler light  4218  traveling through the even index segments. 
     Each of these groups of segments and tuning optical waveguides forms a route. As a result, two routes are present through which signal light  4215  and  4213  and idler light  4217  and  4218  travel within optical waveguide structure  4200 . First route  4251  comprises odd index segments and the associated optical tuning waveguides. In this example, first route  4251  comprises first segment  4201 , third segment  4203 , fifth segment  4205 , first tuning optical waveguide  4241 , and third tuning optical waveguide  4243 . A combination of first tuning optical waveguide  4241  and third tuning optical waveguide  4243  can be, for example, first set of tuning optical waveguides  2941  in  FIG.  29   . Second route  4252  comprises even index segments and the associated optical tuning waveguides. In this example, second route  4252  comprises second segment  4202 , fourth segment  4204 , second tuning optical waveguide  4242 , and fourth tuning optical waveguide  4244 . A combination of second tuning optical waveguide  4242  and fourth tuning optical waveguide  4244  can be, for example, second set of tuning optical waveguides  2942  in  FIG.  29   . 
     Optical waveguide structure  4200  also has tuning optical waveguides that are separate from the nonlinear optical waveguide  4209 . Idler light  4217  and signal light  4215  is routed at a first wavelength selective coupler  4221  out from nonlinear optical waveguide  4209  and then is routed back into nonlinear optical waveguide  4209  at a subsequent second wavelength selective coupler. The first segment  4201  of nonlinear optical waveguide  4209  precedes the first out-coupling point, which is first wavelength selective coupler  4221 . At the first out-coupling point, idler light  4217  and signal light  4215  generated by the nonlinear optical process in the first segment  4201  is diverted into first tuning optical waveguide  4241  in which phases of idler light  4217  and signal light  4215  are adjusted. At the first in-coupling point, which is second wavelength selective coupler  4222 , idler light  4217  and signal light  4215  from first tuning optical waveguide  4241  are routed back into nonlinear optical waveguide  4209  and into third segment  4203 . The phases of the diverted idler light and signal light are adjusted by the electrically controlled tuning performed using first phase shifter  4261  to achieve at and after the first in-coupling point a constructive nonlinear optical interaction between the first generated light from the phase tuning path and the source light, which continues to propagate in the nonlinear optical waveguide  4209 . As a result, additional generated idler light  4217  and signal light  4215  will continue to be produced in the portion of nonlinear optical waveguide  4209  after the first in-coupling point. This portion of nonlinear optical waveguide  4209  is the third segment  4203 . 
     Similarly, idler light  4218  and signal light  4213  generated in second segment  4202  of nonlinear optical waveguide  4209  can be diverted to second tuning optical waveguide  4242  separate from nonlinear optical waveguide  4209  at a second out-coupling point which is third wavelength selective coupler  4223  and then routed back into nonlinear optical waveguide  4209  at a subsequent second in-coupling point which is fourth wavelength selective coupler  4224 . Second segment  4202  of the nonlinear optical waveguide  4209  precedes the second out-coupling point. At the second out-coupling point, idler light  4218  and signal light  4213  generated by the nonlinear optical process in second segment  4202  are routed into second tuning optical waveguide  4242  in which the phases of idler light  4218  and signal light  4213  are adjusted. At the second in-coupling point, idler light  4218  and signal light  4213  are coupled from the second tuning optical waveguide  4242  back into nonlinear optical waveguide  4209 , into fourth segment  4204 . The phases of idler light  4218  and signal light  4213  are adjusted by the electrically controlled tuning by second phase shifter  4262  to achieve at and after the second in-coupling point a constructive nonlinear optical interaction between the second generated light from second tuning optical waveguide  4242  and pump light  4212 , which continues to propagate in the nonlinear optical waveguide  4209 . As a result, idler light  4218  and signal light  4213  will continue to be produced in the portion of nonlinear optical waveguide  4209  after the second in-coupling point. This portion of nonlinear optical waveguide  4209  is fourth segment  4204 . 
     Optical waveguide structure  4200  can be used in a spontaneous parametric down conversion (SPDC) process to generate both signal light  4215  and signal light  4213  both at a signal wavelength and idler light  4217  and idler light  4218  both at an idler wavelength from source light, such as pump light  4212  at a pump wavelength. Pump light  4212  is supplied to nonlinear optical waveguide  4209  from pump input coupler  4232  and continues to propagate in nonlinear optical waveguide  4209  and is not diverted into the tuning optical waveguides. The generated signal and idler light generated prior to the first out-coupling point (i.e., generated in first segment  4201 ) is diverted into first tuning optical waveguide  4241 . Since pump light  4212  still travels in nonlinear optical waveguide  4209 , additional signal light and idler light is generated in the portion of nonlinear optical waveguide  4209  between the first out-coupling point and the first in-coupling point (i.e., in second segment  4202 ). The generated signal and idler light generated in the second segment  4202  is diverted into second tuning optical waveguide  4242  at the second out-coupling point. Again, since the pump light still travels in the NLO waveguide, additional signal and idler is generated in the portion of nonlinear optical waveguide  4209  between the second out-coupling point and the second in-coupling point (i.e., in third segment  4203 ). The generated signal and idler light generated in third segment  4203  is diverted into third tuning optical waveguide  4243  at the third out-coupling point. Since the pump light still travels in nonlinear optical waveguide  4209 , additional signal and idler is generated in the portion of NLO waveguide between the third out-coupling point and the third in-coupling point (i.e., in fourth segment  4204 ). The generated signal light and idler light generated in the fourth segment  4204  is diverted into fourth tuning optical waveguide  4244  at the fourth out-coupling point. 
     In this illustrative example, combiner  4280  combines signal light  4213  and signal light  4415  and also combines idler light  4218  and idler light  4417  together after the end of fifth segment  4205  to produce signal light  4214  and idler light  4216 , respectively. 
     Pump light  4212  is removed from nonlinear optical waveguide  4209  by a pump output coupler  4233  after the fourth out-coupling point. Thus, no additional signal and idler is generated in the portion of nonlinear optical waveguide  4209  between the fourth out-coupling point and the fourth in-coupling point (i.e., in fifth segment  4205 ). Combiner  4280  is located at the fourth in-coupling point. This optical combiner combines the signal light  4213  and idler light  4218  from fourth tuning optical waveguide  4244  with signal light  4215  and idler light  4217  from the fifth segment  4205 . Signal light  4214  and idler light  4216  produced by this optical combiner is the desired output of nonlinear optical waveguide  4209 . Additional at least one of the signal output coupler or idler output coupler can be used to selectively extract at least one of the generated signal light or the generated idler light. 
     Thus, in segments with an odd index contribute constructively to produce even more generated light. The odd-indexed third tuning optical waveguides enable the generation of light in the odd-indexed segments to accumulate constructively from one odd-indexed segment to the next. Thus, the effective length of the nonlinear optical interaction can be equivalent to the total combined length of the multiple odd-indexed segments. Similarly, light generated in those segments with an even index can contribute constructively to produce even more generated light. The even-indexed phase tuning paths enable the generation of light in the even indexed segments to accumulate constructively from one even index segment to the next even index segment. Thus, the effective length of the nonlinear optical interaction can be equivalent to the total combined length of the multiple even indexed segments. 
     When the wavelengths of the idler light  4217  and idler light  4218  and the wavelength of the signal light  4215  and  4213  are sufficiently close to each other, the same wavelength selective coupler can couple both the idler light and the signal light from a nonlinear optical waveguide segment to a tuning optical waveguide. Likewise, the same wavelength selective coupler can couple both the idler light and the signal light from a tuning optical waveguide to a nonlinear optical waveguide segment. Furthermore, the same phase shifter can shift the phase of the idler light and the phase of the signal light such that a desired phase walk-off is achieved. However, when the wavelength of the idler light and the signal light are not sufficiently close together, different wavelength selective coupler must be used to couple the signal light and to couple the idler light. Furthermore, different phase shifters must be used to adjust the phases of the signal light and of the idler light. 
     With reference now to  FIG.  43   , an illustration of a nonlinear optical waveguide structure with separate tuning optical waveguides for signal light and for idler light is depicted in accordance with an illustrative embodiment. In this example, signal light  4314  and idler light  4316  can travel through optical waveguide structure  4300 , using separate tuning optical waveguides. Optical waveguide structure  4300  may be especially useful for a nonlinear optical process such as spontaneous parametric down conversion (SPDC) in which both signal light  4314  and idler light  4316  are generated from source light comprising pump light  4312 . 
     As depicted, optical waveguide structure  4300  comprises nonlinear optical waveguide  4309 , first idler tuning optical waveguide  4341 A, first signal tuning optical waveguide  4341 B, second idler tuning optical waveguide  4342 A, second signal tuning optical waveguide  4342 B, third idler tuning optical waveguide  4343 A, third signal tuning optical waveguide  4343 B, fourth idler tuning optical waveguide  4344 A, fourth signal tuning optical waveguide  4344 B, first idler out wavelength selective coupler  4321 A, first signal out wavelength selective coupler  4321 B, second idler in second idler wavelength selective coupler  4322 A, second signal in second signal wavelength selective coupler  4322 B, third idler out wavelength selective coupler  4323 A, third signal out wavelength selective coupler  4323 B, fourth idler in wavelength selective coupler  4324 A, fourth signal in fourth signal wavelength selective coupler  4324 B, fifth idler out wavelength selective coupler  4325 A, fifth signal out wavelength selective coupler  4325 B, sixth idler in wavelength selective coupler  4336 A, sixth signal in wavelength selective coupler  4336 B, seventh idler out wavelength selective coupler  4357 A, seventh signal out wavelength selective coupler  4357 B, idler combiner  4380 A, signal combiner  4380 B, pump input waveguide  4372 , pump output waveguide  4373 , signal output waveguide  4375 , idler output waveguide  4379 , pump input coupler  4332 , pump output coupler  4333 , signal output coupler  4335 , idler output coupler  4339 , first idler phase shifter  4361 A, first signal phase shifter  4361 B, second idler phase shifter  4362 A, second signal phase shifter  4362 B, third idler phase shifter  4363 A, third signal phase shifter  4363 B, fourth idler phase shifter  4364 A, fourth signal phase shifter  4364 B, and optional fifth phase shifter  4365 . 
     In this illustrative example, nonlinear optical waveguide  4309 , has nonlinear optical waveguide segments. As depicted, these nonlinear optical waveguide segments are first segment  4301 , second segment  4302 , third segment  4303 , fourth segment  4304 , fifth segment  4305 , and an optional output segment  4306 . 
     In this example, pump input coupler  4332  couples pump light  4312  introduced through pump input waveguide  4372  to first segment  4301 . Pump output coupler  4333  couples pump light  4312  from fourth segment  4304  to pump output waveguide  4373  so that no pump light  4312  travels through fifth segment  4305 . Signal output coupler  4335  couples signal light  4314  from optional output segment  4306  to signal output waveguide  4375 . Idler output coupler  4339  couples idler light  4316  from optional output segment  4306  to idler output waveguide  4379 . 
     As depicted, nonlinear optical waveguide  4309  and other components are formed on a yz plane defined by z-axis  4393  and y-axis  4392  in which an x-axis  4391  is perpendicular to the plane. In an illustrative example, the nonlinear optical waveguides can be fabricated from a nonlinear optical material such as x-cut lithium niobate. In this example, x-axis  4391  of the nonlinear optical material is perpendicular to the yz plane of the structure of nonlinear optical waveguide  4309  and the other components. 
     In this illustrative example, idler light  4317  and  4318  and signal light  4315  and signal light  4313  are generated in the different segments in nonlinear optical waveguide  4309 . The generated idler light and signal light are obtained from the output end of nonlinear optical waveguide  4309  in optical waveguide structure  4300 . 
     Also, separate sets of wavelength selective couplers extract idler light and signal light from nonlinear optical waveguide segments into separate tuning optical waveguides and reinsert the idler light and signal light in the separate tuning optical waveguides back into the nonlinear optical waveguide segments. In other words, both idler light and signal travel in routes formed by the odd index segments and the even index segments but the phase tuning is performed separately for idler light and signal light by the phase shifters associated with the tuning optical waveguides through which idler light and signal light are travelling separately. 
     The portion of nonlinear optical waveguide  4309  between the pump input coupler  4332  and first idler out wavelength selective coupler  4321 A defines first segment  4301 . Idler light  4317  generated in first segment  4301  is diverted into first idler tuning optical waveguide  4341 A by the first idler out wavelength selective coupler  4321 A. This wavelength selective coupler diverts idler light  4317  into first idler tuning optical waveguide  4341 A and couples pump light  4312  and signal light  4314  to first signal out wavelength selective coupler  4321 B. Signal light  4315  generated in first segment  4301  is diverted into first signal tuning optical waveguide  4341 B by the first signal out wavelength selective coupler  4321 B. This wavelength selective coupler diverts signal light  4315  into first signal tuning optical waveguide  4341 B but couples pump light  4312  into second segment  4302  in nonlinear optical waveguide  4309 . 
     Thus, idler light  4317  and signal light  4315  are coupled from first segment  4301  into separate tuning waveguides to be re-inserted into third segment  4303 . This process is repeated for each odd index segment with separate tuning optical waveguides for idler light  4317  and signal light  4315 . 
     In an illustrative implementation of optical waveguide structure  4300 , such as depicted in signal light  4214  and idler light  4216 , idler light  4317  has a longer wavelength than signal light  4315 . Both idler light  4317  and signal light  4315  propagate as the fundamental mode in nonlinear optical waveguide  4309 . For the example, an idler out wavelength selective coupler, such as first idler out wavelength selective coupler  4321 A, is located immediately before a signal out wavelength selective coupler, such as first signal out wavelength selective coupler  4321 B. Also, a signal in wavelength selective coupler, such as second signal wavelength selective coupler  4322 B, is located immediately before an idler in wavelength selective coupler, such as second idler wavelength selective coupler  4322 A. However, other arrangements of the out wavelength selective couplers and in wavelength selective couplers for idler light  4317  and signal light  4315  can be used in other implementations. 
     For a given tuning optical waveguide in optical waveguide structure  4300 , the phase shifters for signal light  4315  can be controlled separately from the phase shifters for idler light  4317  with the depicted configuration using separate tuning optical waveguides and phase shifters for idler light  4317  and signal light  4315 . Thus, the phase of the signal light re-inserted into the subsequent segment, such as third segment  4303 , in nonlinear optical waveguide  4309  can be adjusted to have that signal light interact constructively to produce additional signal light newly generated in that segment. The phase of the idler light re-inserted into the subsequent segment, such as third segment  4303 , can be adjusted to have that idler light interact constructively to produce additional idler light newly generated in that segment. 
     As further depicted in  FIG.  43   , the portion of nonlinear optical waveguide  4309  between first signal out wavelength selective coupler  4321 B and third idler out wavelength selective coupler  4323 A defines second segment  4302 . Idler light  4318  generated in second segment  4302  is diverted into second idler tuning optical waveguide  4342 A by the third idler out wavelength selective coupler  4323 A. This wavelength selective coupler diverts idler light  4318  into second idler tuning optical waveguide  4342 A and couples pump light  4312  and signal light  4314  to third signal out wavelength selective coupler  4323 B. Signal light  4313  generated in second segment  4302  is diverted into second signal tuning optical waveguide  4342 B by the third signal out wavelength selective coupler  4323 B. This wavelength selective coupler diverts signal light  4313  into second signal tuning optical waveguide  4342 B but couples pump light  4312  into third segment  4303  in nonlinear optical waveguide  4309 . 
     Thus, idler light  4318  and signal light  4313  are coupled from second segment  4302  into separate tuning waveguides and to be re-inserted into fourth segment  4304 . This process is repeated for each even index segment with separate tuning optical waveguides for idler light  4318  and signal light  4313 . 
     As depicted in this illustrative implementation, idler light  4318  has a longer wavelength than signal light  4313 . Both idler light  4318  and signal light  4313  propagate as the fundamental mode in nonlinear optical waveguide  4309 . For the example, an idler out wavelength selective coupler, such as third idler out wavelength selective coupler  4323 A, is located immediately before a signal out wavelength selective coupler, such as third signal wavelength selective coupler  4323 B. Also, a signal in wavelength selective coupler, such as fourth signal wavelength selective coupler  4324 B, is located immediately before an idler in wavelength selective coupler, such as fourth idler wavelength selective coupler  4324 A. However, other arrangements of the out wavelength selective couplers and in wavelength selective couplers for idler light  4318  and signal light  4313  can be used in other implementations. 
     For a given tuning optical waveguide in optical waveguide structure  4300 , the phase shifters for signal light  4313  can be controlled separately from the phase shifters for idler light  4318  with the depicted configuration using separate tuning optical waveguides and phase shifters for idler light  4318  and signal light  4313 . Thus, the phase of the signal light re-inserted into the subsequent segment, such as fourth segment  4304 , in nonlinear optical waveguide  4309  can be adjusted to have that signal light interact constructively to produce additional signal light newly generated in that segment. The phase of the idler light re-inserted into the subsequent segment, such as fourth segment  4304 , can be adjusted to have that idler light interact constructively to produce additional idler light newly generated in that segment. 
     In optical waveguide structure  4300 , the adjustment of the idler phase for idler light  4317  or idler light  4318  can be controlled separately from the adjustment of the signal phase for signal light  4315  or signal light  4313 . The tuning optical waveguides in the output portion of optical waveguide structure  4300 , such as third idler tuning optical waveguides  4343 A and third signal tuning optical waveguide  4343 B as well as fourth idler tuning optical waveguides  4344 A and fourth signal tuning optical waveguide  4344 B have separate phase shifters for signal light  4315  and for idler light  4317  traveling separately though those tuning optical waveguides,  4343 A and  4343 B, and also have separate phase shifters for signal light  4313  and for idler light  4318  traveling separately through fourth idler tuning optical waveguides  4344 A and fourth signal tuning optical waveguide  4344 B. Thus, the phases of signal light  4315  and signal light  4313  in the two routes can be adjusted to achieve constructive interference at signal combiner  4380 B. Also, the phases of idler light  4317  and  4318  in the two routes can be adjusted separately to achieve constructive interference at idler combiner  4380 A. 
     The material used to fabricate optical waveguide structure  4300  can result in constraints on the lengths of the segments and the phase shifters associated with tuning optical waveguides. For example, materials such as x-cut lithium niobate for which the electro optical effect and the nonlinear optical coefficient is much stronger for TE polarized light traveling in a particular direction with respect to the crystal axes of the material result in constraints such as the phase shifters and nonlinear optical waveguide  4309  needing to be aligned parallel with each other and with the nonlinear optical waveguide  4309  aligned parallel to the material y-axis  4392 . With phase shifters used in the examples such as the optical waveguide structures depicted in  FIG.  35   ,  FIG.  38   ,  FIG.  39   ,  FIG.  42    and  FIG.  43   , the phase shifters and the nonlinear optical waveguides are aligned parallel to the Y-axis of the exemplary lithium niobate nonlinear optical material. For these examples, the tuning optical waveguides for one group of segments (e.g., odd index) are located on one side of the nonlinear optical waveguide, such as nonlinear optical waveguide  4309 , and the tuning optical waveguides of the other group segments (e.g., even index segments) are located on the other side of nonlinear optical waveguide. Such an arrangement provides more space for longer phase shifters that use materials in which both the electro optical (EO) effect and the nonlinear optical (NLO) coefficient are much stronger for TE polarized light traveling in a particular direction with respect to the crystal axes of the material, such that the phase shifters are preferably oriented parallel to the nonlinear optical waveguide. 
     Thus, the illustrative examples described in  FIGS.  34  through  43    describe optical waveguide structures that have tuning optical waveguides that can be used to adjust the phase of light traveling through those tuning optical waveguides. In these examples, phase shifters are used to adjust the phase of light traveling through the tuning optical waveguides to obtain desired generation of light within the different optical waveguide structures. 
     Optical waveguide structure  4300  can be compared with optical waveguide structure  3400 . Optical waveguide structure  3400  has one group of nonlinear optical waveguide segments and has separate tuning optical waveguides for the idler light and the signal light generated in each segment of the nonlinear optical waveguide. For the idler light and separately for the signal light in optical waveguide structure  3400 , the same wavelength selective coupler, rather than two separate couplers, performs the extraction from a nonlinear optical waveguide segment into a tuning optical waveguide and the insertion from that tuning optical waveguide back into another nonlinear optical waveguide segment. Since only one group of segments is present in the example of  FIG.  34   , optical waveguide structure  3400  does not need to have a combiner located near the output of that structure, which can be used to combine the generated light from an odd index group and an even index group of segments. In contrast, optical waveguide structure  4300  has two groups of nonlinear optical waveguide segments that are arranged into an odd index group and an even index group. Furthermore, for the idler light in each group, and separately for the signal light in each group, a wavelength selective coupler is used to out couple the idler light (or the signal light) from a nonlinear optical waveguide segment to a tuning optical waveguide for the idler light (or for the signal light); and a different wavelength selective coupler is used to in couple the idler light (or the signal light) back from the tuning optical waveguide into another nonlinear optical waveguide segment. The presence of two different groups of nonlinear optical waveguide segments that generate different components of idler light (or signal light) is addressed by the combiner that combines those two components of idler light (or signal light). The maximum overall interaction distance for nonlinear optical generation is given by the total length of the segments in a group. Thus, if both optical waveguide structure  3400  and optical waveguide structure  4300  have 7 nonlinear optical waveguide segments each of 1 mm length, for example, and if both structures achieve the desired optimal phase walk-off at the start of each segment, optical waveguide structure  3400  could have higher nonlinear optical generation efficiency than optical waveguide structure  4300 . 
     With reference to  FIG.  44   , an illustration of a nonlinear optical waveguide with two groups of segments in which only one group of segments is associated with tuning optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  4400  is an open-ended nonlinear optical waveguide structure. 
     In this example, optical waveguide structure  4400  comprises a number of different components. As depicted, optical waveguide structure  4400  comprises nonlinear optical waveguide  4409 , first idler tuning optical waveguide  4441 A, first signal tuning optical waveguide  4441 B, third idler tuning optical waveguide  4443 A, third signal tuning optical waveguide  4443 B, first idler out wavelength selective coupler  4421 A, second idler in wavelength selective coupler  4422 A, first signal out wavelength selective coupler  4421 B, second signal in wavelength selective coupler  4422 B, fifth idler out wavelength selective coupler  4425 A, sixth idler in wavelength selective coupler  4426 A, fifth signal out wavelength selective coupler  4425 B, sixth signal in wavelength selective coupler  4426 B, pump input waveguide  4472 , pump output waveguide  4473 , signal output waveguide  4475 , idler output waveguide  4479 , pump input coupler  4432 , pump output coupler  4433 , signal output coupler  4435 , idler output coupler  4439 , first idler phase shifter  4461 A, first signal phase shifter  4461 B, third idler phase shifter  4463 A, and third signal phase shifter  4463 B. 
     In this illustrative example, nonlinear optical waveguide  4409 , has nonlinear optical waveguide segments. As depicted, these nonlinear optical waveguide segments are first segment  4401 , second segment  4402 , third segment  4403 , fourth segment  4404 , and fifth segment  4405 . 
     As depicted, nonlinear optical waveguide  4409  and other components are formed on a yz plane defined by z-axis  4493  and y-axis  4492  in which an x-axis  4491  perpendicular to the plane. In an illustrative example, nonlinear optical waveguides can be fabricated from a nonlinear optical material such as x-cut lithium niobate. In this example, the x-axis of the nonlinear optical material is perpendicular to the yz plane of the structure of nonlinear optical waveguide  4409  and the other components. 
     In this example, pump input coupler  4432  couples pump light  4412  introduced through pump input waveguide  4472  to first segment  4401 . Pump output coupler  4433  couples pump light  4412  from fifth segment  4405  to pump output waveguide  4473 . Signal input coupler couples signal light  4415  introduced through signal input waveguide to first segment  4401 . Signal output coupler  4435  couples signal light  4415  from fifth segment  4405  to signal output waveguide  4475 . Idler output coupler  4439  couples idler light  4417  from fifth segment  4405  to idler output waveguide  4479 . 
     In this illustrative example, first idler out wavelength selective coupler  4421 A extracts idler light  4417  from first segment  4401  into first idler tuning optical waveguide  4441 A. Second idler in wavelength selective coupler  4422 A reinserts idler light  4417  into third segment  4403  after activations have been applied using first idler phase shifter  4461 A associated with first idler tuning optical waveguide  4441 A. Each phase shifter is comprised of three pairs of electrodes in this example. First signal out wavelength selective coupler  4421 B extracts signal light  4415  from first segment  4401  into first signal tuning optical waveguide  4441 B and second signal in wavelength selective coupler  4422 B reinserts signal light  4415  into third segment  4403  after activations have been applied using first signal phase shifter  4461 B associated with first signal tuning optical waveguide  4441 B. 
     In this illustrative example, third idler out wavelength selective coupler  4425 A extracts idler light  4417  from third segment  4403  into third idler tuning optical waveguide  4443 A. Sixth idler in wavelength selective coupler  4426 A reinserts idler light  4417  into fifth segment  4405  after activations have been applied using third idler phase shifter  4463 A associated with third idler tuning optical waveguide  4443 A. Fifth signal out wavelength selective coupler  4425 B extracts signal light  4415  from third segment  4403  into third signal tuning optical waveguide  4443 B, and sixth signal in wavelength selective coupler  4426 B reinserts signal light  4415  into fifth segment  4405  after activations have been applied using third signal phase shifter  4463 B associated with third signal tuning optical waveguide  4443 B. 
     In this example, even index segments are second segment  4402  and fourth segment  4404 . Odd index segments are first segment  4401 , third segment  4403 , and fifth segment  4405 . The even index segments are not associated with a tuning optical waveguide. In this example, odd index segments are associated with tuning optical waveguides. 
     Further, separate tuning optical waveguides are present for idler light  4417  and for signal light  4415 . In other words, each tuning optical waveguide is used for tuning either idler light  4417  or signal light  4415  in this example. 
     Each of these groups of segments and tuning optical waveguides forms a route. As a result, idler route  4456  is present through which idler light  4417  travels within optical waveguide structure  4400 . Idler route  4456  comprises odd index segments, first segment  4401 , third segment  4403  and fifth segment  4405 , and the associated idler tuning optical waveguides, first idler tuning optical waveguide  4441 A and third idler tuning optical waveguide  4443 A for idler light  4417 . Signal route  4454  comprises odd index segments, first segment  4401 , third segment  4403  and fifth segment  4405 , and the associated signal tuning optical waveguides, first signal tuning optical waveguide  4441 B and third signal tuning optical waveguide  4443 B, for signal light  4415 . 
     In optical waveguide structure  4400 , each tuning optical waveguide for idler light  4417  begins at an idler out wavelength selective coupler located at the end of the associated odd index segment. This wavelength selective coupler is designed to selectively couple idler light  4417  out of the odd index segment into a tuning optical waveguide. Each tuning optical waveguide for idler light  4417  ends at an idler in wavelength selective coupler located at the end of the even index segment that follows immediately after the associated odd index segment. This wavelength selective coupler is designed to selectively couple idler light  4417  out of the tuning optical waveguide and reinsert this light into the next odd index segment. 
     Each tuning optical waveguide for signal light  4415  begins at a signal out wavelength selective coupler located at the end of the associated odd index segment. Each tuning optical waveguide for signal light  4415  ends at a signal in wavelength selective coupler located at the end of the even index segment that follows immediately after the associated odd index segment. For this example, the idler out wavelength selective coupler is located immediately before the signal out wavelength selective coupler. Also, the idler in wavelength selective coupler is located immediately after the signal in wavelength selective coupler. 
     In the example of optical waveguide structure  4400 , idler light  4417  is generated from nonlinear optical interaction occurring in odd index segments such as first segment  4401  and third segment  4403 . Signal light  4415  is generated from nonlinear optical interaction occurring in odd index segments such as first segment  4401  and third segment  4403 . Besides the light generated in the odd index segments, idler light  4418  can be generated in even index segments such as second segment  4402  and fourth segment  4404 . Also, signal light  4413  can be generated from nonlinear optical interaction occurring in odd index segments such as first segment  4401  and third segment  4403 . 
     Optical waveguide structure  4400  uses the idler in wavelength selective coupler at the end of each tuning optical waveguide to also couple out and remove idler light  4418  that is generated in the immediately preceding even index segment. This removal of idler light  4418  generated in the even index segments prevents idler light  4418  generated in the even index segments from interfering destructively with idler light  4417  coupled into next odd index segment and also from interacting destructively to reduce or reverse the generation of idler light  4417  in the next odd index segment. 
     Similarly, the signal in wavelength selective coupler at the end of each tuning optical waveguide also couples out and removes signal light  4413  that is generated in the even index segment. This removal of signal light  4413  generated in the even index segments prevents those generated signal light from interfering destructively with signal light  4415  coupled into the next odd index waveguide segment and also from interacting destructively to reduce or reverse the generation of signal light  4415  in the next odd index segment. 
     In optical waveguide structure  4400 , the length of each segment prior to a tuning optical waveguide can be selected to be sufficiently small that the magnitude of the phase walk-off resulting from anticipated fabrication and operational tolerances of optical waveguide structure  4400  is no greater than n radians. The phase shifters in a tuning optical waveguide can be configured to have an applicable length sufficiently large to achieve an electrically controlled phase shift of ±n radians. The overall length of a tuning optical waveguide for idler light  4417  is selected to achieve a relative phase shift that is 0 or a multiple of 2n radians between idler light  4417  coupled out of the tuning optical waveguide path and the newly generated idler light in the subsequent segment. Similarly, the overall length of a tuning optical waveguide for signal light  4415  can be selected to achieve a relative phase shift that is 0 or a multiple of 2n radians between signal light  4415  coupled out of the tuning optical waveguide and the newly generated signal light in the subsequent segment. 
     The optical waveguide structure  4400  can be used to implement a parametric down conversion process, such as difference frequency generation or even spontaneous parametric down conversion, or to implement a parametric up conversion process, such as sum frequency generation and second harmonic generation. Consider, for example, a second order nonlinear optical parametric down conversion process that generates idler light from pump light and signal light supplied to the optical waveguide structure. The idler-wave amplitude M i  of the idler light  4417  in third segment  4403  can be described by 
     
       
         
           
             
               
                 
                   
                     
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      These approximate expressions assume there is negligible change in the amplitudes of the source pump light M p  and source signal light M s , and that only the amplitude of the idler light changes as a result of the nonlinear optical interaction. The generation of the idler light over the length of third segment  4403  considers the nonlinear interactions that occur from the starting point S1 of first segment  4401  to the ending point E3 of the third segment  4403 . Since for this example, we assume the source pump light and source signal light are supplied to the nonlinear optical waveguide  4409  at the starting point S1 of the first segment. Thus, we can set the phase walk-off Φ s1  of the nonlinear optical process at starting point S1 to zero. In many cases, the phase matching in a nonlinear optical waveguide segment, such as third segment  4403 , is not perfect. Thus, there is a non-zero wave-vector mismatch Δk=k p ±k s -k i  between the wave vectors for the pump light k p  and signal light k s  and the wave vector for the generated idler light k i  in a nonlinear optical waveguide segment. The expression for the wave-vector mismatch has a plus sign for an up-conversion, sum-frequency generation process and has a minus sign for a down-conversion, difference-frequency generation process. In an illustrative example, the length of a nonlinear optical waveguide segment, such as from a starting point S3 to an ending point E3 of third segment  4403  with length L S3E3 , is chosen such that the phase walk-off for that segment, ΔkL S3E3 , has a value between zero and n radians. 
     In an illustrative example, the generation of additional idler light in third segment  4403  can build upon the generation of idler light in first segment  4401 . This dependence on the idler light from first segment  4401  is shown in Expression 1 above. The term M i  (S 3 ) represents the amplitude of the idler wave at the starting point of third segment  4403 . To fully benefit from the idler light generated in a preceding segment of nonlinear optical waveguide and thus to have the generation of additional idler light in third segment  4403  be constructive with the generation of idler light in first segment  4401 , it is desirable to have the phase walk-off Φ s3  at the starting point of third segment  4403  equal zero or an even multiple of n radians (or a multiple of 2n radians). The phase walk-off at the starting point of third segment  4403  is given by: 
     
       
         
           
             
               
                 
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      Expression 2 is approximate and neglects the phase shifts for the pump light, signal light and idler light that may result from the wavelength selective couplers. Expression 2 illustrates that the phase walk-off at the starting point of third segment  4403  depends on the phase walk-off obtained at the ending point of first segment  4401 , as described by Φ E1 =(k p -k i -k s )L S1E1 , assuming a down-conversion process. The pump light  4412  travels with wave vector k p2  through length L S2E2  of second segment  4402 . The signal light  4415  travels with wave vector k sT  through length L T1S  of first signal tuning optical waveguide  4441 B. The idler light  4417  from first segment  4401  travels with wave vector k iT  through length L T1i  of first idler tuning optical waveguide  4441 A. 
     Phase shifter  4462  can apply an activation that produces a phase shift of Δφ p1  to the pump light; phase shifter  4464  can apply an activation that produces a phase shift of Δφ p2  to the pump light; first signal phase shifter  4461 B can apply an activation that produces a phase shift of Δφ sT1  to the signal light; and first idler phase shifter  4461 A can apply an activation that produces a phase shift of Δφ iT1  to the idler light. For optical waveguide structure  4400 , the pump light, signal light, and idler light are affected by different phase shifters. Thus, it is possible to apply electro-optic activations to those phase shifters such that the phase shift of the pump light has an opposite sign from the phase shift for the idler light. This form of push-pull control would not be possible if the same phase shifter were to apply an activation that affects both the pump light and the idler light, for example. 
     In this example, a pump-inserting coupler, pump input coupler  4432 , is located at the start of first segment  4401  and the location of this coupler defines the start of the nonlinear optical interaction. A pump-extracting coupler, signal output coupler  4435 , is located at the end of the final segment, fifth segment  4405 , and the location of this coupler defines the end of the nonlinear optical interaction in this open-ended nonlinear optical waveguide structure. An idler output coupler can be located subsequent to the pump-extracting coupler to extract the generated idler light from the NLO waveguide. Similarly, a signal output coupler can be located subsequent to the pump-extracting coupler to extract the generated signal light from the nonlinear optical waveguide. 
     In the different illustrative examples in  FIGS.  34  through  44   , the phase shifters are implemented as electro optical phase shifters in which the electrodes for a phase shifter are constructed using electro-optical material. The use of electro optical phase shifters is not meant to limit the manner in which other illustrative examples can be implemented. For example, in another illustrative example the phase shifters can be implemented using thermal phase shifters in which the electrodes apply activation in the form of heat. 
     The selection of the type electrodes and the configuration of the electrodes for phase shifters can be based on the type of material used for the substrate in which the optical waveguide structure is fabricated. For example, when the substrate is an x-cut material and the electrodes for the optical electrical phase shifters, at least one of folds or overlaps can be used such that the electrodes are aligned to a y-axis on a plane formed by the Y axis and z-axis. This alignment increases the effectiveness of activations applied by the electrodes to the tuning optical waveguides when electro-optical materials used to form the electrodes. Electro optical phase shifters at a faster response and can more quickly control the phase in a tuning electrode as compared to thermal phase shifters. In other words, electro optical phase shifters can provide a faster response time for controlling the phase of light as compared to using other types of phase shifters such as thermal phase shifters. 
     In another example, when thermal phase shifters are used, this type of alignment is unnecessary. As result, folds and overlaps may not be needed. The use of thermal phase shifters can allow for less constraints with respect to the positioning and design of phase shifters and tuning optical waveguides. However, the use of temperature as an activation applied by thermal phase shifters has a slower response time for controlling the phase of light traveling through the tuning optical waveguide. 
     Some features of the illustrative examples are described in the following clauses. These clauses are examples of features and are not intended to limit other illustrative examples. 
     Clause 1 
     An optical waveguide structure comprising: 
     a nonlinear optical waveguide;   a set of tuning optical waveguides;   a set of wavelength selective couplers that couples light between the nonlinear optical waveguide and a tuning optical waveguide based on a wavelength of light; and   a set of phase shifters located along one or more tuning optical waveguides in the set of tuning optical waveguides.   

     Clause 2 
     The optical waveguide structure according to clause 1, wherein the light comprises a first wavelength light and a second wavelength light produced from the first wavelength light through a nonlinear optical interaction occurring within the nonlinear optical waveguide; the optical waveguide structure further comprising: 
     a first segment in the nonlinear optical waveguide;   a second segment in the nonlinear optical waveguide;   a wavelength selective coupler in the set of wavelength selective couplers that couples the first wavelength light from the first segment into the second segment, wherein the wavelength selective coupler couples the second wavelength light from the first segment into the tuning optical waveguide; and   a phase shifter in the set of phase shifters that applies an activation to the tuning optical waveguide to change a phase shift for the second wavelength light in the tuning optical waveguide.   

     Clause 3 
     The optical waveguide structure according to clause 2, wherein the second wavelength light in the tuning optical waveguide is coupled from the tuning optical waveguide to the second segment by the wavelength selective coupler. 
     Clause 4 
     The optical waveguide structure according to clause 3, wherein the phase shifter in the set of phase shifters applies the activation to the tuning optical waveguide to change the phase shift for the second wavelength light in the tuning optical waveguide such that a phase walk-off for the nonlinear optical interaction in the nonlinear optical waveguide from a starting point where the first wavelength light is supplied to the first segment to a junction between the wavelength selective coupler and the second segment is zero or an even multiple of n radians. 
     Clause 5 
     The optical waveguide structure according to one of clauses 2, 3, or 4, wherein the wavelength selective coupler is a first wavelength selective coupler and the optical waveguide structure further comprises: 
     a third segment in the nonlinear optical waveguide; and   a second wavelength selective coupler in the set of wavelength selective couplers, wherein the second wavelength selective coupler in the set of wavelength selective couplers couples first wavelength light from the second segment into the third segment.   

     Clause 6 
     The optical waveguide structure according to clause 5, wherein the second wavelength light in the tuning optical waveguide is coupled from the tuning optical waveguide to the third segment by the second wavelength selective coupler. 
     Clause 7 
     The optical waveguide structure according to clause 6, wherein the phase shifter in the set of phase shifters applies the activation to the tuning optical waveguide to change the phase shift for the second wavelength light in the tuning optical waveguide such that a phase walk-off for the nonlinear optical interaction in the nonlinear optical waveguide from a starting point where the first wavelength light is supplied to the first segment to a junction between the second wavelength selective coupler and the third segment is zero or an even multiple of n radians. 
     Clause 8 
     The optical waveguide structure according to one of clauses 5, 6, or 7 wherein the tuning optical waveguide is a first tuning optical waveguide and the phase shifter in the set of phase shifters is a first phase shifter; the optical waveguide structure further comprising: 
     a second tuning optical waveguide;   a second phase shifter in the set of phase shifters located along the second tuning optical waveguide; and   a third wavelength selective coupler in the set of wavelength selective couplers that couples first wavelength light from the second segment into the third segment and couples second wavelength light from the second segment into the second tuning optical waveguide.   

     Clause 9 
     The optical waveguide structure according to clause 8 further comprising: 
     a fourth segment in the nonlinear optical waveguide; and   a fourth wavelength selective coupler in the set of wavelength selective couplers that couples second wavelength light from the second tuning optical waveguide into the fourth segment, wherein the fourth wavelength selective coupler couples the first wavelength light from the third segment into the fourth segment.   

     Clause 10 
     The optical waveguide structure according to clause 9, wherein the second phase shifter applies an activation to the second tuning optical waveguide to change a phase shift for the second wavelength light in the second tuning optical waveguide such that a phase walk-off for the nonlinear optical interaction in the nonlinear optical waveguide from a first junction between the first wavelength selective coupler and the second segment to a second junction between the fourth wavelength selective coupler and the fourth segment is zero or an even multiple of n radians. 
     Clause 11 
     The optical waveguide structure according to clause 9 further comprising: 
     a third tuning optical waveguide;   a fifth wavelength selective coupler in the set of wavelength selective couplers that couples second wavelength light from the third segment into the third tuning optical waveguide and couples first wavelength light from the third segment into the fourth segment; and   a sixth wavelength selective coupler in the set of wavelength selective couplers that couples second wavelength light from the third tuning optical waveguide into a fifth segment and couples first wavelength light from the fourth segment into the fifth segment.   

     Clause 12 
     The optical waveguide structure according to clause 11, further comprising: 
     a third phase shifter in the set of phase shifters located along the third tuning optical waveguide, wherein the third phase shifter applies an activation to the third tuning optical waveguide to change a phase shift for the second wavelength light in the third tuning optical waveguide such that a phase walk-off for the nonlinear optical interaction in the nonlinear optical waveguide from a third junction between the second wavelength selective coupler and the third segment to a fourth junction between the sixth wavelength selective coupler and the fifth segment is zero or an even multiple of n radians.   

     Clause 13 
     The optical waveguide structure according to one of clauses 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 further comprising: 
     a phase shifter located along a segment in the nonlinear optical waveguide,   wherein the phase shifter located along the segment in the nonlinear optical waveguide applies an activation to the segment to change a phase shift for the first wavelength light in the segment,   and wherein the phase shift for the first wavelength light in the segment resulting from the activation applied to the segment has an opposite sign from the phase shift for the second wavelength light resulting from the activation applied to the tuning optical waveguide.   

     Clause 14 
     The optical waveguide structure according to one of clauses 9, 10, 11, 12, or 13 further comprising: 
     a combiner that combines the second wavelength light from the first segment and the second wavelength light from the second segment to form a combined wavelength light.   

     Clause 15 
     The optical waveguide structure according to clause 14, wherein a third phase shifter in the set of phase shifters located along a third tuning optical waveguide and a fourth phase shifter in the set of phase shifters located along the fourth tuning optical waveguide apply activations that produce a difference between a phase of the second wavelength light from the first segment and a phase of the second wavelength light from the second segment that equals zero or an even multiple of 2 n radians at the combiner. 
     Clause 16 
     The optical waveguide structure according to one of clauses 9, 10, 11, 12, 13, 14, or 15, further comprising: 
     a source output coupler that couples the first wavelength light out of a final segment in the nonlinear optical waveguide.   

     Clause 17 
     The optical waveguide structure according to clause 16 further comprising: 
     a final phase shifter in the set of phase shifters located along the final segment.   

     Clause 18 
     The optical waveguide structure according to one of clauses 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, or 17, wherein the first wavelength light is a pump light and the second wavelength light is one of a signal light and an idler light. 
     Clause 19 
     The optical waveguide structure according to one of clauses 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, or 18, wherein the set of phase shifters is associated with the tuning optical waveguide being at least one of adjacent to part of the tuning optical waveguide, connected to part of the tuning optical waveguide, or integrated as part of the tuning optical waveguide. 
     Clause 20 
     The optical waveguide structure according to one of clauses 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, or 19, wherein the set of phase shifters is selected from at least one of a tuning electrode, a thermal element, shape memory alloy element, or piezo electric element. 
     Clause 21 
     The optical waveguide structure according to one of clauses 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20, wherein the tuning optical waveguide has a set of folds, wherein a pair of electrodes for a phase shifter in the set of phase shifters is present along a length of the tuning optical waveguide occurring after a fold in the set of folds such that the phase shifter and wherein the length is parallel to a crystal axis of an nonlinear optical material in which the optical waveguide structure and the set of tuning waveguides is formed. 
     Clause 22 
     The optical waveguide structure according to clause 21, wherein the nonlinear optical material is an x-cut lithium niobate and wherein the optical waveguide structure is formed on a yz plane and an x-axis of the nonlinear optical material is perpendicular to the yz plane of the optical waveguide structure and the set of tuning optical waveguides. 
     Clause 23 
     An optical waveguide structure comprising: 
     a nonlinear optical waveguide;   a tuning optical waveguide;   a set of wavelength selective couplers that couples light between the nonlinear optical waveguide and the tuning optical waveguide based on a wavelength of light; and   a set of phase shifters located along the set of tuning optical waveguide.   

     Clause 24 
     The optical waveguide structure according to clause 23, wherein the nonlinear optical waveguide comprises segments alternating between odd index segments and even index segments, wherein a first wavelength light travels through the odd index segments and the even index segments and further comprising: 
     tuning optical waveguides including the tuning optical waveguide;   a first route through odd index segments and a first set of wavelength selective couplers that couples an odd index second wavelength light generated in the odd index segments from the odd index segments into a first set of tuning optical waveguides in the tuning optical waveguides and from the first set of tuning optical waveguides back into the odd index segments;   a second route though even index segments and a second set of wavelength selective couplers that couples an even index second wavelength light generated in the even index segments from the even index segments into a second set of tuning optical waveguides in the tuning optical waveguides and from the second set of tuning optical waveguides back into the even index segments;   phase shifters including the set of phase shifters, wherein a first set of phase shifters is associated with the first set of tuning optical waveguides and applies first activations to adjust a first phase of the odd index second wavelength light and a second set of phase shifters is associated with the second set of tuning optical waveguides and applies second activations to adjust a second phase of the even index second wavelength light; and   a combiner, wherein the combiner receives the odd index second wavelength light from a first end of the first route, receives the even index second wavelength light from a second end of the second route and combines the odd index second wavelength light and the even index second wavelength light to form a second wavelength light.   

     Clause 25 
     The optical waveguide structure according to one of clauses 23 or 24, wherein the light comprises a first wavelength light and a second wavelength light produced from the first wavelength light through a nonlinear optical interaction occurring within the nonlinear optical waveguide; the optical waveguide structure further comprising: 
     a first wavelength selective coupler in the set of wavelength selective couplers that couples the second wavelength light from an exit location in the nonlinear optical waveguide to a starting point in the tuning optical waveguide;   a second wavelength selective coupler in the set of wavelength selective couplers that couples the second wavelength light from an ending point in the tuning optical waveguide an entry location in the nonlinear optical waveguide; and   a phase shifter in the set of phase shifters located between the starting point and the ending point in the tuning optical waveguide, wherein the phase shifter applies an activation to the second wavelength light in the tuning optical waveguide to change a phase shift for the second wavelength light in the tuning optical waveguide.   

     Clause 26 
     A method for a nonlinear optical interaction, the method comprising: 
     coupling, by a wavelength selective coupler, a first wavelength light from a first segment in a nonlinear optical waveguide into a second segment in the nonlinear optical waveguide;   coupling, by the wavelength selective coupler, a second wavelength light from the first segment in the nonlinear optical waveguide into a tuning optical waveguide; and   applying, by a phase shifter, an activation to the tuning optical waveguide to change a phase shift for the second wavelength light in the tuning optical waveguide.   

     Clause 27 
     The method according to clause 26, wherein the wavelength selective coupler is a first wavelength selective coupler and further comprising: 
     coupling by a second wavelength selective coupler, the first wavelength light from the second segment in the nonlinear optical waveguide into a third segment in the nonlinear optical waveguide; and   coupling, by the second wavelength selective coupler, the second wavelength light from the tuning optical waveguide into the third segment in the nonlinear optical waveguide.   

     Clause 28 
     The method according to clause 27, wherein the change in the phase shift for the second wavelength light in the tuning optical waveguide modifies a phase walk-off for the nonlinear optical interaction in the nonlinear optical waveguide from an entry location where the first wavelength light is supplied to the first segment to an entry location in the third segment to have a value that is zero or an even multiple of n radians. 
     Clause 29 
     The method according to one of clauses 26, 27, or 28 further comprising: 
     coupling, by the wavelength selective coupler, the second wavelength light from the tuning optical waveguide into the second segment in the nonlinear optical waveguide, wherein the change in the phase shift for the second wavelength light in the tuning optical waveguide modifies a phase walk-off for the nonlinear optical interaction in the nonlinear optical waveguide from an entry location where the first wavelength light is supplied to the first segment to an entry location into the second segment to have a value that is zero or an even multiple of n radians.   

     Clause 30 
     The method according to one of clauses 26, 27, 28, or 29, wherein the tuning optical waveguide is a first tuning optical waveguide and the phase shifter is a first phase shifter and further comprising: 
     coupling, by a third wavelength selective coupler, the first wavelength light from the second segment in the nonlinear optical waveguide into a second tuning optical waveguide;   applying, by a second phase shifter, a second activation to the second tuning optical waveguide to change the phase shift for the second wavelength light in the second tuning optical waveguide;   coupling, by a fourth wavelength selective coupler, the first wavelength light from a third segment in the nonlinear optical waveguide into a fourth segment in the nonlinear optical waveguide; and   coupling, by the fourth wavelength selective coupler, the second wavelength light from the second tuning optical waveguide into the fourth segment in the nonlinear optical waveguide, wherein the phase shift for the second wavelength light is changed by the second activation applied to the second tuning optical waveguide, wherein the change in the phase shift for the second wavelength light in the second tuning optical waveguide modifies a phase walk-off for the nonlinear optical interaction in the nonlinear optical waveguide from an entry location where the first wavelength light is supplied to the second segment to an entry location into the fourth segment to have a value that is zero or an even multiple of n radians.   

     Clause 31 
     The method according to one of clauses 27, 28, 29, or 30 further comprising: 
     coupling, by a combiner, the second wavelength light from a first tuning optical waveguide into an output segment in the nonlinear optical waveguide; and   coupling, by the combiner, the second wavelength light from a second tuning optical waveguide into the output segment in the nonlinear optical waveguide.   

     Clause 32 
     The method according to one of clauses 30 or 31 further comprising: 
     coupling, by a combiner, the second wavelength light from the third segment in the nonlinear optical waveguide into an output segment in the nonlinear optical waveguide; and   coupling, by the combiner, the second wavelength light from the fourth segment into the output segment in the nonlinear optical waveguide.   

     Clause 33 
     The method according to clause 32 further comprising: 
     applying, by a third phase shifter, a third activation to the second wavelength light in the third segment; and   applying, by a fourth phase shifter, a fourth activation the second wavelength light in the fourth segment, wherein the third activation adjusts a phase of the second wavelength light in the third segment, wherein the fourth activation adjusts the phase of the second wavelength light in the fourth segment such that a difference between the phase of the second wavelength light in the third segment and a phase of the second wavelength light in the fourth segment is an even multiple of n radians where the second wavelength light in the third segment and second wavelength light in the third segment and the second wavelength light in the fourth segment are coupled by the combiner into the output segment. The description of the different illustrative embodiments has been presented for purposes of illustration and description and is not intended to be exhaustive or limited to the embodiments in the form disclosed. The different illustrative examples describe components that perform actions or operations. In an illustrative embodiment, a component can be configured to perform the action or operation described. For example, the component can have a configuration or design for a structure that provides the component an ability to perform the action or operation that is described in the illustrative examples as being performed by the component. Further, To the extent that terms “includes”, “including”, “has”, “contains”, and variants thereof are used herein, such terms are intended to be inclusive in a manner similar to the term “comprises” as an open transition word without precluding any additional or other elements.   

     Many modifications and variations will be apparent to those of ordinary skill in the art. Further, different illustrative embodiments may provide different features as compared to other desirable embodiments. The embodiment or embodiments selected are chosen and described in order to best explain the principles of the embodiments, the practical application, and to enable others of ordinary skill in the art to understand the disclosure for various embodiments with various modifications as are suited to the particular use contemplated.