Patent Publication Number: US-2022229345-A1

Title: Optical waveguide structure

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation in part application of U.S. patent application Ser. No. 17/450,044 filed Oct. 5, 2021, and entitled “Directional Phase Matching Optical Waveguide,” which is related to and claims the benefit of priority of provisional U.S. Patent Application Ser. No. 63/088,220, entitled “Directional Phase Matching (DPM) Optical Waveguide”, filed on Oct. 6, 2020; provisional U.S. Patent Application Ser. No. 63/201,661, entitled “Directional Phase Matching Optical Waveguide”, filed on May 7, 2021; and provisional U.S. Patent Application Ser. 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. 
    
    
     BACKGROUND INFORMATION 
     1. Field 
     The present disclosure relates generally to optical waveguide structures and, in particular, to directional phase matching optical waveguide structures. 
     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. 
     Currently, second order nonlinear optical frequency conversion is used. However, 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 the efficiency of second order nonlinear optical processes using waveguides. 
     SUMMARY 
     An embodiment of the present disclosure provides an optical waveguide structure comprising a nonlinear optical waveguide, straight segments in the nonlinear optical waveguide, and curved segments in the nonlinear optical waveguide. The nonlinear optical waveguide comprises a nonlinear optical material having a second order nonlinear optical coefficient for a nonlinear optical process in which the second order nonlinear optical coefficient changes with a direction of light propagation. The straight segments in the nonlinear optical waveguide are oriented such that a nonlinear optical interaction with light generation occurs with an overall constructive manner within the nonlinear optical waveguide in response to a light traveling though the nonlinear optical waveguide. The curved segments have a 90 degree bend, wherein the curved segments connect the straight segments to each other within in the nonlinear optical waveguide. 
     Another embodiment of the present disclosure provides an optical waveguide structure comprising a nonlinear optical waveguide, first segments in the nonlinear optical waveguide, second segments in the nonlinear optical waveguide, and curved segments in the nonlinear optical waveguide. The nonlinear optical waveguide comprises a nonlinear optical material having a second order optical nonlinear coefficient for a nonlinear process in which the second order nonlinear optical coefficient changes with a direction of light propagation. The second segments have an orientation that is perpendicular to the first segments. The first segments and the second segments are oriented such that a nonlinear optical process with light generation occurs within the first segments and the second segments. The curved segments have a 90 degree bend. The curved segments connect the first segments to the second segments. 
     In yet another embodiment of the present disclosure provides a method for moving a light through an optical waveguide structure. A pump light in the light is inputted into a nonlinear optical waveguide. The nonlinear optical waveguide comprises a nonlinear optical material having a second order nonlinear optical coefficient for a nonlinear optical process in which the second order nonlinear optical coefficient changes with a direction of light propagation. The light is propagated through straight segments connected by curved segments in which an overall nonlinear optical interaction in the straight segments is constructive in the nonlinear optical waveguide such that light generation occurs. 
     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 block diagram of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG. 2  is an illustration of a block diagram of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG. 3  is an illustration of a block diagram of a configuration for an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG. 4  is an illustration of a block diagram of a configuration for an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG. 5  is an illustration of a block diagram of another configuration for an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG. 6  is an illustration of an optical waveguide structure having nonlinear optical waveguide with a serpentine path that achieves direction-reversal enhanced coherent interaction (DRECI) in accordance with an illustrative embodiment; 
         FIG. 7  is an illustration of an optical waveguide structure having nonlinear optical waveguide with a racetrack shape that achieves direction-reversal enhanced coherent interaction (DRECI) in accordance with an illustrative embodiment; 
         FIG. 8  is an illustration of the cross-sectional view of a nonlinear optical waveguide in an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG. 9  is an illustration of a graph of an optical field overlap factor as a function of central region top width in accordance with an illustrative embodiment; 
         FIG. 10  is an illustration of optical field profiles that overlap a nonlinear optical material in a nonlinear optical waveguide in accordance with an illustrative embodiment; 
         FIG. 11  is an illustration of optical field profiles that overlap a nonlinear optical material in a nonlinear optical waveguide in accordance with an illustrative embodiment; 
         FIG. 12  is an illustration of a graph of a net coherent interaction length for different configurations of nonlinear optical waveguides in accordance with an illustrative embodiment; 
         FIG. 13  is an illustration of a graph of an optical field overlap factor for different configurations of nonlinear optical waveguides in accordance with an illustrative embodiment; 
         FIG. 14  is an illustration of an optical waveguide structure having a nonlinear optical waveguide with a shape of a circular ring that achieves a direction-reversal enhanced coherent interaction in accordance with an illustrative embodiment; 
         FIG. 15  is an illustration of a graph of phase matching conditions that vary with a propagation angle in accordance with an illustrative embodiment; 
         FIG. 16  is an illustration of graphs illustrating incremental spontaneous parametric down conversion (SPDC) generation rate relative to an accumulated phase walk-off in accordance with an illustrative embodiment; 
         FIG. 17  is an illustration of graphs illustrating a sign of a nonlinear optical coefficient relative to an accumulated phase walk-off in accordance with an illustrative embodiment; 
         FIG. 18  is an illustration of graphs illustrating normalized incremental spontaneous parametric down conversion generation rates relative to a normalized net spontaneous parametric down conversion generation rates in accordance with an illustrative embodiment; 
         FIG. 19  is an illustration of a graph of a net coherent interaction distance in accordance with an illustrative embodiment; 
         FIG. 20  is an illustration of a graph of a ring diameter for a circular ring nonlinear optical waveguide in accordance with an illustrative embodiment; 
         FIG. 21  is an illustration of a graph of a normalized net spontaneous parametric down conversion generation in accordance with an illustrative embodiment; 
         FIG. 22  is an illustration of an optical waveguide structure including a nonlinear optical waveguide with a serpentine path in accordance with an illustrative embodiment; 
         FIG. 23  is an illustration of a graph of real and imaginary parts of a generated field in accordance with an illustrative embodiment; 
         FIG. 24  is an illustration of graphs illustrating a phase walk-off relative to a nonlinear optical coefficient in accordance with an illustrative embodiment; 
         FIG. 25  is an illustration of a graph of a phase walk-off in accordance with an illustrative embodiment; 
         FIG. 26  is an illustration of a graph of a normalized spontaneous parametric down conversion (SPDC) rate in accordance with an illustrative embodiment; 
         FIG. 27  is an illustration of an optical waveguide structure including a nonlinear optical waveguide with a serpentine path in accordance with an illustrative embodiment; 
         FIG. 28  is an illustration of a graph of a phase walk-off in accordance with an illustrative embodiment; 
         FIG. 29  is an illustration of a graph of a phase walk-off in accordance with an illustrative embodiment; 
         FIG. 30  is an illustration of graphs illustrating a phase walk-off relative to a nonlinear optical coefficient and relative to a normalized spontaneous parametric down conversion (SPDC) rate in accordance with an illustrative embodiment; 
         FIG. 31  is an illustration of a graph of a normalized spontaneous parametric down conversion (SPDC) rate in accordance with an illustrative embodiment; 
         FIG. 32  is an illustration of a graph of a phase walk-off in accordance with an illustrative embodiment; 
         FIG. 33  is an illustration of a graph of a normalized spontaneous parametric down conversion rate in accordance with an illustrative embodiment; 
         FIG. 34  is an illustration of a graph of a normalized spontaneous parametric down conversion rate in accordance with an illustrative embodiment; 
         FIG. 35  is an illustration of optical couplers used to couple a pump input optical waveguide to a nonlinear optical waveguide and to couple output light from the nonlinear optical waveguide to an output optical waveguide in accordance with an illustrative embodiment; 
         FIG. 36  is an illustration of a graph of a pump light transmission in accordance with an illustrative embodiment; 
         FIG. 37  is an illustration of a graph of an output light transmission in accordance with an illustrative embodiment; 
         FIG. 38  is an illustration of a graph of a coupled transmittance of light from a nonlinear optical waveguide to an output waveguide in accordance with an illustrative embodiment; 
         FIG. 39  is an illustration of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG. 40  is an illustration of a flowchart of a process for inputting light through an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG. 41  is an illustration of a block diagram of a product management system in accordance with an illustrative embodiment; 
         FIG. 42  is an illustration of an optical waveguide structure is depicted in accordance with an illustrative embodiment; 
         FIG. 43  is an illustration of phase walk-off between points in a nonlinear optical waveguide in accordance with an illustrative embodiment; 
         FIG. 44  is an illustration of an optical waveguide structure with a staircase configuration in accordance with an illustrative embodiment; 
         FIG. 45  is an illustration of a graph illustrating values for nonlinear optical coefficients traveling through nonlinear optical waveguide in accordance with an illustrative embodiment; 
         FIG. 46  is an illustration of a graph of a nonlinear optical coefficient a phase walk-off for light propagating through a nonlinear optical waveguide in accordance with an illustrative embodiment; 
         FIG. 47  is an illustration of a graph of a rate of change in the amplitude of an online propagating through a nonlinear optical waveguide in accordance with an illustrative embodiment; 
         FIG. 48  is an illustration of an amplitude for an idler light propagating through a nonlinear optical waveguide in accordance with an illustrative embodiment; 
         FIG. 49  is an illustrative of an optical waveguide structure with a staircase configuration with phase shifters in accordance with an illustrative embodiment; 
         FIG. 50  is an illustration of an optical waveguide structure in accordance with an illustrative embodiment; 
         FIG. 51  is an illustration of an optical waveguide structure having a serpentine configuration in accordance with an illustrative embodiment; 
         FIG. 52  is an illustration of an optical waveguide structure having two nonlinear optical waveguides connected by connecting optical waveguide in accordance with an illustrative embodiment; and 
         FIG. 53  is an illustration of a flowchart of a process for moving a light through an optical waveguide structure in accordance with an illustrative embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Example embodiments of the claimed structures and methods are disclosed herein; however, it is to be understood that the disclosed embodiments are merely illustrative of the claimed structures and methods that may be embodied in various forms. In addition, each of the examples given in connection with the various embodiments is intended to be illustrative, and not restrictive. 
     Further, the figures are not necessarily to scale, as some features may be exaggerated to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the methods and structures of the present disclosure. 
     For purposes of the description hereinafter, the terms “upper,” “lower,” “right,” “left,” “vertical,” “horizontal,” “top,” “bottom,” and derivatives thereof shall relate to the illustrative examples in the disclosure, as it is oriented in the drawing figures. The terms “positioned on” means that a first element, such as a first structure, is present on a second element, such as a second structure, wherein intervening elements, such as an interface structure, e.g., interface layer, may be present between the first element and the second element. 
     In this disclosure, when an element, such as a layer, a region, or a substrate, is referred to as being “on” or “over” another element, the element can be directly on the other element or intervening elements can also be present. In contrast, when an element is referred to as being “directly on,” “directly over,” or “on and in direct contact with” another element, no intervening elements are present, and the element is in contact with the other element. 
     Any processes, steps, and structures described below do not form a complete process flow for manufacturing integrated circuits. The disclosure can be practiced in conjunction with integrated circuit fabrication techniques currently used in the art, and only so much of the commonly practiced process steps are included as necessary for an understanding of the different examples of the present disclosure. The figures represent cross-sections of a portion of an integrated circuit during fabrication and are not drawn to scale, but instead are drawn so as to illustrate different illustrative features of the disclosure. 
     The illustrative examples pertain to a nonlinear optical interaction and a nonlinear optical process in which one or two input photons can generate one or two output photons from those input photons. A nonlinear optical process involves not only the generation of those photons but also the material in which those photons propagate or travel. Nonlinear optical material can be described by its nonlinear optical susceptibility or nonlinear optical coefficient. A wavelength, frequency, or energy of at least one of the output photons is different from the wavelength, frequency, or energy of at least one of the input photons. 
     A second order nonlinear optical process involves 3 types of photons. These 3 types of photons can be referred to as the photons of a first light, a second light, and a third light. Many second order nonlinear optical processes involve the interaction of 2 input photons to produce 1 output photon. 
     In the illustrative examples, one of the input photons involved in the nonlinear optical interaction is referred to as the pump photon or a photon of the pump light. The second input photon is referred to as the signal photon or a photon of a signal light. The output photon is referred to as the idler photon or a photon of the idler light. Alternatively, the second input photon can be referred to as the idler photon or a photon of the idler light. The output photon can be referred to as the signal photon or a photon of the signal light. 
     Examples of these types of nonlinear optical processes include difference frequency generation (DFG) and sum frequency generation (SFG). In difference frequency generation, the frequency of the output third light (or the energy of the output third photon) is equal to the difference between the frequencies of the input first light and the input second light (or the difference between the energies of the two input photons). In SFG, the frequency of the output third light (or the energy of the output third photon) is equal to the sum of the frequencies of the input first light and the input second light (or the sum of the energies of the two input photons). The energy of a photon is related to the frequency of the light comprising that photon by the Planck constant. Since the frequency (or frequencies) of the output light is different from the frequency (or frequencies) of the input light, these processes can be considered as producing nonlinear optical frequency conversion. 
     For the second order nonlinear optical process in some of the illustrative examples given below, the nonlinear optical process involves 1 input photon (the pump photon) that produces 2 output photons (the signal photon and the idler photon). This nonlinear optical process is called spontaneous parametric down-conversion (SPDC). Spontaneous parametric down-conversion is a form of difference frequency generation in which either the signal photon or the idler photon is not supplied externally as input light but rather can be generated spontaneously due to a noise process or to processes such as Raman scattering. This signal photon or idler photon can act as an internally produced second input to the nonlinear optical process. 
     In an illustrative example, a second order nonlinear optical process involves 3 types of photons in a material. These photons can be referred to as photons of the pump light, photons of the signal light, and photons of the idler light. Among these 3 types of photons, pump photons have the highest energy (and the pump light has the shortest wavelength and highest frequency), idler photons have the lowest energy (and the idler light has the longest wavelength and lowest frequency), and signal photons have an intermediate energy (and the signal light has an intermediate wavelength and intermediate frequency). For light, or a light wave, propagating in vacuum, the frequency of that light is related to the inverse of the wavelength of that light by the speed of light, which is a known constant. 
     The propagation constant or wave vector can be used to describe the change in the phase of the light wave for a given distance of travel in a given material. The value of the propagation constant or wave vector typically is different for different wavelengths of light and can depend on the refractive index of the material through which the light propagates, and depend inversely on the value of the wavelength of the light. Thus, k P , k S , and k I  can be defined as the propagation constants or wave vectors for the pump light, the signal light, and the idler light, respectively. 
     The refractive indices of the materials comprising a waveguide structure and also a geometric construction of the waveguide structure can affect the propagation constant of the light at each wavelength of light propagating in the waveguide structure. Light wave-guided by an optical waveguide and propagating in that optical waveguide can be described as comprising a set of guided modes. The propagation constant for a given guided mode (e.g., mode m) of the pump light propagating in the waveguide structure can be defined by the following expression: 
     
       
         
           
             
               k 
               
                 P 
                 ⁢ 
                 m 
               
             
             = 
             
               2 
               ⁢ 
               
                 
                   
                     ∏ 
                     
                         
                     
                   
                   
                     n 
                     
                       eff 
                       , 
                       Pm 
                     
                   
                 
                 / 
                 
                   λ 
                   P 
                 
               
             
           
         
       
     
     where λ P  is the free-space wavelength of the pump light and n eff , p m  is an effective refractive index of wave-guided mode m of the pump light propagating in the waveguide structure, and Δ P  is the wavelength of the pump light. 
     Similar expressions can be given for the signal light and the idler light. The pump light, signal light, and idler light have different wavelengths. 
     For a second order nonlinear optical process that occurs at a given location, such as involving difference frequency generation, both the frequencies of the pump, signal, and idler light and the energies of the pump, signal, and idler photons are constrained by an energy conservation relation and the propagation constants of the pump, signal, and idler light are constrained by a momentum conservation relation, such as: 
     
       
         
           
             
               
                 1 
                 / 
                 
                   λ 
                   p 
                 
               
               = 
               
                 
                   
                     1 
                     / 
                     
                       λ 
                       s 
                     
                   
                   + 
                   
                     
                       1 
                       / 
                       
                         λ 
                         i 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       k 
                       p 
                     
                   
                 
                 = 
                 
                   
                     k 
                     s 
                   
                   + 
                   
                     k 
                     i 
                   
                 
               
             
             , 
           
         
       
     
     respectively. 
     For a difference frequency generation process that occurs over some travel distance, perfect phase matching is achieved when k P L P =k S L S +k I L I , where L P , L S , and L I  are the distances traveled by the pump light, the signal light, and the idler light, respectively, as they participate in the nonlinear optical process. The phase shift of the pump light is k P L P , the phase shift of the signal light is k S L S , and the phase shift of the idler light is k I L I . 
     In this illustrative example, distance-separated nonlinear optical processes are nonlinear optical processes that occur at two different locations or points in which the two different locations are separated by some distance. The locations can be along a path in an optical waveguide. 
     If the phase matching is not an exact match, a phase walk-off (Δϕ) for the distance-separated nonlinear optical processes can be defined as: 
     
       
         
           
             Δϕ 
             = 
             
               
                 
                   k 
                   P 
                 
                 ⁢ 
                 
                   L 
                   P 
                 
               
               - 
               
                 
                   k 
                   S 
                 
                 ⁢ 
                 
                   L 
                   S 
                 
               
               - 
               
                 
                   k 
                   I 
                 
                 ⁢ 
                 
                   L 
                   I 
                 
               
             
           
         
       
     
     If all 3 wavelengths of light travel the same distance over which they interact in the nonlinear optical process, a propagation-constant mismatch or wave vector mismatch (Δk) for the nonlinear optical process can be defined by the relation: 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               K 
             
             = 
             
               
                 k 
                 P 
               
               - 
               
                 k 
                 S 
               
               - 
               
                 k 
                 I 
               
             
           
         
       
     
     This propagation-constant mismatch leads to a phase mismatch between the light generated at a first location and then propagated to a second location and the light generated at the second location. 
     In the illustrative example, the phase walk-off is between the light produced by the nonlinear optical interaction that occurs in a nonlinear optical material between two locations. 
     A phase walk-off is a phase walk-off between the light produced at two locations, a first location and a second location, on a path in an optical waveguide. For example, the relative phase walk-off can be for light, such as an idler light, at those two locations, where the idler light is generated by a difference frequency generation process involving the signal light and the pump light. More specifically, the relative phase walk-can be the difference between the phase of the idler light generated at the first location and propagated to the second location and the idler light newly generated at the second location. The phase of the newly generated idler light is determined by the phases of the pump light and the signal light at that location, according to the momentum conservation condition of the nonlinear optical process. 
     A relative phase walk-off is a phase walk-off between a first location and a second location on the path and between the first location and additional locations between the first location and the second location on the path in an optical waveguide. A cumulative phase walk-off as defined at a given location in a path is the relative phase walk-off between the starting point of a nonlinear optical process and that given location. In one illustrative example, the starting point of the nonlinear optical process can be the beginning of the nonlinear optical waveguide structure. In another illustrative example, the starting point can be the location of the pump input coupler that couples an input pump light into the nonlinear optical waveguide. The given location can be a second location within the nonlinear optical waveguide. A cumulative phase walk-off can also be referred to as an accumulated phase walk-off. 
     For example, the light propagating in a nonlinear optical waveguide structure can start at location 0 and then progress onto location A and then progress further onto location B and then finally exit the nonlinear optical waveguide structure after passing location C. The relative phase walk-off can be the amount of phase walk-off associated with the light traveling between locations A and B. A different value for the “relative phase walk-off” can be obtained for the light travel between locations B and C. 
     This light can be, for example, a pump light, a signal light, and an idler light. The phase walk-off can be determined for any of all of the types of light. 
     The relative phase shifts and relative phase walk-off can be defined with respect to a particular interaction distance and to the length of a particular segment, section, or portion of the nonlinear optical waveguide. The relative phase shifts and the relative phase walk-off also can be defined with respect to a particular structure and material composition of the nonlinear optical waveguide, which determine the effective refractive index of the waveguided light, as well as to the direction of propagation of light in that waveguide. For some materials, the refractive index varies with the direction of propagation of the light through that material. 
     As an illustrative example, if location A and location B are the two ends of a “first straight segment” of an optical waveguide, the relative phase walk-off could have a first value. However, if location A and location B are the two ends of a “second curved segment” of an optical waveguide, the direction of propagation in at least a portion of the curved segment is different from the direction of propagation in the straight segment. In this case, the relative phase walk-off for that “second curved segment” can have a second value that is different from the first value for the “first straight segment”. 
     The effective index of the waveguided pump, signal and idler light can vary with the location in a waveguide. Other factors such as the nonlinear optical coefficient d eff  and the amplitudes of the contributing optical waves A 1  and A 2  also can vary with the location. Consider the illustrative example of difference frequency generation of idler light from pump light and signal light. The phase walk-off obtained after the source pump and signal light and the generated idler light travel in a waveguide with longitudinal axis  1  can be described as follows: 
     
       
         
           
             
               
                 
                   
                     Δϕ 
                     = 
                     
                       
                         integral 
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 k 
                                 P 
                               
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             - 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 
                                   k 
                                   S 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   k 
                                   I 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                       ⁢ 
                       d 
                       ⁢ 
                       1 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where l is a value of a point location on the longitudinal axis, k P (l) is the propagation constant for the pump light at location l, k S (l) is the propagation constant for the signal light at location l, k I (l) is the propagation constant for the idler light at location l, and dl is the increment value of distance along the longitudinal axis used in the integral. The start and end points of the integral are the two locations (such as location A and location B discussed above) that determine the portion of nonlinear optical waveguide between which the relative phase walk-off is obtained. 
     The expression above can be rewritten as: 
     
       
         
           
             
               
                 
                   Δϕ 
                   = 
                   
                     
                       
                         integral 
                         ⁡ 
                         
                           [ 
                           
                             
                               k 
                               ⁢ 
                               
                                 P 
                                 ⁡ 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                             
                             - 
                             
                                 
                             
                             ⁢ 
                             
                               k 
                               ⁢ 
                               
                                 S 
                                 ⁡ 
                                 
                                   ( 
                                   1 
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                       ⁢ 
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     - 
                     
                       
                         integral 
                         ⁡ 
                         
                           [ 
                           
                             k 
                             ⁢ 
                             
                               I 
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                       ⁢ 
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
               
               
                 
                   
                     ( 
                     1 
                     ) 
                   
                   ] 
                 
               
             
           
         
       
     
     The first integral represents the phase of the newly generated idler light, which is determined from the phases of the pump and signal light that have propagated to the location l. The second integral represents the phase of the previously generated idler light that has propagated to the location l. 
     An integral can be approximated as a sum of successive incremental distances and the values of the integrand for those successive locations. The integral accounts for the variation in the value for the propagation constant or effective refractive index for different locations along the longitudinal axis. This axis can be straight or curved. 
     In the illustrative example, efficiency in generating output photons from input photons can be increased. For example, an increase in the efficiency can be described by (i) an increase in the probability of generating a photon for every photon coming in, (ii) an increase in the number of photons produced (or power of the light produced) for a given number of photons coming in (or power of the light coming in), and (iii) an increase in the rate of photons produced for a given rate of photons coming in. 
     The illustrative examples recognize and take into account that with current techniques, second order nonlinear optical frequency conversion is performed using either modal phase matching or quasi phase matching, but not both together. The illustrative examples recognize and take into account that current waveguides and structures that implement second order nonlinear optical processes are not as efficient as desired. 
     The illustrative embodiments recognize and take into account that a nonlinear optical process can be constructive or destructive. The illustrative embodiments recognize and take into account that constructive or destructive nonlinear optical interaction between the light generated at a first location and the light generation can occur at a second location. In other words, the interaction is the light generated in the first location that propagates to the second location and how that generated light at the second location interacts or affects the light generation occurring in the second location. 
     The illustrative embodiments recognize and take into account that the effect on light generation at the second location can also occur because of the light that is already propagating in addition to the light generated at the first location. The illustrative embodiments recognize and take into account that when the power from the generated light at the second location goes back into the source light, the nonlinear optical interaction is destructive. The illustrative embodiments recognize and take into account that the nonlinear optical interaction is constructive when the power in the light generated increases and the power in the source light decreases. In the illustrative example, the source light can be the pump light or other light input into the nonlinear optical waveguide. 
     The illustrative examples recognize and take into account that with current techniques for nonlinear optical frequency conversion producing light of a second wavelength (or wavelengths) from light of a first wavelength (or wavelengths), a phase matching condition can be maintained such that a relative phase walk-off between a light generated at a first location of the waveguide and a light generation occurring at a second location of the waveguide is less than 180 degrees. The illustrative examples recognize and take into account that these two locations can be, for example, the start locations and end locations of a waveguide or waveguide segment. The illustrative embodiments recognize and take into account that relative phase walk-off for the light generation at these two locations should remain less than 180 degrees for the nonlinear optical frequency conversion to be constructive and thus for the optical power at the second wavelength (or wavelengths) to continue to build up, with current techniques. 
     The illustrative embodiments recognize and take into account that when the relative phase walk-off has a value between 180 degrees and 360 degrees, the nonlinear optical interaction of the light at the second location of these two locations is destructive and the optical power at the second wavelength is reduced as compared to the optical power that can be obtained when the relative phase walk-off has a value of 180 degrees. The illustrative embodiments recognize and take into account that when the relative phase walk-off has a value between 360 degrees and 540 degrees, the nonlinear optical interaction again becomes constructive and the optical power at the second wavelength is increased as compared to the optical power that can be obtained when the relative phase walk-off has a value of 360 degrees. The illustrative embodiments recognize and take into account that a constructive condition can apply to light generation at a specific location on a path in an optical waveguide. However, that light generation is affected by the light generated at preceding locations on the path in the optical waveguide. 
     The illustrative embodiments also recognize and take into account that when the relative phase walk-off between these two locations has a value between 180 degrees and 360 degrees, the nonlinear optical interaction of the light generation at the first of these two locations and the light generation occurring at the second of these two locations is destructive. As a result, the illustrative embodiments recognize and take into account that the optical power at the second wavelength is reduced compared to the optical power that can be obtained if the nonlinear optical interaction were constructive. 
     The illustrative embodiments also recognize and take into account that the relative phase walk-off between the second location and a third location on the path in the optical waveguide can have a value between 360 degrees and 540 degrees. In this case, the nonlinear optical interaction of the light becomes constructive. 
     The illustrative examples recognize and take into account that the phase walk-off maintained should be no greater than 180 degrees for the nonlinear optical interaction that produces the light of the second wavelength (or wavelengths) to continue to be a constructive or coherent process that progressively increases the amount of light at the second wavelength (or wavelengths). The illustrative examples recognize and take into account that when the phase walk-off exceeds 180 degrees and until that phase walk-off reaches 360 degrees, the nonlinear optical process in currently used waveguides is a destructive process, decreasing the amount of light at the second wavelength (or wavelengths) and thereby increasing the amount of light at the first wavelength (or wavelengths). 
     The illustrative embodiments recognize and take into account that an accumulated phase walk-off can be determined for two locations. The accumulated phase walk-off can be the phase walk-off determined between A and location B on a path in an optical waveguide and for locations between location A and location B on the path. 
     The illustrative examples recognize and take into account that with current waveguides, an accumulated amount of nonlinear optical frequency conversion or a net efficiency of that nonlinear optical frequency conversion does not exceed the value reached when the phase walk-off is 180 degrees. Instead, the illustrative examples recognize and take into account that a net amount of power in the second wavelength (or wavelengths) oscillates between this maximum value and zero when the nonlinear optical interaction distance is made larger and larger. 
     In contrast, the illustrative examples recognize and take into account that for the structures that implement direction-reversal enhanced coherent interaction in the illustrative examples, the accumulated amount of nonlinear optical frequency conversion can continue to increase and be much greater than the amount achieved when the phase walk-off is at 180 degrees. In the illustrative examples, despite the large, accumulated phase walk-off, the nonlinear optical interaction continues to be coherent and thus continues to increase the optical power at the second wavelength (or wavelengths). 
     In one illustrative example, a directional phase matching waveguide structure can have a central region with strong nonlinear optical susceptibility or a large nonlinear optical coefficient and side regions comprising a material with weak nonlinear optical susceptibility or a small nonlinear optical coefficient (in comparison to the material of the central region). The efficiency of the second order nonlinear optical process depends on the net overlap between optical fields at the 3 wavelengths and the nonlinear optical material in the waveguide. The optical-field overlap factor, which is the normalized integral of these 3 optical fields within the cross-sectional area of the nonlinear optical material, can be 2 to 10 times larger for this illustrative example of the directional phase matching waveguide structure when compared to a prior-art waveguide structure. Since the efficiency of the optical-frequency conversion is proportional to the square of the optical-field overlap factor, the improvement afforded by this illustrative example of the directional phase matching waveguide structure can result in a 4 to 100 times higher optical-frequency conversion efficiency. 
     In an illustrative example, the directional phase matching waveguide structure can have at least one of input optical waveguides or output optical waveguides containing only material with weak or negligible nonlinear optical susceptibility or a nonlinear optical coefficient. This structure is beneficial because the nonlinear optical frequency conversion is constrained to occur within the nonlinear optical waveguide portion of the directional phase matching waveguide structure, and the nonlinear optical frequency conversion does not occur in other portions of the directional phase matching waveguide structure. In this illustrative example, the nonlinear optical waveguide portion of the directional phase matching waveguide structure can be designed to produce specific wavelengths of output light and at specific instances in time. Such control can be especially useful when the direction-reversal enhanced coherent interaction in this waveguide structure can be used to produce entangled photon pairs and when production of additional, non-entangled photons is not desired. 
     In the illustrative example, the second order nonlinear optical process of parametric down conversion can be operated with the higher frequency (shorter wavelength) pump light supplied as input to the waveguide and without any lower frequency (longer wavelength) signal light and idler light supplied. Some of the signal light and/or the idler light can be generated “spontaneously”. The spontaneous generation of the signal light and/or the idler light can be due to a noise process or other processes such as Raman scattering. The spontaneous parametric down conversion (SPDC) process can be used to produce entangled photon pairs for quantum optical applications. 
     When using second order nonlinear optical processes such as sum frequency generation and difference frequency generation in the illustrative example, the direction-reversal enhanced coherent interaction structure can produce an output photon of a second optical frequency or wavelength from an input photon of a first optical frequency or wavelength. Thus, this illustrative example can be used as an optical-frequency converter for single photons. The optical-frequency converter in the illustrative example enables both generation of the entangled photon pairs and frequency conversion of the single photons, which are useful for quantum networks and quantum processors. 
     In the illustrative example, second harmonic generation (SHG) can be used to generate optical wavelengths for which an optical emitter is not readily available. For example, second harmonic generation can be used to produce blue/green and yellow/green light. Second harmonic generation can be used to generate wavelengths of light useful for through-water optical communication. In the illustrative example, second harmonic generation can be used to produce deep ultraviolet light for solar-blind optical communication, and second harmonic generation can be used to generate ultraviolet light also for disinfection. For example, the second harmonic generation can be used to generate ultraviolet light in categories such as far UV, UVC, UVB, or UVA. The wavelengths can be from about 100 nm to 400 nm depending on the category of the ultraviolet light generated. 
     In the illustrative example, the processes of sum frequency generation and difference frequency generation can be used to produce light of mid-wave infrared (MWIR) and long-wave infrared (LWIR) wavelengths. For example, such processes can be used to produce the mid-wave infrared light used for laser infrared countermeasures (IRCM) sources that protect aircraft. 
     The directional phase matching waveguide structures in the illustrative example can result in optical sources that are more compact as compared to current systems. For example, these optical sources can have a chip-scale size. Further, these optical sources can also be manufactured with a lower cost. For example, optical sources including directional phase matching waveguide structures in the illustrative example can be fabricated using wafer-scale processes. 
     The illustrative examples recognize and take into account that waveguides that accomplish second order nonlinear optical frequency conversion can use techniques such as “modal phase matching” and “quasi phase matching” to accomplish the phase matching that is needed to have a long coherent interaction distance over which the nonlinear optical process can occur. 
     The illustrative examples recognize and take into account that to accommodate the large variation in the material refractive index for a large spectral span of the optical wavelengths involved in a nonlinear optical frequency conversion process occurring in a waveguide, some current techniques use modal phase matching, for which a higher-order transverse mode of the shorter wavelength light is involved in that nonlinear optical frequency conversion. The illustrative examples recognize and take into account that modal phase matching suffers from requiring very precise control of the dimensions of the fabricated waveguide. For example, the 3 wavelengths involved in the second order nonlinear optical process may not be adjustable to compensate for departures of those waveguide dimensions from their as-designed values. Thus, the illustrative examples recognize and take into account that modal phase matching alone cannot sustain desired distances for the coherent nonlinear optical interaction, such as distances of several millimeters and greater. 
     The illustrative examples recognize and take into account that quasi phase matching is a technique that can be used for phase matching nonlinear optical interactions in which the relative phase walk-off is corrected at regular intervals using a structural periodicity built into the nonlinear optical waveguide or into the nonlinear optical medium. Quasi phase matching (QPM) can be used when the phase mismatch Δk of the nonlinear optical process exceeds 180 degrees for a desired nonlinear optical interaction distance. 
     The illustrative examples recognize and take into account that quasi phase matching can be achieved by a periodic modulation of the effective dielectric constant of the waveguide. The illustrative examples recognize and take into account that this modulation can be accomplished by changing the width of the waveguide. The primary feature of quasi phase matching is that a Fourier component of the periodic modulation, mK i , where i is the i th  Fourier component and m is an integer. In this example, the periodic modulation mK i  is equal to the phase mismatch between the input light and the output light of the nonlinear optical process. The following expression is for the case of second harmonic generation in which two photons of input light at a “fundamental” frequency generate one photon of the output light at the second harmonic frequency: 
       Δ k= 2 k   F   −k   SHG   =mK   i  
 
     However, the illustrative examples recognize and take into account that the corrugations in the waveguide, due to the changes in waveguide width, result in substantial optical loss from scattering of the light. 
     The illustrative examples recognize and take into account that other mechanisms can be used in addition to or in place of a periodic modulation in the effective refractive index of the wave-guided light. For example, the illustrative examples recognize and take into account that quasi phase matching also can be achieved using a periodic modulation of the nonlinear optical coefficient. The illustrative examples recognize and take into account that this periodic modulation of the nonlinear optical coefficient can occur using waveguides that have reversals in the material polarizability. 
     To achieve a desired level of efficiency in efficient optical frequency conversion, the illustrative examples recognize and take into account that waveguides that have very strong confinement of the wave-guided light can be used. For example, the transverse spatial extent of the wave-guided light can be on the order of the size of the wavelength of the light in the material comprising the waveguide. In the illustrative examples, the cross-sectional dimensions of such waveguides are small compared to the wavelength of the light guided by the waveguide. 
     The illustrative examples recognize and take into account that one manner for causing these reversals in material polarizability can include periodic poling of a material such as lithium niobate (LiNbO 3 ) and thereby producing periodically poled lithium niobate (PPLN) and potassium titanyl phosphate (KTiOPO 4  or PPKTP). Waveguide structures fabricated in periodically poled lithium niobate (or fabricated in PPKTP) can provide second harmonic generation. For example, the periodic poling can be accomplished by fabricating two sets of phase shifters, such as tuning electrodes, that are located at the sides of a straight waveguide. In this example, the waveguide can be oriented perpendicular to the crystalline Z-axis of an x-cut layer of lithium niobate. A direct current (DC) electric field can be applied for the poling when the material is heated to a high temperature above room temperature. The illustrative examples recognize and take into account that a deficiency of this process is the difficulty in achieving a 50:50 duty factor of the periodic reversals in the material polarizability. Thus, the illustrative examples recognize and take into account that the enhancement in the nonlinear optical frequency conversion achieved by the quasi phase matching can be degraded using this technique. 
     The illustrative examples recognize and take into account that optical waveguides for quasi phase matching periodic reversals in material polarizability also have been achieved in gallium arsenide (GaAs) and gallium phosphide (GaP). For these materials, the illustrative examples recognize and take into account that the crystallographic orientation can be reversed in a periodic pattern. This periodic pattern can be generated using a material growth process and also can be generated by stacking alternate layers of material that have opposite crystallographic orientation. For the growth process, a “seed” layer that has the periodic orientation pattern can be formed. Then, additional materials are grown to form the layers of a waveguide structure. This process can be performed in GaAs and GaP. However, the illustrative examples recognize and take into account that GaAs and GaP are not suitable for nonlinear optical frequency conversion that involves shorter wavelengths of light, which are above the bandgap of and thus can be absorbed by the GaAs or GaP. 
     The illustrative examples recognize and take into account that a waveguide making use of quasi phase matching alone can have a period for the reversals in material nonlinear optical polarizability that ranges from 2 μm to 10 μm when each of the 3 wavelengths has a value shorter than 2 μm. The illustrative examples recognize and take into account that this small period makes the quasi phase matching waveguides more difficult to fabricate and to accurately control the duty factor for nonlinear optical processes involving wavelengths in the visible range of 0.4-0.7 μm and the near-infrared (NIR) to short-wave infrared (SWIR) range of 0.7-3 μm. 
     Further, the illustrative examples recognize and take into account that nonlinear optical waveguides can have cross-sectional structures that comprise the nonlinear optical material as the high-refractive-index core of the waveguide. Examples of a nonlinear optical material include lithium niobate, aluminum nitride, silicon carbide and gallium aluminum arsenide. The illustrative examples recognize and take into account that a nonlinear optical waveguide can have a nonlinear optical core surrounded by another material that has a lower refractive index and that acts as a waveguide cladding. Examples of this cladding material can include silicon dioxide or air. The illustrative examples recognize and take into account that these cladding materials do not have a desired level of nonlinear optical susceptibility. 
     The illustrative examples recognize and take into account that a nonlinear optical waveguide core region can have a slab of lithium niobate nonlinear optical material and a ridge of silicon nitride, located above the laterally continuous lithium niobate slab, which is then surrounded by the cladding materials. The illustrative examples recognize and take into account that this waveguide is used for a second order nonlinear optical process, but the silicon nitride does not have a desired level of nonlinear optical order susceptibility. Thus, the illustrative examples recognize and take into account that only the slab portion of this ridge waveguide comprises a nonlinear optical material. 
     The illustrative examples recognize and take into account that the optical-field overlap factor for waveguide designs is quite low when modal phase matching is used, especially when that phase matching involves certain higher-order transverse modes. For example, the optical-field overlap factor can be less than 0.2. 
     The illustrative examples recognize and take into account that for some nonlinear optical waveguides in which the pump light and the output light in the waveguide are both in the fundamental transverse mode, the nonlinear optical process involves birefringent phase matching and thus a much weaker nonlinear optical coefficient is used. Alternatively, the illustrative examples recognize and take into account that some nonlinear optical waveguides have rib-waveguide structures with a nonlinear optical slab and a nonlinear optical rib region above that laterally continuous slab. The illustrative examples recognize and take into account that these rib-waveguide structures can be used for quasi phase matching accomplished by periodic reversals of the material polarizability and involve pump and output light in the fundamental transverse mode. The fabrication of such periodic reversal in material polarizability can be more complicated than desired. 
     In the illustrative example, a direction-reversal enhancement of the coherent interaction approach implemented in directional phase matching waveguide structures can implement a quasi phase matching approach without needing to change the nonlinear optical material. As a result, the directional phase matching waveguide structure in the illustrative examples can be much easier to fabricate and can have lower loss as compared to other approaches for achieving quasi phase matching. 
     Furthermore, the period of the reversals in propagation direction of the directional phase matching (DPM) waveguide structure can be large in comparison to the wavelengths of the light. For example, a typical cycle length used for a directional phase matching waveguide structure ranges from 100 μm to 1,000 μm for light of wavelengths shorter than 2 μm. Thus, the period and the duty factor of this periodic change in waveguide propagation direction can be controlled precisely, relative to the optical wavelength. In comparison, many common fabrication processes can achieve control that is better than 0.01 μm in the waveguide transverse dimensions and the lengths of the waveguide sections. The illustrative examples recognize and take into account that to obtain a given desired value for the phase walk-off after completing one full cycle through a closed-loop ring or racetrack waveguide, or one full zig-zag cycle of a serpentine waveguide, a directional phase matching waveguide structure can make use of a higher-order transverse mode for the shortest wavelength light involved in the nonlinear optical process. A higher-order transverse mode has a smaller effective refractive index. 
     The illustrative examples recognize and take into account that modal phase matching allows the 3 wavelengths of the second order nonlinear optical process to be farther apart. The cross-section of the nonlinear optical waveguide structure in this illustrative example has a combination of a central region comprising a nonlinear optical material that is located between two side regions comprising materials that have weak nonlinear optical susceptibility, as compared to the nonlinear optical susceptibility of the material in the central region. Thus, compared to the current waveguide structures for modal phase matching, the nonlinear optical waveguide structure in this illustrative example can achieve much larger net overlap of the optical fields with the nonlinear optical material. 
     In the illustrative example, placing the nonlinear optical material at the center of the waveguide structure allows the maximum optical fields for the 3 wavelengths to overlap the nonlinear optical material when the optical field of the wave-guided light at a first wavelength of these 3 wavelengths has 3 peaks separated by 2 zeros, with the sign of the central peak being opposite from the sign of the two outer peaks. The cross-sectional structure of the waveguide in this illustrative example has 3 regions, and places these 3 regions laterally side-by-side of each other, with the region of nonlinear material located at the center. The central region is aligned with the central peak of the optical field of the light at the first wavelength and the two side regions are aligned with the two outer peaks of that optical field. 
     One illustrative example comprises an apparatus that comprises multiple parts and performs specific functions. In the illustrative example, the combination of parts together with the functions they perform can increase performance as compared to current techniques. 
     In the illustrative example, a system can include nonlinear optical frequency conversion for which a change in the sign of the nonlinear optical coefficient is aligned with a walk-off of π radians (or, equivalently, 180 degrees) in the phase match associated with that nonlinear optical process. This phase walk-off is defined with respect to the specific wavelengths or frequencies of the light involved in the nonlinear optical process. 
     Thus, the illustrative embodiments provide an optical waveguide structure that comprises a nonlinear optical waveguide comprising a nonlinear optical material having a second order nonlinear coefficient that changes with a direction of light propagation. A light propagating through a first portion of the nonlinear optical waveguide is affected by a positive value of a second order nonlinear coefficient. A light propagating through a second portion of the nonlinear optical waveguide is affected by a negative value of a second order nonlinear coefficient, wherein a set of dimensions in the nonlinear optical waveguide in the first portion and the second portion is selected to cause the light to have a relative phase walk-off occurring at a location in the first waveguide portion and a location in the second waveguide portion that is an odd multiple of 180 degrees. 
     With reference now to the figures and, in particular, with reference to  FIG. 1 , an illustration of a block diagram of an optical waveguide structure is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  100  comprises nonlinear optical waveguide  102  that comprises nonlinear optical material  104 . In the illustrative example, nonlinear optical waveguide  102  can operate as directional phase matching (DPM) optical waveguide structure  166 . In this example, directional phase matching (DPM) optical waveguide structure  166  can also be referred to as a direction-reversal enhancement of a coherent interaction (DRECI) waveguide structure. 
     Nonlinear optical waveguide  102  can have a shape that is selected from one of a closed path, an open path, a ring, a circular ring, an elliptical ring, a racetrack, a square, a rectangle path, a serpentine path, a zig-zag path, or some other suitable shape. 
     In this illustrative example, nonlinear optical material  104  has second order nonlinear coefficient  108  that changes with direction of light propagation  110 . 
     In this illustrative example, the value of second order nonlinear coefficient  108  depends on the direction of electric-field vectors of the light, typically with respect to the crystallographic orientation of nonlinear optical material  104 . In this example, second order nonlinear coefficient  108  is determined from second order nonlinear susceptibility  150 . Second order nonlinear susceptibility  150  can be a dimensionless proportionality constant x (2)   ijk  that indicates a degree of polarizability of a dielectric material. In this example, i, j, and k are the vector directions of the electric field components of a first light, second light, and third light involved in a second order nonlinear optical process. In this particular example, the first light, the second light, and the third light refer to a pump light, a signal light, and an idler light, but not necessarily in any particular order. For example, the first light can also refer to a signal light. 
     Nonlinear polarization can occur in nonlinear optical material  104  in which the material polarization no longer varies linearly with the electric field amplitude for the light wave which is an electromagnetic field. In other words, both an electric field and a magnetic field are present. This nonlinear relationship can be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     P 
                     = 
                     
                       
                         
                           χ 
                           
                             ( 
                             1 
                             ) 
                           
                         
                         ⁢ 
                         E 
                       
                       + 
                       
                         
                           χ 
                           
                             ( 
                             2 
                             ) 
                           
                         
                         ⁢ 
                         E 
                         ⁢ 
                         E 
                       
                       + 
                       
                         
                           χ 
                           
                             ( 
                             3 
                             ) 
                           
                         
                         ⁢ 
                         E 
                         ⁢ 
                         E 
                         ⁢ 
                         E 
                       
                       + 
                     
                   
                   ⁢ 
                   … 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     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, 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 example, second order nonlinear susceptibility  150  represents a nonlinear part of the dipolar characteristics for nonlinear optical material  104 . 
     As depicted, nonlinear optical waveguide  102  has first portion  112  and second portion  114 . Light  116  propagating in first direction  168  in direction of light propagation  110  through first portion  112  of nonlinear optical waveguide  102  can have first sign  152  of second order nonlinear coefficient  108  for nonlinear optical interaction  171  of light  116  with nonlinear optical material  104 . In this example, first sign  152  of second order nonlinear coefficient  108  is second order nonlinear coefficient  108  with positive value  118 . In other words, light  116  propagating through first portion  112  in first direction  168  can be affected by positive value  118  of second order nonlinear coefficient  108 . 
     In this illustrative example, nonlinear optical waveguide  102  has second portion  114 . Light  116  propagating in second direction  170  in direction of light propagation  110  through second portion  114  of nonlinear optical waveguide  102  can have second sign  154  of second order nonlinear coefficient  108  for nonlinear optical interaction  171  of light  116  with nonlinear optical material  104 . In this example, second sign  154  of second order nonlinear coefficient  108  is second order nonlinear coefficient  108  with negative value  120 . In other words, light  116  propagating through second portion  114  is affected by negative value  120  of second order nonlinear coefficient  108 . 
     In this example, second sign  154  is negative when first sign  152  is positive and second sign  154  is positive when first sign  152  is positive. Also, in this example, second direction  170  is a direction that is opposite of first direction  168 . 
     As depicted, a set of dimensions  122  in nonlinear optical waveguide  102  in first portion  112  and second portion  114  can be selected to cause light  116  to have phase walk-off  124  that is an odd multiple  126  of 180 degrees or n radians. In this illustrative example, nonlinear optical interaction  171  occurring in first portion  112  of nonlinear optical waveguide  102  can produce light  116  that has phase walk-off  124  that is odd multiple  126  of 180 degrees for nonlinear optical interaction  171  occurring in second portion  114  of nonlinear optical waveguide  102 . 
     In this illustrative example, nonlinear optical interaction  171  is a type of nonlinear optical interaction that can occur at multiple locations. For example, nonlinear optical interaction  171  can occur at first location  172  in first portion  112  of nonlinear optical waveguide  102 , and nonlinear optical interaction  171  can occur at second location  174  in second portion  114  of nonlinear optical waveguide  102 . 
     Additionally, phase walk-off  124  at second location  174  can be for previously generated light in light  116  generated at first location  172 , traveling to second location  174 , and affecting the generation of light  116  at second location  174 . Phase walk-off  124  can be between previously generated light in nonlinear optical waveguide  102  and newly generated light in nonlinear optical waveguide  102 . Phase walk-off  124  can have odd multiple  126  of 180 degrees that occurs with a change in a sign of second order nonlinear coefficient  108 . Also, successive sign changes occur in alignment with corresponding successive increments of odd multiples of 180 degrees in phase walk-off  124 . 
     In illustrative example, phase walk-off  124  has odd multiple  126  of 180 degrees in which odd multiple  126  of 180 degrees can occur at a location where a change in a sign of second order nonlinear coefficient  108  occurs. In the illustrative example, the location where phase walk-off  124  reaches 180 degrees can be about the same location where second order nonlinear coefficient  108  changes its sign. In the illustrative example, it can be desirable for second order nonlinear coefficient  108  to have a different sign where phase walk-off  124  is between 180 degrees and 360 degrees. With this situation, the change in sign due to phase walk-off  124  can be compensated by the change in the sign of second order nonlinear coefficient  108 , resulting in a higher level of light generation than would occur if second order nonlinear coefficient  108  does not have a change in its sign. In other words, the sign of second order nonlinear coefficient  108  changes. In this example, second order nonlinear coefficient  108  has one sign where the value of the phase walk-off is between 0 and 180 degrees. Second order nonlinear coefficient  108  has an opposite sign where the value of the phase walk-off is between 180 and 360 degrees. 
     In the illustrative example, phase walk-off  124  has odd multiple  126  of 180 degrees in which odd multiple  126  of 180 degrees is aligned with a change in the sign of second order nonlinear coefficient  108 . In this example, a change in the sign of a nonlinear optical interaction associated with phase walk-off  124  and a change in the sign of second order nonlinear coefficient  108  can occur at the same location, as close as possible to the same location, or at a location that results in a constructive generation of light. 
     In this illustrative example, the design of nonlinear optical waveguide  102  is such that the desired generation of light  116  occurs in second order nonlinear coefficient  108 . In the illustrative example, it can be desirable to have the location where phase walk-off  124  reaches 180 degrees to be about the same place where the sign of second order nonlinear coefficient  108  changes. Further, it is desirable for second order nonlinear coefficient  108  to have a first sign where phase walk-off  124  is between 0 degrees and 180 degrees and to have a second sign, opposite from the first sign, where phase walk-off  124  is between 180 degrees and 360 degrees. In this manner, the change in sign due to phase walk-off  124  can be compensated by the change in sign of second order nonlinear coefficient  108 . 
     In another illustrative example, nonlinear optical waveguide  102  can be designed such that wherein a peak in magnitude  180  of second order nonlinear coefficient  108  is aligned with phase walk-off  124  having a value of odd multiple  126  of 90 degrees. This type of alignment can also increase the generation of light in nonlinear optical waveguide  102 . In one illustrative example, the alignment of a peak in magnitude  180  of second order nonlinear coefficient  108  with phase walk-off  124  for value of odd multiple  126  of π/2 radians can be within π/4 radians. In the illustrative example, the generation can also be produced at desired levels even without this alignment in some illustrative examples. 
     As depicted, light  116  can have a number of different components. Light  116  can include pump light  128 , signal light  130 , and idler light  132 . In this illustrative example, pump light  128  has pump wavelength  134 ; signal light  130  has signal wavelength  136 ; and idler light  132  has idler wavelength  138 . In other words, light  116  can propagate through nonlinear optical waveguide  102  as pump light  128  having pump wavelength  134 ; signal light  130  having signal wavelength  136 ; and idler light  132  having idler wavelength  138 . In this example, pump light  128  can comprise one or more pump photons; signal light  130  can comprise one or more signal photons; and idler light  132  can comprise one or more idler photons. 
     In this example, a nonlinear optical interaction can occur between light  116  and nonlinear optical material  104  as light  116  propagates through nonlinear optical material  104 . This nonlinear optical interaction can be one in which phase walk-off  124 , associated with the phases of pump light  128 , signal light  130 , and idler light  132  traveling through a length of nonlinear optical waveguide  102  is odd multiple  126  of 180 degrees or n radians. In other words, phase walk-off  124  is with respect to the light generation at two different locations. Phase walk-off  124  also can be with respect to the phases of the pump, signal, or idler light present at two different locations in the illustrative example. For example, with spontaneous parametric down conversion, the phase of the pump light at each location determines the phases of the signal and idler light generated at that those locations. 
     Optical waveguide structure  100  can also include other components such as, for example, output optical waveguide  140  and input optical waveguide  139 . Output optical waveguide  140  can comprise a set of materials  156  having second order nonlinear coefficient  158 . In this depicted example, second order nonlinear coefficient  158  can be the same or different from second order nonlinear coefficient  108 . 
     In this illustrative example, output optical waveguide  140  is configured to emit output light  142  as an output from nonlinear optical waveguide  102 . In this example, output light  142  has output wavelength  144  that is different from pump light  128  at pump wavelength  134  input into nonlinear optical waveguide  102 . 
     As depicted, a set of optical couplers  146  can be in a set of regions  147  of nonlinear optical waveguide  102  and output optical waveguide  140 . As used herein, a “set of,” when used with reference to items, means one or more items. For example, a “set of optical couplers  146 ” is one or more optical couplers. 
     In this illustrative example, the set of regions  147  comprises portions of 2 waveguides that are sufficiently close to each other to enable the transmission of light  116  from one optical waveguide to another optical waveguide. For example, optical coupler  149  in the set of optical couplers  146  can be in region  151  in the set of regions  147 . In this example, region  151  can be a portion of nonlinear optical waveguide  102  and input optical waveguide  139  that are sufficiently close to each other such that input light  121  can be transmitted from input optical waveguide  139  to nonlinear optical waveguide  102 . As another example, optical coupler  149  can be formed from portions of nonlinear optical waveguide  102  and output optical waveguide  140  that are sufficiently close to each other such that some or all of light  116  can be transmitted from nonlinear optical waveguide  102  to output optical waveguide  140  in which the output is output light  142 . 
     In this depicted example, an optical coupler in the set of optical couplers  146  can be configured to couple light  116  at pump wavelength  134  from nonlinear optical waveguide  102  to output optical waveguide  140  and to couple light  116  at signal wavelength  136  and light  116  at idler wavelength  138  at a level with a desired level of transmission from nonlinear optical waveguide  102  to output optical waveguide  140 . 
     In this illustrative example, input optical waveguide  139  comprises a set of materials  160  having second order nonlinear coefficient  162 . Second order nonlinear coefficient  162  can be the same or different from second order nonlinear coefficient  158  and second order nonlinear coefficient  108 . 
     Input optical waveguide  139  can provide input light  121  having input wavelength  123  to nonlinear optical waveguide  102 . For example, input light  121  can be pump light  128  at pump wavelength  134 . As depicted, input optical waveguide  139  can be coupled to nonlinear optical waveguide  102  by a set of optical couplers  146 . An optical coupler in the set of optical couplers  146  can be configured to couple light  116  at pump wavelength  134  from input optical waveguide  139  to nonlinear optical waveguide  102  and couple light  116  at pump wavelength  134  at a desired level of intensity or power from input optical waveguide  139  to nonlinear optical waveguide  102 . 
     In some illustrative examples, optical waveguide structure  100  can also include a set of phase shifters  164 . The set of phase shifters  164  can apply activations  165  to nonlinear optical waveguide  102 . The set of phase shifters  164  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 emit energy to change the phase of a light particular wavelength propagating through an optical waveguide such as nonlinear optical waveguide  102 . 
     The set of activations  165  can take a number of different forms. For example, the set of activations  165  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 a light of the particular wavelength propagating through an optical waveguide such as nonlinear optical waveguide  102 . 
     For example, the set of phase shifters  164  can be located adjacent to nonlinear optical waveguide  102 . Phase shifters  164  can be configured as groups of phase shifters  164  in which the phase shifters can be implemented using tuning electrodes. In this example, the tuning electrode comprise positive tuning electrodes and negative tuning electrodes forming one more groups of tuning electrodes for phase shifters  164 . 
     In one illustrative example, phase shifters  164  can comprise a first set of phase shifters  164  located adjacent to first portion  112  of nonlinear optical waveguide  102  and a second set of phase shifters  164  located adjacent to second portion  114  of nonlinear optical waveguide  102 . The first set of phase shifters  164  can be a first set tuning electrodes that can operate to apply activations such as a first voltage and the second set of phase shifters  164  can be a second set of tuning electrodes can operate to apply activations such as a second voltage. 
     In this example, the first voltage and the second voltage can be selected such that phases shift in the wavelengths of at least one of pump light  128 , signal light  130 , or idler light  132  in nonlinear optical waveguide  102  occur in a manner such that a value of phase walk-off  124  changes. 
     As depicted, the configuration of nonlinear optical waveguide  102  can be selected to accomplish an increase in the efficiency in the generating of at least one of signal light  130  or idler light  132  within nonlinear optical waveguide  102 . This configuration can include a selection of parameters selected from at least one of a number of portions, a set of dimensions  122  of the portions, a shape of nonlinear optical waveguide  102 , nonlinear optical material  104 , or other suitable parameters. 
     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. 
     With reference next to  FIG. 2 , an illustration of a block diagram 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. 
     In this depicted example, nonlinear optical waveguide  102  has open path  200 . As depicted, open path  200  has end locations in the form of beginning  204  and ending  206 . In this illustrative example, open path  200  can have configurations selected from at least one of a serpentine path, a zig-zag path, a straight path, or some other type of open path. 
     In this illustrative example, open path  200  has ending  206  in nonlinear optical waveguide  102 . In this example, termination  208  is located at ending  206 . Examples of termination  208  include optical grating couplers, cleaved waveguide end faces, and etched waveguide end faces. Light can be coupled to and from terminations by mechanisms selected from at least one of an optical fiber, a free-space optical beam, or other suitable coupling mechanism. In other illustrative examples, termination  208  can be located in another nonlinear optical waveguide. 
     With reference next to  FIG. 3 , an illustration of a block diagram of a configuration for an optical waveguide structure is depicted in accordance with an illustrative embodiment. As depicted in this example, nonlinear optical waveguide  102  has central region  300  and two side regions, first side region  302  and second side region  304 , located on each side of central region  300 . 
     In this illustrative example, central region  300  comprises first nonlinear optical material  306  in a set of nonlinear optical materials  308  that has first second-order nonlinear coefficient  310  with a magnitude that is at least one picometer/volt. The two side regions, first side region  302  and second side region  304 , have second nonlinear optical material  312  in the set of nonlinear optical materials  308  that has second second-order nonlinear coefficient  314  whose magnitude is equal to or less than one tenth the magnitude of first second-order nonlinear coefficient  310  for first nonlinear optical material  306 . 
     Turning to  FIG. 4 , an illustration of a block diagram of a configuration for an optical waveguide structure is depicted in accordance with an illustrative embodiment. As depicted in this example, nonlinear optical waveguide  102  in  FIG. 1-3  has core region  400 , lower cladding region  404 , and upper cladding region  402 . As depicted, core region  400  is located between lower cladding region  404  and upper cladding region  402 . In this depicted example, the terms “upper” and “lower” are used to indicate relative locations of components with respect to each other. In this example, “upper” and “lower” can be relative locations on a structure in a vertical position. In a cross-sectional configuration, upper and lower are relative vertical positions. Left side and right side are relative horizontal positions. 
     Core region  400  can comprise a single spatially-uniform material and have a single value of its refractive index for a given wavelength of light. Core region  400  also can comprise a spatially non-uniform material that is better described by a “net refractive index” whose value can be determined by the spatially varied refractive index distribution of that material. Core region  400  also can comprise an arrangement of multiple, different materials of different refractive indexes. In this case, a determination can be made for the “net refractive index” of that core region. 
     In this illustrative example, core region  400  can have a number of different configurations. For example, core region  400  can be implemented using central region  300  and side regions, first side region  302  and second side region  304 . 
     In this illustrative example, core region  400  has average refractive index  406 , and upper cladding region  402  has first refractive index  408  that is lower than average refractive index  406 . As depicted, lower cladding region  404  has second refractive index  410  that is lower than average refractive index  406 . 
     In another illustrative example, upper cladding region  402  has height  432  that can be selected to compensate for a variation of the phase walk-off in the nonlinear optical waveguide. In this illustrative example, upper cladding region  402  can have height  432  selected to compensate for a variation in dimension  436  in core region  400  which can be one cause in the variation of the phase walk-off in the nonlinear optical waveguide. 
     For example, height  432  for upper cladding region  402  can be adjusted during fabrication to compensate for a variation in dimension  436  for core region  400  from an as-designed value for dimension  436 . In this illustrative example, dimension  436  can be, for example, a width or a height of core region  400 , a width or height of central region  300 , or a width or height of first side region  302  or second side region  304 . As depicted, height  432  of upper cladding region  402  can be sufficiently small that adjustments of height  432  can affect the effective refractive indices of the nonlinear waveguide modes. 
     With reference now to  FIG. 5 , an illustration of a block diagram of another configuration for an optical waveguide structure is depicted in accordance with an illustrative embodiment. This depicted example illustrates configurations for first portion  112  and second portion  114  in nonlinear optical waveguide  102 . 
     As depicted, first portion  112  of nonlinear optical  102  has first curved segment  500  and first straight segment  502 . These two segments can be a “zig” in first portion  112  in nonlinear optical waveguide  102 . In this example, second portion  114  of nonlinear optical waveguide  102  has second curved segment  504  and second straight segment  506 . These two segments can be a “zag” in second portion  114  in nonlinear optical waveguide  102 . 
     With this configuration, wherein a nonlinear optical interaction in first curved segment  500  has phase walk-off  124  for light  116  between first location  172  and second location  174  along path  509  traveled by light  116  in nonlinear optical waveguide  102 . In this example, phase walk-off  124  can be determined for a combination of pump wavelength  134 , signal wavelength  136 , and idler wavelength  138  between first location  172  and second location  174 . 
     When phase walk-off  124  is determined considering just light  116  from first location  172  in first portion  112  within nonlinear optical waveguide  102  and light  116  at second location  174  in second portion  114  within nonlinear optical waveguide  102 , phase walk-off  124  is relative phase walk-off  511 . In this illustrative example, phase walk-off  124  for the nonlinear optical interaction  171  can be due to the accumulated phases of the pump light, signal light, and idler light occurring from travel of the pump light, signal light, and idler light between the two locations within nonlinear optical waveguide  102 . 
     Phase walk-off  124  can be associated with light  116  in a portion of nonlinear optical waveguide  102  instead of with light  116  in the entire length of nonlinear optical waveguide  102 . In this case, relative phase walk-off  511  is for the two endpoints of the portion of nonlinear optical waveguide  102  being considered. The two endpoints can be first location  508  and second location  510  within nonlinear optical waveguide  102 . 
     When phase walk-off  124  occurs for light  116  from the beginning of nonlinear optical waveguide  102  and light  116  at another location in nonlinear optical waveguide  102  after the beginning of nonlinear optical waveguide  102 , phase walk-off  124  is cumulative phase walk-off  513 . In this illustrative example, cumulative phase walk-off  513  is relative phase walk-off  511  between light  116  from the start of nonlinear optical waveguide  102  and light  116  at the location within nonlinear optical waveguide  102  being considered. In other words, first location  508  is the start of nonlinear optical waveguide  102  and second location  510  is a location within nonlinear optical waveguide  102  at which cumulative phase walk-off  513  is measured or observed. 
     Characteristics of nonlinear optical waveguide  102  such that light  116  generated in first location  508  in a nonlinear optical interaction occurring in first portion  112  of nonlinear optical waveguide  102  propagates to second location  510  in second portion  114  of nonlinear optical waveguide  102  and has phase walk-off  124  for nonlinear optical interaction  171  occurring at second location  510  that is an odd multiple of 180 degrees. 
     In this example, phase walk-off  124  is for light  116  generated in nonlinear optical interaction  171  at first location  508  that then propagates to second location  510 . In these illustrative examples, phase walk-off  124  is for the components of the light  116  that are present at second location  510 . This phase walk-off is due to both the previously generated idler light that has propagated to second location  510  as well as pump light  128  and signal light  130  that also have propagated to second location  510 . 
     In this depicted example, length  512  of first straight segment  502  can be selected such that phase walk-off  124  equals at least one of odd multiple  126  of 180 degrees or n radians. Although this example describes first portion  112  and second portion  114  as both having a curved segment and a straight segment, phase walk-off  124  can be determined for other first and second portions and other combinations of at least one of curved or straight segments. For example, first portion  112  and second portion  114  can be comprised of only curved segments in other illustrative examples. Phase walk-off  124  can be determined for first location  508  in a curved segment in first portion  112  and second location  510  in a curved segment in second portion  114 . 
     The illustration of optical waveguide structure  100  in  FIG. 1  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, although two portions, first portion  112  and second portion  114 , are shown in nonlinear optical waveguide  102 , nonlinear optical waveguide  102  can include any number of additional portions  530  in which nonlinear optical material  104  is also present in the number of additional portions  530 . As used herein, a “number of,” when used with reference to items, means one or more items. For example, a “number of additional portions  530 ” is one or more additional portions. 
     As another example, the set of phase shifters  164  can apply activations  165  to other optical waveguides in addition to or in place of nonlinear optical waveguide  102 . For example, the set of phase shifters can be used to apply activations  165  to at least one of input optical waveguide  139 , output optical waveguide  140 , optical couplers  146 , or other optical waveguides or structures that may be used within optical waveguide structure  100 . 
     In the illustrative examples, directional phase matching (DPM) optical waveguide structure  166  in  FIG. 1  can receive input light of one or more frequencies or wavelengths (first wavelengths) and produce output light of one or more different frequencies or wavelengths (second wavelengths). These waveguide structures can comprise a nonlinear optical (NLO) material, such as lithium niobate. The optical-frequency conversion that produces the output light, of a different frequency from the input light, can be a result of the nonlinear optical interaction of the input light with the nonlinear optical material. 
     In the depicted example, the light propagating through the optical waveguide structure travels first in one direction (a first direction) and then travels in an opposite direction (a second direction) for which the light encounters a first sign of the nonlinear optical coefficient of the material when traveling in the first direction and encounters the opposite (second) sign of the nonlinear optical coefficient when traveling in the opposite direction. Also, the phase walk-off caused by a phase mismatch for the nonlinear optical process reaches 180 degrees (or n radians) at a location where the light reverses direction of propagation. A change in sign of the nonlinear optical coefficient counteracts the change in sign associated with the 180-degree phase walk-off. 
     In this illustrative example, the change in the sign of the nonlinear optical coefficient does not need to occur exactly at the same location as where the phase walk-off reaches 180 degrees. The illustrative embodiments recognize and take into account that it is desirable for the change in sign of the nonlinear optical coefficient to counteract the change in the sign associated with the phase walk-off having a value between 180 degrees and 360 degrees for most of the travel of light in the second direction. 
     When the phase walk-off reaches 360 degrees, the light reverses its direction of travel again, and thus encounters again the first sign of the nonlinear optical coefficient. The reversals in propagation direction and the reversals in the nonlinear optical interaction associated with the net phase walk-off continue in a periodic manner as the light travels in the waveguide. As a result of this direction-reversal enhancement of the coherent interaction (DRECI), the nonlinear optical process can continue to be a coherent interaction and continue to increase the amount of light at the second wavelengths, even though the accumulated phase walk-off has greatly exceeded 180 degrees and even has greatly exceeded 360 degrees. 
     This periodic reversal of the propagation direction for the light can be accomplished by constructing nonlinear optical waveguide  102  in  FIGS. 1-3  and  FIG. 5  in a configuration selected from one of a circular ring, an elliptical ring, a racetrack-shaped ring, a square or rectangular ring, a serpentine path, a zig-zag path, and other suitable configurations. 
     In an illustrative example, a second-order nonlinear optical effect is involved in the optical frequency conversion process. In the illustrative example, nonlinear optical waveguide  102  can comprise nonlinear optical material  104  having relatively large second order nonlinear optical susceptibility χ(2) or second order nonlinear optical coefficient d ij . For example, the values for second order nonlinear coefficient  108  of nonlinear optical material  104  can be at least 1 picometer/Volt. 
     In the illustrative example, nonlinear optical waveguide  102  can also comprise additional materials that have much smaller nonlinear optical susceptibility, or nonlinear optical coefficient, than the nonlinear optical susceptibility of the nonlinear optical material. For example, the values for the second order nonlinear optical coefficient of the additional materials can be no greater than one tenth the value for the second order nonlinear optical coefficient of nonlinear optical material  104 . Nonlinear optical waveguide  102  functioning as directional phase matching (DPM) optical waveguide structure  166  can be located on a substrate. 
     In the illustrative example, second order nonlinear susceptibility  150  or second order nonlinear coefficient  108  of nonlinear optical material  104  in  FIG. 1  can be largest for light  116  propagating in directional phase matching (DPM) optical waveguide structure  166  whose polarization is oriented parallel to the plane of the substrate. An example of nonlinear optical material  104  is x-cut lithium niobate. Examples of the additional materials include silicon nitride, silicon dioxide, titanium dioxide, aluminum oxide, and a polymer, such as bis-benzo-cyclo-butene and polyimide. Examples of the material of the substrate include lithium niobate, silicon carbide, quartz, alumina, and silicon. 
     In some illustrative examples, nonlinear optical waveguide  102  of optical waveguide structure  100  in  FIG. 1  can have central region  300  in  FIGS. 3-4  comprising nonlinear optical material  104  and two outer regions comprising one of the additional materials. These two outer regions are located at the two sides of central region  300  and can be, for example, first side region  302  and second side region  304  in  FIGS. 3-4 . As an illustrative example of this configuration, the nonlinear optical material of central region  300  can be x-cut lithium niobate and the additional material of the side regions, first side region  302  and second side region  304 , can be silicon nitride. 
     Additionally, nonlinear optical waveguide  102  can further comprise lower cladding region  404  in  FIG. 4  that is formed from silicon dioxide. This lower cladding region can be located on a silicon substrate. In some variations of this illustrative example, the nonlinear optical waveguide can also comprise upper cladding region  402  in  FIG. 4  of silicon dioxide. In this illustrative example, air is above upper cladding region  402 . 
     In the illustrative example, the second order nonlinear optical process in nonlinear optical waveguide  102  involves 3 wavelengths of light  116  that are different from each other, with that difference in the wavelengths being greater than 10% of the wavelength values. The wave-guided light of the shortest wavelength in light  116  propagates in a higher-order transverse mode that is, in particular, the TE yz =TE 31  mode. In this example, y and z subscripts in TE yz  indicate the optical field components parallel to the Y axis and the Z axis, respectively, of the x-cut lithium niobate crystal. 
     The optical field profile of this TE 31  mode has a peak of one sign located near the center of the waveguide and two peaks of the opposite sign from the center peak that are located at the sides, with one of these opposite-sign peaks located at each side of the central peak. In the illustrative example, the optical field designates the electric field component E of an electromagnetic wave such as light. 
     In this illustrative example, the wave-guided light of the other two wavelengths in light  116  propagate in the fundamental transverse mode, i.e., the TE yz =TE 11  mode, and have a single peak that is maximum near the center of the waveguide. The width of the central region of the waveguide can be selected such that a majority (&gt;50% in one illustrative example and &gt;80% in another illustrative example) of the central peak of the TE 31  optical-field profile overlaps the waveguide central region having the nonlinear optical material and also such that a minority (&lt;50% in one illustrative example and &lt;30% in another illustrative example) of the two side peaks of the TE 31  optical-field profile overlaps the waveguide central region having the nonlinear optical material. 
     Furthermore, in some illustrative examples, directional phase matching (DPM) optical waveguide structure  166  can also include optical waveguide components that comprise the additional materials and do not include a nonlinear optical material. The waveguide sections that do not comprise the nonlinear optical material can function as input optical waveguides and output optical waveguides that supply input light to the nonlinear optical waveguide, which contains the nonlinear optical material, or that selectively extract output light or input light from the nonlinear optical waveguide. The directional phase matching waveguide structure can also comprise wavelength-selective optical coupling regions between the nonlinear optical waveguide and the input and output optical waveguides. 
     In the depicted example, optical waveguide structure  100  can provide direction-reversal enhanced coherent interaction (DRECI) of the nonlinear optical process occurring in nonlinear optical waveguide  102 . The second order nonlinear optical frequency conversion process facilitated by the direction-reversal enhanced coherent interaction waveguide structures can accomplish functions such as a second-harmonic generation (SHG), a difference frequency generation (DFG), a parametric down conversion (PDC), a spontaneous parametric down conversion (SPDC), a sum frequency generation (SFG), and a parametric up conversion (PUC). 
     Turning now to  FIG. 6 , an illustration of an optical waveguide structure having a nonlinear optical waveguide with a serpentine path that achieves direction-reversal enhanced coherent interaction (DRECI) is depicted in accordance with an illustrative embodiment. As depicted, optical waveguide structure  600  is an example of one implementation for optical waveguide structure  100  shown in block form in  FIG. 1 . 
     In this illustrative example, optical waveguide structure  600  comprises nonlinear optical waveguide  602  with a serpentine shape in which light travels in a serpentine path. Further, nonlinear optical waveguide  602  also includes pump input optical waveguide  604 , output optical waveguide  606 , and output optical waveguide  608 . In this example, optical waveguide structure  600  also includes sets of phase shifters in the form of tuning electrodes. In the depicted example, the sets of tuning electrodes are tuning electrodes  610 , tuning electrodes  612 , tuning electrodes  614 , and tuning electrodes  616 . 
     As depicted, pump input optical waveguide  604  is depicted as a separate waveguide from nonlinear optical waveguide  602 . In some illustrative examples, pump input optical waveguide  604  can be an extension of nonlinear optical waveguide  602 . Further, optical waveguide structure  600  can also include additional input optical waveguides and output optical waveguides. 
     In the illustrative example, optical couplers can be used to couple light into and out of nonlinear optical waveguide  602 . In this illustrative example, input optical coupler  601  couples light from pump input optical waveguide  604  to nonlinear optical waveguide  602 ; output optical coupler  603  couples light to output optical waveguide  606  from nonlinear optical waveguide  602 ; and output optical coupler  605  couples light to output optical waveguide  608  from nonlinear optical waveguide  602 . 
     In this depicted example, the light travels in a zig-zag path within nonlinear optical waveguide  602 . Further, the polarization of the light traveling through nonlinear optical waveguide  602  is aligned parallel to the yz plane of nonlinear optical waveguide  602 , which is defined by z-axis  622  and y-axis  624 . 
     The polarization of the light in nonlinear optical waveguide  602  is transverse to the direction of propagation of the light. In nonlinear optical waveguide  602 , the optical-field polarization can be predominantly aligned parallel to the plane of the structure. For waveguides fabricated from a thin-film material such as thin-film lithium niobate, this optical-field polarization is considered to be transverse electric (TE) polarization. 
     In an illustrative example, the nonlinear optical waveguides can be fabricated from x-cut lithium niobate, such that the material X-axis is perpendicular to the plane of the structure. For lithium niobate, the strongest nonlinear optical coefficient is for light whose polarization is aligned parallel to the material Z-axis. The strongest nonlinear optical coefficient is the d 33  coefficient for lithium niobate. The nonlinear optical coefficient d ijk  is equal to one half the second order nonlinear optical susceptibility χ (2)   ijk . 
     The d 33  nonlinear optical coefficient can be strongest when the light travels in the upper straight waveguide segment between the 11 o-clock position and the 1 o-clock position and again in the lower straight waveguide segment between the 5 o-clock position and the 7 o-clock position. 
     The sign of the nonlinear optical coefficient depends on the direction of propagation of the light with respect to the crystal +Z-axis. For example, the nonlinear optical coefficient has one sign for light traveling from the 11 o-clock position to the 1 o-clock position and has the opposite sign for light traveling from the 5 o-clock position to the 7 o-clock position along that serpentine path for nonlinear optical waveguide  602 . 
     The optical field amplitude, or the amplitude of the electric-field component, of the light generated in a nonlinear optical waveguide can increase as the pump light (and the additional input light when that input light also is supplied) propagates in the nonlinear optical waveguide. In the illustrative examples, additional input light, when supplied, is an idler light and the nonlinear optical generated light is a signal light. An increase in the signal field amplitude, or the electric-field amplitude of the signal light, depends on the relative phases of the pump field (the electric field component of the pump light), the signal field (the electric field component of the signal light), and the idler field (the electric field component of the idler light). 
     In the illustrative example, the nonlinear optical process is a cumulative effect which also depends on interaction of the optical fields with each other and with the nonlinear optical material. Thus, the net nonlinear optical generation rate (and nonlinear optical generation efficiency) and, equivalently, the optical-frequency conversion efficiency can depend on the interaction between the photons present at a given location in the nonlinear optical waveguide and includes the photons generated at all of the locations between that given location and the start of the nonlinear optical waveguide. 
     The nonlinear optical interaction associated with photons for two different sets of locations (the given location “B” and a previous location “A”) can depend on the relative phase walk-off for the photons at and/or generated at those two locations. The nonlinear optical process for generating a photon at the given location “B” is determined by the phase of the input pump photon (and also the phase of the input idler photon if an input idler photon is supplied) that has traveled to that given location “B”. The nonlinear optical process for generating a photon at the given location “B” also is determined by the phase of the previously generated photon (idler photon and/or signal photon) that is determined by the phase of the input pump photon (and also the phase of the input idler photon if the input idler photon is supplied) that has traveled to previous location “A” plus the additional phase shift of the photon (the idler photon, the signal photon, or both) previously generated at location “A” that has traveled from location “A” to location “B”. 
     The effect of this interaction can be described as follows: 
     
       
         
           
             
               
                 
                   
                     
                       d 
                       ⁢ 
                       
                         A 
                         3 
                       
                     
                     
                       d 
                       ⁢ 
                       z 
                     
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         i 
                         ⁢ 
                         
                           d 
                           eff 
                         
                         ⁢ 
                         
                           ω 
                           3 
                           2 
                         
                       
                       
                         
                           k 
                           3 
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       A 
                       1 
                     
                     ⁢ 
                     
                       A 
                       2 
                     
                     ⁢ 
                     
                       e 
                       
                         i 
                         ⁢ 
                         Δ 
                         ⁢ 
                         k 
                         ⁢ 
                         z 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where dz is an incremental distance along the path taken by the photons from location “A” to location “B”, d eff  is the nonlinear optical coefficient, A 1  is the first wavelength of the light (producing the generated light), A 2  is the second wavelength of the light (involved in the NLO generation process), A 3  is the third wavelength of light (which is of the generated light), k 3  is the wave vector for the light at the third wavelength, ω 3  is the frequency of light at the third wavelength, c is the speed of light, and i is an index value. The factor Δkz is the phase walk-off from some starting point to the point z on the path. As depicted, the phase is the product of the wave vector k and the distance traveled to reach point z. 
     In this example, phase walk-off affects the generation of light, and equation (1) describes the generation of light. This equation describes the generation of light over the incremental distance dz. 
     In this example, Δk is the wave vector mismatch for the light generated at the location at point z. The phase walk-off incurred between two locations, location A and location B, is described by Δkz, which is the difference between the phase of newly generated light at location B and the phase of the light generated at A that travels to location B. 
     This expression describes the change in the amplitude of the optical field of the light at the third wavelength A 3  as generated by the nonlinear optical process occurring over an incremental distance dz. This generation depends on the amplitudes of the optical fields of the light at the first wavelength A 1  and at the second wavelength A 2 . The generation also depends on the frequency of the light at the third wavelength ω 3  (given as radians per second in this expression) and on the wave vector for the light at the third wavelength k 3 . The generation also depends on the nonlinear optical coefficient d eff . In this expression, the phase walk-off is given by Δkz and has a sinusoidal variation with changes in the z location along the path. 
     The nonlinear optical generation that occurs at a given location, such as location “B”, is the result of integrating the sinusoidal variation of the net phase walk-off from location “A” to location “B” where the overall distance between those two locations is L: 
     
       
         
           
             
               
                 
                   
                     
                       A 
                       3 
                     
                     ⁡ 
                     
                       ( 
                       L 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           ω 
                           3 
                           2 
                         
                         
                           
                             k 
                             3 
                           
                           ⁢ 
                           
                             c 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         
                           ∫ 
                           A 
                           B 
                         
                         ⁢ 
                         
                           
                             
                               2 
                               ⁢ 
                               
                                 id 
                                 eff 
                               
                               ⁢ 
                               
                                 A 
                                 1 
                               
                               ⁢ 
                               
                                 A 
                                 2 
                               
                             
                             1 
                           
                           ⁢ 
                           
                             e 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               kz 
                             
                           
                           ⁢ 
                           dz 
                         
                       
                     
                     ∼ 
                     
                       
                         
                           2 
                           ⁢ 
                           
                             id 
                             eff 
                           
                           ⁢ 
                           
                             ω 
                             3 
                             2 
                           
                           ⁢ 
                           
                             A 
                             1 
                           
                           ⁢ 
                           
                             A 
                             2 
                           
                         
                         
                           
                             k 
                             3 
                           
                           ⁢ 
                           
                             c 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               e 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 kL 
                               
                             
                             - 
                             1 
                           
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             k 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where dz is an incremental distance, d eff  is the nonlinear optical coefficient, A 1  is the optical field amplitude at the first wavelength, A 2  is the optical field amplitude at the second wavelength, A 3  is the optical field amplitude at the third wavelength of light, k 3  is the wave vector for the light at the third wavelength, ω 3  is the frequency of light at the third wavelength, c is the speed of light, i is an index value, L is a distance between the 2 locations, Δk is the mismatch between the wave vectors for the light at the three wavelengths, and ΔkL is the accumulated phase walk-off affecting the nonlinear optical generation that occurs at the second location z=B assuming the nonlinear optical generation process begins at the first location z=A. In this example, the right-most expression in equation (2) assumes the various factors remain constant in the portion of a nonlinear optical waveguide between those two locations. 
     In some subsequent examples, the value for Δk can change from one location to another location. Also, the value for d eff  can change from one location to another. 
     The intensity of the generated light (such as the power of the generated signal photons traveling in the waveguide or exiting the waveguide) is related to the square of the optical field amplitude, such as described below. The intensity of an electromagnetic wave, such as light, is given by the magnitude of the time-averaged Poynting vector which for our definition of field amplitude is given by: 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       i 
                     
                     = 
                     
                       2 
                       ⁢ 
                       
                         n 
                         i 
                       
                       ⁢ 
                       
                         ɛ 
                         0 
                       
                       ⁢ 
                       c 
                       ⁢ 
                       
                         
                            
                           
                             A 
                             i 
                           
                            
                         
                         2 
                       
                     
                   
                   , 
                   
                     i 
                     = 
                     1 
                   
                   , 
                   2 
                   , 
                   3 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where n i  is the refractive index of a wavelength of light, A i  is the ith wavelength of light, ϵ 0  is vacuum permittivity, and i is an index value. 
     The net refractive index of the waveguide for light of the first, second, or third wavelength is given by n i  where i=1,2,3. In these expressions, the speed of light is designated by c and the vacuum permittivity is designated by ϵ 0 . 
     Thus, using equation (3) and right-most expression in equation (2), the intensity of the light at the third wavelength can be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     I 
                     3 
                   
                   = 
                   
                     
                       
                         8 
                         ⁢ 
                         
                           n 
                           3 
                         
                         ⁢ 
                         
                           ϵ 
                           0 
                         
                         ⁢ 
                         
                           d 
                           eff 
                           2 
                         
                         ⁢ 
                         
                           ω 
                           3 
                           4 
                         
                         ⁢ 
                         
                           
                              
                             
                               A 
                               1 
                             
                              
                           
                           2 
                         
                         ⁢ 
                         
                           
                              
                             
                               A 
                               2 
                             
                              
                           
                           2 
                         
                       
                       
                         
                           k 
                           3 
                           2 
                         
                         ⁢ 
                         
                           c 
                           3 
                         
                       
                     
                     ⁢ 
                     
                       
                          
                         
                           
                             
                               e 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 kL 
                               
                             
                             - 
                             1 
                           
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             k 
                           
                         
                          
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     The squared modulus that appears in this equation can be expressed as: 
     
       
         
           
             
               
                 
                   
                     
                        
                       
                         
                           
                             e 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               kL 
                             
                           
                           - 
                           1 
                         
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           k 
                         
                       
                        
                     
                     2 
                   
                   = 
                   
                     
                       
                         
                           L 
                           2 
                         
                         ( 
                         
                           
                             
                               e 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 kL 
                               
                             
                             - 
                             1 
                           
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             kL 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   i 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 kL 
                               
                             
                             - 
                             1 
                           
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             kL 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       2 
                       ⁢ 
                       
                         L 
                         2 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               kL 
                             
                           
                           ) 
                         
                         
                           
                             ( 
                             
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               kL 
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Finally, the expression for I 3  can be written in terms of the intensities of the incident fields by using equation (3) to express |A i | 2  in terms of the intensities, yielding the result: 
     
       
         
           
             
               
                 
                   
                     I 
                     3 
                   
                   = 
                   
                     
                       
                         8 
                         ⁢ 
                         
                           d 
                           eff 
                           2 
                         
                         ⁢ 
                         
                           ω 
                           3 
                           2 
                         
                         ⁢ 
                         
                           I 
                           1 
                         
                         ⁢ 
                         
                           I 
                           2 
                         
                       
                       
                         
                           n 
                           1 
                         
                         ⁢ 
                         
                           n 
                           2 
                         
                         ⁢ 
                         
                           n 
                           3 
                         
                         ⁢ 
                         
                           ϵ 
                           0 
                         
                         ⁢ 
                         
                           c 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       L 
                       2 
                     
                     ⁢ 
                     
                       
                         sinc 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             kL 
                           
                           2 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Note that the effect of wave vector mismatch is included entirely in the factor sinc 2 (ΔkL/2). This factor is also known as the phase mismatch factor. 
     The term 
     
       
         
           
             
               L 
               2 
             
             ⁢ 
             
               
                 sinc 
                 2 
               
               ⁡ 
               
                 ( 
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     kL 
                   
                   2 
                 
                 ) 
               
             
           
         
       
     
     indicates that the phase mismatch limits the improvement in nonlinear optical generation efficiency (or generation rate) that can be achieved by increasing the overall length L of the nonlinear optical waveguide (assuming locations “A” and “B” are the start and end points of the nonlinear optical waveguide). This term has a maximum value of 1 when ΔkL=π. A coherent interaction length or coherent interaction distance can be defined as the value for the distance or length L at which the phase walk-off (e.g., ΔkL) equals π radians. 
     When the wave vector match is not perfect and thus the phase match is not perfect, an increasing walk-off can be present between the phases of the generated optical fields for longer distances of the nonlinear optical interaction. As a result, the net phase walk-off becomes larger and larger, and the nonlinear optical generation of the signal can be degraded. The accumulated phase walk-off is equal to the difference in the wave vectors, as given for each location, multiplied by the incremental distance traveled and integrated over an overall distance traveled, as indicated by the mathematical expressions above. In other words, the accumulated phase walk-off covers all portions of a path from the starting point on the path where the nonlinear optical interaction begins to occur to the location on the path where the accumulated phase walk-off is evaluated, while a relative phase walk-off covers the phase walk-off from between two locations on the path. 
     When the phase match is not perfect and as the lengths of the nonlinear optical waveguide increase, as well as for an increasing number of cycles of travel around a closed-loop nonlinear optical waveguide, such as nonlinear optical waveguide  702  in  FIG. 7 , the efficiency of the nonlinear optical generation process in these nonlinear optical waveguides decreases. This decrease in efficiency can occur because when the interaction length is greater than approximately the inverse of the net difference in the wave vectors of the generated signal light and the contributing pump light and the contributing idler light (for an example in which both the pump light and idler light are supplied as inputs), the output signal light can become out of phase with its driving polarization. In this example, the driving polarization can be determined by the phases of the pump light and the idler light. Thus, power can flow from the signal light back into the pump light and the idler light. 
     Essentially, the phases of the participating optical fields of the pump light, the signal light, and the idler light can contribute a factor to the nonlinear optical generation efficiency, whose sign can change. This change in sign can occur when the net phase walk-off equals a multiple of π, as indicated by the mathematical expressions above. 
     In this illustrative example, the sign associated with the phase mismatch can reverse each time the net phase walk-off equals a multiple of π radians. In the illustrative example, a coherent interaction length or distance is defined as being the length of travel in the nonlinear optical waveguide at which the net phase walk-off equals π radians. 
     For the directional phase matching (DPM) optical waveguide structure, the phase match can be such that the sign change associated with a phase mismatch (or wave vector mismatch) occurs when a reversal is present in the direction of propagation of the light that produces a reversal in the sign of the nonlinear optical coefficient. Thus, the sign change due to the phase mismatch can be counteracted by a sign change in the nonlinear optical coefficient. As a result, the efficiency of the nonlinear optical generation process can continue to increase as the overall interaction distance increases. 
     The accumulated nonlinear optical generation or the net generation rate or efficiency for a nonlinear optical process, such as a spontaneous parametric down conversion process in a directional phase matched waveguide structure, can build up with the interaction distance as a series of steps. The total number of steps that can occur before the nonlinear optical interaction loses its coherence and begins to decline can depend on the relative error between the net coherent interaction length and the physical distance traveled by the light between reversals in the sign of the nonlinear optical coefficient. 
     For the illustrative example in  FIG. 6 , the length of one “zig” through the serpentine path or the length of one “zag” through the serpentine path is equal to the coherent interaction length. The coherent interaction length can depend on the detailed structure of the waveguide, which then determines the effective refractive indices of the specific wave-guided optical modes of the pump light, the signal light, and the idler light that participate in the nonlinear optical process. The coherent interaction length also can depend on the specific wavelengths of the pump light, the signal light, and the idler light. 
     As depicted, the directional phase matching optical waveguide structure also can have one or more sets of tuning electrodes, as depicted in  FIG. 6 . The waveguide sections that have these tuning electrodes function as voltage-controlled optical phase shifters and are examples of phase shifters  164  in  FIG. 1 . These tuning electrodes can tune the phases of the pump light, the signal light, and the idler light. If the pump optical field, the signal optical field, and the idler optical field have different amounts of overlap with the electro-optic material in these waveguide sections, these fields can receive different amounts of phase shift due to the applied voltage and the electric-field resulting from that applied voltage. Thus, the net phase walk-off can be changed by the voltage applied to each set of tuning electrodes. 
     Tuning electrodes can be used to increase the efficiency of nonlinear optical generation in nonlinear optical waveguide  602 . For a nonlinear optical waveguide, such as nonlinear optical waveguide  602 , formed in an anisotropic material such as x-cut lithium niobate, the electro-optic coefficient which affects the optical phase shift resulting from an applied electrical voltage can depend on a propagation direction of light. This behavior is similar to the behavior of the second order nonlinear coefficient in the illustrative examples. 
     The electro-optic coefficient also can have one sign for light traveling in one direction and an opposite sign for light traveling in an opposite direction. The voltage dependent phase shift is determined by both the sign of the electro-optic coefficient and the sign of the applied voltage. The voltage dependent phase shift is proportional to the arithmetic product (i.e., multiplication) of the electro-optic coefficient and the electric field resulting from the applied voltage. 
     In this example, nonlinear optical waveguide  602  is fabricated in x-cut lithium niobate. Light propagates in the yz plane of the lithium niobate material in nonlinear optical waveguide  602 . Light propagating in the +Y direction experiences one sign of the electro-optic coefficient and light propagating in −Y direction experiences the opposite sign of the electro-optic coefficient. 
     The light propagating in the upper-most straight segment propagates in the +Y direction. The positive electrode is at the left side from the point-of-reference of the propagating light and the negative electrode is at the right side. The light propagating in the second from the upper-most straight segment propagates in the −Y direction. The positive electrode is at the right side from the point-of-reference of the propagating light and the negative electrode is at the left side. Thus, with this arrangement of the electrodes, the sign of the applied voltage and the sign of the resulting electric field for light propagating in the +Y direction is opposite from the sign of the applied voltage and the sign of the resulting electric field for light propagating in the −Y direction. As a result, the product of the electro-optic coefficient and the electric field has one sign for light propagating in the +Y direction and the same sign for light propagating in the −Y direction. 
     Turning now to  FIG. 7 , an illustration of an optical waveguide structure having a nonlinear optical waveguide with a racetrack shape that achieves direction-reversal enhanced coherent interaction (DRECI) is depicted in accordance with an illustrative embodiment. As depicted, optical waveguide structure  700  is an example of one implementation for optical waveguide structure  100  shown in block form in  FIG. 1 . 
     In this illustrative example, optical waveguide structure  700  comprises nonlinear optical waveguide  702 , which operates as a direction reversal enhanced coherent interaction waveguide structure. As depicted, nonlinear optical waveguide  702  has a closed path in the shape of a racetrack. As depicted, a nonlinear optical (NLO) frequency conversion process occurs in the racetrack shape of nonlinear optical waveguide  702 . As depicted, nonlinear optical waveguide  702  lies on a zy plane, which is defined by z-axis  720  and y-axis  722 . 
     In this illustrative example, optical waveguide structure  700  further comprises pump input optical waveguide  704  into which a pump light is supplied and through which the pump light is provided to nonlinear optical waveguide  702 . Optical waveguide structure  700  can also include one or more additional inputs such as input optical waveguide  706 . 
     Further, optical waveguide structure  700  can have a set of outputs. In this illustrative example, the outputs can be output optical waveguide  708  and output optical waveguide  710 . 
     Additionally, optical waveguide structure  700  can also include input optical coupler  701 , input optical coupler  703 , output optical coupler  705 , and output optical coupler  707 . As depicted, input optical coupler  701  couples pump input optical waveguide  704  to nonlinear optical waveguide  702 ; input optical coupler  703  couples input optical waveguide  706  to nonlinear optical waveguide  702 ; output optical coupler  705  couples output optical waveguide  708  to nonlinear optical waveguide  702 ; and output optical coupler  707  couples output optical waveguide  710  to nonlinear optical waveguide  702 . 
     In this illustrative example, the light travels in a clockwise path through nonlinear optical waveguide  702  in the optical waveguide structure  700  functioning as a direction-reversal enhancement of the coherent interaction waveguide structure. In the illustrative example, one half of the circumference of the racetrack-shaped loop in nonlinear optical waveguide  702  is equal to the coherent interaction length. 
     As depicted in  FIG. 7 , sets of phase shifters such as tuning electrodes  712  and tuning electrodes  714  can be present in optical waveguide structure  700 . Each set of tuning electrodes operates to apply a voltage in a manner that causes phases to shift in the wavelengths of light moving within nonlinear optical waveguide  702 . In other words, these sets of tuning electrodes can operate as voltage control optical phase shifters and are examples of phase shifters  164  in  FIG. 1 . In this manner, phase walk-off of light traveling within nonlinear optical waveguide  702  can be changed as desired. 
     In this depicted example, the nonlinear optical process that operates within nonlinear optical waveguide  702  converts photons of the pump light received by at least one of pump input optical waveguide  704  or input optical waveguide  706  into photons of an output light of a different optical frequency. This output light can be output by at least one of output optical waveguide  708  or output optical waveguide  710 . 
     In this illustrative example, the number of additional input optical waveguides and output optical waveguides can depend on the specific nonlinear optical process being used and the application selected for the nonlinear optical frequency generation. For example, a spontaneous parametric down conversion (SPDC) process can use pump input optical waveguide  704  and one or two outputs, such as output optical waveguide  708  and output optical waveguide  710 . 
     In this example, the pump photons, supplied through pump input optical waveguide  704 , have a higher energy than the output photons. In this example, the higher energy means that the pump photons have a higher frequency and a shorter wavelength. 
     The use of one or two outputs for optical waveguide structure  700  can depend on whether the spontaneous parametric down conversion process is phase matched to produce frequency degenerate output in which both output photons resulting from an input pump photon have the same frequency or frequency non-degenerate outputs in which the frequencies of the two output photons produced from an input pump photon are very different from each other. For the case of two outputs comprising photons with different frequencies, some illustrative examples can separate the photons of the two frequencies into two output optical waveguides, such as output optical waveguide  708  and output optical waveguide  710 , for optical waveguide structure  700 . 
     As another example, a parametric down conversion (PDC), a parametric up conversion (PUC), a difference frequency generation (DFG), or a sum frequency generation (SFG) process can be implemented with a direction-reversal enhanced coherent interaction waveguide structure, such as optical waveguide structure  700 , that has inputs for the pump light, such as pump input optical waveguide  704  and input optical waveguide  706 . 
     For difference frequency generation (DFG), the nonlinear optical process operating in nonlinear optical waveguide  702  produces an output photon whose optical frequency is the difference between the optical frequencies of the pump photon received through pump input optical waveguide  704  and the additional input photon received through input optical waveguide  706 . 
     For sum frequency generation (SFG), the nonlinear optical process in nonlinear optical waveguide  702  produces an output photon whose optical frequency is a sum of the optical frequencies of the pump photon and the additional input photon. The output photons can be extracted from output optical waveguide  708 . 
     Whether the process is considered a down-conversion process or an up-conversion process can depend on whether the parametric input photon has a higher or lower energy than the output photon resulting from the nonlinear optical frequency conversion. 
     Second harmonic generation (SHG) can be considered a specific case of sum frequency generation. In this case, the pump photon received by pump input optical waveguide  704  and the additional input photon received by input optical waveguide  706  have the same optical frequency. Both of the input photons can be supplied through pump input optical waveguide  704 . In this illustrative example, the output photons produced by second harmonic generation have twice the optical frequency of the input photons. These output photons can be extracted through an output optical waveguide, such as output optical waveguide  708  or output optical waveguide  710 . 
     The effectiveness of a nonlinear optical generation process, such as the power in the idler light generated by a spontaneous parametric down conversion for a given pump power, can depend on several factors such as the magnitude of the nonlinear optical coefficient, the degree of phase matching, and the physical interaction length. The effectiveness of a nonlinear optical generation process also can depend on the cross-sectional area of the wave-guided light because the nonlinear optical generation process depends on the pump intensity. Further, the effectiveness of the nonlinear optical generation process depends on the net overlap of the pump, signal, and idler optical fields with the nonlinear optical material in a cross-section of the nonlinear optical waveguide. 
     With reference now to  FIG. 8 , an illustration of a cross-sectional view of a nonlinear optical waveguide in an optical waveguide structure is depicted in accordance with an illustrative embodiment. Nonlinear optical waveguide  800  is an example of an implementation for nonlinear optical waveguide  102  shown in block form in  FIG. 1  and in  FIG. 4 . In this illustrative example, nonlinear optical waveguide  800  has core region  802 . In this illustrative example, core region  802  comprises a nonlinear optical material, such as x-cut lithium niobate (LiNbO3). As depicted, nonlinear optical waveguide  800  also has cladding regions. Nonlinear optical waveguide  800  has lower cladding  806  and upper cladding  808 . In this example, lower cladding  806  is comprised of silicon oxide. In this depicted example, the cladding regions can comprise silicon dioxide region and air. As depicted, a first portion of upper cladding  808  is comprised of silicon dioxide and a second portion of upper cladding  808  is comprised of air. In this example, silicon oxide in upper cladding  808  has upper cladding height  807 . In this illustrative example, upper cladding  808  can be comprised of silicon dioxide, air, or a combination of silicon dioxide and air. 
     Further, nonlinear optical waveguide  800  can have side regions on either side of central region  804  within core region  802 . As depicted, these two side regions are located laterally adjacent to central region  804 . In this illustrative example, the side regions include side region  810  and side region  812 , which are comprised of silicon nitride (Si 3 N 4 ). 
     As depicted, nonlinear optical waveguide  800  has strip width  814 . Additionally, central region  804  in nonlinear optical waveguide  800  has center region top width  816 . 
     In this illustrative example, silicon nitride can be a suitable material for side region  810  and side region  812  because silicon nitride has a minimal second order optical nonlinearity and the refractive index of silicon nitride is slightly smaller than the refractive index of lithium niobate, the nonlinear optical material used in central region  804 . In this depicted example, the refractive index of silicon nitride can be less than 10% smaller than the refractive index of lithium niobate. 
     As depicted, nonlinear optical waveguide  800  can be especially suitable for modal phase matching in which the shortest wavelength of the light involved in the nonlinear optical process is in the TE xy =TE 31  mode (or in the TM xy =TM 31  mode). For this nomenclature, the x-axis of the cross-section is in the horizontal direction and the y-axis of the cross-section is in the vertical direction. These axes are reference directions in a cross-sectional depiction and are not necessarily the same as the X, Y, and Z axes of a lithium niobate crystal. For a spontaneous parametric down conversion nonlinear optical process, a pump light has the shortest wavelength (highest energy) and is in the TE 31  mode. 
       FIGS. 9-13  are graphs illustrating characteristics of nonlinear optical waveguide  800  in  FIG. 8 . With reference next to  FIG. 9 , an illustration of a graph of an optical field overlap factor as a function of a central region top width is depicted in accordance with an illustrative embodiment. In this illustrative example, graph  900  illustrates an optical field overlap factor as a function of center top width  816  for central region  804  in nonlinear optical waveguide  800  in  FIG. 8 . As depicted, y-axis  902  represents optical field overlap factor, and x-axis  904  represents center region top width  816  for central region  804  in micrometers. 
     In this illustrative example, line  906  illustrates values for the optical field overlap factor as center region top width  816  increases. In this example, upper clad height  807  for the SiO 2  portion of upper cladding  808  in  FIG. 8  is 0.5 micrometers and is comprised of air. The strip height for central region  804  in  FIG. 8  is 0.3 micrometers. 
     As depicted, line  906  shows that the optical field overlap factor can be optimized by selecting the width of the central region. The optical field profile of the TE 31  mode has a central peak of one sign and two side peaks of the opposite sign, as illustrated in section  908  in graph  900 . In one illustrative example, a design goal can include maximizing the overlap of the central peak of the optical field profile and minimizing the overlap of the side peaks of that optical field profile with the nonlinear optical central region of the waveguide. 
     Turning now to  FIG. 10 , an illustration of field profiles that overlap a nonlinear optical material in a nonlinear optical waveguide is depicted in accordance with an illustrative embodiment. In this illustrative example, optical field profiles  1000  are field profiles for a nonlinear optical waveguide, such as nonlinear optical waveguide  800  in  FIG. 8 . 
     As depicted, optical field profiles  1000  are illustrated for pump mode  1002 , signal mode  1004 , and idler mode  1006  that overlap nonlinear material in nonlinear optical waveguide  800  in  FIG. 8 . In this illustrative example, the pump light is in the TE 31  mode and the signal light and the idler light are in the TE 11  (or fundamental) mode. As depicted, optical field profiles  1000  depict side peaks of the pump optical field in pump mode  1002  having only minimal overlap with the nonlinear optical material. In this depicted example, substantial portions of the peaks of the signal field in signal mode  1004  and the idler field in idler mode  1006  overlap the nonlinear optical material. 
     In comparison,  FIG. 11  is an illustration of optical field profiles that overlap a nonlinear optical material in a nonlinear optical waveguide depicted in accordance with an illustrative embodiment. As depicted, optical field profiles  1100  are illustrated for pump mode  1102 , signal mode  1104 , and idler mode  1106  that overlap the nonlinear material in the nonlinear optical waveguide that does not have side regions such as those depicted for nonlinear optical waveguide  800  in  FIG. 8 . 
     The side peaks of the TE 31  mode for the pump light in pump mode  1102  substantially overlap the nonlinear optical material and the contribution of those side peaks can partially cancel out the contribution of the central peak to the nonlinear optical frequency conversion. For example, an optical field overlap factor for nonlinear optical waveguide  800  in  FIG. 8  can be larger than 0.33 (33%). This value for the optical field overlap factor is nearly twice as large as the best optical field overlap factor that can be achieved with nonlinear optical waveguides that do not have side regions for the same set of pump, signal, and idler wavelengths. 
     With reference next to  FIG. 12 , an illustration of a graph of a net coherent interaction length, obtained for one round trip, for different configurations of nonlinear optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, graph  1200  illustrates net coherent interaction length as a function of strip width. 
     In graph  1200 , y-axis  1202  represents the net coherent interaction length in millimeters, and x-axis  1204  represents strip width in micrometers. The lines in graph  1200  illustrate that net coherent interaction length for various configurations of nonlinear optical waveguides. 
     As depicted, the lines in section  1206  depict net coherent interaction lengths for nonlinear optical waveguides with a spatially uniform core region rather than a core region that comprises a central region and two side regions, such as depicted in  FIG. 8 . In section  1206 , line  1220  is for a nonlinear optical waveguide a spatially uniform lithium niobate core region and an upper cladding height of 0.45 μm, and line  1222  is for a nonlinear optical waveguide with a spatially uniform lithium niobate core region and an upper cladding height of 0.50 μm. In the illustrative example, the upper cladding height is the height for a first portion of the upper cladding. This upper cladding height corresponds to upper cladding height  807  for upper cladding  808  in  FIG. 8 . In the depicted example, air is above the upper cladding. 
     In this illustrative example, the lines in section  1208  show net coherent interaction lengths for nonlinear optical waveguides that include side regions, such as the waveguide depicted in  FIG. 8 . In section  1208 , line  1224  is for nonlinear optical waveguide  800  in  FIG. 8  with lithium niobate center region and silicon nitride side regions, a center region width of 0.3 μm, and an upper cladding height of 0.47 μm, and line  1226  is for nonlinear optical waveguide  800  in  FIG. 8  with lithium niobate center region and silicon nitride side regions, a center region width of 0.3 μm, and an upper cladding height of 0.46 μm. 
     Turning now to  FIG. 13 , an illustration of a graph of an optical field overlap factor for different configurations of nonlinear optical waveguides is depicted in accordance with an illustrative embodiment. In this illustrative example, graph  1300  illustrates an optical field overlap factor as a function of strip width. In this example, y-axis  1302  represents the optical field overlap factor, and x-axis  1304  represents strip width in micrometers. The lines in graph  1300  illustrate values of the optical field overlap factor obtained for various configurations of nonlinear optical waveguides. 
     As depicted, the lines in section  1306  depict optical field overlap factors for nonlinear optical waveguides that have a spatially uniform lithium niobate core region. In section  1306 , line  1352  is for a waveguide with a spatially uniform lithium niobate core region and an upper cladding height of 0.50 μm, and line  1354  is for a waveguide with a spatially uniform lithium niobate core region and an upper cladding height of 0.45 μm. 
     In this illustrative example, the lines in section  1308  illustrate optical field overlap factors for nonlinear optical waveguides whose core region comprises a central region and two side regions, such as the nonlinear optical waveguide  800  in  FIG. 8  with lithium niobate center region and silicon nitride side regions. In section  1308 , line  1356  is for a waveguide such as nonlinear optical waveguide  800  in  FIG. 8  with a center region width of 0.3 μm, and an upper cladding height of 0.46 μm; and line  1358  is for nonlinear optical waveguide  800  in  FIG. 8  with lithium niobate center region and silicon nitride side regions, a center region width of 0.3 μm, and an upper cladding height of 0.47 μm. 
     In some illustrative examples, one or more input optical waveguides and one or more output optical waveguides for an optical waveguide structure can be implemented in a material that has negligible or weak nonlinear optical susceptibility as compared to nonlinear optical material used in the nonlinear optical waveguide. For example, an optical waveguide structure whose nonlinear optical waveguide contains lithium niobate as a nonlinear optical material can have input and output optical waveguides with silicon nitride (Si 3 N 4 ) or titanium dioxide (TiO 2 ) as the waveguide-core material of those input and output optical waveguides. The higher refractive-index core region of the input and output optical waveguides can be surrounded by lower refractive-index cladding that comprises a material such as silicon dioxide or air. 
     In the mathematical expression describing nonlinear optical generation and generation efficiency such as expressions (1) through (6) discussed above, the contribution of the optical field overlap factor can be included in the value used for the effective nonlinear optical coefficient d eff . 
     With reference next to  FIG. 14 , an illustration of an optical waveguide structure having a nonlinear optical waveguide with a shape of a circular ring that achieves a direction-reversal enhanced coherent interaction is depicted in accordance with an illustrative embodiment. As depicted, optical waveguide structure  1400  is an example of one implementation for optical waveguide structure  100  shown in block form in  FIG. 1 . The circular ring can be thought of as a simpler version of a racetrack shaped ring for which the length of the straight segments in the racetrack is zero. 
     In this illustrative example, optical waveguide structure  1400  comprises circular ring nonlinear optical waveguide  1402  which is a nonlinear optical waveguide in which light travels in a closed path that is in the shape of a circular ring. Further, optical waveguide structure  1400  also includes pump input optical waveguide  1404  and output optical waveguide  1406 . As depicted in this illustrative example, optical waveguide structure  1400  also includes optical coupler  1401  and optical coupler  1403 . Optical coupler  1401  couples light into circular ring nonlinear optical waveguide  1402  from pump input optical waveguide  1404 . Optical coupler  1403  couples light from circular ring nonlinear optical waveguide  1402  to output optical waveguide  1406 . In this depicted example, optical waveguide structure  1400  also includes sets of phase shifters such as tuning electrodes  1408  and tuning electrodes  1410 . 
     As depicted, circular ring nonlinear optical waveguide  1402  has a shape of a circular ring that provides a closed circular path. In this illustrative example, circular ring nonlinear optical waveguide  1402  has zy plane as defined by z-axis  1412  and y-axis  1414 . 
     In this example, a pump light, a signal light, and an idler light travel within circular ring nonlinear optical waveguide  1402  in a counter-clockwise direction. The propagation angle can be defined relative to z-axis  1412 . 
     In one illustrative example, circular ring nonlinear optical waveguide  1402  can be implemented in x-cut lithium niobate. With this example, z-axis  1412  in the positive direction can correspond to the +Z crystallographic direction of the lithium niobate material. 
     The direction of travel and the propagation angles for light traveling in a counter-clockwise direction within circular ring nonlinear optical waveguide  1402  are illustrated by arrow  1420 , arrow  1422 , arrow  1424 , arrow  1426 , and arrow  1428 . A propagation angle of zero degrees for arrow  1420  corresponds to travel along the +Z-axis of the lithium niobate material. TE polarized light at this propagation angle for arrow  1420  can experience the +d 22  nonlinear optical coefficient. A propagation angle of 90 degrees for arrow  1424  corresponds to travel along the minus Y-axis of the x-cut lithium niobate material. TE polarized light at this propagation angle for arrow  1424  can experience the +d 33  nonlinear optical coefficient. 
     In this depicted example, TE polarized light at a propagation angle of 180 degrees for arrow  1426  can travel along the −Z-axis of the x-cut lithium niobate material and can experience the −d22 nonlinear optical coefficient. In a similar fashion, TE polarized light at a propagation angle of 270 degrees for arrow  1428  can travel along the +Y axis of the x-cut lithium niobate material and can experience the −d33 nonlinear optical coefficient. 
     Light traveling around the ring at an intermediate propagation angle θ, such as 45 degrees for arrow  1422 , can experience a combination of the d 33 , d 31 , and d 22  nonlinear optical coefficients. For example, the propagation-angle dependent nonlinear optical coefficient d eff  can be described by the expression: 
     
       
         
           
             
               d 
               eff 
             
             = 
             
               
                 
                   + 
                   
                     d 
                     
                       2 
                       ⁢ 
                       2 
                     
                   
                 
                 ⁢ 
                 
                   cos 
                   3 
                 
                 ⁢ 
                 θ 
               
               + 
               
                 3 
                 ⁢ 
                 
                   d 
                   
                     3 
                     ⁢ 
                     1 
                   
                 
                 ⁢ 
                 
                   cos 
                   2 
                 
                 ⁢ 
                 θ 
                 ⁢ 
                 sin 
                 ⁢ 
                 θ 
               
               + 
               
                 
                   d 
                   
                     3 
                     ⁢ 
                     3 
                   
                 
                 ⁢ 
                 
                   sin 
                   3 
                 
                 ⁢ 
                 θ 
               
             
           
         
       
     
     TE polarized light propagating at different angles also can experience different values of the material refractive index. For the x-cut lithium niobate material, the material refractive index varies between the extra-ordinary index experienced by light traveling at propagation angles of 90 degrees and 270 degrees to the ordinary index experienced by light traveling at propagation angles of 0 degrees and 180 degrees. 
     Turning next to  FIG. 15 , an illustration of a graph of phase matching conditions that vary with a propagation angle is depicted in accordance with an illustrative embodiment. In this depicted example, graph  1500  illustrates the coherent interaction distance obtained at different propagation angles around circular ring nonlinear optical waveguide  1402  in  FIG. 14  and the dependence on the strip width of circular ring nonlinear optical waveguide  1402  in  FIG. 14 . As depicted, y-axis  1502  is the equivalent coherent interaction distance in millimeters, and x-axis  1504  is strip width in micrometers. 
     In graph  1500 , phase matching conditions vary with propagation angle around the circular path of the nonlinear optical waveguide. In this illustrative example, line  1510  shows the equivalent coherent interaction distance for light propagating in the +Z direction in a nonlinear optical waveguide having the cross-section of circular ring nonlinear optical waveguide  1402  in  FIG. 14 . For propagation in this direction, which is equivalent to an angle of 0-degrees relative to the +Z axis, the light of the three wavelengths experience the ordinary refractive index, n_ord, of lithium niobate. Line  1506  shows the equivalent coherent interaction distance for light propagating in the −Y direction in a nonlinear optical waveguide having the cross-section of circular ring nonlinear optical waveguide  1402  in  FIG. 14 . For propagation in this direction, which is equivalent to an angle of 90-degrees relative to the +Z axis, the light of the three wavelengths experience the extra-ordinary refractive index, n_ext, of lithium niobate. Line  1508  shows the equivalent coherent interaction distance for light propagating in a direction equivalent to a 45-degree angle relative to the +Z axis, as depicted in  FIG. 14 . For propagation in this direction, the light of the three wavelengths experience a combination of the ordinary index and the extra-ordinary index of lithium niobate. Other materials in the waveguide structure such as silicon nitride and silicon dioxide are isotropic and the refractive index of those materials do not change with the direction of propagation of the light. 
     With the varying material refractive index, the equivalent coherent interaction distance that is obtained for a given value of the waveguide width can be different if the light were traveling in a straight waveguide at the angles of 0 degrees, 45 degrees, or 90 degrees, relative to the +Z axis of the x-cut lithium niobate. 
     The coherent interaction distance obtained for a given waveguide cross-section design can vary with the propagation angle, as illustrated in graph  1500 . When the coherent interaction distance is longer, the additional phase walk-off contributed at that propagation angle is smaller. Conversely, when the coherent interaction distance is shorter, the additional phase walk-off is greater. 
     With reference now to  FIGS. 16-21 , illustrations of graphs illustrating a nonlinear optical coefficient, an accumulated phase walk-off, a nonlinear optical generation, and an accumulated nonlinear optical generation at different accumulated propagation angles around a nonlinear optical waveguide having a shape of a circular ring are depicted in accordance with illustrative embodiments. In this example, the circular ring nonlinear optical waveguide can be, for example, circular ring nonlinear optical waveguide  1402  in  FIG. 14 . 
     In  FIG. 16 , illustrations of graphs illustrating the incremental generation by spontaneous parametric down conversion (SPDC) relative to an accumulated phase walk-off are depicted in accordance with an illustrative embodiment. As depicted, graph  1600  illustrates incremental photon generation rate or generated power from spontaneous parametric down (conversion (SPDC). 
     In this illustrative example, y-axis  1602  is a normalized incremental spontaneous parametric down (SPDC) generation in power or photons/sec, and x-axis  1604  is an angle propagated in degrees in graph  1600 . Line  1606  in graph  1600  represents incremental spontaneous parametric down conversion (SPDC) generation as light travels within a circular ring nonlinear optical waveguide. 
     As illustrated, graph  1620  shows accumulated phase walk-off in accordance with an illustrative embodiment. In this illustrative example, y-axis  1622  is accumulated phase walk-off in radians, and x-axis  1624  is an angle propagated in degrees. Line  1626  in graph  1620  represents accumulated phase walk-off as light travels within circular ring nonlinear optical waveguide  1402  in  FIG. 14 . 
     In anisotropic material such as the x-cut lithium niobate material, the refractive index of the material can vary with the direction of the light propagation. Since the material refractive index changes, the refractive index of the wave-guided mode also can change with the propagation direction, and the propagation constant or wave vector also changes with the propagation direction. Thus, the propagation-constant mismatch or wave vector mismatch Δk also can change as the propagation direction changes. As a result, the accumulated phase walk-off exhibits a somewhat oscillatory behavior with respect to the angle propagated. In this depicted example, the propagation angles corresponding to successive half-cycles are indicated by line  1610 , line  1612 , and line  1614 . The ring circumference of circular ring nonlinear optical waveguide  1402  in  FIG. 14  can be set equal to twice the equivalent coherent interaction distance for a round trip around the ring. 
     In this depicted example, accumulated phase walk-off represented by line  1626  equals a multiple of π radians after every half-cycle of travel around circular ring nonlinear optical waveguide  1402 . 
     In  FIG. 17 , illustrations of graphs illustrating a value of a nonlinear optical coefficient relative to an accumulated phase walk-off is depicted in accordance with an illustrative embodiment. As depicted, graph  1700  illustrates the sign of an optical nonlinear coefficient reversing for light traveling through circular ring nonlinear optical waveguide  1402  in  FIG. 14 . 
     In this illustrative example, y-axis  1702  is nonlinear optical coefficient (D eff ) in pm/V, and x-axis  1704  is angle propagated in degrees. Line  1706  represents a value of the nonlinear optical coefficient (D eff ) as light travels within circular ring nonlinear optical waveguide  1402 . 
     In this figure, graph  1720  depicts an accumulated phase walk-off in accordance with an illustrative embodiment. In this illustrative example, y-axis  1722  is accumulated phase walk-off in radians, and x-axis  1724  is angle propagated in degrees. Line  1726  represents accumulated phase walk-off as light travels within a circular ring nonlinear optical waveguide. 
     In the illustrative example, circular ring nonlinear optical waveguide  1402  in  FIG. 14  can be a directional phase matching waveguide structure designed such that the magnitude of the nonlinear optical coefficient indicated by line  1706  in graph  1700  is larger at those propagation angles for which the accumulated phase walk-off is closer to an odd multiple of π/2 radians, as illustrated by line  1726  in graph  1720 . 
     As depicted, line  1606  in  FIG. 16  indicates that a greatest nonlinear optical generation can occur at propagation angles for which the nonlinear optical coefficient has larger magnitude as shown by line  1706  in  FIG. 17  and the net phase walk-off is approximately an odd multiple of π/2 radians as shown in graph  1720  in  FIG. 17 . Comparatively low nonlinear optical generation occurs at those propagation angles for which the net phase walk-off is a multiple of π radians as can be seen as being high at angle of 100 degrees in line  1606  in  FIG. 16  as compared to being low at an angle 180 degrees in line  1606 . Also, with circular ring nonlinear optical waveguide  1402  in  FIG. 14 , the changes in the phase walk-off are greatest when small incremental spontaneous parametric down conversion generation is present as seen in line  1606  in graph  1600  in  FIG. 16 . 
     In this depicted example, line  1706  in graph  1700  in  FIG. 17  shows that the sign of the nonlinear optical coefficient reverses after each half cycle (or 180 degrees) of travel around the circular ring nonlinear optical waveguide. Thus, the reversals in the sign of the nonlinear optical coefficient can match the change in the net sign of the interaction between the optical fields and the nonlinear optical material polarization due to the phase walk-off. For spontaneous parametric down conversion, both a signal photon and an idler photon can be generated from the interaction of a pump photon with the nonlinear optical material. 
     In the illustrative example, it is also desirable to have a magnitude of the second order nonlinear coefficient to be a peak when the factor for the phase walk-off is one. In this illustrative example, the factor for phase walk-off is one at an odd multiple of 180 degrees or π/2. As can be seen in  FIG. 17 , line  1706  has a peak magnitude can be seen, for example, at point  1710  and point  1712 . This can be compared to the accumulated phase walk-off at point  1714  and point  1716 . The alignment of the peaks in line  1706  with the odd multiples of 180 degrees or π/2 for phase walk-off in line  1726  can provide a desired level of light generation. For a suitably designed direction-reversal enhanced coherent interaction nonlinear optical waveguide, each increment in a spontaneous parametric down conversion generation process can add to the total power in the signal or idler in a coherent manner, as illustrated in  FIG. 18 . 
     With reference now to  FIG. 18 , an illustration of graphs illustrating normalized net spontaneous parametric down conversion generation rates relative to normalized incremental spontaneous parametric down conversion generation rates is depicted in accordance with an illustrative embodiment. 
     As depicted, graph  1800  illustrates a normalized incremental spontaneous parametric down conversion (SPDC) generation rate. In this illustrative example, y-axis  1802  is normalized incremental spontaneous parametric down conversion (SPDC) generation rate in power or photons/sec, and x-axis  1804  is angle propagated in degrees. Line  1806  represents the normalized incremental spontaneous parametric down conversion (SPDC) generation rate as light travels within a circular ring nonlinear optical waveguide. 
     In  FIG. 18 , graph  1820  of normalized net spontaneous parametric down conversion generation is depicted in accordance with an illustrative embodiment. In this illustrative example, y-axis  1822  is length normalized net spontaneous parametric down conversion generation rate in photons per second or power per mm, and x-axis  1824  is angle propagated in degrees. Line  1826  represents normalized net spontaneous parametric down conversion generation as light travels within a circular ring nonlinear optical waveguide. By comparing line  1826  with line  1806 , one can see that the net spontaneous parametric down conversion generation rate has larger increases at those values of travel distance, or propagated angle, for which the incremental spontaneous parametric down conversion generation rate is larger. 
     For this example, the net spontaneous parametric down conversion generation rate can decrease instead of increase for certain values of the travel distance or propagated angle. For these travel distances or propagated angles, the sign of the nonlinear optical coefficient does not match the sign of the interaction between the optical fields and the nonlinear optical material polarization due to the phase walk-off. Thus, the additional contribution to the net spontaneous parametric down conversion generation is destructive instead of constructive. 
     In the illustrative examples, the net coherent interaction length can be the distance of travel around a loop or zig-zag or serpentine path in an optical nonlinear waveguide at which the net phase walk-off equals π. If the nonlinear optical waveguide in the optical waveguide structure has the shape of a circular ring, the diameter of that ring can be equal to 2/π times the net coherent interaction distance, in one illustrative example. 
     In another illustrative example, if the nonlinear optical waveguide in the optical waveguide structure is a closed loop with a racetrack path, the circumference of the loop can be twice the net coherent interaction distance. In yet another illustrative example, if the nonlinear optical waveguide in the optical waveguide structure has a serpentine shape, each zig and each zag in this illustrative example can have a length that is equal to the net coherent interaction distance. Since the value for the material refractive index of x-cut lithium niobate varies with the propagation angle in the x-cut lithium niobate, a determination of the net coherent interaction distance can be made after the light has traveled over at least 180 degrees of propagation angle. 
     The cross-sectional dimensions of the nonlinear optical waveguide can be designed to achieve a given value for the net coherent interaction distance. Turning next to  FIG. 19 , an illustration of a graph of a net coherent interaction distance is depicted in accordance with an illustrative embodiment. In this illustrative example, graph  1900  illustrates a net coherent interaction as a function of strip width. Y-axis  1902  represents net coherent interaction distance in millimeters, and x-axis  1904  represents strip width in micrometers. Line  1906  is the net coherent interaction distance as a function of strip width. In an illustrative example, the value for the strip width can be in accordance with strip width  814  depicted in  FIG. 8 . 
     As depicted, examples of strip width used for direction reversal enhancement are shown in section  1901  and section  1903  of line  1906  in graph  1900 . An example of a strip width used for regular modal phase matching is shown in section  1905  of line  1906 . 
     In a typical chip-scale nonlinear optical waveguide, the selected net coherent interaction distance may not be the maximum achievable value. Instead, the selected net coherent interaction distance can be substantially smaller such that the physical size of the nonlinear optical waveguide can be compatible with the desired size of a photonic chip. The physical size of the structure can be, for example, the diameter of a closed loop ring or a racetrack-shaped nonlinear waveguide or the curved segment of a serpentine-shaped nonlinear waveguide. 
       FIG. 20  is an illustration of a graph of a ring diameter for a circular ring nonlinear optical waveguide depicted in accordance with an illustrative embodiment. In this illustrative example, graph  2000  illustrates a ring diameter for a circular ring nonlinear optical waveguide, such as circular ring nonlinear optical waveguide  1402  in  FIG. 14 , as a function of strip width. 
     In this illustrative example, y-axis  2002  represents the ring diameter for a circular ring nonlinear optical waveguide in micrometers, and x-axis  2004  represents strip width in micrometers. 
     In graph  2000 , line  2006  is the ring diameter as a function of strip width. Line  2006  in graph  2000  illustrates how the ring diameter can depend on the width of a core region of a nonlinear optical waveguide, such as core region  400  illustrated in  FIG. 4 . 
     A lower limit on the size of a nonlinear optical waveguide can be constrained by factors such as optical loss from having a radius of curvature that is too small. Graph  2000  illustrates a change in the diameter of circular ring nonlinear optical waveguide  1402  in  FIG. 14  that can be made to accommodate a small (e.g., ±1 nm) change in the waveguide width. 
     For example, a ±1 nm change in the width in section  2020  can result in a first ring diameter range as depicted in section  2022 . As another example, a ±1 nm change in section  2024  can result in a second ring diameter range as shown in section  2026 . The percent change in the ring diameter needed can be smaller when circular ring nonlinear optical waveguide  1402  in  FIG. 14  is used with a smaller net coherent interaction length, and thus a smaller ring diameter. 
     With a circular ring nonlinear optical waveguide, such as circular ring nonlinear optical waveguide  1402  in  FIG. 14 , a departure of the achieved net coherent interaction distance from a value that is one-half of the circular ring can reduce the number of round trips or cycles around circular ring nonlinear optical waveguide  1402  before the enhancement in total interaction distance achieved by the direction-reversal enhancement of the coherent interaction approach becomes limited. With a directional phase matching waveguide structure, the net nonlinear optical generation, such as of the signal light and idler light in a spontaneous parametric down conversion, increases with the overall interaction distance, as illustrated in  FIG. 21 . 
       FIG. 21  is an illustration of a graph of a normalized net spontaneous parametric down conversion generation depicted in accordance with an illustrative embodiment. In this illustrative example, graph  2100  illustrates a length normalized net spontaneous parametric down conversion generation rate as a function of interaction distance. 
     In this example, y-axis  2102  represents the length normalized net spontaneous parametric down conversion generation rate with units of photons per second or power per mm, and x-axis  2104  represents interaction distance in millimeters. 
     The lines in graph  2100  illustrate a normalized net spontaneous parametric down conversion generation rate as a function of interaction distance for various waveguide core widths and waveguide circumference configurations for a circular ring optical waveguide such as circular ring nonlinear optical waveguide  1402  in  FIG. 14 . 
     In this illustrative example, line  2106  is for a configuration of circular ring nonlinear optical waveguide  1402  with a width of 0.930 μm and a circumference of 226 μm; line  2108  is for a configuration of circular ring nonlinear optical waveguide  1402  with a width of 0.930 μm and a circumference of 238 μm; line  2110  is for a configuration of circular ring nonlinear optical waveguide  1402  with a width of 0.930 μm and a circumference of 236 μm; line  2112  is for a configuration of circular ring nonlinear optical waveguide  1402  with a width of 0.930 μm and a circumference of 238.6 μm; line  2114  is for a configuration of circular ring nonlinear optical waveguide  1402  with a width of 0.930 μm and a circumference of 232 μm; and line  2116  is for a configuration of circular ring nonlinear optical waveguide  1402  with a width of 0.930 μm and a circumference of 242 μm. 
     When a large enough difference between the net coherent interaction distance and one-half the circumference of a loop is present, the normalized net nonlinear optical generation reaches a maximum value and begins to decline as illustrated by line  2106  in graph  2100 . 
     With reference to  FIG. 22 , an illustration of an optical waveguide structure including a nonlinear optical waveguide with a serpentine path is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  2200  is an example of one implementation for optical waveguide structure  100  shown in block form in  FIG. 1 . 
     As depicted in this example, optical waveguide structure  2200  includes a number of different components. In this illustrative example, optical waveguide structure  2200  comprises nonlinear optical waveguide  2202 , pump input optical waveguide  2204 , output optical waveguide  2206 , idler output optical waveguide  2208 , input optical coupler  2201 , output optical coupler  2203 , and output optical coupler  2205 . As depicted, optical waveguide structure  2200  lies in an yz plane defined by z-axis  2210  and y-axis  2212 . 
     In this illustrative example, a pump input light can be input through pump input optical waveguide  2204  into nonlinear optical waveguide  2202  via input optical coupler  2201 . At least one of an input idler light or an input signal light can be supplied at end  2207  of nonlinear optical waveguide  2202 . 
     As depicted, an idler light can be extracted from idler output optical waveguide  2208 . An output signal light can be extracted from nonlinear optical waveguide  2202  at output  2209  of nonlinear optical waveguide  2202 . 
     In this depicted example, nonlinear optical waveguide  2202  has a shape in the form of a serpentine path. As depicted, nonlinear optical waveguide  2202  has a serpentine path with curved waveguide segments and without straight segments. In this illustrative example, nonlinear optical waveguide  2202  has curved segment  2220 , curved segment  2222 , curved segment  2224 , curved segment  2226 , curved segment  2228 , curved segment  2230 , curved segment  2232 , curved segment  2234 , curved segment  2236 , and curved segment  2238 . 
     As depicted, nonlinear optical waveguide  2202  is a serpentine waveguide with two zig-zag cycles. A first zig can be from location  2251  to location  2253 . A first zag can be from location  2253  to location  2255 . The first zig and the first zag form a first cycle for the zig-zag. A second zig is from location  2255  to location  2257 . A second zag is from location  2257  to location  2259 . The second zig and the second zag form a second cycle for the zig-zagging serpentine path. 
     In this depicted example, the location of input optical coupler  2201  is the location where the pump light is input from pump input optical waveguide  2204  into nonlinear optical waveguide  2202 . This location defines the start of the first zig-zag cycle. The location of output optical coupler  2203  is the location where the pump light is extracted from nonlinear optical waveguide  2202  to output optical waveguide  2206  which defines the end of the last zig-zag cycle. 
     A nonlinear optical process such as difference frequency generation and sum frequency generation can involve two input wavelengths. In this example, the input wavelength whose optical power is substantially higher than the optical power of the other input wavelength typically is considered the “pump” light. 
     Additionally, optical waveguide structure  2200  also comprises output optical coupler  2205  that is used to physically separate the two wavelengths of light that are not the pump light. 
     As used herein, the terms “portion” and “part,” as used herein, are interchangeable. For example, portions can be the curved segments. A portion can be the entire curved segment that is between two straight segments or a part of that curved segment. In the illustrative example, curved segments can be present at both ends of a straight segment in nonlinear optical waveguide  2202 . 
     In this illustrative example,  FIGS. 23-26  are graphs that illustrate the operation of nonlinear optical waveguide  2202  with a serpentine path having only curved segments, such as depicted in  FIG. 22 .  FIGS. 23  and  FIG. 24  illustrate the nonlinear optical process of spontaneous parametric down conversion that occurs in the first cycle through a serpentine structure, such as nonlinear optical waveguide  2202 . In  FIG. 23 , an illustration of a graph of real and imaginary parts of a generated field is depicted in accordance with an illustrative embodiment. As depicted, graph  2300  illustrates real and imaginary parts of the generated field as a function of interaction distance. 
     In this illustrative example, y-axis  2302  is normalized amplitude of the real and imaginary parts of a generated field, and x-axis  2304  is interaction distance in millimeters. In graph  2300 , line  2306  represents the real part of a net field, and line  2308  represents the imaginary part of a net field. The complex exponential factor in the mathematical expressions (1) and (2) discussed above can be represented as a sum of a real part and an imaginary part. 
       FIG. 24  is an illustration of graphs illustrating a phase walk-off relative to a nonlinear optical coefficient depicted in accordance with an illustrative embodiment. As illustrated, graph  2400  depicts a phase walk-off as a function of interaction distance. In this illustrative example, y-axis  2402  is phase walk-off in radians, and x-axis  2404  is interaction distance in millimeters. Line  2406  represents changes in the phase walk-off as the interaction distance increases. 
     In this figure, graph  2420  depicts the nonlinear optical coefficient as a function of interaction distance. As depicted, y-axis  2422  is the nonlinear optical coefficient in pm/V, and x-axis  2424  is interaction distance in millimeters. Line  2426  represents the change in the nonlinear optical coefficient as interaction distance increases. 
     In one example, the curved portion of nonlinear optical waveguide  2202  has a 25 μm radius of curvature. In nonlinear optical waveguide  2202 , the total nonlinear optical interaction distance after one cycle is about 0.157 mm. 
     In this depicted example, the net phase walk-off for the wave-guided optical modes at the 3 wavelengths that participate in the nonlinear optical process reaches n radians, or 180 degrees, at the halfway point of the first cycle at location  2430 , as depicted in graph  2400 . This halfway point is the end of the “zig” portion of the cycle and the start of the “zag” portion of the cycle. 
     In this illustrative example, nonlinear optical waveguide  2202  can be fabricated from x-cut lithium niobate and the zig and zag portions of a cycle can be oriented such that the nonlinear optical coefficient has primarily one sign (e.g., negative) for the zig portion of the cycle and primarily the opposite sign (e.g., positive) for the zag portion of the cycle. For the zig portion, the phase walk-off is close to −π/2 whereas for the zag portion, the phase walk-off is close to −3π/2. 
     Turning to  FIG. 25 , an illustration of a graph of a phase walk-off is depicted in accordance with an illustrative example. As depicted, graph  2500  illustrates a phase walk-off as a function of strip width for nonlinear optical waveguide  2202  in  FIG. 22 . In this illustrative example, y-axis  2502  is phase walk-off in radians, and x-axis  2504  is waveguide strip width in micrometers. In this illustrative example, the strip width shown in  FIG. 25  can be strip width  814  in nonlinear optical waveguide  800  illustrated in  FIG. 8 . 
     Line  2506  is the phase walk-off from traversing through a zig portion of nonlinear optical waveguide  2202 , and line  2508  is the phase walk-off from traversing through the combination of a zig portion and a zag portion of nonlinear optical waveguide  2202 . As shown in  FIG. 25 , the additional phase walk-off from traversing through a zig portion or through a zag portion is −3.1436 radians when the strip width is 0.884 μm for nonlinear optical waveguide  2202  in this particular example. 
     With reference to  FIG. 26 , an illustration of a graph of a normalized spontaneous parametric down conversion (SPDC) rate is depicted in accordance with an illustrative embodiment. As depicted, graph  2600  illustrates a normalized spontaneous parametric down conversion (SPDC) rate as a function of interaction distance for nonlinear optical waveguide  2202  in  FIG. 22 . In this illustrative example, y-axis  2602  is normalized spontaneous parametric down conversion (SPDC) rate in photons per second or power, and x-axis  2604  is interaction distance in millimeters. 
     The optical field generated (e.g., by the spontaneous parametric down conversion) after a given interaction distance in nonlinear optical waveguide  2202  can be described by its real and imaginary components as depicted in graph  2300  in  FIG. 23 . Graph  2300  shows that for this example, the optical field magnitude, which combines the contributions from the real and imaginary components of the optical field, increases gradually with greater interaction distance. The optical power generated, which is shown in graph  2600  in  FIG. 26 , is given by summing the squares of the real and the imaginary field components, such as those shown in lines  2306  and  2308  of graph  2300  in  FIG. 23 . A comparison of graph  2300  in  FIG. 23  and graph  2420  in  FIG. 24  shows that the greatest increases in the optical field, and in the optical power, occur when the nonlinear optical coefficient has a larger magnitude. Also, a comparison of graph  2300  in  FIG. 23  and graph  2400  in  FIG. 24  shows that the greatest increases in the optical field, and in the optical power, occur when the phase walk-off has a value close to an odd multiple of π/2 radians. The greatest increases occur when the combination of the nonlinear optical coefficient and the phase walk-off are aligned properly. 
     The different lines in graph  2600  represent the normalized spontaneous parametric down conversion rate for different strip widths and upper cladding height for nonlinear optical waveguide  2202  in  FIG. 22 . The normalized spontaneous parametric down conversion rate can be a measure of efficiency, assuming the pump power is kept constant. As depicted, line  2606  is for a strip width of 0.884 μm with an upper cladding height of 0.500 μm; line  2608  is for a strip width of 0.883 μm with an upper cladding height of 0.492 μm; and line  2610  is for a strip width of 0.883 μm with an upper cladding height of 0.500 μm. 
     For a strip width of 0.884 μm, the normalized spontaneous parametric down conversion rate achieved for an interaction distance of 1 mm is about 15, as shown by line  2606  in graph  2600 . However, the normalized spontaneous parametric down conversion rate achieved for this interaction distance is only about 4 for a strip width of 0.883 μm and the same upper cladding height, as shown by line  2610  in graph  2600 . The lower SPDC rate is associated with the differing values for the phase walk-off achieved for the two strip widths. 
     Referring back to line  2506  in graph  2500  of  FIG. 25 , the phase walk-off for a strip width of 0.883 μm is roughly 10% more negative than is the phase walk-off for a strip width of 0.884 μm. As shown in graph  2600  in  FIG. 26 , the normalized spontaneous parametric down conversion rate at the interaction distance of 1 mm is less than 5, with the maximum normalized spontaneous parametric down conversion rate being about 5. Thus, for a 10% change in the phase walk-off, the spontaneous parametric down conversion rate is reduced by a factor of 3. Whether a factor of 3 degradation in the generation rate of photons is acceptable depends on the particular implementation. Thus, whether a 10% departure from π/2 is acceptable or not depends on the implementation. 
     For a different strip width, such as 0.883 μm as illustrated in  2600  in  FIG. 26 , the phase walk-off after a zig portion departs slightly from being equal to an odd multiple of π. Thus, nonlinear optical interaction eventually is no longer coherent after a larger number of cycles and the spontaneous parametric down conversion generation reaches a maximum value and declines, as shown by the line  2610  in  FIG. 26 . 
     For the waveguide cross-sectional structure of nonlinear optical waveguide  2202  in  FIG. 22 , a compensation can be made for a change in a waveguide parameter, such as the strip width, by a corresponding change in another waveguide parameter, such as the upper cladding height. Line  2608  in  FIG. 26  shows that, for this example, changing the upper cladding height from 0.500 μm to 0.492 μm can be suitable for adjusting the effective refractive indices of the optical modes at the pump, signal, and idler wavelengths participating in the nonlinear optical process, and thus having the phase walk-off be an odd multiple of π at the end of the zig portion. 
     For the nonlinear optical process in nonlinear optical waveguide  2202  in  FIG. 22  to remain coherent over many zig and zag cycles through a serpentine waveguide, the phase walk-off after each zig portion should be an odd multiple of π and the phase walk-off after each zag portion should be a multiple of 2π. Graph  2500  in  FIG. 25  shows that this condition can be met in the present example for a strip width of 0.884 μm. Graph  2600  in  FIG. 26  shows that for a strip width of 0.884 μm, the net generation of signal light or idler light by a spontaneous parametric down conversion process does continue to increase with additional zig-zag cycles, and thus greater interaction distance. 
     In this example, when the waveguide is designed such that the sign change due to the phase walk-off and the sign change of the second order nonlinear coefficient are aligned in a desired manner, the results are like those shown in line  2608  and line  2606 . 
     If a level of alignment is not as great, then the result shown in line  2610  can occur. However, the results in line  2610  can be sufficient in some implementations made in accordance with an illustrative example. In other words, the perfect or exact alignment is not necessary to obtain desired light generation. In other words, the amount of alignment depends on the amount of light generation desired. 
     Turning now to  FIG. 27 , an illustration of an optical waveguide structure including a nonlinear optical waveguide with a serpentine path is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  2700  is an example of one implementation for optical waveguide structure  100  shown in block form in  FIG. 1 . 
     As depicted in this example, optical waveguide structure  2700  includes a number of different components. In this illustrative example, optical waveguide structure  2700  includes nonlinear optical waveguide  2702 , pump input optical waveguide  2704 , pump removal optical waveguide  2706 , idler output optical waveguide  2708 , input optical coupler  2701 , output optical coupler  2703 , and output optical coupler  2705 . As depicted, optical waveguide structure  2700  lies in an yz plane defined by z-axis  2710  and y-axis  2712 . 
     In this illustrative example, a pump input light can be input through pump input optical waveguide  2704 . At least one of an input idler light or an input signal light can be supplied at end  2707  of nonlinear optical waveguide  2702 . 
     As depicted, an idler light can be extracted from idler output optical waveguide  2708 . An output signal light can be extracted from nonlinear optical waveguide  2702  at end  2709  of nonlinear optical waveguide  2702 . 
     Nonlinear optical waveguide  2702  has a serpentine path that has straight segments in addition to curved segments. In this example, nonlinear optical waveguide  2702  has curved segment  2721 , straight segment  2720 , curved segment  2722 , curved segment  2723 , straight segment  2724 , curved segment  2725 , curved segment  2726 , straight segment  2728 , curved segment  2727 , curved segment  2730 , straight segment  2732 , curved segment  2729 , and curved segment  2734 . 
     As depicted, nonlinear optical waveguide  2702  has two cycles of zigs and zags. For a structure that has both straight and curved segments, the relative contributions of straight segment  2724  and the two curved segments, curved segment  2733  and curved segment  2725  on either side of straight segment  2724 , in a zig can be considered. Additionally, the relative contributions of straight segment  2728  and the two curved segments, curved segment  2726  and curved segment  2727  on either side of straight segment  2728  in a zag can be considered. 
     Turning to  FIG. 28 , an illustration of a graph of a phase walk-off is depicted in accordance with an illustrative embodiment. As depicted, graph  2800  illustrates a phase walk-off as a function of strip width for nonlinear optical waveguide  2702  in  FIG. 27 . The strip width for this illustrative example can be as defined by strip width  814  in nonlinear optical waveguide  800  depicted in  FIG. 8 . In this illustrative example, y-axis  2802  is phase walk-off in radians, and x-axis  2804  is strip width in micrometers. Line  2806  is the phase walk-off for a straight segment in nonlinear optical waveguide  2702  in  FIG. 27 , and line  2808  is the phase walk-off for a curved segment in nonlinear optical waveguide  2702  in  FIG. 27 . In this depicted example, a straight segment has a length of about 100 μm. In this example, the curved segments include the two portions of curved segments that are on either end of a straight segment of a zig or of a zag. 
     For this example, the contribution to the phase walk-off from the curved segments in a zig (or a zag) is shown by line  2808  in graph  2800 . This contribution can vary with the parameters of the waveguide cross-section structure, such as strip width. 
     The phase walk-off due to the straight segment can depend on the waveguide cross-sectional structure and on the length of that straight segment. For the example, line  2806  in graph  2800  represents the contribution from a straight segment of 100 μm length. Line  2806  becomes steeper as the length of the straight segment is made larger. 
     Thus, for a given strip width, one can choose a length for the straight segment at which the net phase walk-off due to both the curved and straight segments of a zig is an odd multiple of π, and can be either +π or −π. The following examples illustrate considerations and trade-offs that can be made when choosing a waveguide cross-sectional dimensional parameter, such as strip width, and when choosing the straight segment length. 
     In an illustrative example, the phase walk-off in the curved segments in nonlinear optical waveguide  2702  in  FIG. 27  can be chosen to have a value that is close to the desired odd multiple of π/2. An example of this condition is illustrated in  FIGS. 29 and 30 . 
     Before turning to  FIGS. 29 and 30 , consider graph  2800  in  FIG. 28 . Line  2808  of this graph indicates that the phase walk-off from the curved segments of a zig can be approximately −π radians when the strip width is 0.884 μm. Thus, to have the net phase walk-off due to the combination of both the curved segments and a straight segment be an odd multiple of π radians, one would want the straight segment to contribute a phase walk-off that is zero or is an even multiple of π radians. Line  2806  in graph  2800  is for a straight segment length of 100 μm. For a strip width of 0.884 μm, this straight segment length gives an additional phase walk-off that is greater than 2π and is approaching 3π radians. Thus, the desired condition for direction phase matching can be achieved with a shorter straight segment length. 
     Turning to  FIG. 29 , an illustration of a graph of a phase walk-off is depicted in accordance with an illustrative embodiment. As depicted, graph  2900  illustrates a phase walk-off as a function of strip width for nonlinear optical waveguide  2702  in  FIG. 27 . In this illustrative example, y-axis  2902  is phase walk-off in radians, and x-axis  2904  is strip width in micrometers. 
     In graph  2900 , line  2906  is the phase walk-off for a straight segment in nonlinear optical waveguide  2702 , and line  2908  is phase walk-off for a curved segment in nonlinear optical waveguide  2702 . In this depicted example, nonlinear optical waveguide  2702  in  FIG. 27  has an upper cladding height of 0.50 μm. For graph  2900  in  FIG. 29 , the straight segment has a length of 75.44 μm, which was chosen so that the contribution to the phase walk-off from the straight segment would be +2π radians when the strip width is 0884 μm and for an upper cladding height of 0.50 μm. 
     Turning now to  FIG. 30 , an illustration of graphs illustrating a phase walk-off relative to a nonlinear optical coefficient and relative to a normalized spontaneous parametric down conversion (SPDC) rate is depicted in accordance with an illustrative embodiment. As illustrated, graph  3000  depicts a phase walk-off as a function of interaction distance. In this illustrative example, y-axis  3002  is phase walk-off in radians, and x-axis  3004  is interaction distance in millimeters. Line  3006  represents accumulated phase walk-off as the interaction distance increases. Line  3008  represents incremental phase walk-off as the interaction distance increases. 
     In  FIG. 30 , graph  3020  depicts the nonlinear optical coefficient as a function of interaction distance. As depicted, y-axis  3022  is the nonlinear optical coefficient in pm/V, and x-axis  3024  is interaction distance in millimeters. Line  3026  represents the change in the nonlinear optical coefficient as interaction distance increases. 
     The results shown in  FIG. 30  are for a waveguide with a straight segment length of 75.44 μm. For this length of the straight segment, the net phase walk-off due to the contributions of both the curved segments and the straight segment of a zig is +π radians when the strip width is 0.884 μm. This value for the net phase walk-off can be obtained by adding the contributions indicated by lines  2906  and  2908  in graph  2900  of  FIG. 29 . 
     Graph  3000  in  FIG. 30  shows that the accumulated phase walk-off does equal +π radians at the end of the zig portion of the serpentine waveguide structure. For this illustrative example, the end of the zig corresponds to an interaction distance slightly larger than 0.15 mm and is indicated by the dashed vertical line that extends through graphs  3000  and  3020 . Also, at the end of a combination of a zig and a zag, the accumulated phase walk-off equals +2π radians. 
     For this illustrative example, line  3008  in graph  3000  shows that the incremental phase walk-off for the straight segment has a value that is not zero. As a result, the accumulated phase walk-off has a large change as the interaction distance increases while the light traverses the straight segment. In fact, the accumulated phase walk-off changes from a value of approximately −π/2 radians to a value of approximately +3π/2 radians. 
     Graph  3040  of  FIG. 30  depicts the normalized spontaneous parametric down conversion generation rate as a function of interaction distance. As depicted, y-axis  3042  is normalized spontaneous parametric down conversion generation rate in photons per second or power, and x-axis  3044  is interaction distance in millimeters. Line  3046  represents the change in the spontaneous parametric down conversion generation rate as the interaction distance increases. Since the phase walk-off that occurs in each of the straight segments exceeds 180 degrees and equals 360 degrees, the contribution to the spontaneous parametric down conversion generation of light from a first portion of a straight segment would be cancelled by the contribution from a second portion of the straight segment. As a result, the only overall increase in the spontaneous parametric down conversion generation rate is from the curved segments of the zig and zag portions of this exemplary serpentine waveguide. Nevertheless, the spontaneous parametric down conversion generation rate does become higher and higher for more and more zig-zag cycles through the serpentine waveguide. 
     With reference to  FIG. 31 , an illustration of a graph of a normalized spontaneous parametric down conversion (SPDC) rate is depicted in accordance with an illustrative embodiment. As depicted, graph  3100  illustrates a normalized spontaneous parametric down conversion rate as a function of interaction distance for nonlinear optical waveguide  2702  in  FIG. 27 . In this illustrative example, y-axis  3102  is normalized spontaneous parametric down conversion (SPDC) rate, and x-axis  3104  is the interaction distance in millimeters. 
     The different lines in graph  3100  represent the normalized spontaneous parametric down conversion rate for different strip widths for nonlinear optical waveguide  2702  in  FIG. 27 . The spontaneous parametric down conversion rates obtained for 10 zig plus zag cycles through the serpentine shape of nonlinear optical waveguide  2702  are shown in these lines. As depicted, line  3106  is for a strip width of 0.884 μm with an upper cladding height of 0.499 μm; line  3108  is for a strip width of 0.883 μm with an upper cladding height of 0.492 μm; line  3110  is for a strip width of 0.883 μm with an upper cladding height of 0.496 μm; and line  3112  is for a strip width of 0.885 μm with an upper cladding height of 0.506 μm. Thus, for each value of the strip width, there is a different value for the upper cladding height that results in a higher spontaneous parametric down conversion generation rate. For those examples having a more optimal choice of waveguide parameters, such as indicated by line  3106 , line  3108 , and line  3112 , the normalized spontaneous parametric down conversion generation rate continues to increase as the number of zig-zag cycles and thus the overall interaction distance increases. 
     Similar to nonlinear optical waveguide  2202  in  FIG. 22  with only curved segments, the serpentine path in nonlinear optical waveguide  2702  in  FIG. 27  with both curved and straight segments can have one of its cross-sectional waveguide parameters adjusted to compensate for a change in another cross-sectional waveguide parameter. 
     As depicted in graph  3100  in  FIG. 31 , adjustments can be made to an upper cladding height. In graph  3100 , a combination of a strip width and an upper cladding height can be optimized to obtain a net spontaneous parametric down conversion generation that continues to be coherent over many zig-zag cycles and to have desired levels of spontaneous parametric down conversion photon-generation rates, or spontaneous parametric down conversion efficiency. For example, the spontaneous parametric down conversion efficiency is improved for a waveguide with strip width of 0.883 μm by changing the upper cladding height from 0.496 μm to 0.492 μm, as illustrated by comparing lines  3110  and  3108  in graph  3100 . 
     In the illustrative example, a determination can be made as to whether the phase walk-off is sufficiently close. This determination can be made using the value for the normalized spontaneous parametric down conversion rate obtained for that phase walk-off and whether that normalized spontaneous parametric down conversion rate is considered to be acceptable in a particular implementation. As a result, a value for the phase walk-off can be sufficiently close, but another value for the phase walk-off can be even closer. 
     In the depicted example, the straight segment in nonlinear optical waveguide  2702  can produce a large change in the phase walk-off. Graph  2800  in  FIG. 28  also shows that the waveguide parameters can be chosen such that the phase walk-off due to the straight segments can be quite small as compared to the phase walk-off due to the curved segments of a zig or a zag. As depicted in graph  2800 , this regime of operation occurs when the strip width is approximately 0.859 μm. The phase walk-off due to the curved segments is not equal to +π or to −π in graph  2800 . However, the phase walk-off can still be close to being an odd multiple of π, such as −3π. 
     Turning next to  FIG. 32 , an illustration of a graph of a phase walk-off is depicted in accordance with an illustrative embodiment. As depicted, graph  3200  illustrates a phase walk-off as a function of interaction distance for nonlinear optical waveguide having a serpentine path, such as nonlinear optical waveguide  2702  in  FIG. 27 . In this illustrative example, y-axis  3202  is phase walk-off in radians, and x-axis  3204  is interaction distance in millimeters. 
     The different lines in graph  3200  represent a phase walk-off for different waveguide strip widths and for different lengths of straight segments in a nonlinear optical waveguide. As depicted, line  3206  depicts an incremental phase walk-off for a strip width of 0.884 μm with a straight segment length of 75.44 μm; line  3208  depicts an accumulated phase walk-off for a strip width of 0.884 μm with a line segment length of 75.44 μm; line  3210  depicts an incremental phase walk-off for a strip width of 0.859 μm with a line segment length of 631.7 μm; and line  3212  depicts an accumulated phase walk-off for a strip width of 0.859 μm with a line segment length of 631.7 μm. The data plotted in lines  3206  and  3208  of graph  3200  is the same as the data plotted in lines  3006  and  3008  of graph  3000  in  FIG. 30 . 
     In this depicted example, line  3210  and line  3212  in graph  3200  show the phase walk-off obtained for the first zig-zag cycle of a nonlinear optical waveguide having a serpentine path with a straight segment having a strip width of 0.859 μm and curved segments with 25 μm radius of curvature. The length of the straight segment in this example is 631.7 μm and can be selected to achieve a net phase walk-off at the end of the zig portion that is nearly exactly −3π radians. This phase walk-off is due solely to the curved segments of the zig portion. As illustrated by line  3210 , the incremental phase walk-off for the straight segment of the zig portion, and also for the straight segment of the zag portion, is almost exactly zero. 
     The phase walk-off in the straight segment of nonlinear optical waveguide  2702  in  FIG. 27  having a serpentine path with a strip width of 0.859 μm is much smaller than 180 degrees. The 631.7 μm length of this straight segment is much smaller than the coherent interaction length, ˜4,457 μm, for that straight nonlinear optical waveguide. 
     As a result, the spontaneous parametric down conversion increases as the square of the interaction distance in the straight segment, as depicted in  FIG. 33 . In the illustrative example,  FIG. 33  is an illustration of a graph of a normalized spontaneous parametric down conversion rate depicted in accordance with an illustrative embodiment. As depicted, graph  3300  illustrates a normalized spontaneous parametric down conversion rate as a function of interaction distance for a nonlinear optical waveguide having a serpentine path, such as nonlinear optical waveguide  2702  in  FIG. 27 . In this illustrative example, y-axis  3302  is normalized spontaneous parametric down conversion rate in photons per second or in a unit of power such as Watts, and x-axis  3304  is the interaction distance in millimeters. 
     The different lines in graph  3300  represent normalized spontaneous parametric down conversion rates for different waveguide strip widths and different lengths for the straight segments in a serpentine nonlinear optical waveguide. As depicted, line  3306  depicts a normalized spontaneous parametric down conversion rate for a strip width of 0.884 μm with a line segment length of 75.44 μm; and line  3308  depicts a normalized spontaneous parametric down conversion rate for a strip width of 0.859 μm with a line segment length of 631.7 μm. 
     Each straight segment in nonlinear optical waveguide  2702  in  FIG. 27  essentially can act like a nonlinear optical waveguide with close-to-perfect modal phase matching. The directional phase matching allows successive zig and zag segments to function substantially like one longer waveguide having their combined lengths, as also depicted in graph  3300  in  FIG. 33 . 
     Direction-reversal enhanced coherent interaction allows the overall interaction distance in a serpentine waveguide, such as nonlinear optical waveguide  2702  in  FIG. 27 , to be much larger than the coherent interaction length of the straight waveguide segment. This enhancement of the interaction distance is a result of the resetting of the phase walk-off to exactly a multiple of 2π after each cycle due to the combined phase walk-offs of the curved segments and the straight segments of a cycle. 
     Turning next to  FIG. 34 , an illustration of a graph of a normalized spontaneous parametric down conversion rate is depicted in accordance with an illustrative embodiment. As depicted, graph  3400  illustrates a normalized spontaneous parametric down conversion rate as a function of interaction distance for a nonlinear optical waveguide having a serpentine path, such as nonlinear optical waveguide  2702  in  FIG. 27 . In this illustrative example, y-axis  3402  is normalized spontaneous parametric down conversion rate in photons per second or in a unit of power such as Watts, and x-axis  3404  is the interaction distance in millimeters. 
     Line  3406  in graph  3400  represents the normalized spontaneous parametric down conversion rate in a nonlinear optical waveguide for a strip width of 0.859 μm with a line segment length of 631.7 μm. 
     In  FIG. 34 , the normalized spontaneous parametric down conversion photon-generation rate (or efficiency) that is obtained after 10 zig-zag cycles is shown. This spontaneous parametric down conversion generation rate is more than 18 times higher than the maximum spontaneous parametric down conversion generation rate for a single straight nonlinear optical waveguide with a 0.859 μm strip width. 
     Thus, the result shown in graph  3400  illustrates a benefit of using a nonlinear optical waveguide with directional phase matching that occurs from direction-reversal enhanced coherent interaction as compared to a waveguide that uses only modal phase matching. 
     Other components in an optical waveguide structure having directional phase matching include optical couplers. Optical couplers can be present between a nonlinear optical waveguide and the input and output optical waveguides used with a nonlinear optical waveguide. 
     For example, an optical coupler can be used to couple a pump input optical waveguide to a nonlinear optical waveguide. For example, input optical coupler  601  can be used to couple pump light from pump input optical waveguide  604  to nonlinear optical waveguide  602  in  FIG. 6 . In this example, input optical coupler  601  can couple the pump light into the nonlinear optical waveguide  602 . As another example, the output optical coupler  603  can be configured to couple only the pump light and not couple the signal light and the idler light from nonlinear optical waveguide  602  out to output optical waveguide  606 . 
     Turning next to  FIG. 35 , an illustration of optical couplers used to couple a pump input optical waveguide to a nonlinear optical waveguide and output light from the nonlinear optical waveguide to an output optical waveguide is depicted in accordance with an illustrative embodiment.  FIG. 35  depicts a cross-sectional top view of waveguide structures as taken by a plane that intersects through core regions of both nonlinear optical waveguide  3502 , input optical waveguide  3504 , and output optical waveguide  3507  with the structure viewed from above (perpendicular to that plane). 
     In this illustrative example, input optical coupler  3500  is defined by region  3501  in this figure. As depicted, input optical coupler  3500  lies on an yz plane defined by z-axis  3513  and y-axis  3514 . Input optical coupler  3500  is formed by a portion of nonlinear optical waveguide  3502  and a portion of input optical waveguide  3504 . In this example, input optical coupler  3500  is indicated by the portions of these two waveguides that are within region  3501 . 
     As depicted, output optical coupler  3503  is defined by region  3505  in this figure. As depicted, output optical coupler  3503  lies on an yz plane defined by z-axis  3513  and y-axis  3514 . Output optical coupler  3503  is formed by a portion of nonlinear optical waveguide  3502  and a portion of output optical waveguide  3507 . In this example, output optical coupler  3503  is indicated by the portions of these two waveguides that are within region  3505 . As depicted, nonlinear optical waveguide  3502  has a circular configuration with radius  3523 , which is 100 μm in this example. In this illustrative example, nonlinear optical waveguide  3502  has a waveguide core region that is comprised of ring  3510 , ring  3516 , and ring  3512 . Ring  3510  is comprised of silicon nitride (SiNx) and has a width of 0.9 μm; ring  3516  is comprised of lithium niobate (LN) and has a width of 0.3 μm; and ring  3512  is comprised of silicon nitride (SiNx) and has a width of 0.9 μm. 
     Input optical waveguide  3504  has core region  3511  comprised of silicon nitride (SiNx). For input optical coupler  3500 , core region  3511  of input optical waveguide  3504  and core region comprising portions of ring  3512 , ring  3516 , and ring  3510  of nonlinear optical waveguide  3502  are separated by gap  3515 . Nonlinear optical waveguide  3502  and input optical waveguide  3504  share the same cladding material in gap  3515 . 
     Output optical waveguide  3507  has core region  3521  comprised of silicon nitride (SiNx). For output optical coupler  3503 , core region  3521  of output optical waveguide  3507  and core region comprising portions of ring  3612 , ring  3516 , and ring  3510  of nonlinear optical waveguide  3502  are separated by gap  3525 . Nonlinear optical waveguide  3502  and output optical waveguide  3507  share the same cladding material in gap  3525 . In this illustrative example, gap  3525  can be a different distance from gap  3515 . In other words, the distance feature can depend on the particular characteristics desired for coupling light. 
     The cross-sectional illustration of nonlinear optical waveguide  800  depicted in  FIG. 8  can represent a cross-sectional side view of a portion of nonlinear optical waveguide  3502  in input optical coupler  3500  in  FIG. 35 . In input optical coupler  3500 , a part of the core region comprising parts of ring  3510 , ring  3516 , and ring  3512  can be represented by side region  810 , central region  804 , and side region  812  in  FIG. 8 . A part of upper cladding  808  can be located between these regions and core region  3511  of input optical waveguide  3504 . The core regions of both nonlinear optical waveguide  3502  and input optical waveguide  3504  can be located above lower cladding  806  in  FIG. 8 . 
     The coupling of light between nonlinear optical waveguide  3502  and input optical waveguide  3504  can depend on the cross-sectional dimensions of their core regions in input optical coupler  3500 , on the size or width of gap  3515 , and on the overall length of input optical coupler  3500 . In a general optical coupler, these dimensions can vary along the length direction of the optical coupler. 
     In this illustrative example, input optical coupler  3500  can couple pump light between input optical waveguide  3504  and nonlinear optical waveguide  3502 . The pump light has a wavelength of 655 nm. 
     With reference now to  FIG. 36 , an illustration of a graph of a pump light transmission is depicted in accordance with an illustrative embodiment. As depicted, graph  3600  illustrates a pump light transmission as a function of the size or width of gap  3515  between the core region of nonlinear optical waveguide  2702  and the core region of pump input optical waveguide  2704  in  FIG. 27  operating as a pump input optical waveguide. In this illustrative example, y-axis  3602  is pump light transmittance or normalized transmission, which has a maximum value of 1, and x-axis  3604  is the gap size in micrometers. 
     Line  3606  in graph  3600  represents the transmittance or normalized power coupling of pump light, having a wavelength of 655 nm, from input optical waveguide  3504  to nonlinear optical waveguide  3502  in  FIG. 35 . Since an optical coupler is a reciprocal device, line  3606  can also represent the transmittance of pump light from the nonlinear optical waveguide  3502  back to the input optical waveguide  3504  in  FIG. 35 . 
     As depicted, input optical coupler  3500  couples 655 nm light that is in the fundamental TE 11  mode of input optical waveguide  3504  when configured as a pump input optical waveguide into the TE 31  mode of nonlinear optical waveguide  3502 . In some implementations, input optical coupler  3500  can provide coupling such that as much pump power from input optical waveguide  3504  operating as a pump input optical waveguide is supplied into nonlinear optical waveguide  3502  as is lost from nonlinear optical waveguide  3502 . Power can be lost by mechanisms such as absorption, scattering, and nonlinear optical frequency conversion. The amount of pump light coupled (or transmitted) into nonlinear optical waveguide  3502  depends on the width of the gap between input optical waveguide  3504  configured to operate as a pump input optical waveguide and nonlinear optical waveguide  3502 , as illustrated in  FIG. 36 . 
     Input optical waveguide  3504  comprises a material with a nonlinear optical coefficient that is small compared to the nonlinear optical coefficient of the nonlinear optical material in nonlinear optical waveguide  3502 . Thus, the nonlinear optical interaction that generates at least one of an idler light or a signal light from the pump light occurs only in nonlinear optical waveguide  3502  and does not occur in input optical waveguide  3504 . An example of a material with a weak nonlinear optical coefficient is silicon nitride or aluminum oxide. In comparison, the center region of the core region of nonlinear optical waveguide  3502  can comprise lithium niobate, which has a much larger nonlinear optical coefficient. The constraints on the optical coupler for the output waveguide of a nonlinear optical waveguide structure can depend on whether that nonlinear optical waveguide structure has a closed loop configuration, such as the circular ring illustrated in  FIG. 14  or the racetrack-shaped ring illustrated in  FIG. 7 , or has an open configuration, such as the serpentine waveguide illustrated in  FIG. 6 . 
     With reference now to  FIG. 37 , an illustration of a graph of an output light transmission is depicted in accordance with an illustrative embodiment. As depicted, graph  3700  illustrates an output light transmission as a function of gap size or width of output optical waveguide  3507  in  FIG. 35 . In this illustrative example, y-axis  3702  is normalized idler light transmittance, and x-axis  3704  is the gap size in micrometers. 
     Line  3706  in graph  3700  represents the transmittance of an output light of 1558 nm wavelength from an optical coupler. In this example, input optical coupler  3500  in  FIG. 35  couples a circular ring nonlinear optical waveguide having a 100 μm radius, such as nonlinear optical waveguide  3502  illustrated in  FIG. 35  to an output optical waveguide. For this illustrative example, output optical waveguide  3507  can be an output optical waveguide with core region  3521  comprising silicon nitride, like core region  3511  of input optical waveguide  3504 , but having a different width than that of output optical waveguide  3507 . Core region  3521  of output optical waveguide  3507  is separated from ring  3512  of nonlinear optical waveguide  3502  by gap  3525 . 
     The output light coupled by input optical coupler  3500  can be at least one of a 1558 nm idler light or a 1130 nm signal light. Line  3706  in graph  3700  illustrates that the coupling of the light at a 1558 nm wavelength by this exemplary optical coupler becomes weaker in an exponential manner as the gap size is increased. 
     When the nonlinear optical waveguide structure has a closed-loop configuration, output optical coupler  3503  can extract a percentage of the signal light or the idler light from nonlinear optical waveguide  3502  having a ring-shape and into output optical waveguide  3506 , and leave the rest of the signal light or the idler light to continue propagating in the closed-loop or ring-shape of nonlinear optical waveguide  3502 . 
     In the illustrative example, the amount of light output optical coupler  3503  is designed to leave in the ring-shape of nonlinear optical waveguide  3502  depends on the desired optical loss limited propagation distance in the nonlinear optical waveguide  3502 . That loss-limited interaction distance can be approximately equal to the interaction distance limited by the accuracy with which the phase walk-off is achieved as discussed with reference to  FIG. 21 . The loss of the signal light or the idler light from a ring-shaped nonlinear optical waveguide can be caused by both the coupling of the light out through the output coupler and by other loss mechanisms such as absorption and scattering of the signal light or the idler light while the signal light or the idler light circulates around the nonlinear optical waveguide. 
     The amount of light coupled can depend on what percentage of coupling is desired for a particular implementation. In an illustrative example, four optical couplers, input optical coupler  701 , input optical coupler  703 , output optical coupler  705 , and output optical coupler  707  are present in optical waveguide structure  700  in  FIG. 7 . With this example, input optical coupler  701  can be designed to couple or transmit a certain percentage of the input pump light from pump input optical waveguide  704  into nonlinear optical waveguide  702 . The design of input optical coupler  701  can be similar to the design illustrated in  FIG. 35  for input optical coupler  3500 . For this example, output optical coupler  705  is intended to couple signal light out from nonlinear optical waveguide  702  to output optical waveguide  708 . Also, output optical coupler  707  is intended to couple idler light out from nonlinear optical waveguide  702  to output optical waveguide  710 . 
     Additionally, output optical coupler  705  and output optical coupler  707  in  FIG. 7  can be configured such that only the light of the desired wavelength is coupled out and the light of the other two wavelengths is not coupled out. As discussed previously with reference to  FIG. 36 , an optical coupler for the pump light can be designed to couple light of the 655 nm pump wavelength, but have minimal coupling of the 1130 nm signal wavelength and minimal coupling of the 1558 nm idler wavelength. 
     With reference next to  FIG. 38 , an illustration of a graph of a coupled transmittance of light from a nonlinear optical waveguide to an output waveguide is depicted in accordance with an illustrative embodiment. As depicted, graph  3800  illustrates a coupled transmittance into an output waveguide as a function of couple length of an optical coupler. In this illustrative example, y-axis  3802  is normalized coupled transmittance (dimensionless), and x-axis  3804  is coupler length in micrometers. 
     As depicted in this illustrative example, a coupler gap of 0.500 μm is present between the core region of the nonlinear optical waveguide, such as nonlinear optical waveguide  800  in  FIG. 8 , and the core of the output waveguide. The output waveguide can have a core region comprising a material such as silicon nitride or titanium dioxide. For the illustrative example of  FIG. 38 , the core region of the output waveguide comprises silicon nitride. 
     As depicted, line  3806  in graph  3800  represents the coupled transmittance for a signal light having a wavelength of 1130 nm. Line  3808  in graph  3800  represents the coupled transmittance for an idler light having a wavelength of 1558 nm. 
     As illustrated in graph  3800 , output optical coupler  705  in  FIG. 7  can be designed to be wavelength-selective. For example, output optical coupler  705  can couple out 1130 nm signal light from nonlinear optical waveguide  702  into output optical waveguide  3608 . Further, output optical coupler  705  can couple 1558 nm idler light or 655 nm pump light at a much lower percentage. 
     For example, when output optical coupler  705  has a coupler length of about 51 μm, the coupled transmittance of the 1130 nm signal light between nonlinear optical waveguide  702  and output optical waveguide  708  is about 99 percent, as shown in line  3806 . 
     In the depicted example, a coupler length of about 56 μm can be selected to obtain a coupled transmittance for the 1558 nm idler light of only 0.1%, as depicted in line  3808 . With a coupler length 56 μm, the coupled transmittance for the 1130 nm signal light is about 97%, as shown in line  3806 . 
     Thus, the coupler length for output optical coupler  705  can be selected in a manner that obtains a desired level of coupling for at least one of a signal light or an idler light as depicted in graph  3800 . A selection of coupler lengths can also be made to obtain a desired amount of pump light from output optical coupler  705 . 
     The illustrative examples of an optical waveguide structure with directional phase matching can involve an open, as opposed to closed-loop, nonlinear optical waveguide, such as the serpentine path depicted for nonlinear optical waveguide  602  in  FIG. 6 . Nonlinear optical waveguide  602  can also be described as having a zig-zag path. 
     With a serpentine path or zigzag path, the output optical waveguides can be located near the end of the nonlinear optical waveguide. The optical coupler for coupling the signal light or the idler light into its output optical waveguide can be designed to couple as much of the signal light or the idler light as possible into the output optical waveguide because the signal and idler light do not need to recirculate in the nonlinear optical waveguide having an open path for those wavelengths of light. 
     Turning next to  FIG. 39 , an illustration of an optical waveguide structure is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  3900  comprises nonlinear optical waveguide  3902 , pump input optical waveguide  3904 , output optical waveguide  3906 , output optical waveguide  3908 , optical coupler  3910 , optical coupler  3912 , and optical coupler  3914 . In this illustrative example, optical waveguide structure  3900  also includes a set of phase shifters, such as tuning electrodes  3916 , tuning electrodes  3918 , tuning electrodes  3920 , and tuning electrodes  3922 . 
     In this illustrative example, nonlinear optical waveguide  3902  is a nonlinear optical waveguide with a serpentine path. This path can also be referred to as a zigzag path. 
     A pump light can be supplied from pump input optical waveguide  3904  via optical coupler  3910 . Light can be output from nonlinear optical waveguide  3902  through output optical waveguide  3906  using optical coupler  3912  and through output optical waveguide  3908  using optical coupler  3914 . 
     Additional light can be input and output of nonlinear optical waveguide  3902  using additional input and output optical waveguides. Each wavelength can be supplied or output through a single optical waveguide. In other illustrative examples, an optical waveguide can input or output multiple wavelengths of light. 
     In some illustrative examples, one or both ends of a nonlinear optical waveguide can have a termination region. For example, nonlinear optical waveguide  3902  has termination  3930  and termination  3932 . In some illustrative examples, at least one of termination  3930  or termination  3932  in nonlinear optical waveguide  3902  can absorb the pump light and prevent recirculation of that pump light in nonlinear optical waveguide  3902 . 
     In this illustrative example, nonlinear optical waveguide  3902  lies on an yz plane defined by z-axis  3901  and y-axis  3903 . 
     For other examples, termination  3930  and termination  3932  can be reflecting terminations. In some illustrative examples, the reflecting terminations form an optical cavity for the pump light. Having the pump light confined within an optical cavity can increase the pump power that contributes to the nonlinear optical process and make that “intra-cavity” pump power much higher than the pump power that is supplied into the input optical waveguide for the pump light, such as a factor of 2 higher to more than a factor of 100 higher. 
     Nonlinear optical waveguide  702  in  FIG. 7  and circular ring nonlinear optical waveguide  1402  in  FIG. 14  have pump light, signal light, and idler light circulating in an optical cavity in the racetrack or circular ring. In contrast, in nonlinear optical waveguide  3902 , only the pump light circulates in an optical cavity in nonlinear optical waveguide  3902 . In this example, the signal light and the idler light do not circulate in nonlinear optical waveguide  3902 . The signal light and the idler light make one pass through that waveguide. 
     In some illustrative examples, at least one of termination  3930  or termination  3932  in nonlinear optical waveguide  3902  can reflect the pump light. Examples of optical-frequency (or wavelength) selective reflector regions that can be used in termination  3930  and termination  3932  include at least one of a waveguide loop mirror, a micro-ring waveguide resonator, a distributed feedback grating, or a photonic crystal structure. 
     In illustrative examples, a directional phase matching optical waveguide structure that has a serpentine or zig-zag nonlinear optical waveguide and has pump-wavelength selecting reflective terminations at each of the two ends of the nonlinear optical waveguide has a linear optical cavity for the pump light. The pump power in the nonlinear optical waveguide can be much higher than the pump power supplied to the nonlinear optical waveguide via the pump input optical waveguide. Optical waveguide structure  600  with nonlinear optical waveguide  602  in  FIG. 6 , optical waveguide structure  2200  with nonlinear optical waveguide  2202  in  FIG. 22 , optical waveguide structure  2700  with nonlinear optical waveguide  2702  in  FIG. 27 , and optical waveguide structure  3900  with nonlinear optical waveguide  3902  in  FIG. 39  are examples of nonlinear optical waveguides that can have terminations in the illustrative examples. 
     In another example, a directional phase matching optical waveguide structure that has a ring, racetrack or other closed-loop nonlinear optical waveguide shape forms a closed path nonlinear optical waveguide that has an optical cavity for the pump light and also can have optical cavities for either or both of the signal light and the idler light. Optical waveguide structure  700  with nonlinear optical waveguide  702  in  FIG. 7  and optical waveguide structure  1400  with circular ring nonlinear optical waveguide  1402  in  FIG. 14  are examples of closed path nonlinear optical waveguides. 
     With a closed path nonlinear waveguide, the signal light and idler light also recirculate in that closed path optical cavity in the nonlinear optical waveguide. In this example, optical couplers can be used to extract the signal light and the idler light. 
     With an open path nonlinear optical waveguide having pump-wavelength reflecting terminations, only the pump light recirculates in that optical cavity. The signal light and the idler light are not reflected by the reflecting terminations and do not recirculate in this illustrative example. 
     Furthermore, the path length for one round trip through an optical cavity can determine the spectral density of the optical-cavity or resonator modes (i.e., how closely spaced in wavelength those resonator modes are). A nonlinear waveguide with a long round-trip path length has resonator modes that are more closely spaced in wavelength than a nonlinear waveguide with a shorter round-trip path length. The tuning electrodes in the nonlinear optical waveguide can be used to adjust the net phase shift of the pump light such that the pump wavelength is aligned with a resonator mode of the nonlinear optical waveguide cavity. 
     Thus, the illustrative examples provide an optical waveguide structure that comprises a nonlinear optical waveguide comprising a nonlinear optical material having a second order nonlinear coefficient that changes with a direction of light propagation. A first portion of the nonlinear optical waveguide in which a light propagating through the first portion is affected by a positive value of a second order nonlinear coefficient. A second portion of the nonlinear optical waveguide in which the light propagating through the first portion is affected by a negative value of a second order nonlinear coefficient, wherein a set of dimensions in the nonlinear optical waveguide in the first portion and the second portion is selected to cause the light to have a relative phase walk-off that is an odd multiple of 180 degrees. 
     In the illustrative examples, direction-reversal enhanced coherent interaction can match a phase walk-off that is an odd multiple of π radians to a reversal in the sign of the nonlinear optical coefficient. For a second order nonlinear optical process in the different illustrative examples, the nonlinear optical process involves 1 input photon (the pump photon) that produces 2 output photons (the signal photon and the idler photon). This nonlinear process is called spontaneous parametric down conversion (SPDC). Since the nonlinear optical processes are quite inefficient, most of the input pump photons are not converted to signal and idler photons. Thus, those “un-used” pump photons can be part of the output from a nonlinear optical waveguide. 
     Further, in the illustrative examples, additional structures can be present in the optical waveguide structure in addition to the nonlinear optical waveguide. These additional structures can be, for example, optical couplers that separate the pump light, the signal light, and the idler light into different output optical waveguides. In other words, each different type of light can be output into a different output optical waveguide. 
     The efficiency of the nonlinear optical process can be the inverse of the number of input photons of a given type of photons that are needed to produce one output photon or one pair of output photons as a result of their interaction with the nonlinear optical material. Examples of input photons can be pump photons, signal photons and idler photons. In the illustrative example, the output photon can be an idler photon or a signal photon. The pair of output photons can be a signal photon and an idler photon when spontaneous parametric down conversion is present. 
       FIGS. 16-18  illustrate the effect of a phase matching approach on the nonlinear optical generation in a nonlinear optical waveguide, such as circular ring nonlinear optical waveguide  1402  in  FIG. 14 . The results shown in graphs in  FIGS. 16-18  also are relevant to the other configurations of the directional phase matching waveguide structure. The value of the nonlinear optical coefficient is shown in graph  1700  in  FIG. 17 . The nonlinear optical coefficient D eff  (or d eff ) has a positive value when the direction of travel for the light is primarily along the −Y direction of the x-cut lithium niobate material (propagation angles between 30 and 150 degrees). The nonlinear optical coefficient has a negative value when the direction of travel for the light is primarily along the +Y direction of the x-cut lithium niobate material (propagation angles between 210 and 330 degrees). 
     In the illustrative example, the nonlinear optical generation is an interaction of the optical fields rather than the optical power. This interaction is illustrated in equation (2) above. 
     The nonlinear optical coefficient can be multiplied with the term 
     
       
         
           
             
               
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     describing the effect of the phase walk-off. This term has a sinusoidal dependence with the phase walk-off and can have positive or negative values. The nonlinear optical waveguides in the illustrative examples are constructed such that the sign of the nonlinear optical coefficient remains the same as the sign of this term or remains opposite to the sign of this term. Therefore, the multiplication of the nonlinear optical coefficient with this term gives a result whose value continues to have the same sign, rather than alternating between being positive and being negative. This result is illustrated in graph  1800  in  FIG. 18 . 
     Thus, the nonlinear optical generation efficiency (or generation rate) of at least one of the output signal or idler photons continues to increase as the interaction distance is increased, as illustrated in graph  1820  in  FIG. 18 . The graphs in  FIGS. 23-26  and  FIGS. 28-31  also illustrate this increase in the nonlinear optical generation efficiency (or generation rate), for other configurations of nonlinear optical waveguides. 
     Turning next to  FIG. 40 , an illustration of a flowchart of a process for inputting light through an optical waveguide structure is depicted in accordance with an illustrative embodiment. The process in  FIG. 40  can be implemented in physical waveguide structure such as nonlinear optical waveguide  102  in  FIG. 1  in the different physical implementation shown in the different illustrative examples. 
     The process begins by inputting a light at a pump wavelength into an optical waveguide structure comprising a nonlinear optical material having a second order nonlinear coefficient that changes with a direction of light propagation (operation  4000 ). In operation,  4000 , the light input into the nonlinear optical waveguide can be a pump light supplied by an input optical waveguide. 
     The process propagates the light along a path in the optical waveguide structure from a first location in a first portion of the nonlinear optical waveguide having a first sign of a second order nonlinear coefficient for a nonlinear optical interaction of the light with the nonlinear optical material in the first portion of the nonlinear optical waveguide (operation  4002 ). In operation  4002 , the light propagated can have a pump wavelength. Also, in operation  4002 , the light generation can occur at the first location to generate at least one of a signal light or idler light. For example, in operation  4002 , at least one of a signal light or an idler light can be generated at the first location such that the light in the nonlinear optical interaction of the light with the nonlinear optical material in the second portion of the nonlinear optical waveguide comprises the pump light and at least one of the signal light or the idler light at the second location. In one illustrative example, the nonlinear optical interaction involves the light of the pump wavelength as well as the light of the signal wavelength and idler wavelength. 
     The process propagates the light along the path in the optical waveguide structure to a second location in a second portion of the nonlinear optical waveguide having a second sign of the second order nonlinear coefficient for the nonlinear optical interaction of the light with the nonlinear optical material in the second portion of the nonlinear optical waveguide (operation  4004 ). In operation  4004 , the light propagated can have a pump wavelength. Further, in operation  4004 , the interaction involves light of the pump wavelength as well as the light of the signal wavelength and the idler wavelength. The light generated in the first location in the nonlinear optical interaction occurring in the first portion of the nonlinear optical waveguide propagates to the second location in the second portion of the nonlinear optical waveguide and the nonlinear optical interactions occurring in the first location and in the second location have a phase walk-off that is an odd multiple of 180 degrees. In this example, the phase walk-off is for the nonlinear optical interaction occurring in the second location in the second portion of the nonlinear optical waveguide in which the phase walk-off is an odd multiple of 180 degrees. 
     A portion of the light is output from the nonlinear optical waveguide to an output optical waveguide, wherein the portion of the light comprises at least one of the signal light or the idler light (operation  4006 ). The process terminates thereafter. 
     Further, in propagating the light on the path through the nonlinear optical waveguide, a configuration of nonlinear optical waveguide can be selected such that a peak in a magnitude of the second order nonlinear coefficient is aligned with a phase walk-off of an odd multiple of π/2 radians. The alignment of the peak in the magnitude of the second order nonlinear coefficient with the phase walk-off of an odd multiple of π/2 radians can be within π/4 radians. Other amounts of alignment can be used in other illustrative examples. 
     In the flowchart in  FIG. 40 , at least one of a signal light or an idler light can be generated at the first location such that the light in the nonlinear optical interaction of the light with the nonlinear optical material in the second portion of the nonlinear optical waveguide comprises the pump light and at least one of the signal light or the idler light at the second location. The interaction can involve the light of the pump wavelength as well as the light of the signal wavelength and the idler wavelength. 
     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. 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. 41 , an illustration of a block diagram of a product management system is depicted in accordance with an illustrative embodiment. Product management system  4100  is a physical hardware system. In this illustrative example, product management system  4100  includes at least one of manufacturing system  4102  or maintenance system  4104 . 
     Manufacturing system  4102  is configured to manufacture products. As depicted, manufacturing system  4102  includes manufacturing equipment  4106 . Manufacturing equipment  4106  includes at least one of fabrication equipment  4108  or assembly equipment  4110 . 
     Fabrication equipment  4108  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. For example, both closed-loop structures such as those depicted in  FIG. 6  and  FIG. 14  and  FIG. 35  as well as open structures, such as those depicted in  FIG. 7 ,  FIG. 38 ,  FIG. 22 ,  FIG. 27 , can be fabricated on the same substrate wafer. The substrate wafer can comprise a material such as silicon or lithium niobate or quartz or sapphire or silicon carbide. Fabrication equipment  4108  can be used to fabricate at least one of optical waveguide structures, nonlinear optical waveguides, 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  4108  can include machines and tools. With respect to fabricating semiconductor components and optical waveguide components, fabrication equipment  4108  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  4110  is equipment used to assemble parts to form a product such as a chip, an integrated circuit, a computer, an aircraft, or some other product. Assembly equipment  4110  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, an elevator system, a rail-based system, or a robot. 
     In this illustrative example, maintenance system  4104  includes maintenance equipment  4112 . Maintenance equipment  4112  can include any equipment needed to perform maintenance on and evaluation of a product. Maintenance equipment  4112  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  4112  may include optical inspection devices, x-ray imaging systems, surface-profile measurement systems, drills, vacuum leak checkers, and other suitable devices. In some cases, maintenance equipment  4112  can include fabrication equipment  4108 , assembly equipment  4110 , or both to produce and assemble parts that needed for maintenance. 
     Product management system  4100  also includes control system  4114 . Control system  4114  is a hardware system and may also include software or other types of components. Control system  4114  is configured to control the operation of at least one of manufacturing system  4102  or maintenance system  4104 . In particular, control system  4114  can control the operation of at least one of fabrication equipment  4108 , assembly equipment  4110 , or maintenance equipment  4112 . 
     The hardware in control system  4114  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  4106 . For example, robots, computer-controlled machines, and other equipment can be controlled by control system  4114 . In other illustrative examples, control system  4114  can manage operations performed by human operators  4116  in manufacturing or performing maintenance on a product. For example, control system  4114  can assign tasks, provide instructions, display models, or perform other operations to manage operations performed by human operators  4116 . 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  4114 . 
     In the different illustrative examples, human operators  4116  can operate or interact with at least one of manufacturing equipment  4106 , maintenance equipment  4112 , or control system  4114 . 
     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  4114  can be used to adjust manufacturing of nonlinear optical waveguides, optical waveguides, optical couplers and terminations dynamically 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. 
     For example, the height of the upper cladding region can be selected to achieve the desired value for the phase walk-off. The phase walk-off depends on the values of the effective refractive indices n eff,P , n eff,S , and n eff,I  for the wave-guided modes at the pump, signal, and idler wavelengths. For example, one point in the fabrication process is after the waveguide core region has been fabricated and before the upper cladding material has been deposited over the waveguide core region. 
     The dimensions of the fabricated core region can be measured and optical waveguide design simulations can be done to determine the values of the effective refractive indices that can be obtained for various candidate values of the upper cladding height. The upper cladding height that gives the desired value for the phase walk-off can be chosen accordingly. Upper cladding material can then be deposited that has the desired thickness or height. 
     Another point in the fabrication process is after the upper cladding material has been deposited to a value that is greater than what might be desired. Test devices such as asymmetric Mach-Zehnder interferometers and micro-ring resonators can be fabricated in addition to the nonlinear optical waveguide. 
     These test devices can be characterized to extract values for the effect refractive indices for the upper cladding height of those test devices. The upper cladding height can then be reduced by etching away some of the upper cladding material, possibly in an iterative manner accompanied by additional measurements of the test structures. In this way, the desired value for the upper cladding height can be approached and then achieved. 
     Thus, in one illustrative example, the optical waveguide structure is constructed such that the change in the sign in the phase walk-off is aligned with a change in sign the second order linear coefficient in the nonlinear optical material in the nonlinear optical waveguide. The alignment of the changes can occur based on the configuration of the nonlinear optical waveguide in the optical waveguide structure. Additionally, the optical waveguide structure can also include electrodes that can supply voltages that are used to adjust the phase walk-off to provide a desired level of alignment between sign changes in the phase walk-off and the second order nonlinear coefficient to have a desired amount of alignment. 
     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 nonlinear optical waveguide comprising a nonlinear optical material having a second order nonlinear coefficient for a second order nonlinear susceptibility in which the second order nonlinear coefficient changes with a direction of light propagation; 
     wherein a light propagating in a first direction through a first portion of the nonlinear optical waveguide has a first sign of the second order nonlinear coefficient for a nonlinear optical interaction of the light with the nonlinear optical material in the first portion of the nonlinear optical waveguide and the light propagating in a second direction through a second portion of the nonlinear optical waveguide has a second sign of the second order nonlinear coefficient for the nonlinear optical interaction of the light with the nonlinear optical material in the second portion of the nonlinear optical waveguide; and 
     wherein the light generated in a first location of a nonlinear optical interaction occurring in the first portion of the nonlinear optical waveguide propagates to a second location in the second portion of the nonlinear optical waveguide and has a phase walk-off between the first location and the second location that is an odd multiple of 180 degrees. 
     Clause 2: 
     The optical waveguide structure according to clause 1 further comprising: 
     an output optical waveguide configured to output an output light from the nonlinear optical waveguide, wherein the output light has an output wavelength that is different from a pump light at a pump wavelength input into the nonlinear optical waveguide. 
     Clause 3: 
     The optical waveguide structure according to one of clause 1 or 2 further comprising: 
     an input optical waveguide configured to input an input light into the nonlinear optical waveguide. 
     Clause 4: 
     The optical waveguide structure according to one of clause 1, 2, or 3, wherein the phase walk-off is between previously generated light in the waveguide and newly generated light in the waveguide. 
     Clause 5: 
     The optical waveguide structure according to one of clause 1, 2, 3, or 4, wherein the phase walk-off of the nonlinear optical interaction occurs in the second portion of the nonlinear optical waveguide from the light generated in the first portion of the nonlinear optical waveguide. 
     Clause 6: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, or 5, wherein the phase walk-off is an odd multiple of 180 degrees and wherein the phase walk-off is the odd multiple of 180 degrees that occurs at a location where a change in a sign of the second order nonlinear coefficient occurs. 
     Clause 7: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, or 6, wherein the phase walk-off is an odd multiple of 180 degrees and wherein a location at which the phase walk-off has the odd multiple of 180 degrees is aligned with the location at which a change in a sign of the second order nonlinear coefficient occurs. 
     Clause 8: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, or 7, wherein successive sign changes of the second order nonlinear coefficient occur in alignment with corresponding successive increments of odd multiples of 180 degrees in the phase walk-off. 
     Clause 9: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, or 8, wherein a configuration of nonlinear optical waveguide is selected to cause an increase in efficiency in generating at least one of a signal light or an idler light within the nonlinear optical waveguide. 
     Clause 10: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, or 9, wherein a configuration of nonlinear optical waveguide is selected such that a peak in a magnitude of the second order nonlinear coefficient is aligned with a phase walk-off of an odd multiple of π/2 radians. 
     Clause 11: 
     The optical waveguide structure according to clause 10, wherein an alignment of the peak in the magnitude of the second order nonlinear coefficient with the phase walk-off of an odd multiple of π/2 radians is within π/4 radians. 
     Clause 12: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or 11, wherein the nonlinear optical waveguide is selected from one of a closed path, a ring, a circular ring, an elliptical ring, a racetrack, a square, or a rectangle path. 
     Clause 13: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, wherein the nonlinear optical waveguide is selected from one of an open path, a serpentine path, or a zig-zag path. 
     Clause 14: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, or 13, wherein the nonlinear optical waveguide has an open path with an ending at a termination in a set of waveguide structures. 
     Clause 15: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, or 14, wherein the nonlinear optical waveguide has an open path with ends points at reflecting terminations in a set of waveguide structures that increases a power of a pump light in the light. 
     Clause 16: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, or 15, wherein the nonlinear optical waveguide has a central region and two side regions on each side of the central region, wherein the central region comprises a first nonlinear optical material in a set of nonlinear optical materials that has a first second-order nonlinear coefficient with a magnitude that is at least one picometer/volt, and wherein the two side regions have a second nonlinear optical material in the set of nonlinear optical materials that has a second second-order nonlinear coefficient whose magnitude is equal to or less than one tenth the magnitude of the first second-order nonlinear coefficient for the first nonlinear optical material. 
     Clause 17: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16, wherein the nonlinear optical waveguide has a core region, a lower cladding region, and an upper cladding region, wherein the core region is located between the lower cladding region and the upper cladding region and wherein the upper cladding region has a height selected to compensate for a variation of the phase walk-off in the nonlinear optical waveguide. 
     Clause 18: 
     The optical waveguide structure according to claim  17 , wherein the core region has a central region and two side regions on each side of the central region, wherein the central region comprises a first nonlinear optical material in a set of nonlinear optical materials that has a first second-order nonlinear coefficient with a magnitude that is at least one picometer/volt and wherein the two side regions have a particular nonlinear optical material in the set of nonlinear optical materials that has a second second-order nonlinear coefficient whose magnitude is one tenth the magnitude of the first second-order nonlinear coefficient for the first nonlinear optical material. 
     Clause 19: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, or 18, wherein the nonlinear optical waveguide has a first curved segment and a second curved segment with a first straight segment located between the first curved segment and the second curved segment, and the second portion of the nonlinear optical waveguide has a third curved segment and a fourth curved segment with a second straight segment located between has the third curved segment and the fourth curved segment. 
     Clause 20: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, or 19, wherein the first portion has a first curved segment and a first straight segment, and the second portion of the nonlinear optical waveguide has a second curved segment and a second straight segment, wherein the second curved segment in the second portion is connected to the first curved segment in the first portion. 
     Clause 21: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20, wherein the first portion has a first curved segment and the second portion of the nonlinear optical waveguide has a second curved segment that is connected to the first curved segment. 
     Clause 22: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or 21 further comprising: 
     an optical coupler for the nonlinear optical waveguide and an output optical waveguide. 
     Clause 23: 
     The optical waveguide structure according to clause 22, wherein the optical coupler is configured to couple the light having at least one of a signal wavelength or an idler wavelength from the nonlinear optical waveguide to the output optical waveguide. 
     Clause 24: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, or 23 further comprising: 
     an optical coupler for an input of an input optical waveguide and the nonlinear optical waveguide. 
     Clause 25: 
     The optical waveguide structure according to clause 24, wherein the optical coupler is configured to couple the light having a pump wavelength from the input optical waveguide to the nonlinear optical waveguide. 
     Clause 26: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, or 25 further comprising: 
     a set of phase shifters adjacent to the nonlinear optical waveguide. 
     Clause 27: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, or 25 further comprising: 
     a first set of phase shifters located adjacent to the first portion of the nonlinear optical waveguide; and 
     a second set of phase shifters located adjacent to the second portion of the nonlinear optical waveguide, wherein the first set of phase shifters operates to apply a first voltage and the second set of phase shifters operates to apply a second voltage in which the first voltage and the second voltage cause phase shifts in wavelengths of the light selected from at least one of a pump light, a signal light, or an idler light in the nonlinear optical waveguide such that a value of the phase walk-off changes. 
     Clause 28: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, or 27, wherein the second direction is opposite to the first direction. 
     Clause 29: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, or 28, wherein the second sign is negative when the first sign is positive and the second sign is positive when the first sign is positive. 
     Clause 30: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, or 29, wherein the light propagates through the nonlinear optical waveguide as a pump light having a pump wavelength, a signal light having a signal wavelength, and an idler light having an idler wavelength. 
     Clause 31: 
     The optical waveguide structure according to one of clause 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, or 30, wherein the phase walk-off is one of a relative phase walk-off and a cumulative phase walk-off. 
     Clause 32: 
     An optical waveguide structure comprising: 
     a nonlinear optical waveguide comprising: 
     a nonlinear optical material having a second order nonlinear coefficient that changes with a direction of light propagation; 
     a first portion of the nonlinear optical waveguide in which a light propagating through the first portion is affected by a positive value of the second order nonlinear coefficient; and 
     a second portion of the nonlinear optical waveguide in which the light propagating through the first portion is affected by a negative value of the second order nonlinear coefficient, wherein a set of dimensions in the nonlinear optical waveguide in the first portion and the second portion is selected to cause the light in a first location in the first portion and a second location in the second portion to have a phase walk-off that is an odd multiple of 180 degrees. 
     Clause 33: 
     The optical waveguide structure according to clause 32 further comprising: 
     an output optical waveguide configured to output an output light from the nonlinear optical waveguide, wherein the output light has an output wavelength that is different from a pump light at a pump wavelength input into the nonlinear optical waveguide. 
     Clause 34: 
     The optical waveguide structure according to one of clause 32 or 33, wherein the light propagates through the nonlinear optical waveguide as a pump light having a pump wavelength, a signal light having a signal wavelength, and an idler light having an idler wavelength and wherein a phase of the signal light and the idler light generated at the first location and the phase of the signal light and the idler light generated at the second location have the phase walk-off that is an odd multiple of 180 degrees. 
     Clause 35: 
     The optical waveguide structure according to one of clause 32, 33, or 34 further comprising: 
     a set of optical couplers for the nonlinear optical waveguide and an output optical waveguide. 
     Clause 36: 
     The optical waveguide structure according to one of clause 32, 33, 34, or 35, wherein a configuration of nonlinear optical waveguide is selected such that a peak in a magnitude of the second order nonlinear coefficient is aligned with a phase walk-off of an odd multiple of π/2 radians. 
     Clause 37: 
     The optical waveguide structure according to one of clause 32, 33, 34, 35, or 36, wherein an alignment of the peak in the magnitude of the second order nonlinear coefficient with the phase walk-off of an odd multiple of π/2 radians is within π/4 radians. 
     Clause 38: 
     The optical waveguide structure according to one of clause 32, 33, 34, 35, 36, or 37, wherein the phase walk-off is one of a relative phase walk-off and a cumulative phase walk-off. 
     Clause 39: 
     A method for moving a light through an optical waveguide structure, the method comprising: 
     inputting the light at a pump wavelength into the optical waveguide structure comprising a nonlinear optical material having a second order nonlinear coefficient that changes with a direction of light propagation; 
     propagating the light at the pump wavelength along a path in the optical waveguide structure from a first location in a first portion of a nonlinear optical waveguide having a first sign of the second order nonlinear coefficient for a nonlinear optical interaction of the light with the nonlinear optical material in the first portion of the nonlinear optical waveguide; and 
     propagating the light at the pump wavelength along the path in the optical waveguide structure to a second location in a second portion of the nonlinear optical waveguide having a second sign of the second order nonlinear coefficient for the nonlinear optical interaction of the light with the nonlinear optical material in the second portion of the nonlinear optical waveguide, wherein the light generated in the first location in the nonlinear optical interaction occurring in the first portion of the nonlinear optical waveguide propagates to the second location in the second portion of the nonlinear optical waveguide and has a phase walk-off for the nonlinear optical interaction occurring in the second location in the second portion of the nonlinear optical waveguide that is an odd multiple of 180 degrees. 
     Clause 40: 
     The method according to clause 39 further comprising: 
     generating at least one of a signal light or an idler light at the first location such that the light in the nonlinear optical interaction of the light with the nonlinear optical material in the second portion of the nonlinear optical waveguide comprises a pump light and at least one of the signal light or the idler light at the second location. 
     Clause 41: 
     The method according to one of clause 39 or 40 further comprising: 
     outputting a portion of the light from the nonlinear optical waveguide to an output optical waveguide, wherein the portion of the light comprise at least one of a signal light or an idler light. 
     In another illustrative example, optical waveguide structures can be implemented in which straight segments are connected to each other by curved segments having a 90 degree bend. The configuration of these structures can be arranged to provide a coherent interaction length of for a nonlinear optical process, having a distance for which the phase mismatch becomes equal to π. 
     An optical waveguide structure can be used with at least one material that has a sufficiently large χ (2)  nonlinear optical (NLO) susceptibility for light generation, and can be fabricated with cross-sectional geometries on the order of several microns or less (width, height). Light traveling in a nonlinear optical waveguide can undergo various nonlinear optical processes. For example, in spontaneous parametric down conversion (SPDC), a χ (2)  NLO process, an input light, such as pump light, spontaneously decays into two other types of light, such as signal light and idler light, having different wavelengths. 
     In this type of process, energy is conserved as follows: 
     
       
         
           
             
               
                 
                   
                     ℏω 
                     p 
                   
                   = 
                   
                     
                       ℏω 
                       s 
                     
                     + 
                     
                       ℏω 
                       i 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     where ωp, ωs, and ωi are the angular frequencies of pump light, signal light, and idler light, respectively. For a significant nonlinear optical effect to occur, phase walk-off of the pump light, signal light, and idler light is taken into account. Phase walk-off is also referred to as phase mismatch, momentum mismatch, or wavevector mismatch. 
     In this illustrative example, phase walk-off is described in terms of wavevectors. The wavevector, k, of a coherent optical field is given by: 
     
       
         
           
             
               
                 
                   k 
                   = 
                   
                     
                       
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           n 
                           ⁡ 
                           
                             ( 
                             ω 
                             ) 
                           
                         
                       
                       c 
                     
                     = 
                     
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           n 
                           ⁡ 
                           
                             ( 
                             ω 
                             ) 
                           
                         
                       
                       λ 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     where n(ω) is the refractive index of the material at the relevant angular frequency, or in the case of guided optical modes the effective index of that mode, c is the speed of light, and λ is the vacuum wavelength of the optical field. 
     Thus, the phase mismatch (Δk) for spontaneous parametric down conversion on linear optical involving three types of light having different wavelengths, such as pump light (p), signal light (s), and idler light (i), can be described as follows: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     k 
                   
                   = 
                   
                     
                       
                         
                           ω 
                           p 
                         
                         ⁢ 
                         
                           
                             n 
                             p 
                           
                           ⁡ 
                           
                             ( 
                             
                               ω 
                               p 
                             
                             ) 
                           
                         
                       
                       c 
                     
                     - 
                     
                       
                         
                           ω 
                           s 
                         
                         ⁢ 
                         
                           
                             n 
                             s 
                           
                           ⁡ 
                           
                             ( 
                             
                               ω 
                               s 
                             
                             ) 
                           
                         
                       
                       c 
                     
                     - 
                     
                       
                         
                           ω 
                           i 
                         
                         ⁢ 
                         
                           
                             n 
                             i 
                           
                           ⁡ 
                           
                             ( 
                             
                               ω 
                               i 
                             
                             ) 
                           
                         
                       
                       c 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Similar equations can be derived, without loss of generality, for other relevant nonlinear optical processes, such as difference frequency generation, sum frequency generation, and second harmonic generation. 
     The change in amplitude of the idler light and signal light in this example of spontaneous parametric down conversion, assuming the slowly varying amplitude approximation and assuming transverse electric (TE) polarized light propagating parallel to the y axis, is as follows: 
     
       
         
           
             
               
                 
                   
                     
                       dM 
                       
                         i 
                         , 
                         s 
                       
                     
                     dy 
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         
                           id 
                           33 
                         
                         ⁢ 
                         
                           ω 
                           
                             i 
                             , 
                             s 
                           
                         
                       
                       
                         
                           n 
                           
                             i 
                             , 
                             s 
                           
                         
                         ⁢ 
                         c 
                       
                     
                     ⁢ 
                     
                       M 
                       p 
                     
                     ⁢ 
                     
                       M 
                       
                         i 
                         , 
                         s 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       exp 
                       ⁡ 
                       
                         ( 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ky 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Where Mi,s,p are the amplitudes of the idler, signal, and pump optical fields, respectively, and d33 is the nonlinear optical (NLO) coefficient. 
     A similar expression can be obtained for propagation in the z-axis, where the relevant nonlinear optical coefficient is d22. A more general form of this equation can be used to describe the change in amplitude of in the optical fields for signal and idler light of arbitrary polarization propagating in an arbitrary direction. 
     Thus, the idler light and signal light increase or decrease in amplitude according to the magnitude of the phase walk-off and the sign (positive or negative) of the nonlinear optical coefficient. For a given, non-zero phase mismatch the coherent interaction length of the nonlinear optical process, Lcoh, is defined as the distance for which the phase mismatch becomes equal to π: 
     
       
         
           
             
               
                 
                   
                     L 
                     coh 
                   
                   = 
                   
                     π 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       k 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     If an assumption made that the spontaneous parametric down conversion process begins at some point of origin and that the nonlinear optical coefficient in the direction of propagation is positive, then the amplitude of the signal light and idler light reach a maximum at Lcoh. Beyond this length, and up to a distance of 2×Lcoh, the amplitude of the signal light and idler light decrease and reach 0 at a propagation distance of exactly 2×Lcoh. Then from a distance of 2×Lcoh up to 3×Lcoh the amplitude of the signal light and idler light increase again. 
     This process continues in a periodic fashion for as long as the optical fields remain in the nonlinear optical material. Without any phase-matching devices such as phase shifters, the amplitude of the signal light and idler light can only reach a maximum value consistent with one coherent interaction length. 
     The nonlinear optical process can be enhanced beyond a single Lcoh by avoiding or reducing the subsequent decrease in amplitude after the optical fields for light travel one Lcoh. If some of the signal light and idler light are present at the beginning of the next cycle of increasing amplitude for idler light and signal light, then the cumulative amplitude of the signal light and idler light will continue to increase and a substantial nonlinear optical process will occur, beyond the maximum expected for a single Lcoh. 
     The efficiency of the nonlinear optical process increases as the amplitude of signal light and idler light increase, assuming any decrease in the amplitude of the pump light is negligible. Thus, it is desirable to have the nonlinear optical process occur over many coherent interaction lengths. The optical waveguide structure can be designed and fabricated to enable this phenomenon in which a nonlinear optical waveguide has a configuration that the direction of propagation near every successive Lcoh. 
     In the following illustrative examples, a nonlinear optical process of spontaneous parametric down conversion (SPDC) is used. However, in other illustrative examples, other types of χ (2)  nonlinear optical processes can be used. Other types of materials can be used in place of or in addition to x-cut lithium niobate. The materials used can be selected as ones that provide desired level of χ (2)  nonlinear optical process susceptibility. 
     With reference to  FIG. 42 , an illustration of an optical waveguide structure is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  4200  comprises nonlinear optical waveguide  4202 . In this example, nonlinear optical waveguide  4202  is comprised of nonlinear optical material  4204  having second order nonlinear optical coefficient  4206  for nonlinear optical process  4208 . Nonlinear optical process  4208  can be a second order nonlinear optical process selected from a group comprising a second-harmonic generation (SHG), a difference frequency generation (DFG), a parametric down conversion (PDC), a sum frequency generation (SFG), a parametric up conversion (PUC), and other types of light generation. 
     In fabricating optical waveguide structure  4200 , nonlinear optical waveguide  4202  can be formed from a material such as x-cut lithium niobate  4210 . Nonlinear optical waveguide  4202  can be formed on plane  4212  in which an x-axis  4214  of x-cut lithium niobate  4210  is perpendicular to plane  4212 . 
     In this illustrative example, nonlinear optical waveguide  4202  can be comprised of a number of different types of components. As depicted, nonlinear optical waveguide  4202  is comprised of straight segments  4216  and curved segments  4218 . In this illustrative example, curved segments  4218  connect straight segments  4216  to each other to form at least one of a cascaded configuration, a stair case configuration, or a serpentine configuration for the nonlinear optical waveguide. Additionally, straight segments  4216  can have a first length that is greater than a second length of curved segments  4218 . 
     Straight segments  4216  are oriented such that nonlinear optical interaction  4220  with light generation  4222  occurs with overall constructive manner  4224  within nonlinear optical waveguide  4202  in response to light  4226  traveling through nonlinear optical waveguide  4202 . 
     In these illustrative examples, light  4226  can take number of forms. For example, light  4226  can be comprised of at least one of pump light  4228 , signal light  4230 , or idler light  4232 . In one illustrative example, light  4226  comprises pump light  4228 . Nonlinear optical interaction  4220  of pump light  4228  within nonlinear optical waveguide  4202  generates at least one of signal light  4230  or idler light  4232  in light  4226 . 
     As depicted, curved segments  4218  have 90 degree bend  4234 . Curved segments  4218  connect straight segments  4216  to each other within nonlinear optical waveguide  4202 . 
     In this illustrative example, straight segments  4216  can be comprised of first segments  4236  and second segments  4238 . Second segments  4238  have an orientation that is perpendicular to first segments  4236 . With this example, curved segments  4218  connect first segments  4236  to the second segments  4238 . 
     Light  4226  travels in first direction  4240  in first segments  4236  and in second direction  4242  in second segments  4238  in which second direction  4242  is perpendicular to first direction  4240  in first segments  4236 . Nonlinear optical interaction  4220  of light  4226  traveling in first direction  4240  is constructive. In this illustrative example, depending on the configuration of second segments  4238 , the travel of light  4226  within second segments  4238  can also be constructive. 
     In the illustrative example, optical waveguide structure  4200  can also include other components in addition to nonlinear optical waveguide  4202 . For example, optical waveguide structure  4200  can also include a set of phase shifters  4246  and a set of optical couplers  4248 . 
     A set of phase shifters  4246  can be present in a set of locations relative to the nonlinear optical waveguide  4202 . The set of phase shifters  4246  operates to apply a set of activations  4250  to change phase  4252  of light  4226 . The set of phase shifters  4246  can be selected from at least one of a tuning electrode, a thermal element, shape memory alloy element, Piezo electric element, or some other suitable component. 
     The set of phase shifters  4246  can be used to change the phase-matching condition, such that the light which experience the nonlinear process can be tuned in an “on-demand” fashion. Further, the selection of phase shifters  4246  can be made for use using optical waveguide structure  4200  in a wide variety of operating environments. These environments can be, for example, such as slightly above room temperature or even at 4 Kelvin. 
     The set of optical couplers  4248  can be connected to nonlinear optical waveguide  4202 . The set of optical couplers  4248  operate at least one of couple light  4226  into nonlinear optical waveguide  4202  or out of nonlinear optical waveguide  4202 . These optical couplers can include at least one of a directional coupler, multimode interferometer, a micro ring, a grating coupler, or some other suitable device type. 
     With reference next to  FIG. 43 , an illustration of phase walk-off between points in a nonlinear optical waveguide is depicted in accordance with an illustrative embodiment. In this example, first curved segment  4306  in curved segments  4218  is connected to straight segment  4312  in straight segments  4216 . Second curved segment  4311  are also connected to straight segment  4312 . Distance  4310  is present between first point  4304  in first curved segment  4306  and second point  4308  in second curved segment  4311 . 
     In this illustrative example, phase walk-off  4300  of a multiple of π occurs between first point  4304  in first curved segment  4306  in curved segments  4218  and second point  4308  in second curved segment  4311  in curved segments  4218 . Distance  4310  between first point  4304  in first curved segment  4306  and second point  4308  in second curved segment  4311  is selected to provide phase walk-off  4300  that is a multiple of π. In this example, this selection of distance  4310  is coherent interaction length  4330  (Lcoh) for nonlinear optical process  4208 . 
     Further, length  4319  of curved segments  4218  can be selected to be longer than the coherent interaction length of the fundamental modes of the optical fields, higher-order modes can be used in order to increase the coherent interaction length. 
     The selection of geometries for straight segments  4216  and curved segments  4218  can be made such that the connection of straight segments  4216  and curved segments  4218  provide multiple coherent interaction length in nonlinear optical waveguide  4202 . 
     The illustration of optical waveguide structure in  FIGS. 42-43  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 optical waveguides can be present in optical waveguide structure  4200  in addition or in place of the ones depicted. Phase shifters  4246  and optical couplers  4248  are optional components. In other examples, wavelength selective couplers can be used in optical waveguide structure  4200  to couple portion of light  4226  to another optical waveguide from nonlinear optical waveguide  4202 . For example, signal light  4230  can be coupled from light  4226  in nonlinear optical waveguide  4202  to another optical waveguide while pump light  4228  remains in light  4226 , traveling in nonlinear optical waveguide  4202 . 
     These could include various directional couplers, multimode interferometers, micro rings, grating couplers, or other suitable devices. In some instances, including these structures at some point or points in-between the start and end of optical waveguide structure  4200  may be useful as a way of monitoring the nonlinear optical process in a specific section of the device. 
     As yet another example, reflective components can be at the start and end of the nonlinear optical waveguide  4202 . This configuration can increase the magnitude of the light as the light propagates back and forth in nonlinear optical waveguide  4202  over many cycles. The reflective components can be placed at positions in nonlinear optical waveguide  4202  that preserves the phase-matching conditions described above. 
     With reference next to  FIG. 44 , an illustration of an optical waveguide structure with a staircase configuration is depicted in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  4400  is an example of one implementation for optical waveguide structure  4200  shown in block form in  FIG. 42 . 
     As depicted, optical waveguide structure  4400  comprises nonlinear optical waveguide  4402  formed in a nonlinear optical material in the form of x-cut lithium niobate  4404 . As depicted, nonlinear optical waveguide  4402  lies on plane  4406  defined by y-axis  4408  and z-axis  4410  in crystal axes  4411 . Crystal axes  4411  are defined based on the crystalline structure of x-cut lithium niobate  4404 . In this example, x-axis  4412  in crystal axes  4411  is perpendicular to plane  4406 . In this example, z-axis  4410  is the crystal optical axis in crystal axes  4411 . 
     In this example, nonlinear optical waveguide  4402  has straight segments and curved segments. This illustrative example, the straight segments are straight segment A 1   4420 , straight segment C 1   4422 , straight segment A 2   4424 , straight segment C 2   4426 , and straight segment A 3   4428 . As depicted, straight segment A 1   4420 , straight segment A 2   4424 , and straight segment A 3   4428  are examples of first segments  4236  in  FIG. 42 , and straight segment C 1   4422  and straight segment C 2   4426  are examples for second segments  4238  in  FIG. 42 . 
     The curved segments are curved segment B 1   4430 , curved segment D 1   4432 , curved segment B 2   4434 , and curved segment D 2   4436 . 
     In this example, x-cut lithium niobate  4404  has crystal axes  4411  which is used to describe the propagation direction and polarization orientation of light in nonlinear optical waveguide  4402 . For an input light, such as a pump light, with transverse electric (TE) polarization, propagation in the y direction enables the nonlinear optical process to utilize nonlinear optical coefficient d33  4440  of x-cut lithium niobate  4404 , which has the greatest magnitude. In this example, nonlinear optical coefficient d33  4440  is positive. 
     Thus, the nonlinear optical process is most efficient in the following sections that are aligned along y-axis  4408 : straight segment A 1   4420 , straight segment A 2   4424 , and straight segment A 3   4428 . Each of these straight segments is considered part of a repeating structure in optical waveguide structure  4400 . 
     In contrast, the nonlinear optical process in straight segment C 1   4422  and straight segment C 2   4426  utilize nonlinear optical coefficient d22  4442  for x-cut lithium niobate  4404 , which is different from nonlinear optical coefficient d33  4440 . In this example, nonlinear optical coefficient d22  4442  is negative. 
     In optical waveguide structure  4400  the orientation of straight segments, straight segment A 1   4420 , straight segment C 1   4422 , straight segment A 2   4424 , straight segment C 2   4426 , and straight segment A 3   4428  can be used to obtain desired values for the nonlinear optical coefficients. For example, light propagating in direction  4444  in straight segment A 1   4420 , straight segment A 2   4424 , and straight segment A 3   4428  has a positive value for nonlinear optical coefficient d33  4240 . Light propagating in direction  4446  in straight segment C 1   4422  and straight segment C 2   4426  has a negative value for nonlinear optical coefficient d 22   4442 . 
     The curved segments, curved segment B 1   4430 , curved segment D 1   4432 , curved segment B 2   4434 , and curved segment D 2   4436  have 90 degree bends. These curved segments are used to change propagation direction of the light traveling through nonlinear optical waveguide  4402 . For example, curved segment B 1   4430  can change light traveling in direction  4444  in straight segment  4420  to direction  4446  in curved segment C 1   4422 . 
     The lengths of the straight and curved segments are selected such that phase walk-off in the straight segments, straight segment A 1   4420 , straight segment A 2   4424 , and straight segment A 3   4428  can be a value between at least one of from 0 to π radians or from an even-numbered integer of π radians to a next larger odd-numbered integer of π radians for the nonlinear optical interaction that occurs. For example, the phase walk-off can be between 0 and π, 2π and 3π, 4π and 5π, and so on. 
     The phase walk-off in straight segment C 1   4422  and straight segment C 2   4426  can be an odd number from π radian to a next larger even numbered integer of π radians. For example, the phase walk-off can be between π and 2π, 3π and 4π, 5π and 6π, and so on. The approximate location and value of the phase walk-off is denoted in the drawing. 
     In this example, curved segments follow a circular path that can be described by a radius of curvature (r). Light traveling in the curved segments, experience a combination of nonlinear optical coefficients. The net value of the combination of nonlinear optical coefficients can be described by an effective nonlinear optical coefficient (d eff ), which is as follows: 
     
       
         
           
             
               
                 
                   
                     
                       d 
                       eff 
                     
                     ⁡ 
                     
                       ( 
                       θ 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           d 
                           
                             2 
                             ⁢ 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         cos 
                         3 
                       
                       ⁢ 
                       θ 
                     
                     + 
                     
                       3 
                       ⁢ 
                       
                         d 
                         
                           3 
                           ⁢ 
                           1 
                         
                       
                       ⁢ 
                       
                         cos 
                         2 
                       
                       ⁢ 
                       θ 
                       ⁢ 
                       sin 
                       ⁢ 
                       θ 
                     
                     + 
                     
                       
                         d 
                         
                           3 
                           ⁢ 
                           3 
                         
                       
                       ⁢ 
                       
                         sin 
                         3 
                       
                       ⁢ 
                       θ 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Where θ, the propagation angle, is the angle between the wave vector of the optical fields and the crystal axes, which is the z axis in this example. 
     With reference next to  FIG. 45 , an illustration of a graph illustrating values for nonlinear optical coefficients traveling through nonlinear optical waveguide is depicted in accordance with an illustrative embodiment. In this example, graph  4500  illustrates values for nonlinear optical coefficients at different propagation angles. Y-axis  4502  is the effective nonlinear optical coefficient (pm/v). X-axis  4504  is the propagation angle in radians. Line  4506  identifies the effective nonlinear coefficient for different propagation angles. Line  4508  and line  4510  indicate angles where the nonlinear optical coefficient is equal to zero. 
     In graph  4500 , values of effective nonlinear optical coefficients (d eff ) are calculated for angles between 0 radian and 2 radians depicted by line  4506 . A radian is equivalent to π in these examples. Values of the nonlinear optical coefficients for lithium niobate used are d22=2.4 pm/V, d31=−4.52 pm/V, and d33=−31.5 pm/V. As shown in graph  4500 , (d eff ) in line  4506  reaches a value of zero at a selected propagation angle, which is referred to as θ crit . 
     For a radius of curvature r, the length of the curved segment between the start of curved segment B 1   4430  in  FIG. 44  and the point θ crit  is: 
     
       
         
           
             
               
                 
                   
                     L 
                     ⁡ 
                     
                       ( 
                       
                         AB 
                         ⁢ 
                         
                           : 
                         
                         ⁢ 
                         
                           θ 
                           crit 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     r 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Δθ 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     To achieve a phase walk-off of π at this point in the curved segment, phase walk-off in curved segment B 1   4430  and then the length of straight segment A 1   4420  in  FIG. 44  is selected accordingly. 
     The phase walk-off (Φ) for straight segment A 1   4420  in  FIG. 44  is the product of the phase mismatch and distance that the light has propagated. However, the refractive index in birefringent media is not constant in curved segments. The refractive index as a function of angle can be determined analytically or through simulations. Once the refractive index in curved waveguide sections is known, the phase mismatch can be calculated as a function of the angle θ, and the phase walk-off (Φ) can be calculated by: 
     
       
         
           
             
               
                 
                   Φ 
                   = 
                   
                     ∫ 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         k 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                       ⁢ 
                       rd 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       θ 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Thus, segment A 1   4420  can be designed to have a phase walk-off that satisfies the following condition: 
     
       
         
           
             
               
                 
                   
                     Φ 
                     
                       A 
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     π 
                     - 
                     
                       Φ 
                       
                         AB 
                         : 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           ⁢ 
                           crit 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     where Φ AB:θcrit  is the phase walk-off experienced in the curved segment starting from the end of straight segment A 1   4420  and ending at θ crit , the point where the nonlinear optical coefficient changes sign. Next, the length of straight segment A 1   4420  is calculated as follows: 
     
       
         
           
             
               
                 
                   
                     L 
                     
                       A 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       Φ 
                       
                         A 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         k 
                         ⁡ 
                         
                           ( 
                           A 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Where Δk(A) is the phase mismatch in waveguide segments have the orientation of straight segment A 1   4420  is constant value, since these segments are straight. 
     Once the light has passed θ crit  in curved segment B 1   4430 , the light continues to propagate on into straight segment C 1   4422 . Because of the specific orientation of this segment relative to the crystal axes and the phase walk-off of the light, the light experiences a negative value of the nonlinear optical coefficient. The length of curved segment B 1   4430  can be designed such that a phase walk-off of π is experienced as the optical fields propagate between the critical angle in curved segment B 1   4430 , through curved segment B 1   4430 , and up until the critical angle in curved segment D 1   4432 . The phase walk-off in curved segment B 1   4430 , from the critical angle up until the end of curved segment B 1   4430 , and curved segment D 1   4432 , from the start of this curved segment until the critical angle, can be calculated via Equation 14. The relative phase walk-off in straight segment C 1   4422  satisfies the following condition 
     
       
         
           
             
               
                 
                   
                     Φ 
                     
                       C 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     π 
                     - 
                     
                       Φ 
                       
                         
                           θ 
                           ⁢ 
                           crit 
                         
                         : 
                         
                             
                         
                         ⁢ 
                         BC 
                       
                     
                     - 
                     
                       Φ 
                       
                         CD 
                         : 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           ⁢ 
                           crit 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     The length of straight segment C 1   4422  is selected as follows: 
     
       
         
           
             
               
                 
                   
                     L 
                     Ci 
                   
                   = 
                   
                     
                       Φ 
                       Ci 
                     
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         k 
                         ⁡ 
                         
                           ( 
                           C 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Where Δk(C) is the phase mismatch in straight segment C 1   4422  is constant value, since this segment is straight. 
     Next, the light travels through the rest of the curved segment D 1   4432 , propagates through straight segment A 2   4424  (where i&gt;1), and into curved segment B 2   4434 . The length of subsequent straight segments ‘A i ’ (i&gt;1) after straight segment A 1   4420  is selected to be designed differently from straight segment A 1   4420  because the phase walk-off cannot be neglected from preceding segments, such as curved segment D 1   4432 , which are not present in straight segment A 1   4420 . Straight segments ‘A i ’ are segments having the same orientation as straight segment A 1   4420 . 
     First, required phase walk-off in waveguide straight segments ‘A i ’ is determined from the following: 
     
       
         
           
             
               
                 
                   
                     Φ 
                     
                       A 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     π 
                     - 
                     
                       Φ 
                       
                         
                           θ 
                           ⁢ 
                           crit 
                         
                         : 
                         
                             
                         
                         ⁢ 
                         DA 
                       
                     
                     - 
                     
                       Φ 
                       
                         AB 
                         : 
                         
                             
                         
                         ⁢ 
                         
                           θ 
                           ⁢ 
                           crit 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     and the length is selected as follows: 
     
       
         
           
             
               
                 
                   
                     L 
                     
                       A 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       Φ 
                       
                         A 
                         ⁢ 
                         i 
                       
                     
                     
                       Δ 
                       ⁢ 
                       
                         k 
                         ⁡ 
                         
                           ( 
                           A 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     With selection of the length of the straight segments ‘A i ’, optical waveguide structure  4400  with nonlinear optical waveguide  4402 , device can enhance nonlinear optical processes such as spontaneous parametric down conversion (SPDC). 
     Examples of results from light propagation through a nonlinear optical waveguide having a staircase configuration such as that depicted for nonlinear optical waveguide  4402  in  FIG. 42  are shown by graphs depicted in  FIGS. 47-49 . In this illustrative example, the calculations for the results in these graphs are made with ordinary refractive index (experienced by optical fields propagating parallel to the z-axis), n 0 , taken to be n 0 =n e +0.05. Furthermore, the refractive index experienced in curved segments is taken to be simply the arithmetic mean of the ordinary and extraordinary refractive indices. Other parameters used in the calculations are as follows: speed of light, c=299792458 m/sp; Pump wavelength=655 nm; ne(pump)=1.72; signal wavelength=1130 nm; ne(signal)=1.8; idler wavelength=1558 nm; ne(idler)=1.6; Mp=−1, Ms=1; and radius of curvature, r=10 μm. In this example, Mp is the amplitude of the optical field for a pump light, and Ms is the amplitude of the optical field for a signal light. 
     With reference to  FIG. 46 , an illustration of a graph of a nonlinear optical coefficient a phase walk-off for light propagating through a nonlinear optical waveguide is depicted in accordance with an illustrative embodiment. In graph  4600 , Y axis  4602  represents phase walk-off in radians, Y axis  4604  represents the nonlinear optical coefficient in pm/V, and x-axis  4608  represents distance propagated in m. 
     As depicted, graph  4600  depicts how the nonlinear optical coefficient, deff, and the phase walk-off change as light propagate through nonlinear optical waveguide  4402  in  FIG. 44 . In this example, the graph shows parameters for nonlinear optical waveguide  4402  beginning at the origin and ending with straight segment A 2   4424 . A nonlinear optical waveguide can be simulated by including more waveguide sections, specifically the repeating unit of the structure, ‘segment Bi’, ‘segment Ci’, ‘curved segment Di’, and ‘segment Ai+1’. 
     In this example, straight segment Ai is a straight segment having the same orientation as straight segment A 1   4420 ; curved segment Bi is a curve segment having the same orientation as curved segment B 1   4430 ; straight segment Ci is a straight segment having the same orientation as straight segment C 1   4422 ; curved segment Di is a curve segment having the same orientation as curved segment D 1   4432  in  FIG. 44 . 
     Horizontal line  4610  and horizontal line  4612  indicate multiples of π. Vertical line  4614  and vertical line  4616  show the point in the nonlinear optical waveguide at which the nonlinear optical coefficient is equal to 0. In this example, line  4601  is the response for straight segment A 1   4420 . As depicted, curved segment B 1   4430 , straight segment C 1   4422 , curved segment D 1   4432 , and straight segment A 2   4424  are in lines  4603 . 
     From the origin up until line intersection  4617 , the phase walk-off is between 0 and π and the nonlinear optical coefficient is greater than 0. In-between the first and second intersection points of the dotted lines, the phase walk-off is between π and 2π, and the nonlinear optical coefficient is less than 0. According to Equation 10 (after being generalized for any arbitrary propagation direction) this ensures that the change in amplitude of the idler optical field is always greater than or equal to 0. 
     A longer nonlinear optical waveguide can be simulated by including more waveguide sections, specifically the repeating unit of the structure, ‘segment Bi’, ‘segment Ci’, ‘curved segment Di’, and ‘segment Ai+1’. In this example, segment Ai is a straight segment having the same orientation as segment A 1   4420 ; curved segment Bi is a curve segment having the same orientation as curved segment B 1   4430 ; straight segment Ci is a straight segment having the same orientation as straight segment C 1   4422 ; curved segment Di is a curve segment having the same orientation as curved segment D 1   4432  in  FIG. 44 . 
     Turning next to  FIG. 47 , an illustration of a graph of a rate of change in the amplitude of an online propagating through a nonlinear optical waveguide is depicted in accordance with an illustrative embodiment. 
     In graph  4700 , Y axis  4702  represents a change in amplitude of an idler light. X-axis  4704  is the distance propagated in meters. 
     Graph shows the rate of change in an idler light as the idler light as light propagates through nonlinear optical waveguide having a staircase configuration. The rates of change are calculated from a generalized form of Equation 10, where the parameters are determined for each individual waveguide section and then the rate of change is calculated as a function of position in nonlinear optical waveguide having a staircase configuration. 
     The length of the nonlinear optical waveguide simulated in this example begins at the origin and terminates after straight waveguide segment ‘A 4 ’. Lines  4710  indicates the rate of change in the idler light traveling through the different segments in the nonlinear optical waveguide as indicated by legend  4711 . Line  4712  indicates the rate of change in the idler light for a straight waveguide parallel to an y axis, such as y-axis  4408  in x-cut lithium niobate  4404  in  FIG. 44 . 
     Using an optical waveguide structure having a nonlinear optical waveguide with a staircase configuration, the rate of change in a signal light and an idler light can be greater than or equal to zero everywhere as shown for an idler light in line  4710 . In contrast, idler light in a straight waveguide has a rate fluctuates periodically between positive and negative values as depicted by line  4712 . 
     In  FIG. 48 , an illustration of an amplitude for an idler light propagating through a nonlinear optical waveguide is depicted in accordance with an illustrative embodiment. In graph  4800 , y-axis  4802  represents idler light amplitude. X axis  4804  represents distance propagated in m. Line  4806  represents idler light propagating through a nonlinear optical waveguide having a staircase configuration. Line  4808  represents idler light propagating through a straight waveguide. 
     As depicted in graph  4800 , the amplitude of the idler light in a nonlinear optical waveguide having a staircase configuration is calculated by taking the integral of the generalized form of Equation 10, which is also simply the area under the curve in  FIG. 47 . The idler light in line  4808  is calculated for a straight waveguide section oriented parallel to a y-axis, such as y-axis  4408  in x-cut lithium niobate  4404  in  FIG. 44 . Line  4806  as compared to line  4808  clearly indicate the ability of a nonlinear optical waveguide having a staircase configuration to provide desired level of light generation. 
     In the manufacturing optical waveguide structures, the fabrication processes can have some tolerances. For example, the designed waveguide geometries may not perfectly meet specifications. In manufacturing optical waveguide structures, the structures can be subject to random and systematic fabrication errors. Thus, in order to maintain the phase-matching conditions over many cycles of the “staircase” pattern, tuning the relative phase walk-off in the individual waveguide sections ‘A i ’, ‘B i ’, ‘C i ’, ‘D i ’, or some combination thereof, can be performed by adding tuning structures such as phase shifters. 
     With reference next to  FIG. 49 , an illustrative of an optical waveguide structure with a staircase configuration is depicted with phase shifters in accordance with an illustrative embodiment. In this illustrative example, optical waveguide structure  4400  depicted with the addition of a shifters to compensate for fabrication tolerances. 
     In this illustrative example, phase shifters are associated with straight segments in nonlinear optical waveguide  4402 . As depicted, phase shifters in the form of tuning electrodes can be incorporated into waveguide sections ‘A i ’ and ‘C i ’. In this example, tuning electrodes  4900  are associated with straight segment A 1   4420 ; tuning electrodes  4902  are associated with straight segment C 1   4422 , tuning electrodes  4904  are associated with straight segment A 2   4424 , tuning electrodes  4906  are associated with straight segment C 2   4426 , and tuning electrodes  4908  are associated with straight segment A 3   4428 . 
     Due to the χ 2  NLO susceptibility of a nonlinear optical material, an electric field applied across a segment in nonlinear optical waveguide  4202  can result in a change of the refractive index in the nonlinear optical material. This change is a phenomenon known as the electro-optic effect. Consequently, the phase walk-off in these sections will be modified in accordance with the magnitude and direction of the applied electric field in the waveguide. 
     These optional tuning electrodes associated with nonlinear optical waveguide  4202  can be very tolerant to fabrication processing as well as capable of maintaining the desired phase-matching conditions over many cycles of the “staircase” pattern. In other illustrative examples, thermo-optic phase-shifters can be used in place of or in addition instead of the electro-optic modulators, or both types of modulators could be used in some combination. In still other illustrative examples, the phase shifters, in part or in whole, could be based on charge-carrier depletion or injection. 
     In some examples, the tuning range of the phase shifting elements can be as large as desired to correct for fabrication tolerances and errors. With this situation, the length of waveguide segments, such as straight segments ‘A i ’ and ‘C i ’, can be extended such that the designed increase in relative phase walk-off in those sections is an odd multiple of π. Specifically, Equations 15, 17, and 19 can have a value of mπ on the right-hand-side of the equations instead of just a value of π, where m is any odd integer. 
     This type of adjustment can allow the rate of change in the signal light and idler light to oscillate between positive and negative values, ensuring the phase walk-off is an odd multiple of π between successive critical angles will maintain a net positive increase in the signal and idler optical field amplitudes. 
     For additional phase walk-off tuning, a cumulative phase walk-off, Φ, can be defined as follows: 
     
       
         
           
             
               
                 
                   Φ 
                   = 
                   
                     
                       l 
                       ⁢ 
                       Δ 
                       ⁢ 
                       k 
                     
                     = 
                     
                       l 
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 ω 
                                 p 
                               
                               ⁢ 
                               
                                 n 
                                 p 
                               
                             
                             c 
                           
                           - 
                           
                             
                               
                                 ω 
                                 s 
                               
                               ⁢ 
                               
                                 n 
                                 s 
                               
                             
                             c 
                           
                           - 
                           
                             
                               
                                 ω 
                                 i 
                               
                               ⁢ 
                               
                                 n 
                                 i 
                               
                             
                             c 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     where l is the distance that the optical fields have propagated. A phase shifting element is selected that can produce a change in the effective index of the optical fields whose magnitude depends on some function ƒ(ρ) where ρ is some parameter of the phase shifting element that a user can adjust. For example, in the case of electro-optic phase-shifters, the adjustable parameter could be voltage. Thus, the cumulative phase walk-off with some phase shifting element is now given by 
     
       
         
           
             
               
                 
                   
                     Φ 
                     ⁡ 
                     
                       ( 
                       ρ 
                       ) 
                     
                   
                   = 
                   
                     l 
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               ω 
                               p 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   n 
                                   p 
                                 
                                 + 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                     n 
                                     p 
                                   
                                   ⁢ 
                                   
                                     
                                       f 
                                       p 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       ρ 
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           c 
                         
                         - 
                         
                           
                             
                               ω 
                               s 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   n 
                                   s 
                                 
                                 + 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                     n 
                                     s 
                                   
                                   ⁢ 
                                   
                                     
                                       f 
                                       s 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       ρ 
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           c 
                         
                         - 
                         
                           
                             
                               ω 
                               i 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   n 
                                   i 
                                 
                                 + 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                     n 
                                     i 
                                   
                                   ⁢ 
                                   
                                     
                                       f 
                                       i 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       ρ 
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           c 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     from which it follows that 
     
       
         
           
             
               
                 
                   
                     
                       d 
                       ⁢ 
                       
                         Φ 
                         ⁡ 
                         
                           ( 
                           ρ 
                           ) 
                         
                       
                     
                     
                       d 
                       ⁢ 
                       ρ 
                     
                   
                   ∝ 
                   l 
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     Thus, the cumulative phase walk-off can be more efficiently adjusted for longer waveguide sections, enabling a greater tuning range for a finite operational range of ρ in the phase shifting element. 
     In some instances, the radius of curvature in the waveguide bends may need to be excessively small in order to satisfy the design criteria of Equations 15, 17, and 19. Such cases are undesirable because one or more of the type of light, such as signal light or idler light, may experience significant optical losses in these curved waveguide sections with small radius of curvature. Furthermore, the nonlinear optical coefficient is largest in waveguide sections ‘A i ’. As a result, as the length of these sections are longer these sections relative to the curved waveguide sections, greater nonlinear optical efficiency enhancement occurs. In other words, it is desirable to have length L coh »radius r. Although changing the cross-sectional geometry of the waveguide may provide some tunability of length L coh , this tuning range may not be as large as desired. 
     Using a higher-order mode for one (or more) of the optical fields can provide a considerable change in the effective index of that optical field in the waveguide. Consequently, length L coh  can be significantly increased. Another manner in which length L coh  can be increased is to add cladding of another material to the main nonlinear optical waveguide. This addition can result in increasing length L coh  when such a cladding induces a change in effective index that is greater for some of the optical fields than for others. These are examples of dispersion engineering in the waveguide in order to produce a more optimal length L coh . These adjustments are optional ones that can be made. Other types of adjustments can also be made depending on the particular implementation. 
     In this illustrative example, specific orientations of the segments are selected relative to the crystal axes of the nonlinear optical material in order to maximize the efficiency of the nonlinear optical process. However, in some case, such as when d 22 &lt;d 33 , the propagation direction parallel to the z-axis may not significantly affect the overall nonlinear optical efficiency. For example, a variation of the configuration shown for nonlinear optical waveguide  4402  in  FIG. 44  can be used. 
     With reference to  FIG. 50 , an illustration of an optical waveguide structure is depicted in accordance with an illustrative embodiment. Optical waveguide structure  5000  is an example of an implementation for optical waveguide structure  4200  in  FIG. 42 . 
     As depicted, optical waveguide structure  5000  comprises nonlinear optical waveguide  5002  formed in x-cut lithium niobate  5004 . As depicted, nonlinear optical waveguide  5002  lies on plane  5006  defined by y-axis  5008  and z-axis  5010  in crystal axes  5011 . In this example, x-axis  5012  in crystal axes  5011  is perpendicular to plane  5006 . In this example, z-axis  5010  is the crystal optical axis in crystal axes  5011 . 
     In this example, nonlinear optical waveguide  5002  has straight segments and curved segments. This illustrative example, the straight segments are straight segment A 1   5020 , straight segment C 1   5022 , straight segment A 2   5024 , straight segment C 2   5026 , and straight segment A 3   5028 . The curved segments are curved segment B 1   5030 , curved segment D 1   5032 , curved segment B 2   5034 , and curved segment D 2   5036 . 
     With this configuration, nonlinear optical coefficient d33  5040  of x-cut lithium niobate  5004 , which has the greatest magnitude. Further with this configuration, nonlinear optical coefficient d33  5040  is positive. Thus, the nonlinear optical process is most efficient in the following segments are aligned along y-axis  5008 . 
     Nonlinear optical coefficient d22  5042  for x-cut lithium niobate  5004  is present for segments aligned along z-axis  5010 . In this example, nonlinear optical coefficient d22  5042  is positive. 
     In nonlinear optical waveguide  5002 , the main nonlinear optical contributions would be produced in segments ‘A i ’. A decrease in the nonlinear optical contribution would be experienced in segments ‘C i ’. 
     With reference next to  FIG. 51 , an illustration of an optical waveguide structure having a serpentine configuration is depicted in accordance with an illustrative embodiment. Optical waveguide structure  5100  is an example of an implementation for optical waveguide structure  4200  in  FIG. 42 . 
     As depicted, optical waveguide structure  5100  comprises nonlinear optical waveguide  5102  formed in x-cut lithium niobate  5104  and has a serpentine configuration. As depicted, nonlinear optical waveguide  5102  lies on plane  5106  defined by y-axis  5108  and z-axis  5110  in crystal axes  5111 . In this example, x-axis  5112  in crystal axes  5111  is perpendicular to plane  5106 . In this example, z-axis  5110  is the crystal optical axis in crystal axes  5111 . 
     In this example, nonlinear optical waveguide  5102  has straight segments and curved segments. The straight segments in this example are straight segment Al  5120 , straight segment C 1   5120 , straight segment A 2   5122 , straight segment F 1   5124 , and straight segment A 3   5126 . The curved segments are curved segment B 1   5128 , curved segment D 1   5130 , curved segment E 1   5132 , and curved segment G 1   5134 . 
     With this configuration, nonlinear optical coefficient d33  5140  of x-cut lithium niobate  5104  is present for segments aligned along y-axis  5108 , which has the greatest magnitude. Further with this configuration, nonlinear optical coefficient d33  5140  is positive. Nonlinear optical coefficient d22  5142  for x-cut lithium niobate  5104  is present for segments aligned along z-axis  5110  In this example, nonlinear optical coefficient d22  5142  is negative for straight segment C 1   5120 , and nonlinear optical coefficient d22  5144  is positive for straight segment F 1   5124 . 
     With this serpentine configuration, the direction of propagation in waveguide sections parallel to the z-axis alternates with every repetition of the segments. In nonlinear optical waveguide  5102 , the nonlinear optical processes that occur in straight segments ‘C i ’ are essentially canceled out by the nonlinear optical processes that occur in straight segments ‘F i ’ because to the change in sign of the nonlinear optical coefficient d22. Thus, enhancement of the nonlinear optical process occurs almost entirely in straight segments ‘A i ’. 
     This example may have desirable features when certain geometric constraints of the structure are imposed. For example, it may be preferable to reduce the footprint of nonlinear optical waveguide  5102  relative to z-axis  5110 . In this example, phase shifters can optionally be placed on waveguide segments, such as straight segment ‘A i ’, curved segment ‘B i ’, straight segment ‘C i ’, curved segment ‘D i ’, curved segment ‘Ei’, straight segment ‘Fi’, curved segment ‘Gi’ or some combination thereof. 
     In other embodiments of this invention, a combination of the “staircase” and “serpentine” structures could be used. In other words, the orientation of one curved segment relative to the curved segments sections preceding and following it can be in any arbitrary pattern with as the arrangement of the curved segments maintaining a single propagation direction in segments ‘Ai’ and using the design criteria for the lengths of each section as described above, resulting in a net increase of nonlinear optical efficiency from the proper phase-matching. This example can be used to control the overall footprint of nonlinear optical waveguide structure. 
     With reference next to  FIG. 52 , an illustration of an optical waveguide structure having to nonlinear optical waveguides connected by connecting optical waveguide is depicted in accordance with an illustrative embodiment. As depicted, optical waveguide structure  5200  is an example of an implementation for optical waveguide structure  4200  shown in block form in  FIG. 42 . 
     As depicted, optical waveguide structure  5200  is formed in x-cut lithium niobate  5204  and has a serpentine configuration. As depicted, nonlinear optical waveguide  5214  and nonlinear optical waveguide  5216  lie on plane  5206  defined by y-axis  5208  and z-axis  5210  in crystal axes  5211 . In this example, x-axis  5212  in crystal axes  5211  is perpendicular to plane  5206 . In this example, z-axis  5210  is the crystal optical axis in crystal axes  5211 . 
     In this example, optical waveguide structure  5200  comprises nonlinear optical waveguide  5214  and nonlinear optical waveguide  5216  connected to each other by connecting optical waveguide  5218 . As depicted, nonlinear optical waveguide  5214  is comprised of first straight segments and first curved segments connecting the first straight segments to each other. In this illustrative example, nonlinear optical waveguide  5216  is comprised of second straight segments and second curved segments that connect the second set segments to each other. 
     Connecting optical waveguide  5218  connects first segment  5220  in the first straight segments in nonlinear optical waveguide  5214  to second straight  5222  in second straight segments in nonlinear optical waveguide  5216 . Connecting optical waveguide  5218  can be comprised of the nonlinear optical material having the second order nonlinear coefficient for the nonlinear optical process in which the second order nonlinear coefficient changes with the direction of light propagation. Alternatively, connecting optical waveguide  5218  can be comprised of a material different material from the nonlinear optical material. 
     The material used in connecting optical waveguide  5218  can also be a combination of segments that include both nonlinear optical waveguide materials and optical waveguide materials other than nonlinear optical waveguide materials. The selection and configuration of connecting optical waveguide  5218  can be selected to preserve the light of interest that does not result in an undesired optical loss. 
     It can bis desirable to maintain the same propagation direction in segments ‘Ai’ to increase or enhance the nonlinear optical process. This type of design, however, can have a limitation with respect to the overall length of optical waveguides and optical waveguide structure, relative to y-axis for x-cut lithium niobate. However, the use of two nonlinear optical waveguides as depicted in optical waveguide structure  5200  can both begin at some −y position in x-cut lithium niobate  5204 , end at some position in the +y direction in x-cut lithium niobate  5204 . The structures can also be offset from each other by some distance relative to z-axis  5210  with connecting optical waveguide  5218  connecting the two nonlinear optical waveguides to each other. 
     Connecting optical waveguide  5218  can have a relative degree of phase walk-off so that the nonlinear optical process is more efficiently enhanced in the straight segments ‘Ai’. Further, in another example connecting optical waveguide bridges can be located at the end of a nonlinear optical waveguide with its origin, effectively turning the optical waveguide structure into a resonator. 
     In illustrative example, segments with a lower deff can comprise a material different than that which segments with the largest deff. For example, at least one of straight segments ‘Ci’ or ‘Fi’ can be replaced with a material that has a smaller χ (2)  NLO susceptibility, such as SiN. With this configuration, essentially no nonlinear optical processes occur in these waveguide sections. However, the light still experiences a phase walk-off in line with the design criteria described above, enabling the nonlinear optical enhancement to still occur in straight segments ‘Ai’. 
     The illustration of optical waveguide structure  5200  is presented is depicted as one example of multiple nonlinear optical waveguides connected by connecting optical waveguide, and not meant to limit the manner in which other illustrative examples can be implemented. For example, other illustrative examples can connect additional nonlinear optical waveguides depending on the particular implementation. Further, other illustrative examples can use other configurations such as a serpentine configuration in addition to or in place of a cascading or staircase configuration. 
     In another illustrative example, other types of mechanisms can be used in addition to or in place of phase shifters which can be incorporated each iteration of segments incurred segments for a coherent interaction length of the nonlinear optical process. Instead of using the phase shifters to correct for fabrication tolerances, the phase shifters they could be used to intentionally change the wavelengths (frequencies) of the pump light, signal light, and idler light in the nonlinear which satisfy Equations 15, 17, and 19. Furthermore, the phase shifters can be used to change the effective indices of the three types of light, changing the wavelengths to enhance the nonlinear optical process. For example, if the target nonlinear optical process in an optical waveguide structure is spontaneous parametric down conversion, using phase shifters on at least one of a straight segment or a curved segment enables tuning, on-demand, the wavelengths of signal and idler optical fields which are enhanced by the nonlinear optical process, energy conservation still being satisfied. Constraints taken into account for this feature for the tuning bandwidth are (i) the cross-sectional geometry of the waveguide, which still supports guided modes at the target wavelengths and (ii) the efficiency (and operating range) of the phase shifting elements. 
     In the illustrative examples, wavelength-selective components are not required. As a result, fabrication tolerances may not impact the efficiency of the nonlinear optical process. In other words, even if the fabrication deviates slightly from the design, some combination of signal light and idler light will be present that meet the criteria above for phase matching and are ultimately enhanced by the optical waveguide structure. 
     This feature can be useful in applications where the precise wavelengths produced by the nonlinear optical process are not required. For example, if the application produces photon pairs from spontaneous parametric down conversion and the target wavelength has a large tolerance. 
     Although the illustrative examples employ curved segments described having a circular curvature, this type of curvature is not required. In other illustrative examples, some other curvature type can be used. Furthermore, segments ‘Ci’ and ‘Fi’ do not necessarily have to be oriented perpendicular (90°) to waveguide sections ‘Ai’. As long as the general design criteria outlined above are met, and deff is largest in waveguide sections ‘Ai’, then the nonlinear optical enhancement will still occur at the desired level. 
     With reference now to  FIG. 53 , an illustration of a flowchart of a process for moving a light through an optical waveguide structure is depicted in accordance with an illustrative embodiment. The process in  FIG. 53  can be implemented in physical waveguide structure such as optical waveguide structure  4200  in  FIG. 42  and in the different physical implementations shown in the different illustrative examples. 
     The process begins by inputting a pump light in the light into a nonlinear optical waveguide, wherein the nonlinear optical waveguide comprises a nonlinear optical material having a second order nonlinear coefficient for a nonlinear optical process in which the second order nonlinear coefficient changes with a direction of light propagation (operation  5300 ). The process propagates the light through straight segments connected by curved segments in which an overall nonlinear optical interaction in the straight segments is constructive in the nonlinear optical waveguide such that light generation occurs (operation  5302 ). With the process terminating thereafter. 
     Thus, the illustrative examples provide an optical waveguide structure that enables increasing the efficiency of nonlinear optical processes for light traveling within the optical waveguide structure. The straight segments and the curved segments are configured such that energy is conserved in nonlinear optical processes. In the illustrative examples, the propagation direction and distance of propagation of light is controlled within optical waveguide structures with respect to the orientation of crystal axes in the material from which the optical waveguide structures are manufactured. Also, with the use of phase shifters, increased coherent interaction lengths can be achieved that are greater than with current devices. 
     Thus, with the different optical waveguide structures the properties of optical waveguide structures described in  FIGS. 42-53 , improving nonlinear optical processes occur making optical waveguide structures in the illustrative examples useful for various implementations. For example, the optical waveguide structures can be used in single photon or entangled photon sources in quantum applications. The frequency conversion that can be achieved through nonlinear optical processes can be used to generate light at wavelengths that are not readily available in currently available devices. For example, nonlinear optical processes can be used to generate ultraviolet light from visible light. This ultraviolet light can be used in in disinfection, chemical catalysis, solar-blind optical communications, as well as other applications. As another example, the optical waveguide structures can implement nonlinear optical processes that generate mid-wave infrared and long-wave infrared light, which are wavelengths often used in aerospace applications. 
     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 nonlinear optical waveguide comprising a nonlinear optical material having a second order nonlinear optical coefficient for a nonlinear optical process in which the second order nonlinear optical coefficient changes with a direction of light propagation; 
     straight segments in the nonlinear optical waveguide, the straight segments are oriented such that a nonlinear optical interaction with light generation occurs with an overall constructive manner within the nonlinear optical waveguide in response to a light traveling though the nonlinear optical waveguide; and 
     curved segments in the nonlinear optical waveguide with a 90 degree bend, wherein the curved segments connect the straight segments to each other within in the nonlinear optical waveguide. 
     Clause 2 
     The optical waveguide structure according to clause 1 further comprising: 
     first segments in the straight segments; and 
     second segments in the straight segments, wherein the second segments have an orientation that is perpendicular to the first segments and the curved segments connect the first segments to the second segments. 
     Clause 3 
     The optical waveguide structure according to one of clauses 1 or 2, wherein the light travels in a first direction in the first segments and in a second direction in the second segments in which the second direction is perpendicular to the first direction in the first segments, wherein the nonlinear optical interaction of the light traveling in the first direction is constructive. 
     Clause 4 
     The optical waveguide structure according to one of clauses 1 2, or 3, wherein a phase walk-off of a multiple of π occurs between a first point in a first curved segment in the curved segments and a second point in a second curved segment in the curved segments, wherein the first curved segment and the second curved segment are connected to a straight segment in the straight segments. 
     Clause 5 
     The optical waveguide structure according to one of clauses 1 2, 3, or 4, wherein the straight segments are first straight segments and the curved segments are second curved segments and further comprising: 
     second straight segments; 
     second curved segments, wherein the second curved segments connect first straight segments to each other; and 
     a connecting optical waveguide that connects a first straight segment in the first straight segments to a second straight segment in the second straight segments. 
     Clause 6 
     The optical waveguide structure according to clause 5, wherein the connecting optical waveguide is comprised of the nonlinear optical material having the second order optical nonlinear coefficient for the nonlinear optical process in which the second order nonlinear optical coefficient changes with the direction of light propagation. 
     Clause 7 
     The optical waveguide structure according to clause 5, wherein the connecting optical waveguide is comprised of a material that is a different material from the nonlinear optical material. 
     Clause 8 
     The optical waveguide structure according to one of clauses 1 2, 3, 4, 5, 6, or 7, wherein the curved segments connect the straight segments to each other form at least one of a cascaded configuration, a stair case configuration, or a serpentine configuration for the nonlinear optical waveguide. 
     Clause 9 
     The optical waveguide structure according to one of clauses 1 2, 3, 4, 5, 6, 7, or 8, wherein the straight segments have a first length that is greater than a second length of the curved segments. 
     Clause 10 
     The optical waveguide structure according to one of clauses 1 2, 3, 4, 5, 6, 7, or 8, wherein the nonlinear optical waveguide is formed from an x-cut lithium niobate and wherein the nonlinear optical waveguide is formed on a plane in which an x-axis of an x-cut lithium niobate is perpendicular to the plane. 
     Clause 11 
     The optical waveguide structure according to one of clauses 1 2, 3, 4, 5, 6, 7, 8, or 9, wherein the nonlinear optical process selected from a group comprising a second-harmonic generation (SHG), a difference frequency generation (DFG), a parametric down conversion (PDC), a sum frequency generation (SFG), and a parametric up conversion (PUC). 
     Clause 12 
     The optical waveguide structure of according to one of clauses 1 2, 3, 4, 5, 6, 7, 8, 9, or 10, wherein the light comprises a pump light and wherein the nonlinear optical interaction of the pump light generates at least one of a signal light or an idler light. 
     Clause 13 
     The optical waveguide structure according to one of clauses 1 2, 3, 4, 5, 6, 7, 8, 9, 10, or 11 further comprising: 
     a set of phase shifters in a set of locations relative to the nonlinear optical waveguide, wherein the set of phase shifters operates to apply a set of activations to change a phase of the light. 
     Clause 14 
     The optical waveguide structure according to clause 13, 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 15 
     The optical waveguide structure according to one of clauses 1 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, or 14 further comprising: 
     a set of optical couplers connected to the nonlinear optical waveguide, wherein the set of optical couplers operate at least one of couple light into the nonlinear optical waveguide or out of the nonlinear optical waveguide. 
     Clause 16 
     An optical waveguide structure comprising: 
     a nonlinear optical waveguide comprising a a nonlinear optical material having a second order nonlinear optical coefficient for a nonlinear process in which the second order nonlinear optical coefficient changes with a direction of light propagation; 
     first segments in the nonlinear optical waveguide; 
     second segments in the nonlinear optical waveguide, wherein the second segments have an orientation that is perpendicular to the first segments, the first segments and the second segments oriented such that a nonlinear optical process with light generation that occurs within the first segments and the second segments; and 
     curved segments in the nonlinear optical waveguide with a 90 degree bend, wherein the curved segments connect the first segments to the second segments. 
     Clause 17 
     The optical waveguide structure according to clause 16, wherein the nonlinear optical waveguide is formed from an x-cut lithium niobate and wherein the optical waveguide structure is formed on a plane in which an x-axis of an x-cut lithium niobate is perpendicular to the plane. 
     Clause 18 
     The optical waveguide structure according to one of clause 16 or 17, wherein the nonlinear optical process selected from a group comprising second-harmonic generation (SHG), a difference frequency generation (DFG), a parametric down conversion (PDC), a sum frequency generation (SFG), and a parametric up conversion (PUC). 
     Clause 19 
     A method for moving a light through an optical waveguide structure, the method comprising: 
     inputting a pump light in the light into a nonlinear optical waveguide, wherein the nonlinear optical waveguide comprises a nonlinear optical material having a second order nonlinear optical coefficient for a nonlinear optical process in which the second order nonlinear optical coefficient changes with a direction of light propagation; and 
     propagating the light through straight segments connected by curved segments in which an overall nonlinear optical interaction in the straight segments is constructive in the nonlinear optical waveguide such that light generation occurs. 
     Clause 20 
     The method of according to clause 19, wherein a phase walk-off of a multiple of π occurs between a first point in a first curved segment in the curved segments and a second point in a second curved segment in the curved segments connecting, wherein the first curved segment and the second curved segment are connected to a straight segment in the straight segments. 
     The different illustrative embodiments have 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.