Patent Publication Number: US-2016245999-A1

Title: Low Loss Optical Crossing and Method of Making Same

Description:
This application is a continuation of U.S. patent application Ser. No. 14/165,229, entitled “Low Loss Optical Crossing and Method of Making Same,” filed on Jan. 27, 2014, which application is hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     This invention relates generally to photonic integrated circuits (PICs) and, more specifically, to an optical crossing and method of making the same. 
     BACKGROUND 
     A PIC is a device that integrates multiple photonic circuit elements, analogous to electronic integrated circuits. PICs are distinct from electronic integrated circuits in that they use light rather than electrons to carry out a variety of optical functions. PICs allow optical systems to be made more compact, more efficient, more capable, and less expensive than with discrete optical components. PICs are often found in optical communication systems and photonic computing systems, where demand for high-speed and high-bandwidth circuits is ever increasing. The need for denser, more complex PICs grows with the demand for speed and bandwidth. Low-loss photonic circuit elements, such as self-imaging crossings and diffractive beam propagation crossings, allow these demands to be met in a wide variety of devices, including photonic switches, adaptive filters, multi-carrier transceivers, modulators, multiplexers, and demultiplexers, among many others. 
     PICs generally include multiple optical waveguides and are fabricated from a variety of materials, including silicon, silica, lithium niobate (LiNbO3), gallium arsenide (GaAs), indium phosphide (InP), lead lanthanum zirconate titanate (PLZT), and silicon nitride (Si3N4). For example, in silicon optical waveguides, a typical structure includes a silicon core having a high refractive index surrounded by silicon dioxide (silica) cladding having a low refractive index, which is typically fabricated on a silicon wafer. This structure is common for communication wavelengths, such as the 1310 nm band, the 1490 nm band, and the 1550 nm band. A PIC can be formed by lithographic techniques, including optical lithography and electron-beam lithography. Optical proximity correction techniques can be used to enhance the optical lithography to improve the fabrication precision of photonic circuit elements by more accurately creating the desired element shapes in the PIC material. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention provide an optical crossing and a method for making an optical crossing. 
     A PIC embodiment having an optical crossing includes a crossing region having a crossing length, wherein a light path through the crossing region is laterally unbound. The PIC embodiment also includes an input waveguide and an output waveguide. The input waveguide has an input crossing end and an input distal end, and is coupled to the crossing region at the input crossing end, thereby partially forming the light path. The output waveguide has an output crossing end and an output distal end, and is also coupled to the crossing region at the output crossing end, partially forming the light path. A crossing width of the output waveguide at the output crossing end is larger than a crossing width of the input waveguide at the input crossing end, the difference being set according to the crossing length. 
     A method embodiment for making an optical crossing in a PIC includes forming a waveguide. Then a crossing waveguide is formed that bisects the waveguide into an input waveguide and an output waveguide, thereby forming a crossing region. At the crossing region, the output waveguide is wider than the input waveguide. 
     The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a schematic diagram of one embodiment of a PIC; 
         FIG. 2  is an illustration of a cross section of one embodiment of a very wide multi-mode optical ridge waveguide; 
         FIG. 3  is an illustration of one embodiment of an optical crossing; 
         FIG. 4  is an illustration of one embodiment of a series of optical crossings; and 
         FIG. 5  is a flow diagram of one embodiment of a method of forming a PIC. 
     
    
    
     Corresponding numerals and symbols in different figures generally refer to corresponding parts unless otherwise indicated. The figures are drawn to clearly illustrate the relevant aspects of embodiments of the present invention and are not necessarily drawn to scale. To more clearly illustrate certain embodiments, a letter indicating variations of the same structure, material, or process step may follow a figure number. 
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     The making and using of embodiments are discussed in detail below. It should be appreciated, however, that the present invention provides many applicable inventive concepts that may be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use the invention, and do not limit the scope of the invention. 
     A typical PIC waveguide includes a dielectric region of high refractive index surrounded vertically and laterally by at least one dielectric region of lower refractive index, forming a rectangular or square optical waveguide. Such a waveguide supports zero or more optical modes that are bound, where a bound optical mode propagates along the waveguide without radiating away from the waveguide. The bound optical mode with the highest propagation constant is known as the lowest-order mode. The lowest-order mode has a peak amplitude toward the center of the waveguide core, decaying monotonically away from the peak. Generally, there is a lowest-order mode of a transverse electrical (TE) polarization and a lowest-order mode of a transverse magnetic (TM) polarization, where the strongest electromagnetic field component is respectively an electrical field (TE) or magnetic field (TM) that is parallel to the plane of the substrate. 
     Complex PICs often include at least one optical waveguide that physically crosses one or more other optical waveguides, forming a crossing region at the intersection. In some PICs, a single lightpath can have 100 or more optical crossings in series. The crossings can be at any angle, for example, a crossing at 90 degrees, a crossing at 45 degrees, a crossing at 30 degrees, or any other angle. Optical crossings can introduce loss and crosstalk to the optical signals propagating through. As a light beam propagates through the crossing region, signal power is lost into the crossing waveguide, causing crosstalk into the crossing waveguide. Similarly, the light beam also experiences crosstalk from the signal propagating through the crossing waveguide. Light is also lost from the light beam by scattering and radiation in the vertical and lateral directions out of the wave guiding regions. 
     As a light beam leaves the narrow aperture of an input waveguide, entering the crossing region, the light beam diffracts and gets larger as it propagates through the crossing region. When the light beam reaches the output waveguide, it presents in a larger output mode. Many PIC technologies support a single optical layer, with all crossings in-plane. Consequently, the lightpath through the crossing region is typically bound vertically and unbound laterally, where vertical describes a plane that is normal to the PIC chip surface and lateral refers to the plane of the chip and perpendicular to the direction of propagation of the light beam. Furthermore, expansion of the light beam propagating through the crossing region is typically lateral. Additional layers are possible, in which case the crossing region would be further unbound vertically and vertical beam expansion would be expected. 
     Some PICs use very wide multi-mode waveguides that experience low loss when only the lowest order optical mode is excited. The high refractive index contrast of a silicon waveguide enhances scattering loss at the core-cladding boundary. These waveguides use a very large core with a shallow ridge, or shoulder. These waveguides are sometimes referred to as wide-ridge waveguides, or simply ridge waveguides. By exciting only the lowest order optical mode, most of the electromagnetic (EM) field is confined within the silicon core such that the amplitude of the electromagnetic field is small at the core-cladding boundary to reduce scattering effects, and scattering is further reduced by the small height of the core-cladding boundary of the shallow silicon ridge relative to the overall size of the core. One way for these multi-mode waveguides to cross each other is by diffractive beam crossings. As the light of the lowest order optical mode reaches the crossing region, the optical mode becomes a light beam that propagates through the crossing region and, again, the electromagnetic field of the light beam is well confined to the core and scattering is reduced by the shallow ridge, resulting in a low-loss crossing. 
     It is realized herein the already low-loss crossing with very wide multi-mode waveguides can be improved by further accounting for beam expansion as a light beam propagates through a crossing region from an input waveguide to an output waveguide. It is realized herein the output waveguide should have a larger mode size than the input waveguide, thereby maximizing the overlap of the light beam and optical mode of the output waveguide. The increase in mode size can be computed according to an expected beam expansion through the crossing region. For example, beam expansion can be computed using a paraxial Gaussian beam calculation, which depends on the propagation distance across the crossing region, among other parameters, including the refractive index of the materials in the crossing, the electromagnetic cross-section of the input optical mode, and the electromagnetic cross-section of the output optical mode. For example, for an input waveguide having a width of 6.00 micrometers of silicon intersecting a crossing waveguide of the same width, the corresponding output waveguide could be 6.13 micrometers based on a calculated beam expansion for a given free-space wavelength of 1550 nm. 
     It is also realized herein the already low-loss crossing can be further improved by accounting for the angular alignment of the light beam propagating through the crossing region. It is realized herein that when the output crossing waveguide is larger than the input crossing waveguide, the crossing end of the input waveguide is no longer perpendicular to the input waveguide. Consequently, the optical beam refracts at the crossing end of the input waveguide and propagates at a small angle laterally. The diffracted optical beam in the crossing is also refracted as it enters the crossing. It is further realized herein, the output waveguide should be displaced laterally by an offset from the input waveguide, according to an expected refraction of the light beam as it enters the crossing region, among other parameters, including the refractive index of the materials in the crossing, the electromagnetic cross-section of the input optical mode, and the electromagnetic cross-section of the output optical mode. Rather than the input and output waveguides being co-linear, it is realized herein, the displaced output waveguide is centered on the diffracted light beam at the crossing end of the output waveguide, thereby further maximizing the overlap of the diffracted light beam with the optical mode of the output waveguide. 
     It is further realized herein the optimum difference in width between the input and output waveguides is related to the lateral offset between the input and output waveguides. A PIC designer should calculate them together with a goal of optimization. For example, larger lateral offsets generally accompany larger differences in widths between the input and output waveguides. 
     It is also realized herein that crossings often occur in series, creating a practical problem for output waveguides that are progressively larger as the lightpath spans each crossing. It is also realized herein the output waveguide of a crossing can be tapered down to the width of the input waveguide between crossings. In this arrangement, in a PIC having a series of crossings, the width of the input waveguide is the same entering each crossing, and the output waveguide is larger at the crossing and tapers back down to the width of the input waveguide as the light beam propagates. 
       FIG. 1  is a schematic diagram of one embodiment of a PIC  100  within which the optical crossing and method of making an optical crossing introduced herein may be embodied or carried out. PIC  100  includes four columns of switch elements, column  110 - 1 , column  110 - 2 , column  110 - 3 , and column  110 - 4 , arranged to form a portion of a photonic switch. As light paths  140  enter the switch elements of column  110 - 1 , PIC  100  routes them to various switch elements in column  110 - 2 , causing most light paths to incur multiple crossings. For example, a light path  120  (emphasized in bold) passes through seven crossings between column  110 - 1  and column  110 - 2 , three crossings between column  110 - 2  and column  110 - 3 , and one crossing between column  110 - 3  and column  110 - 4 , totaling eleven crossings. Other embodiments of PIC  100  can include hundreds of crossings for a single light path before it exits as switched light beams  150 . 
       FIG. 2  is an illustration of one embodiment of a very wide multi-mode optical ridge waveguide  200 . Section A illustrates a propagation dimension of waveguide  200 , and Section B illustrates a cross section of waveguide  200 . Waveguide  200  is wide enough to support multiple optical modes, only the lowest order mode, or the fundamental mode, of waveguide  200  is excited. Typically, this is achieved by forming the light path with a narrow single-mode waveguide (not shown in  FIG. 2 ) that supports only a lowest-order mode. The narrow single-mode waveguide gradually tapers to the wide multi-mode waveguide  200 . So long as the taper is gentle, the light remains in the lowest-order mode. An optical signal passing through waveguide  200  in the lowest order mode experiences very low loss. 
     Waveguide  200  includes a core  260  having a ridge  230  surrounded laterally by a shoulder  210  and another shoulder  240 . Core  260  is surrounded by a cladding  220 . In certain embodiments, cladding  220  is homogeneous, while in alternative embodiments, cladding  220  can vary among the sides of core  260 . Waveguide  200  can be formed using a variety of material systems. For example, in one embodiment using silicon and silica, core  260  is made of silicon. The silicon of ridge  230  has a larger depth than shoulder  210  and shoulder  240 , forming a sidewall  250  at the boundary of ridge  230  and shoulder  240 , and another sidewall at the boundary of ridge  230  and shoulder  210  that is not visible in  FIG. 2 . The sidewalls are formed by etching, leaving the sidewalls rough, which contributes to scattering loss. The top and bottom surfaces of ridge  230 , shoulder  210 , and shoulder  240  are typically much smoother and contribute little loss. Shoulder  240  and shoulder  210  push a portion of core  260 &#39;s sidewalls out wider, such that the fundamental mode in waveguide  200  is confined in the center, further from the sidewalls, thus reducing scattering loss for the fundamental mode. 
       FIG. 3  is an illustration of one embodiment of an optical crossing  300 . Optical crossing  300  may be embodied in a PIC made using a variety of material systems, including silica on silicon, LiNbO3, and GaAs, among others. Optical crossing  300  includes an input waveguide  302  and an output waveguide  304 . Input waveguide  302  and output waveguide  304  form a primary light path  312  through a crossing region  310 . Primary light path  312  intersects a crossing light path  318  at crossing region  310 , which bisects input waveguide  302  and output waveguide  304 . Crossing light path  318  is formed by an input crossing waveguide  306  and an output crossing waveguide  308 , which is also bisected by crossing region  310 . 
     Input waveguide  302  has an input width  332  and refractive index cross section that defines a fundamental optical mode. Input width  332  is defined in the lateral dimension for input waveguide  302 . As primary light path  312  reaches crossing region  310  through input waveguide  302 , it assumes a mode shape represented by an input mode spot  324 . Input mode spot  324  is centered laterally upon input waveguide  302 . Crossing region  310  is unbound laterally with respect to primary light path  312 . As a light beam propagates through input waveguide  302  and arrives at crossing region  310 , it refracts slightly, angling primary light path  312  to a refracted light path  314 . Additionally, as the light beam propagates through crossing region  310 , it experiences beam expansion due to diffraction. The resulting output mode shape is slightly larger than that represented by input mode spot  324 . The output mode shape is represented an output mode spot  326 , which is slightly larger than input mode spot  324 . 
     Output waveguide  304  has a crossing end disposed near crossing region  310  and a distal end disposed away from crossing region  310 . Output waveguide  304  is displaced laterally with respect to input waveguide  302 . The displacement is intended to center output mode spot  326  laterally on output waveguide  304 , thereby improving the overlap of refracted and diffracted light path  314  with the fundamental mode for output waveguide  304 . The displacement reduces loss otherwise experienced when the fundamental mode for output waveguide  304  is co-linear with input waveguide  302 , therefore not accounting for refraction as light path  312  enters crossing region  310 . The displacement is quantified by a lateral offset of output mode spot  326  from input mode spot  324 . The lateral offset can be computed based on the expected refraction and diffraction through crossing region  310 , which is typically a function of the dimensions of crossing region  310 . 
     Output waveguide  304  has an output crossing width  334 , in the lateral dimension, at its crossing end. Output crossing width  334  is slightly larger than input width  332 . The slight increase in width accounts for beam expansion experienced as a light beam propagates through crossing region  310 . Output crossing width  334  can be computed according to the expected beam expansion, which is typically computed as a function of the dimensions of crossing region  310 . The computation can be based on a paraxial Gaussian beam calculation, which uses the length of crossing region  310  along the direction of propagation of the light path. Alternatively, the propagation computation can be based on a beam propagation calculation or a finite difference time domain calculation. The larger width of output crossing width  334  further improves the overlap of the diffracted light path and slightly larger output mode shape with the fundamental mode of output waveguide  304 , thereby further reducing loss. The optical efficiency at the proximal end of output waveguide  304  can be computed as an overlap integral of the electromagnetic fields of light path  314  and output mode spot  326 . The optical efficiency computation can alternatively be based on a beam propagation calculation or a finite difference time domain calculation. 
     As diffracted light path  314  enters output waveguide  304  at its crossing end, it refracts again, assuming a primary output light path that is parallel to primary light path  312 . Output waveguide  304  tapers down to an output distal width  336  that is equal to input width  332 . The taper of output waveguide  304  compensates for the beam expansion experienced through crossing region  310 . The taper, from output crossing width  334  to output distal width  336  can be made over a short distance, such as the distance between crossing region  310  and another crossing region in series. The taper allows serial crossing regions to have a consistent input width. Otherwise, the waveguide width would get progressively larger, which presents practical issues with use of the crossing. 
     Similar to primary light path  312 , crossing light path  318  refracts as it enters crossing region  310 , diffracts and expands as it spans crossing region  310 , and refracts as it leaves crossing region  310 . Input crossing waveguide  306  has an input crossing width  338  that defines a fundamental mode. The fundamental mode assumes a crossing mode shape at the boundary of crossing region  310 . The crossing mode shape is represented by a crossing input mode spot  328  that is centered laterally with respect to input crossing waveguide  306 . As a crossing light beam propagates through input crossing waveguide  306  and reaches crossing region  310 , it diffracts, shifting crossing light path  318  to a refracted crossing light path  320 . Crossing region  310  is unbound laterally with respect to input crossing waveguide  306 , just as it is with respect to input waveguide  302 . 
     As in output waveguide  304 , output crossing waveguide  308  has a crossing end disposed near crossing region  310  and a distal end disposed away from crossing region  310 . Output crossing waveguide  308  has an output crossing width  340  that is slightly larger than input crossing width  338  to accommodate a slightly larger crossing output mode shape represented by a crossing output mode spot  330 . Output crossing waveguide  308  also tapers from output crossing width  340  at its crossing end to an output crossing distal width  342  at its distal end, which is equal to input crossing width  338 . Additionally, output crossing waveguide  308  is displaced laterally with respect to input crossing waveguide  306  to account for refraction as light path  318  enters crossing region  310  and the propagation of refracted and diffracted crossing light path  320  through crossing region  310 . The lateral offset is represented by crossing output mode spot  330  centered laterally upon output crossing waveguide  308 . 
     The refraction, diffraction, and beam expansion of a light beam propagating from input crossing waveguide  306 , through crossing region  310 , and to output crossing waveguide  308  can be computed as a function of the dimensions of crossing region  310 , similar to the refraction, diffraction, and beam expansion experienced along primary light path  312 . The lateral displacement and larger output crossing width  340  improve the overlap of refracted diffracted crossing light path  320  and crossing output mode spot  330  with the fundamental mode of output crossing waveguide  308 , thereby reducing loss otherwise experienced due to beam expansion and diffraction. 
     The lateral dimensions of input waveguide  302  and output waveguide  304  relative to input crossing waveguide  306  and output crossing waveguide  308  can vary by application. Input width  332  can be larger, equal, or smaller than input crossing width  338 . In certain embodiments, one light path may have more crossings than another, in which case the application calls for more crossings along primary light path  312  than along crossing light path  318 . In those cases, dimensions of the respective waveguides are considered, as it impacts the length of crossing region  310  and therefore the amount of diffraction and beam expansion experienced. If possible, the number of crossings along lengthy crossing regions is minimized. 
       FIG. 4  is an illustration of one embodiment of a series of optical crossings  400 . Optical crossings  400  may be embodied in a PIC made using a variety of material systems, including silica on silicon, LiNbO3, and GaAs, among others. Optical crossings  400  include a primary light path  442  formed by an input waveguide  402 , an intermediate waveguide  404 , and an output waveguide  406 . Primary light path  442  passes through a first crossing region  416  that bisects input waveguide  402  and intermediate waveguide  404  at an intersection with a first crossing input waveguide  408  and a first crossing output waveguide  412 . Primary light path  442  also passes through a second crossing region  418  that bisects intermediate waveguide  404  and output waveguide  406  at an intersection with a second crossing input waveguide  410  and a second crossing output waveguide  414 . 
     First crossing region  416  and second crossing region  418  are similar to crossing region  310  of  FIG. 3 . At first crossing region  416 , intermediate waveguide  404  is displaced laterally with respect to input waveguide  402 . Additionally, intermediate waveguide  402  has a first crossing width  422  that is slightly larger than an input width  420  of input waveguide  402 . The displacement and enlargement of intermediate waveguide  404  at first crossing region  416  accounts for beam refraction, diffraction, and expansion experienced as primary light path  442  passes through first crossing region  416 . 
     Intermediate waveguide  404  tapers from first crossing width  422  to a second crossing width  424  that is equal to input width  420 . In other words, along primary light path  442 , the input width of first crossing region  416  is equal to the input width of second crossing region  418 . At second crossing region  418 , output waveguide  406  is displaced laterally with respect to intermediate waveguide  404 . Additionally, output waveguide  406  has a crossing width  426  that is slightly larger than second crossing width  424  of intermediate waveguide  404 . The displacement and enlargement of output waveguide  406  at second crossing region  418  accounts for beam refraction, diffraction, and expansion experienced as primary light path  442  passes through second crossing region  418 . Again, as in intermediate waveguide  404 , output waveguide  406  tapers from crossing width  426  to an output width  428  that is equal to input width  420  and second crossing width  424 . 
     First crossing input waveguide  408  and second crossing input waveguide  410  are similar to input crossing waveguide  306  of  FIG. 3 . First crossing output waveguide  412  and second crossing output waveguide  414  are similar to output crossing waveguide  308 , also of  FIG. 3 . A first crossing light path  444  begins in first crossing input waveguide  408 , passes through first crossing region  416 , and then on through first crossing output waveguide  412 . As a light beam propagating along first crossing light path  444  propagates through first crossing region  416 , it experiences refraction, diffraction, and beam expansion. The expected refraction, diffraction, and beam expansion are accounted for by a first crossing output waveguide crossing width  432  being slightly larger than a first crossing input waveguide width  430 . Additionally, first crossing output waveguide  412  is displaced laterally with respect to first crossing input waveguide  408 . The displacement and enlargement improve the overlap of first crossing light path with the fundamental mode of first crossing output waveguide  412 . First crossing output waveguide  412  also tapers from first crossing output waveguide crossing width  432  down to a first crossing output waveguide distal width  434  that is equal to first crossing input waveguide width  430 . 
     As in first crossing light path  444 , second crossing light path  446  begins in second crossing input waveguide  410 , passes through second crossing region  418 , and then on through second crossing output waveguide  414 . As a light beam propagating along second crossing light path  446  propagates through second crossing region  418 , it experiences refraction, diffraction, and beam expansion. The expected refraction, diffraction, and expected beam expansion is accounted for by a second crossing output waveguide crossing width  438  being slightly larger than a second crossing input waveguide width  436 . Additionally, second crossing output waveguide  414  is displaced laterally with respect to second crossing input waveguide  410 . The displacement and enlargement improve the overlap of second crossing light path  446  with the fundamental mode of second crossing output waveguide  414 . Second crossing output waveguide  414  also tapers from second crossing output waveguide crossing width  438  down to a second crossing output waveguide distal width  440  that is equal to second crossing input waveguide width  436 . 
     In some embodiments, the system performance requirements on input waveguide  402  are more stringent than those on first crossing input waveguide  408 . For example, primary light path  442 , which includes input waveguide  402 , can have a lower optical loss budget than first crossing light path  444 , which includes first crossing input waveguide  408 . This can occur, for example, when input waveguide  402  has many crossings and first crossing input waveguide  408  has only a few. In that case, the crossing loss required for input waveguide  408  is different than the crossing loss for first crossing input waveguide  408 . In embodiments where this occurs, the light path requiring lower optical loss can use wider waveguides. In the embodiment of  FIG. 4 , input waveguide  402  would be wider than first crossing input waveguide  408  and second crossing input waveguide  410 , which is to say that input width  420  is larger than first crossing input waveguide width  430  and second crossing input waveguide width  436 . Consequently, first crossing region  416  and second crossing region  418  would be more rectangular-shaped, as opposed to more square-shaped when input width  420 , first crossing input waveguide width  430 , and second crossing input waveguide width  436  are equal. 
     Generally, larger beams entering a crossing region experience lower loss, because the diffraction in the crossing region is lower and larger beams diffract less than small beams. Wider waveguides have larger modes, and are therefore better suited for light paths requiring lower optical loss. This is advantageous where one light path has many crossings, for example, 100 or more, and other light paths have relatively few crossings, for example, on the order of ten. In the embodiment of  FIG. 4 , primary light path  442  has two crossings, while first crossing light path  444  and second crossing light path  446  have only one, although  FIG. 4  illustrates a small section of a likely much larger PIC that can include hundreds of crossings. 
     Another consideration in determining the width of waveguides is any additional optical loss incurred by tapering from a narrow single-mode waveguide, which are often found in active devices such as modulators, switches, etc., to a wide multi-mode waveguide. This tapering loss increases with the width of the wide multi-mode waveguide. The taper loss, propagation losses through wide multi-mode waveguides, and losses in crossings can be balanced according to the number of crossings in a given light path. For example, in the embodiment of  FIG. 4 , input width  420 , first crossing input waveguide width  430 , and second crossing input waveguide width  436 , and, consequently, the shapes of first crossing region  416  and second crossing regions  418 , can be determined according to the number of crossings along primary light path  442 , first crossing light path  444 , and second crossing light path  446 , as well as losses incurred while propagating through input waveguide  402 , intermediate waveguide  404 , output waveguide  406 , first crossing input waveguide  408 , first crossing output waveguide  412 , second crossing input waveguide  410 , and second crossing output waveguide  414 . Additionally, although no tapers from single-mode waveguide to wide multi-mode waveguide are illustrated in  FIG. 4 , any taper losses should also be considered. 
       FIG. 5  is a flow diagram of one embodiment of a method of making an optical crossing in a PIC. The method begins at a start step  510 . At a step  520 , a first waveguide is formed. At a step  530 , a crossing waveguide is formed that bisects the first waveguide into an input waveguide and an output waveguide. The intersection of the first waveguide and the crossing waveguide forms a crossing region. The output waveguide is slightly larger than the input waveguide. The increase is in a lateral dimension, or width, perpendicular to a light path through the first waveguide. The increased width of the output waveguide accounts for light beam expansion that is experienced as a light beam propagating through the first waveguide propagates through the crossing region formed in step  530 . The increase in width, or the difference in width between the input waveguide and the output waveguide, is computable according to an expected light beam expansion as a function of the dimensions of the crossing region and, more specifically, a function of the length of the crossing region in the dimension of the light path through the first waveguide. 
     The output waveguide is also displaced laterally by an offset value that is computable according to the dimensions of the crossing region. The displacement is with respect to the input waveguide and is such that the input waveguide and output waveguide are not co-linear. The displacement accounts for light beam refraction as a light beam enters and propagates through the crossing region along the light path through the first waveguide. 
     In certain embodiments, the output waveguide tapers from the increased width at the crossing region down to a width equal to that of the input waveguide. This allows the crossing formed in step  530  to be repeated in series without progressively growing the first waveguide as it crosses each crossing waveguide. The method then ends at a step  540 . 
     While this invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments, as well as other embodiments of the invention, will be apparent to persons skilled in the art upon reference to the description. It is therefore intended that the appended claims encompass any such modifications or embodiments.