Patent Publication Number: US-2016246009-A1

Title: Photonic Chip Surface Grating Coupler (SGC)-Based Optical Splitter and Optical Combiner

Description:
TECHNICAL FIELD 
     The present invention relates to a system and method for optical communications, and, in particular, to a surface grating coupler (SGC)-based optical splitter and optical combiner. 
     BACKGROUND 
     Optical fibers have been widely used for the propagation of optical signals, especially to provide high-speed data communication links. Optical links using fiber optics may have various advantages over electrical links, for example, comparatively large bandwidths, comparatively high noise immunity, comparatively reduced power dissipation, and comparatively minimal crosstalk. Optical signals carried by optical fibers may be processed by a wide variety of optical devices, optoelectronic devices, and/or integrated circuits, such as photonic integrated circuits (PICs) and/or planar lightwave circuits (PLCs). 
     Recently, PICs have gained interest in research and industry for use in optical systems since PICs may provide high functionality, stability, reliability, compactness, and/or level of integration. One of the basic building components of PICs may be photonic waveguides, for example, for interconnecting optical components and/or optical circuits and interfacing with external connections for inputs and/or outputs. PICs may be integrated on various material platforms, such as silica-on-silicon, silicon-on-insulator, and/or other semiconductor materials. Some example applications of PICs may include optical modulators, optical switches, and/or optical wavelength-division multiplexers. Mach-Zehnder interferometer (MZI)-based structures are widely employed in implementing such applications. 
     Coupling light in and out of a PIC may be challenging due to the large difference in dimensions between an optical waveguide and an optical fiber. For example, the core diameter of a single-mode fiber (SMF) core may be in the order of micrometers (μm) (e.g., about 5 μm to about 9 μm), whereas the core diameter of an optical waveguide may be less than 1 μm. 
     SUMMARY 
     In one embodiment, the disclosure includes an optical device comprising a first optical interface comprising a first optical waveguide disposed on a surface of a substrate, wherein the first optical waveguide comprises a first wide middle portion that tapers to a first narrow end along a first direction of light propagation and a second narrow end along a second direction of light propagation opposite to the first direction, a first diffraction grating disposed at about the first wide middle portion of the first optical waveguide, and a first optical fiber in optical communication with the first optical waveguide and the first diffraction grating, wherein the first optical fiber is positioned at about perpendicular to the surface and directed towards the first diffraction grating to cause an incoming light signal from the first optical fiber to split into a first portion and a second portion through a diffraction at the first diffraction grating, and wherein the diffraction causes the first portion to propagate towards the first narrow end along the first direction and the second portion to propagate towards the second narrow end along the second direction. 
     In another embodiment, the disclosure includes a photonic integrated circuit (PIC) comprising a first optical interface comprising a first tapered waveguide disposed on a plane of the PIC, wherein the first tapered waveguide comprises a first wide middle portion that tapers to a first narrow end along a first direction of light propagation and a second narrow end along a second direction of light propagation opposite to the first direction, a first diffraction grating disposed at about the first wide middle portion of the first tapered waveguide, and a first out-of-plane optical fiber in optical communication with the first tapered waveguide and the first diffraction grating, wherein the first out-of-plane optical fiber is positioned at about 90 degrees (°) with respect to the plane and directed towards a surface of the first diffraction grating such that a first light signal propagating along the first direction towards the first diffraction grating and a second light signal propagating along the second direction towards the first diffraction grating are combined and transferred to the first out-of-plane optical fiber. 
     In yet another embodiment, the disclosure includes a method comprising disposing a tapered optical waveguide on a plane of an integrated circuit, wherein the tapered optical waveguide comprises a wide middle portion that tapers to a first narrow end along a first direction of light propagation and a second narrow end along a second direction of light propagation opposite to the first direction, disposing an SGC at about the wide middle portion of the tapered optical waveguide, and coupling an optical fiber to the SGC such that the optical fiber is oriented at about ninety degrees with respect to the plane to provide optical couplings between a first light signal propagating through the optical fiber, a second light signal propagating through the tapered optical waveguide in the first direction, and a third light signal propagating through the tapered optical waveguide in the second direction. 
     These and other features will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts. 
         FIG. 1  is a schematic diagram of an MZI device. 
         FIG. 2  is a schematic diagram of another MZI device. 
         FIG. 3  is a perspective view of a fiber and a PIC in a coupling position. 
         FIG. 4  is a top view of a waveguide grating coupler structure comprising a single tapered section. 
         FIG. 5  is a schematic diagram of an SGC-based optical splitter according to an embodiment of the disclosure. 
         FIG. 6  is a schematic diagram of an SGC-based MZI according to an embodiment of the disclosure. 
         FIG. 7  is a schematic diagram of a hybrid SGC-based MZI device according to an embodiment of the disclosure. 
         FIG. 8  is a top view of a waveguide grating coupler structure comprising two tapered sections according to an embodiment of the disclosure. 
         FIG. 9  is a cross-sectional view of a waveguide grating coupler structure according to an embodiment of the disclosure. 
         FIG. 10  is a schematic diagram of an embodiment of a grating diffraction scheme. 
         FIG. 11  is a flowchart of an embodiment of a method for configuring an SGC-based optical coupler. 
     
    
    
     DETAILED DESCRIPTION 
     It should be understood at the outset that, although an illustrative implementation of one or more embodiments are provided below, the disclosed systems and/or methods may be implemented using any number of techniques, whether currently known or in existence. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary designs and implementations illustrated and described herein, but may be modified within the scope of the appended claims along with their full scope of equivalent. 
     One approach to coupling light in and out of a PIC may be to employ a grating-based vertical coupling method, in which an optical fiber may be vertically coupled to a waveguide grating coupler at a small incidence angle, for example, less than about 20° with respect to an axis perpendicular to the plane of the waveguide grating coupler. The incidence angle is designed to provide coupling through a first-order grating diffraction at the waveguide grating coupler and may depend on the design of the waveguide grating coupler. In such vertical coupling methods, the coupling efficiency may depend on the alignment accuracies (e.g., incidence angle) between the optical fiber and the PIC, and thus may increase manufacturing and/or packaging cost. 
       FIG. 1  is a schematic diagram of an MZI device  100 . The device  100  may comprise a 1×1 MZI  160 , SGCs  151  and  152 , tapered waveguides  171  and  172 , an input waveguide  181 , and an output waveguide  182  disposed on a plane  140  of the device  100 . The plane  140  may be a surface of a substrate platform built from silicon, silica, and/or other semiconductor materials. The plane  140  may also be referred to as a chip-plane. Thus, the MZI  160 , the SGCs  151  and  152 , the tapered waveguides  171  and  172 , the input waveguide  181 , and the output waveguide  182  may be referred to as on-chip components and/or in-plane components. The MZI  160  may be coupled to an input fiber  110  via the SGC  151 , the tapered waveguide  171 , and the input waveguide  181 . Similarly, the MZI  160  may be coupled to an output fiber  120  via the SGC  152 , the tapered waveguides  172 , and the output waveguide  182 . The input fiber  110  and the output fiber  120  may be nearly vertically coupled to the plane  140 , and thus may be referred to as out-of-plane fibers. 
     The MZI  160  may be a standard 1×1 MZI, which may receive one input and produce one output. The MZI  160  may comprise a pair of interferometer arms  162  coupled to a first optical coupler  161  at an input end and a second optical coupler  164  at an output end. The first optical coupler  161  may be a standard optical coupler, such as an optical splitter, a Y-junction coupler, a multi-mode interference (MMI) coupler, a directional coupler, configured to split a light signal into a first portion and a second portion. For example, the optical coupler  161  may be a power splitter that splits an input signal into two portions, each comprising a substantially similar power. Each portion of the light signal may propagate through one of the interferometer arms  162 . The second optical coupler  164  may be substantially similar to the first optical coupler  161 . However, the second optical coupler  164  may be configured as a standard optical combiner, which may combine light signals instead of splitting a light signal. 
     The interferometer arms  162  may be photonic wire waveguides (e.g., silicon nanowire), each configured to direct and guide the first portion or the second portion of the light signal along an optical path. The MZI  160  may further comprise at least one phase shifter  163  coupled to one of the interferometer arms  162  to provide a phase differential between the optical paths of the interferometer arms  162 , for example, by changing the refractive index or the length of at least one of the interferometer arms  162 . Depending on the phase differential, the output light signals from the interferometer arms  162  may be recombined more efficiently (e.g., constructively), less efficiently, or not at all (e.g., destructively) at the second optical coupler  164 . As such, the MZI  160  may provide optical modulation, optical switching, and/or wavelength de-multiplexing functions. The input end of the MZI  160  and/or the first optical coupler  161  may be coupled to the input waveguide  181  and the output end of the MZI  160  and/or the second optical coupler  164  may be coupled to the output waveguide  182 . 
     The input waveguide  181  and the output waveguide  182  may be photonic wire waveguides (e.g., silicon nanowire). The input waveguide  181  may be coupled to the tapered waveguide  171  such that the input waveguide  181  is positioned between the input end of the MZI  160  and the tapered waveguide  171 . The input waveguide  181  may be configured to provide an optical path from the tapered waveguide  171  to the input end of the MZI  160 . The output waveguide  182  may be coupled to the tapered waveguide  172  such that the output waveguide  182  is positioned between the output end of the MZI  160  and the tapered waveguide  172 . The output waveguide  182  may be configured to provide an optical path from the output end of the MZI  160  to the tapered waveguide  172 . 
     The tapered waveguides  171  and  172  may comprise a core layer (not marked) and a cladding layer (not marked). The cladding layer may be formed around the core layer along a direction of light propagation. The core layer may be built from a higher index material than the cladding layer such that a light signal propagating along the core layer may be confined to the core layer. For example, the core layer may be constructed from silicon and the cladding layer may be constructed from silica. In some embodiments, the cladding layer may be constructed from several different layers of materials. The core layer may comprise a tapered structure with a wide end that tapers into a narrow tip. For example, the wide end may comprise a width substantially close to a single-mode fiber (SMF) core diameter (e.g., about 5 μm to 9 μm) and the narrow tip may comprise a substantially smaller width (e.g., less than about 1 μm). As such, the tapered waveguides  171  and  172  may provide adiabatic optical mode conversions between optical components with different dimensions. For example, the tapered waveguide  171  may couple light signals between the input fiber  110  and the input waveguide  181  and the tapered waveguide  172  may couple light signals between the output fiber  120  and the output waveguide  182 . In order to couple light signals from the input fiber  110  and/or to the output fiber  120 , the tapered waveguides  171  and  172  may be incorporated with an SGC. Specifically, the SGC  151  may be disposed on the wide end of the tapered waveguide  171 , and the SGC  152  may be disposed on the wide end of the tapered waveguide  172 . 
     The SGCs  151  and  152  may comprise a periodic structure comprising a finite number of grating teeth (e.g., ridges) separated by spaces and/or slits, where the periodicity of the teeth may be referred to as the grating period. The periodic structure may split and diffract an incident light signal into several light signals travelling in different path directions. The incidence angle of the light signal, the grating period, and/or the wavelength of the light signal may determine the different path directions. By positioning the input fiber  110  and the output fiber  120  appropriately, described more fully below, the SGC  151  may be configured to diffract a light signal from the input fiber  110  into the tapered waveguide  171 , while the SGC  152  may be configured to diffract a light signal from the tapered waveguide  172  into the output fiber  120 . 
     The input fiber  110  may comprise a core  111  surrounded by a cladding  112 . The core  111  may be built from a material (e.g., glass or plastic) comprising a higher refractive index than the cladding  112  such that the cladding  112  may confine a light signal propagating along the input fiber  110  in the core  111 . In some embodiments, the input fiber  110  may be an SMF and the core  111  may comprise a cross-sectional diameter of about 5 μm to about 9 μm. The output fiber  120  may be substantially similar to the input fiber  110 . 
     In order to couple an input light signal from the input fiber  110  to the MZI  160 , the input fiber  110  may be coupled to the SGC  151  by positioning the input fiber  110  at an angle  190 , represented by θ, to the SGC  151  in an about normal position such that the SGC  151  may diffract the input light signal from the input fiber  110  into the tapered waveguide  171 . For example, the angle  190  may be less than about 20° with respect to an axis about perpendicular to the plane  140 , and the input fiber  110  may be configured to tilt away from the MZI  160 . The angle  190  may be designed to provide a first-order diffraction at the SGC  151 . The tapered waveguide  171  may couple the input light signal from the SGC  151  to the input waveguide  181 . The input waveguide  181  may couple the input light signal from the tapered waveguide  171  to the first optical coupler  161 . 
     Similarly, the MZI  160  output signal may be coupled out of the plane  140  to the output fiber  120  by employing substantially similar mechanisms as in the input coupling mechanisms described above, but may be in a reverse direction. For example, the output waveguide  182  may couple the output light signal from the second optical coupler  164  to the tapered waveguide  172 , the tapered waveguide  172  may couple the output light signal to the SGC  152 , and the SGC  152  may couple the output light signal to the output fiber  120  through diffraction, where the output fiber may be positioned in a substantially similar angle, θ, as the input fiber  110 . 
       FIG. 2  is a schematic diagram of another MZI device  200 . The device  200  may be substantially similar to the device  100 , but may comprise a 1×2 MZI  260  instead of a 1×1 MZI. The MZI  260  may comprise a pair of interferometer arms  262  positioned between a first optical coupler  261  and a second optical coupler  264 . The interferometer arms  262 , the first optical coupler  261 , and the second optical coupler  264  may be substantially similar to the interferometer arms  162 , the first optical coupler  161 , and the second optical coupler  164 , respectively. However, the second optical coupler  264  may provide two outputs, for example, switching an input signal received from the first optical coupler  261  between the two outputs depending on the phase differentials between the interferometer arms  262 . Each output may be coupled to an output waveguide  282 , followed by an output fiber  220 , by employing substantially similar output coupling mechanisms as described for the device  100 . The output waveguides  282  and the output fibers  220  may be substantially similar to the output waveguide  182  and the output fiber  120 , respectively. 
       FIG. 3  is a perspective view  300  of a fiber  310  and a PIC  340  in a coupling position. The perspective view  300  illustrates a more detailed view of the input fiber-to-chip coupling mechanisms described above in the device  100  and  200 . The PIC  340  may comprise an SGC  350  disposed on a tapered waveguide  370  positioned on a plane  341  of the PIC  340 . The SGC  350 , the tapered waveguide  370 , and the plane  341  may be substantially similar to the SGC  151 , the tapered waveguide  171 , and the plane  140 , respectively. The fiber  310  may be substantially similar to the fiber  110  and may comprise a core  311 , similar to the core  111 , surrounded by a cladding  312 , similar to the cladding  112 . 
     The tapered waveguide  370  may comprise a core layer  371 , a lower cladding layer  372 , and an upper cladding layer (not shown). The core layer  371  may comprise a tapered structure with a wider end  374  that is linearly tapered into an opposite narrower end  375  to provide optical mode conversions, for example, between a fiber and a silicon nanowire waveguide. The core layer  371  may be built from a high-index material (e.g., silicon) and the cladding layer  372  may be built from a lower-index material (e.g., silica) such that the cladding layer  372  may confine a light signal propagating along the tapered waveguide  370  in the core layer  371 . 
     The SGC  350  may be disposed on a portion of the wider end  374  of the core layer  371 . The fiber  310  may be positioned at a pre-determined angle  390 , represented by θ, to the surface of the SGC  350  in an about normal position such that the SGC  350  may diffract an incident light signal  313  travelling through the core  311  of the fiber  310  into the core layer  371  of the tapered waveguide  370 . The angle  390  may be configured to cause a first-order Bragg grating diffraction at the SGC  350  such that a major portion of the incident light signal  313  may be directed into the tapered waveguide  370  towards the narrower end  375 . For example, the angle  390  may be about 10°. The Bragg grating diffraction may refer to optical interference caused by slits in a grating structure. The order of diffraction may be dependent on various factors, such as wavelength of an optical signal, the grating period of a grating structure, and/or the angle of diffraction, discussed more fully below. 
     The tapered waveguide  370  may direct and transition the wider incident light signal  313  towards a narrow photonic wire waveguide and/or couple to other optical components on the PIC  340  for optical signal processing. It should be noted that the polarization of the SGC  350  may determine the polarization component that may travel along the tapered waveguide  370 . For example, when the SGC  350  is a transverse electric (TE)-polarized SGC, the TE polarization component of the incident light signal  313  may propagate along the tapered waveguide  370  (e.g., as shown in  FIG. 3 ). Alternatively, when the SGC  350  is a transverse-magnetic (TM)-polarized SGC, the TM polarization component of the incident light signal  313  may propagate along the tapered waveguide  370 . 
       FIG. 4  is a top view of a waveguide grating coupler structure  400  comprising a single tapered section. The structure  400  may be disposed on a surface of a substrate platform or a plane of a PIC, similar to the PIC  340 , to facilitate light coupling in and/or out of the PIC. The structure  400  may comprise an SGC  450  disposed on a tapered core layer  471  that is surrounded by a cladding layer  472 . The SGC  450 , the tapered core layer  471 , and the cladding layer  472  may be substantially similar to the SGC  350 , the core layer  371 , and the cladding layer  372 , respectively. However, the SGC  450  may comprise curved gratings instead of linear gratings as in the SGC  350 . The curved gratings may comprise teeth separated by gaps and may be structurally similar to the linear gratings, but may be curved in the plane to focus light signals down to the dimensions of the narrow end, for example, for coupling to a photonic wire waveguide. The SGC  450  may be disposed on a portion at about the wide end  473  of the tapered core layer  471  to facilitate coupling of light signals from an out-of-plane fiber, such as the fiber  310 . The region  413  may represent the spot size of an incident light signal, for example, from the out-of-plane fiber vertically coupled to the structure  400 . 
     Disclosed herein are techniques for efficiently implementing SGC-based optical couplers for PIC integration. Instead of an SGC performing PIC I/O coupling and being indirectly coupled to a splitter or a combiner, the disclosed embodiments may provide a single optical interface that facilitates fiber-to-chip coupling and optical splitting or a single optical interface that facilitates chip-to-fiber coupling and optical combining without standard optical splitters, combiners, and couplers (e.g., Y-junction couplers, MMI couplers, and/or directional couplers). The optical interface may comprise a single tapered waveguide, an SGC, and an input/output (I/O) fiber. The tapered waveguide may comprise a wide middle portion that tapers into two opposite narrow tips in a direction of light propagation and may be fabricated on a substrate platform (e.g., silicon, silica, and/or semiconductor materials). The SGC may be disposed at about the wide middle portion of the tapered waveguide. The I/O fiber may be positioned at about 90° to a surface of the SGC to cause a second-order Bragg grating diffraction. The second-order Bragg grating diffraction may cause an incident light signal from the I/O fiber to diffract into the tapered waveguide, where the diffracted light signal may split into two portions propagating in opposite directions along the tapered waveguide. Conversely, the second-order Bragg grating diffraction may cause two light signals traveling in opposite directions in the tapered waveguide from the narrow tips to the wide middle portion to diffract into the I/O fiber, and thus provide an optical combining function. To improve coupling efficiency, the SGC coupling region may be coated with an anti-reflective (AR) coating on a surface opposite to the substrate platform and/or disposing a distributed Bragg reflector (DBR) between the tapered waveguide and the substrate platform. In an embodiment, on-chip MZIs, Michaelson interferometers, and/or any suitable types of interferometers may be built from one or more SGC-based optical couplers instead of employing standard optical couplers and additional I/O waveguides for coupling I/O ports to the standard optical couplers. Thus, the disclosed embodiments may provide PICs with more compact footprints and may enable more efficient utilization of the chip area. In addition, by positioning the fiber in an about perpendicular position to the PIC instead of at a particular small angle (e.g., about 5° to about 20°), packaging may be simpler, and thus may lower packaging and/or manufacturing cost. 
       FIG. 5  is a schematic diagram of an SGC-based optical splitter  500  according to an embodiment of the disclosure. The SGC-based optical splitter  500  may be disposed on a chip-plane  540 , which may be a plane of a PIC, such as the PIC  340 . The SGC-based optical splitter  500  may be integrated with other optical components in the PIC. The SGC-based optical splitter  500  may comprise a fiber  510  perpendicularly coupled to an SGC  550  disposed on a portion of a tapered waveguide  570  to provide a splitting ratio of about 50:50 (e.g., about equal power), where the fiber  510  and the SGC  550  may be substantially similar to the input fiber  110  and the SGC  350 . In some embodiments, the angle of the fiber  510  may be adjusted to provide a different splitting ratio. 
     The tapered waveguide  570  may comprise a core layer  571  and a cladding layer  572  formed along a direction of light propagation, where the core layer  571  may be formed in about the middle of the tapered waveguide  570  and the cladding layer  572  may be formed around the core layer  571 . The core layer  571  may be built from a material (e.g., silicon) comprising a higher refractive index than the cladding layer  572  (e.g., silica) such that the cladding layer  572  may confine a light signal propagating along the tapered waveguide  570  in the core layer  571 . The core layer  571  may comprise a tapered structure with a wide middle portion (e.g., a width of about 8-10 μm) that is linearly tapered into two opposite narrow ends (e.g., a width of less than about 1 μm) to provide adiabatic optical mode conversions, for example, between a fiber and two silicon nanowire waveguides, one at each narrow end. 
     The SGC  550  may be positioned at about the wide middle portion of the core layer  571 . The fiber  510  may be positioned about perpendicular to a surface (e.g., light incident surface) of the SGC  550  such that an input light signal  513  from the fiber  510  may be vertically incident (e.g., incidence angle of about 90°) to the surface of the SGC  550 . The about 90° incidence angle may cause a second-order Bragg grating diffraction at the SGC  550 . The second-order Bragg grating diffraction may cause the input light signal  513  entering the SGC  350  to propagate into opposite directions along the tapered waveguide  570  towards the narrow ends of the tapered waveguide  570  to provide a first output signal  514  and a second output signal  515 . As such, the SGC-based optical splitter  500  may provide both fiber-to-chip coupling and power splitting functionalities. Similarly, the SGC-based optical splitter  500  may provide both chip-to-fiber coupling and power combining functionalities when operating in a reverse direction. It should be noted that the splitting ratio between the first output signal  514  and the second output signal  515  may be dependent on the incidence angle of the input light signal  513 . For example, when the incidence angle is at about 90°, the splitting ratio may be about 50/50. 
       FIG. 6  is a schematic diagram of an SGC-based MZI  600  according to an embodiment of the disclosure. The SGC-based MZI  600  may be disposed on a chip-plane  640 , similar to chip-plane  540 . The SGC-based MZI  600  may be integrated with other optical components. The SGC-based MZI  600  may comprise a pair of interferometer arms  662  positioned between an SGC-based optical splitting section  680  and an SGC-based optical combining section  690 . The interferometer arms  662  may be substantially similar to the interferometer arms  162  and at least one of the interferometer arms  662  may comprise a phase shifter (not shown), such as the phase shifter  163 . Both the SGC-based optical splitting section  680  and the SGC-based optical combining section  690  may comprise substantially similar structures as in the SGC-based optical splitter  500 , but the SGC-based optical combining section  690  may couple a light signal in a reverse direction. For example, the SGC-based optical combining section  690  may comprise an output fiber  620 , similar to the fiber  510 , vertically coupled to an SGC  652 , similar to the SGC  550 , at an angle of about 90° with respect to a surface of the SGC  652 . The SGC  652  may be disposed on a tapered waveguide  672 , similar to the tapered waveguide  570 . 
     In the SGC-based optical combining section  690 , the SGC  652  may combine the light signals propagating through each of the interferometer arms  662  and transfer the combined signal into the output fiber  620  through a second-order Bragg grating diffraction in a reverse direction, for example, to cause convergence of light signals. As such, the SGC-based MZI  600  may be realized on a PIC without standard optical couplers and/or additional waveguides to couple light signals into and/or out of the optical couplers. Thus, the SGC-based MZI  600  may provide a PIC with a more compact footprint and may simplify packaging, and thus may reduce packaging cost. The combining ratio in the SGC-based optical combining section  690  may be dependent on the angle of the output fiber  620 . For example, when the output fiber  620  is coupled at about 90° to the SGC  652 , the combining ratio may be about 50/50. 
       FIG. 7  is a schematic diagram of a hybrid SGC-based MZI device  700  according to an embodiment of the disclosure. The hybrid SGC-based MZI  700  may be disposed on a chip-plane  740 , similar to the chip-plane  640 . The hybrid SGC-based first MZI  700  may comprise a first MZI  760 , an optical circuit  750 , and a second MZI  770 . The optical circuit  750  may be positioned between the first MZI  760  and the second MZI  770 . 
     The first MZI  760  may comprise a pair of interferometer arms  762 , similar to the interferometer arms  662 , positioned between an SGC-based optical splitting section  761 , similar to the SGC-based optical splitting section  680 , and a standard optical coupler  764 , similar to the second optical coupler  164 . The SGC-based optical splitting section  761  may comprise an input fiber  710 , similar to the fiber  510 , and may couple an input light signal  713  into the device  700  by employing substantially similar input coupling mechanisms as in the SGC-based splitter  500 . 
     The second MZI  770  may comprise a pair of interferometer arms  772 , similar to the interferometer arms  662 , positioned between a standard optical coupler  771 , similar to the first optical coupler  161 , and an SGC-based optical combining section  774 , similar to the SGC-based optical combining section  690 . The SGC-based optical combining section  774  may comprise an output fiber  720 , similar to the fiber  620 , and may couple a light signal  723  from the device  700  to the output fiber  720  by employing substantially similar output coupling mechanisms as in the SGC-based optical combining section  690 . 
     The optical circuit  750  may comprise a plurality of interconnecting optical components, such as optical splitters, optical combiners, waveguides, wavelength filters, wavelength-division multiplexers and demultiplexers, etc., to perform various optical signal processing functions. As such, the input light signal  713  may be processed by the first MZI  760 , followed by the optical circuit  750 , and then the second MZI  770  to produce the output light signal  723 . 
       FIG. 8  illustrates a top view of a waveguide grating coupler structure  800  comprising two tapered sections  874  according to an embodiment of the disclosure. The structure  800  may be disposed on a chip-plane, similar to the chip-plane  540  and/or a surface of a substrate platform. The structure  800  may comprise an SGC  850  disposed on a tapered core layer  871  and a cladding layer  872  formed around the tapered core layer  871 , where the tapered core layer  871  comprises a wide middle section  873  that transitions to the two tapered sections  874 . The SGC  850 , the tapered core layer  871 , and the cladding layer  872  may be substantially similar to the SGC  550 , the core layer  571 , and the cladding layer  572 , respectively. It should be noted that the top view is shown with the cladding layer  872  removed from the top of the structure  800 . 
       FIG. 9  is a cross-sectional view of a waveguide grating coupler structure  900  according to an embodiment of the disclosure. The cross-sectional view may correspond to a cross-sectional area along a line  801  in the structure  800 . The structure  900  may comprise a tapered waveguide  970 , similar to the tapered waveguide  570 , disposed on a substrate layer  940 . The tapered waveguide  970  may comprise a core layer  971  formed between a first cladding layer  973  and a second cladding layer  972 . The core layer  971  may be substantially similar to the tapered core layer  871 . The first cladding layer  973  and the second cladding layer  972  may be substantially similar to the cladding layer  872 . The second cladding layer  972  may be disposed on the substrate layer  940 . The structure  900  may further comprise an SGC  950 , similar to the SGC  850 , disposed on a surface of the core layer  971  opposite to the substrate layer  940  and at about the middle portion of the core layer  971 . 
     The SGC  950  may comprise a periodic structure with a plurality of teeth  951  separated by gaps  952  such that the SGC  950  may cause an incident light signal  911  to split into two about equal portions  913  propagating in opposite directions along the core layer  971  of the tapered waveguide  970  through a second-order Bragg grating diffraction. 
     The structure  900  may further comprise an anti-reflective coating  903  disposed on a surface of the first cladding layer  973  opposite to the substrate layer  940  and a DBR  904  disposed between the second cladding layer  972  and the substrate layer  940 . The structure  900  may be built from various optical materials, such as silica-on-silicon, indium phosphide (InP), silicon oxynitride (SiON), silicon nitride (Si 3 N 4 ), etc. 
       FIG. 10  is a schematic diagram of an embodiment of a grating diffraction scheme  1000 . The scheme  1000  may be similar to the grating diffraction scheme as described at http://www.physics.smu.edu/˜scalise/emmanual/diffraction/lab.html, which is incorporated by reference. The grating diffraction scheme  1000  may be employed in an SGC-based optical splitter, such as the splitter  500 , an SGC-based MZI, such as the MZI  600 , and/or a hybrid SGC-based MZI, such as the MZI  700 . In the scheme  1000 , a light signal  1010  comprising a plurality of parallel light rays  1011  may incident on a surface of an SGC  1050 , similar to the SGC  950 , at incidence angles of about 90° with respect to the surface. The wavefronts of the light rays  1011  may be perpendicular to the light rays  1011  and about parallel to the surface of the SGC  1050 . The SGC  1050  may comprise a plurality of periodic teeth  1051 , similar to the teeth  951 , separated by gaps  1052 , similar to the gaps  952 . When the light rays  1011  travel through the SGC  1050 , the light rays  1011  may diffract at the gaps  1052  causing the light rays  1011  to propagate in different directions to produce diffracted light rays  1021 . The directions of the diffracted light rays  1021  may depend on the gaps  1052  and the wavelength of the light signal  1010 . The path difference between two diffracted light rays  1021  may be expressed as shown below: 
       d sin θ=nλ,  (1)
 
     where d may represent the distance between the gaps  1052 , θ may represent the diffraction angle, n may represent the diffraction order, λ may represent the wavelength of the light signal  1010 , and nλ may represent the path difference. An example of path difference is marked as  1023  in  FIG. 10 . 
     When the light rays  1011  are incident to the surface of the SGC  1050  at about 90°, the diffraction angles θ on the left of 0° (shown as  1030 ) and on the right of the 0° may be about equal and in opposite directions. As such, the diffracted light rays  1021  may comprise two portions  1040  and  1050  propagating in about opposite directions. 
       FIG. 11  is a flowchart of an embodiment of a method  1100  for configuring an SGC-based optical coupler, such as the SGC-based optical splitter  500 , an SGC-based MZI, such as MZI  600 , and/or a hybrid SGC-based MZI, such as MZI  700 . The method  1100  may be implemented when designing, manufacturing, and/or packaging PICs that employ optical couplers and/or MZI structures. At step  1100 , method  1100  may dispose a DBR on a substrate for producing an integrated circuit. For example, the DBR may be disposed on a plane (e.g., plane  140 ,  341 ,  540 ,  640 , and/or  740 ) of the integrated circuit. 
     At step  1120 , method  1000  may dispose a tapered optical waveguide (e.g., tapered waveguide  570 ), on the plane of the integrated circuit. For example, method  1100  may dispose a lower cladding layer of the tapered optical waveguide on the substrate, a core layer of the tapered optical waveguide on the lower cladding layer, and then followed by an upper cladding layer of the tapered optical waveguide on the core layer. The core layer may comprise a wide middle portion that tapers into two opposite narrow ends along a direction of light propagation. 
     At step  1130 , method  1100  may dispose an SGC (e.g., SGC  151 ,  152 ,  350 ,  450 ,  550 ,  652 ,  850 , and/or  950 ) at about the middle portion of the tapered optical waveguide (e.g., on the core layer). 
     At step  1140 , method  1100  may coat a surface of the upper cladding layer opposite to the plane of the integrated circuit with an AR coating. 
     At step  1150 , method  1100  may couple an optical fiber (e.g., fiber  110 ,  120 ,  220 ,  310 ,  510 ,  620 ,  710 , and/or  720 ) to the SGC such that the optical fiber is oriented at about 90° with respect to the plane of the integrated circuit to cause a second-order Bragg grating diffraction. As described in the scheme  1000 , the second-order Bragg grating diffraction may provide optical couplings between a first light signal propagating through the optical fiber, a second light signal propagating through the tapered waveguide in a first direction, and a third light signal propagating through the tapered optical waveguide in a second direction opposite to the first direction. 
     When the first light signal is an incident light signal traveling through the fiber towards the SGC, the SGC may diffract the first light signal into the tapered optical waveguide such that the first light signal is split into two about equal portions (e.g., travelling towards the two opposite narrow ends), which may correspond to the second light signal and the third light signal. Alternatively, when the second light signal and the third light signal are traveling from the narrow ends of the tapered optical waveguide towards the middle portion, the SGC may diffract the second light signal and the third light signal into the optical fiber to produce a combined light signal (e.g., corresponding to the first light signal) and output the combined light signal through the optical fiber. 
     It should be noted that the AR coating may improve optical coupling efficiency, for example, by reducing reflection of the first light signal when the first light signal is an incident light signal from an external source. The DBR may further improve efficiency, for example, by reflecting any light signal that is scattered outside of the tapered optical waveguide towards the tapered optical waveguide. It should be noted that method  1100  may be suitable for implementing MZI-based optical signal processing functions, such as optical switching, optical modulation, optical de-multiplexing, etc. For example, method  1100  may further couple interferometer waveguide arms to the narrow ends of the tapered optical waveguide, where the interferometer waveguide arms may be coupled to other optical circuits. In addition, the sequence of operations depicted in  FIG. 11  is for illustrative purposes and may be performed in any suitable order. 
     At least one embodiment is disclosed and variations, combinations, and/or modifications of the embodiment(s) and/or features of the embodiment(s) made by a person having ordinary skill in the art are within the scope of the disclosure. Alternative embodiments that result from combining, integrating, and/or omitting features of the embodiment(s) are also within the scope of the disclosure. Where numerical ranges or limitations are expressly stated, such express ranges or limitations should be understood to include iterative ranges or limitations of like magnitude falling within the expressly stated ranges or limitations (e.g., from about 1 to about 10 includes, 2, 3, 4, etc.; greater than 0.10 includes 0.11, 0.12, 0.13, etc.). For example, whenever a numerical range with a lower limit, R l , and an upper limit, R u , is disclosed, any number falling within the range is specifically disclosed. In particular, the following numbers within the range are specifically disclosed: R=R l +k*(R u −R l ), wherein k is a variable ranging from 1 percent to 100 percent with a 1 percent increment, i.e., k is 1 percent, 2 percent, 3 percent, 4 percent, 7 percent, . . . , 70 percent, 71 percent, 72 percent, . . . , 97 percent, 96 percent, 97 percent, 98 percent, 99 percent, or 100 percent. Moreover, any numerical range defined by two R numbers as defined in the above is also specifically disclosed. Unless otherwise stated, the term “about” means±10% of the subsequent number. Use of the term “optionally” with respect to any element of a claim means that the element is required, or alternatively, the element is not required, both alternatives being within the scope of the claim. Use of broader terms such as comprises, includes, and having should be understood to provide support for narrower terms such as consisting of, consisting essentially of, and comprised substantially of. Accordingly, the scope of protection is not limited by the description set out above but is defined by the claims that follow, that scope including all equivalents of the subject matter of the claims. Each and every claim is incorporated as further disclosure into the specification and the claims are embodiment(s) of the present disclosure. The discussion of a reference in the disclosure is not an admission that it is prior art, especially any reference that has a publication date after the priority date of this application. The disclosure of all patents, patent applications, and publications cited in the disclosure are hereby incorporated by reference, to the extent that they provide exemplary, procedural, or other details supplementary to the disclosure. 
     While several embodiments have been provided in the present disclosure, it should be understood that the disclosed systems and methods might be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted, or not implemented. 
     In addition, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, modules, techniques, or methods without departing from the scope of the present disclosure. Other items shown or discussed as coupled or directly coupled or communicating with each other may be indirectly coupled or communicating through some interface, device, or intermediate component whether electrically, mechanically, or otherwise. Other examples of changes, substitutions, and alterations are ascertainable by one skilled in the art and could be made without departing from the spirit and scope disclosed herein.