Abstract:
An integrated polarization splitter and rotator (PSR) employs the TE0 and TE1 modes of propagating light, rather than the TE0 and TM0 modes used in conventional prior art PSR. The integrated PSR exhibits appreciably flatter wavelength response because it does not require a directional coupler to de-multiplex incoming polarizations. The PSR allows tuning of the TM0 loss to reduce polarization dependent loss (PDL). This integrated polarization splitter and rotator is applicable to all integrated platforms including Silicon-on-Insulator (SOI) and III-V semiconductor compound systems. The PSR may be very compact (12×2 μm 2 ), and provides low loss (&lt;0.3 dB across the C-band) and ultra-broadband operation. The PSR also affords better control of polarization dependent losses.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application No. 62/132,742, filed Mar. 15, 2015 and U.S. Provisional Application No. 62/118,420, filed Feb. 19, 2015, each of which is hereby incorporated by reference herein in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The invention relates to optical waveguide devices and particularly to optical waveguide devices that employ polarization splitters and rotators. 
     BACKGROUND OF THE INVENTION 
     Polarization handling, including splitting and rotation of optical modes, is an important topic in integrated optics, including systems that transmit optical signals over optical fibers. 
     For coherent transmission, dual polarization division multiplexing (DPDM) helps to increase the bandwidth by a factor of two. DP-QPSK is one of the most important modulation mechanisms for long-haul coherent transmission. A polarization splitter and rotator (PSR) is one of the fundamental building blocks of a DP-QPSK transceiver. In order to launch two polarizations from a photonic integrated circuit (PIC) to an optical fiber, a PSR is required to multiplex polarizations on the transmission (TX) side. A PSR can also de-multiplex polarizations at the receiver (RX) side to ensure the PIC receives only light of a single polarization. 
     Also known in the prior art is Thompson, U.S. Pat. No. 5,493,624, issued Feb. 20, 1996, which is said to disclose an integrated optics polarization state converter that comprises optically in series a first TM 0  to TM 1  mode converter that is substantially transparent to TE 0 , a concatenation of total internal reflectors and a second TM 0  to TM 1  converter, similarly substantially transparent to TE 0 , which is connected the way round so as to operate as a TM 1  to TM 0  converter. Each TM 0  to TM 1  converter may comprise a tandem arrangement of a 2×2 TE 0 /TM 0  polarization beam splitting coupler and a mismatched, 3 dB maximum, 2×2 beam splitting coupler. The place of the TM 0  to TM 1  converters substantially transparent to TE 0  may be taken by TE 0  to TE 1  converters substantially transparent to TM 0 . 
     Also known in the prior art is Roth, U.S. Pat. No. 8,855,449, issued Oct. 7, 2014, which is said to disclose embodiments of an invention that enable polarization diversity using a more general component than current polarization splitter and rotator solutions. Devices such as an optical receiver, transmitter or duplexer may utilize polarization diversity to efficiently process incoming signals regardless of the signal&#39;s polarization. Embodiments of the invention may be described as enabling polarization diversity via an adiabatic waveguide polarization converter. When utilized in an optical system of discrete components or in a photonic integrated circuit (PIC), this adiabatic waveguide polarization converter may receive an unknown single-mode polarization of light. This light may, for example, originate from a remote location and come through a single mode fiber. As described in further detail herein, embodiments of the invention reduce the requirements and component complexity for polarization handling for polarization diversity systems. By reducing the component complexity, insertion loss is reduced, device footprint is reduced, and device reliability and tolerances may be improved. 
     TM0-TE1 tapers have been reported in publications such as D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Opt. Express 19, 10940-10949 (2011) and D. Dai, Y. Tang, and J. E. Bowers, “Mode conversion in tapered submicron silicon ridge optical waveguides,” Opt. Express 20, 13425-13426 (2012), but those adiabatic tapers usually have long device lengths. 
     Y-junctions used to split both TE0 and TE1 has been reported in in various publications, including the Dai and Bowers 2011 paper and Y. Ding, H. Ou, and C. Peucheret, “Wideband polarization splitter and rotator with large fabrication tolerance and simple fabrication process,” Opt. Lett. 38, 1227-1229 (2013). 
     There is a need for improved integrated polarization splitters and rotators. 
     SUMMARY OF THE INVENTION 
     Accordingly the present invention relates to integrated optical apparatus, comprising: a substrate; and a waveguide structure disposed on the substrate. 
     The waveguide structure comprising: a first port at a first end of said waveguide structure; and second and third ports at a second end of said waveguide structure. 
     A first region in optical communication with said first port, said first region configured to pass a TE0 optical signal received from said first port as an intermediate TE0 optical signal, and configured to convert a TM0 optical signal received from said first port to an intermediate TE1 optical signal, comprised of first and second out of phase TE0 portions. 
     A second region in optical communication with said first region and in optical communication with said second and third ports, said second region configured to receive said intermediate TE0 and TE1 signals, configured to split said intermediate TE0 into first and second in phase TE0 portions and said intermediate TE1 signal into the first and second portions out of phase portions, and configured to mix the first portions of the TE0 and TE1 signals to produce a first output TE0 signal at said second port and to mix the second portions of the TE0 and TE1 signals to produce a second output TE0 signal at said third port. 
     Preferably, a third region is provided between, said first and second regions, for tuning the PDL of the first and second output TE0 signals, the third region including gradually increasing and/or decreasing widths for expanding and/or compressing the intermediate TE0 and TE1 signals. 
     The foregoing and other objects, aspects, features, and advantages of the invention will become more apparent from the following description and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The objects and features of the invention can be better understood with reference to the drawings described below, which represent preferred embodiments thereof. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the invention. In the drawings, like numerals are used to indicate like parts throughout the various views. 
         FIG. 1  is a schematic diagram of a conventional polarization splitter and rotator. 
         FIG. 2  a schematic diagram of a polarization rotator and splitter that operates according to principles of the invention. 
         FIG. 3A  is a simulation diagram illustrating a TM0-TE1 taper that operates according to principles of the invention. 
         FIG. 3B  is a diagram that shows the simulated loss curve in a TM0-TE1 taper as a function of wavelength. 
         FIG. 4A  is a simulated image of a splitter operating at the TE0 mode. 
         FIG. 4B  is a simulated image of a splitter operating at the TE1 mode. 
         FIG. 4C  is a graph of the simulated splitting efficiency of the TE0 mode as a function of index. 
         FIG. 4D  is a graph of the simulated splitting efficiency of the TE1 mode as a function of index. 
         FIG. 5A  is a graph of the simulated reflection of TE1 mode as a function of wavelength. 
         FIG. 5B  is a graph of the simulated reflection of TE0 mode as a function of wavelength. 
         FIG. 6  is a plan view of a first embodiment of an integrated polarization splitter and rotator that operates according to principles of the invention. 
         FIG. 7  is a plan view of a second embodiment of an integrated polarization splitter and rotator that operates according to principles of the invention. 
         FIG. 8  is a schematic diagram in plan view of a bi-directional photodetector. 
         FIG. 9  is a schematic diagram of an illustrative polarization insensitive WDM receiver (RX). 
         FIG. 10A  is an eye diagram recorded under 10 Gbps modulation using 1530.5 nm illumination at maximum Vpp. 
         FIG. 10B  is an eye diagram recorded under 10 Gbps modulation using 1530.5 nm illumination at minimum Vpp. 
         FIG. 10C  is an eye diagram recorded under 10 Gbps modulation using 1537 nm illumination at maximum Vpp. 
         FIG. 10D  is an eye diagram recorded under 10 Gbps modulation using 1537 nm illumination at minimum Vpp. 
         FIG. 10E  is an eye diagram recorded under 10 Gbps modulation using 1543.5 nm illumination at maximum Vpp. 
         FIG. 10F  is an eye diagram recorded under 10 Gbps modulation using 1543.5 nm illumination at minimum Vpp. 
         FIG. 10G  is an eye diagram recorded under 10 Gbps modulation using 1550 nm illumination at maximum Vpp. 
         FIG. 10H  is an eye diagram recorded under 10 Gbps modulation using 1550 nm illumination at minimum Vpp. 
         FIG. 11  is a diagram of an example of cascaded PSR structure. 
         FIG. 12  is a schematic diagram of a PSR having a Y-junction, according to principles of the invention. 
         FIG. 13  is a graph of insertion loss as a function of wavelength for the TE mode and the TM mode. 
         FIG. 14  is a schematic of an on-chip polarization controller that includes 2 PSR devices and an interposed phase or power tuning element. 
         FIG. 15  is a schematic of a polarization diversity laser that includes two PSR devices. 
         FIG. 16  is a schematic of a polarization diversity MUX/DEMUX that includes a plurality of PSR devices. 
         FIG. 17  is a schematic of a polarization diversity switch that includes a plurality of PSR devices. 
     
    
    
     DETAILED DESCRIPTION 
     Acronyms 
     A list of acronyms and their usual meanings in the present document (unless otherwise explicitly stated to denote a different thing) are presented below. 
     AMR Adabatic Micro-Ring 
     APD Avalanche Photodetector 
     ARM Anti-Reflection Microstructure 
     ASE Amplified Spontaneous Emission 
     BER Bit Error Rate 
     BOX Buried Oxide 
     CMOS Complementary Metal-Oxide-Semiconductor 
     CMP Chemical-Mechanical Planarization 
     DBR Distributed Bragg Reflector 
     DC (optics) Directional Coupler 
     DC (electronics) Direct Current 
     DCA Digital Communication Analyzer 
     DPDM Dual Polarization Division Multiplexing 
     DP-QPSK Dual Polarization Quadrature Phase Shift Keying 
     DRC Design Rule Checking 
     DUT Device Under Test 
     ECL External Cavity Laser 
     FDTD Finite Difference Time Domain 
     FOM Figure of Merit 
     FSR Free Spectral Range 
     FWHM Full Width at Half Maximum 
     GaAs Gallium Arsenide 
     InP Indium Phosphide 
     LiNO 3  Lithium Niobate 
     LIV Light intensity(L)-Current(I)-Voltage(V) 
     MFD Mode Field Diameter 
     MPW Multi Project Wafer 
     NRZ Non-Return to Zero 
     PDL Polarization Dependent Loss 
     PIC Photonic Integrated Circuits 
     PSO Particle Swarm Optimization 
     PSR Polarization Splitter and Rotator 
     Q Quality factor which can be defined by the relationships 
     
       
         
           
             Q 
             = 
             
               
                 2 
                 ⁢ 
                 π 
                 × 
                 
                   
                     Energy 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Stored 
                   
                   
                     Energy 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     dissipated 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     per 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     cycle 
                   
                 
               
               = 
               
                 2 
                 ⁢ 
                 π 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   f 
                   r 
                 
                 × 
                 
                   
                     
                       Energy 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Stored 
                     
                     
                       Power 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Loss 
                     
                   
                   . 
                 
               
             
           
         
       
     
     QD Quantum Dot 
     RSOA Reflective Semiconductor Optical Amplifier 
     RX Receiver 
     SOI Silicon on Insulator 
     SEM Scanning Electron Microscope 
     SMSR Single-Mode Suppression Ratio 
     TEC Thermal Electric Cooler 
     TX Transmitter 
     WDM Wavelength Division Multiplexing 
     The Conventional PSR 
       FIG. 1  is a schematic diagram of a conventional polarization splitter and rotator (PSR)  100 . In the conventional PSR  100  illustrated in  FIG. 1 , the arrows on the left side represent the TE0 mode and TM0 modes (also referred to as TE0 polarization and TM0 polarization) of an optical signal propagating in a waveguide  101  that enters a splitter  110  and are split into separate TM0 and TE0 modes. The TM0 mode then enters a polarization rotator  120  and is then rotated to a TE0 mode. As illustrated on the right side of  FIG. 1 , two separate TE0 modes are then communicated to other on-chip devices. In particular, this is a reciprocal passive system. It can function as a polarization combiner if light comes in from the right side. 
     As is well known in the relevant arts, transverse electric (TE) modes are those in which no electric field points in the direction of propagation. These are sometimes called H modes because there is only a magnetic field along the direction of propagation, where H is the conventional symbol for magnetic field. 
     As is well known in the relevant arts, transverse magnetic (TM) modes are those in which no magnetic field points in the direction of propagation. These are sometimes called E modes because there is only an electric field along the direction of propagation. 
     For the TM0 mode both the magnetic field and the electric field are transverse to the wave propagation direction, so this mode is also known as the transverse electromagnetic (TEM) mode. 
     A directional coupler (DC) based structure, as in the aforementioned Dai et al reference may be provided to split the polarizations. The coupling ratio of directional couplers is usually wavelength sensitive. It is hard to get a flat wavelength response across the wavelength range comprising the C band for long-haul optical transmission. This inherent defect degrades the polarization extinction ratio of the system. The splitting efficiency can be viewed as an insertion loss. Moreover, the TM0-TE0 mode rotator induces additional loss. 
     One can write a transfer matrix for a conventional PSR as shown in Eqn. (1): 
                   M   =     [         1       0           0       1         ]             (   1   )               
in which the orthogonal bases of polarization are the TE0 and TM0 modes of the waveguide.
 
45° PSR
 
       FIG. 2  a schematic diagram of a polarization rotator and splitter (PSR)  200  that operates according to principles of the present invention. As illustrated in the embodiment shown in  FIG. 2 , the arrows on the left side represent the TE0 mode and TM0 modes of an optical signal propagating in a waveguide, e.g. optical fiber,  201  that enter a rotator  210  at a first port  202 , which may be coupled to an edge coupler  203  at an edge of a photonic optical chip (PIC)  204 . The PSR  200  may comprise a high-index contrast semiconductor waveguide structure, e.g. a high index contrast silicon waveguide structure, including a tapered rotator  210  and a Y-splitter  220 . The high-index contrast semiconductor waveguide structure may be fabricated on a semiconductor substrate, such as silicon, SOI or other suitable Group III/V semiconductor material. 
     The TM0 mode is rotated into a TE1 mode by a tapered rotator  210 . The TE0 mode is left undisturbed. Expressed in mathematical terms, the rotator  210  converts the orthogonal basis of polarizations from TE0+TM0 to TE0+TE1. The TE0 and TE1 modes are then split in splitter  220  which produces two distinct TE0 modes at second and third ports  222  and  223 . The splitter  220  functions as a 3 dB divider just as a Y-junction. With reference to  FIG. 4B , a first portion of the TE0 mode is transmitted to the second port  222 , while a second portion of the TE0 mode is transmitted to the third port  223 . Typically, the first and second portions are equal, e.g. 50%; however, any percentage may be provided, depending on the design of the splitter  220  and the requirements of the components on the PIC  204 . 
     In a preferred embodiment, a PDL tuning section  250  may be provided between the rotator  210  and the splitter  220 . Typically, the shape of the TE0 and TE1 modes may be deformed, i.e. expanded and/or compressed, by the shape of the PDL tuning section  250 , e.g. gradual narrowing to widths less than the wide end of the tapered rotator  210  and the splitter  220  and/or broadening to widths greater than the wide end of the tapered rotator  210  and the splitter  220 , whereby the phase may be delayed between the portions of the TE0 and TE1 modes during splitting. The PDL tuning second  250  enables the PSR  200  to generate a specific PDL, a minimum PDL, a higher splitting efficiency, or a minimum PDL with highest achievable splitting efficiency. Ideally, the PDL tuning section  250  is symmetrical, about a longitudinal axis along the direction of light propagation, to provide equal splitting for the TE0 and TE1 modes. 
     With reference to  FIGS. 3A and 4A , the TE1 mode exits the tapered rotator  210  appearing as two superposed TE0 modes, which are out of phase by 180° (it). Similar to the TE0 mode, a first portion of the TE1 mode, i.e. one of the superposed TE0 modes, is transmitted to the second port  222 , while a second portion of the TE1 mode, i.e., the other TE0 mode, is transmitted to the third port  223 . Accordingly, the first portion of the TE0 mode combines with the first portion of the TE1 mode at the second port  222 , and the second portion of the TE0 mode combines with the second portion of the TE1 mode as the third port  223 . 
     In the polarization splitter and rotator  200  of the invention, very broadband performance can be achieved because a directional coupler is absent. The polarization extinction ratio is expected to be high across a wide range of wavelength. 
     The transfer matrix of this PSR  200  can be written as shown in Eqn. (2): 
     
       
         
           
             
               
                 
                   M 
                   = 
                   
                     
                       
                         2 
                       
                       2 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                         
                           
                             1 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     For the TE0 input, the two TE0 output portions have the same amplitude and are in phase, which can be expressed as in Eqn. (3): 
     
       
         
           
             
               
                 
                   
                     E 
                     
                       TE 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       0 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               E 
                               up 
                             
                           
                         
                         
                           
                             
                               E 
                               down 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         M 
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   E 
                                   0 
                                 
                               
                             
                             
                               
                                 0 
                               
                             
                           
                           ] 
                         
                       
                       = 
                       
                         
                           
                             2 
                           
                           2 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   E 
                                   0 
                                 
                               
                             
                             
                               
                                 
                                   E 
                                   0 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     For the TM0 input, the two output portions have the same amplitude but are out of phase, which can be expressed as in Eqn. (4): 
     
       
         
           
             
               
                 
                   
                     E 
                     
                       TM 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       0 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               E 
                               up 
                             
                           
                         
                         
                           
                             
                               E 
                               down 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         M 
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 0 
                               
                             
                             
                               
                                 
                                   E 
                                   0 
                                 
                               
                             
                           
                           ] 
                         
                       
                       = 
                       
                         
                           
                             2 
                           
                           2 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   - 
                                   
                                     E 
                                     0 
                                   
                                 
                               
                             
                             
                               
                                 
                                   E 
                                   0 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In general, any arbitrary input polarization can be considered as a superposition of TE0 and TM0, thus the output can be expressed as in Eqn. (5): 
                     E   Arb     =       M   ⁡     [           aE   0               bE   0           ]       =       aE     TE   ⁢           ⁢   0       +     bE     TM   ⁢           ⁢   0                   (   5   )               
where a and b are normalized superposition coefficients, such that a 2 +b 2 =1.
 
     In particular, if an input polarization has equal projected component to TE0 and TM0 (45 degree polarized), the output can be completely routed to the bottom branch, because the first portion of the TE0 mode is completely out or phase with the first portion of the TE1 mode, i.e. 180°, and the second portion of the TE0 mode is in phase with the second portion of the TE1 mode, as expressed by Eqn. (6): 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             E 
                             up 
                           
                         
                       
                       
                         
                           
                             E 
                             down 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           E 
                           
                             TE 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                       
                       + 
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           E 
                           
                             TM 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                       
                     
                     = 
                     
                       [ 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             
                               E 
                               0 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     It can also be routed into the top branch of the output if the input light is polarized at an angle of −45 degrees (e.g. equivalent to 315 degrees), because the second portion of the TE0 mode is completely out or phase with the second portion of the TE1 mode, i.e. 180°, and the first portion of the TE0 mode is in phase with the first portion of the TE1 mode, as expressed by Eqn. (7): 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             E 
                             up 
                           
                         
                       
                       
                         
                           
                             E 
                             down 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           E 
                           
                             TE 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                       
                       - 
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           E 
                           
                             TM 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                       
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               E 
                               0 
                             
                           
                         
                         
                           
                             0 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     That is the reason that this PSR is called 45 degree PSR. The amount of light transmitted to each of the second and third ports  222  and  223  does not matter, as long as all of the light has the same polarization, e.g. ideally TE0. 
     The PSR  200  may be completely reciprocal, i.e. light of a single polarization, e.g., TE0, may be launched into the second and third ports  222  and  223 , combined by the splitter  220 , partially rotated by the tapered rotator  210 , and then launched onto an output waveguide, e.g., fiber  201 . 
     FDTD Simulation and PSO Optimization 
     An analysis of this device was carried using finite-difference time-domain (FDTD) simulation. In performing the analysis, particle swarm optimization (PSO) was coupled with FDTD to optimize the geometry of embodiments of the invention. FDTD software is available from various vendors (FDTD Solutions 8.11 available from Lumerical Solutions, Inc., Suite 300-535 Thurlow Street, Vancouver, BC V6E 3L2, Canada; XFdtd® EM Simulation Software available from Remcom®, 315 South Allen Street, Suite 416, State College, Pa. 16801 USA; and FullWAVE availalble from Synopsys Optical Solutions Group, 199 S. Los Robles Avenue, Suite 400, Pasadena, Calif. 91101 USA). 
       FIG. 3A  is a simulation diagram illustrating a TM0-TE1 taper that operates according to principles of the invention. 
       FIG. 3B  is a diagram that shows the simulated loss curve  310  in a TM0-TE1 taper as a function of wavelength. The simulated loss of the TM0-TE1 taper is less than 0.2 dB across the C-band. 
       FIG. 4A  is a simulated image of a splitter operating at the TE0 mode. 
       FIG. 4B  is a simulated image of a splitter operating at the TE1 mode. 
       FIG. 4C  is a graph of the simulated splitting efficiency of the TE0 mode as a function of index. 
       FIG. 4D  is a graph of the simulated splitting efficiency of the TE1 mode as a function of index. 
     The efficiency of TE1-TE0 is greater than 97% (i.e., 0.13 dB insertion loss) across the C band. The splitting efficiency of TE0-TE0 is greater than 94% (i.e., 0.27 dB insertion loss) across the C-band. 
       FIG. 5A  is a graph of the simulated reflection of TE1 mode as a function of wavelength. In  FIG. 5A , the backward reflection is given by curve  510  and the total reflection is given by curve  520 . Reflection denoted R_TE1 is less than −33 dB across the C-band. 
       FIG. 5B  is a graph of the simulated reflection of TE0 mode as a function of wavelength. In  FIG. 5B , the backward reflection is given by curve  530  and the total reflection is given by curve  540 . Reflection denoted R_TE0 is less than −23 dB across the C-band. 
     The PSR device has a very compact footprint. The total length of the PSR is only 12 μm, comprising a length of 9 μm for the TM0-TE1 taper and 3 μm for the TE1-TE0 splitter. The area is 12×2 μm 2 . 
     The simulation results shown in  FIG. 4A  through  FIG. 4D  and  FIG. 5A  and  FIG. 5B  describe only one of the many possible embodiments. One can adjust the splitting ratio of TE1 and TE0 in the splitter  220  with assistance of the PSO analysis. One can design a PSR that has complimentary fiber coupling loss to decrease the polarization dependent loss (PDL) of the coherent system. 
     Application and Reduction to Practice 
       FIG. 6  is a plan view of a first embodiment of an integrated polarization splitter and rotator  600  that operates according to principles of the invention. As shown in  FIG. 6 , the integrated polarization splitter and rotator  600  comprises a waveguide structure, which includes: an input port  610 , a tapered rotator  620 , a splitter, e.g. Y-splitter,  630 , and two output ports  640 ,  642 . The integrated polarization splitter and rotator  600  lacks a directional coupler. In the embodiment shown in  FIG. 6 , the dimensions of the integrated polarization splitter and rotator  600  may be 45 μm in length by 7 μm in width, but smaller dimensions are possible. This requires an area of 315 μm 2  or less per integrated polarization splitter and rotator  600 . 
     In a preferred embodiment, a PDL tuning section  650  may be provided between the tapered rotator  620  and the splitter  630 . Typically, the shape of the TE0 and TE1 modes may be deformed, i.e., expanded and/or compressed, by the shape of the PDL tuning section  650 , e.g. gradual narrowing to widths less than the wide end of the tapered rotator  620  and the splitter  630  and/or broadening to widths greater than the wide end of the tapered rotator  620  and the splitter  630 , whereby the phase may be delayed between the portions of the TE0 and TE1 modes during splitting. The PDL tuning second  650  enables the PSR  600  to generate a specific PDL, a minimum PDL, a higher splitting efficiency, or a minimum PDL with highest achievable splitting efficiency. Ideally, the PDL tuning section  650  is symmetrical, about a longitudinal axis along the direction of light propagation, to provide equal splitting for the TE0 and TE1 modes. 
       FIG. 7  is a plan view of a second embodiment of an integrated polarization splitter and rotator  700  that operates according to principles of the invention. As shown in  FIG. 7 , the integrated polarization splitter and rotator  700  comprises a waveguide structure including: an input port  705 , a tapered rotator  710 , a splitter, e.g. Y-splitter,  720 , two waveguides  730 , and two output ports  740 ,  742 . The integrated polarization splitter and rotator  700  lacks a directional coupler. In the embodiment shown in  FIG. 7 , the dimensions of the integrated polarization splitter and rotator  700  may be 20 μm length by 4 μm width or less overall. This requires an area of 80 μm 2  or less per integrated polarization splitter and rotator  700 . It is believed that an operational integrated polarization splitter and rotator  700  can be reduced in size to approximately 12.7 μm length by 1.55 μm width overall. This requires an area of 19.685 μm 2  per integrated polarization splitter and rotator. By reducing the footprint required to construct and operate the integrated polarization splitter and rotator, one can dramatically increase the number of components, and the capacity to receive and transmit optical signals, on a per chip basis. 
     In a preferred embodiment, a PDL tuning section  750  may be provided between the tapered rotator  710  and the splitter  720 . Typically, the shape of the TE0 and TE1 modes may be deformed, i.e. expanded and/or compressed, by the shape of the PDL tuning section  750 , e.g. gradual narrowing to widths less than the wide end of the tapered rotator  710  and the splitter  720  and/or broadening to widths greater than the wide end of the tapered rotator  710  and the splitter  720 , whereby the phase may be delayed between the portions of the TE0 and TE1 modes during splitting. The PDL tuning second  750  enables the PSR  700  to generate a specific PDL, a minimum PDL, a higher splitting efficiency, or a minimum PDL with highest achievable splitting efficiency. Ideally, the PDL tuning section  750  is symmetrical, about a longitudinal axis along the direction of light propagation, to provide equal splitting for the TE0 and TE1 modes. 
     One application for the 45° PSR is for use in on-chip polarization insensitive designs. An example is a polarization insensitive wavelength-division multiplexing (WDM) receiver (RX) system. 
       FIG. 8  is a schematic diagram in plan view of a bi-directional photodetector  800 . In  FIG. 8 , a semiconductor, e.g. silicon, substrate  810 , such as an active device layer in a SOI wafer is provided. An absorber, e.g. germanium,  820  is deposited on the silicon substrate  810 . Two optical waveguides  830 ,  832 , such as high index contrast silicon waveguides, provide paths for illumination to reach the photodetector  800  formed by the Si—Ge region from either of two directions. This forms the bi-directional photodetector  800 . For a polarization diversity receiver, the second port  640  or  740  is optically coupled to one of the optical waveguides, e.g.  830 , while the third port  642  or  742  is optical coupled to the other of the optical waveguides, e.g.  832 . 
       FIG. 9  is a schematic diagram of an illustrative polarization insensitive WDM receiver (RX). As illustrated in the embodiment shown in  FIG. 9 , a 45° PSR  910  is used to split two orthogonal polarization states and rotate them into TE0 modes, as hereinbefore described. Then each signal is multiplexed by a 1×4 WDM MIA  920 ,  930 . The two TE0 signals separated by the 1×4 WDM MLA  920 ,  930  into separate constituent wavelength signals, having wavelengths given by λ 1 , λ 2 , λ 3 , and λ 4 , where λ 1 &gt;λ 2 &gt;λ 3 &gt;λ 4 . The various wavelength signals arrive at respective bi-directional PD  940 . The bi-directional PD  940  collects a signal from both polarizations for each wavelength, making the entire RX system polarization insensitive. In other embodiments, numbers of discrete wavelengths other than 4 may be used. In different embodiments, using N wavelengths, where N is greater than one, the wavelengths λ i  for 1≦i≦N are all different from each other. 
       FIG. 10A  through  FIG. 10H  are eye diagrams of an illustrative WDM RX such as that shown in  FIG. 9  that was fabricated and tested. 
       FIG. 10A  is an eye diagram recorded under 10 Gbps modulation using 1530.5 nm illumination at maximum Vpp. 
       FIG. 10B  is an eye diagram recorded under 10 Gbps modulation using 1530.5 nm illumination at minimum Vpp. 
       FIG. 10C  is an eye diagram recorded under 10 Gbps modulation using 1537 nm illumination at maximum Vpp. 
       FIG. 10D  is an eye diagram recorded under 10 Gbps modulation using 1537 nm illumination at minimum Vpp. 
       FIG. 10E  is an eye diagram recorded under 10 Gbps modulation using 1543.5 nm illumination at maximum Vpp. 
       FIG. 10F  is an eye diagram recorded under 10 Gbps modulation using 1543.5 nm illumination at minimum Vpp. 
       FIG. 10G  is an eye diagram recorded under 10 Gbps modulation using 1550 nm illumination at maximum Vpp. 
       FIG. 10H  is an eye diagram recorded under 10 Gbps modulation using 1550 nm illumination at minimum Vpp. 
     Eye diagram testing at 10 Gbps verified that the device is operational. By rotating the polarization state of the input signal, one can obtain the best case and worst case of eye diagram. The results showed that the worst-case polarization dependent loss (PDL) is 0.6 dB. The calculated PDL is listed in Table 1. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Wavelength 
                 max Vpp 
                 min Vpp 
                 PDL 
               
               
                   
                 (nm) 
                 (mV) 
                 (mV) 
                 (dB) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 1530.5 
                 20.7 
                 18 
                 −0.61 
               
               
                   
                 1537 
                 19 
                 18.7 
                 −0.07 
               
               
                   
                 1543.5 
                 21.8 
                 21.4 
                 −0.08 
               
               
                   
                 1550 
                 20.6 
                 19.5 
                 −0.24 
               
               
                   
                   
               
             
          
         
       
     
     In some embodiments, one may have an application that involves excitation of a TM mode on-chip for some purpose. In such an application, a plurality of PSRs may be employed, and the footprint can be further scaled down. 
       FIG. 11  is a diagram of an example of a cascaded PSR structure. One application of such a structure is as an on-chip test structure. In  FIG. 11 , elements  1110  and  1110 ′ are optical waveguides used to connect successive test modules in the integrated test structure. Element  1120  is a PSR, element  1130  is a structure similar to an MZI with no required elements provided to apply a modulation signal and element  1140  is a combiner based on the PSR  1120  operated in the reciprocal sense from  1120  used as a rotator and splitter, and  1110 ′,  1120 ′,  1130 ′ and  1140 ′ are another example of each of  1110 ,  1120 ,  1130  and  1140 , respectively, in a serial connection. Elements  1120 ,  1130  and  1140  form a butt-coupled PSR pair.  1120 ′,  1130 ′ and  1140 ′ are another example of a second butt-coupled PSR pair. 
     By cascading these pairs with different numbers, one can accurately extract the insertion loss of the device and thus measure the PDL. An embodiment of a test structure with 10 cascaded PSR pairs using the technology described herein will have an accumulated length that is shorter than 250 μm. Such a test structure can be easily provided in the spare space of a large system to enable device characterizations in wafer scale fabrication. 
     In another embodiment, the compact PSR design of  FIG. 11  is very attractive for use in low-power, high-density system integration (such as in WDM systems) enabled by silicon micro-rings where the bend radius is smaller than 10 μm. In such systems, the footprint of an entire system is only several hundred square microns. Such systems are discussed in co-pending U.S. Patent Publication 2015/0104176 filed Oct. 15, 2014 in the name of Baehr-Jones et al, which is incorporated herein by reference. See also Yang Liu, Ran Ding, Yangjin Ma, Yisu Yang, Zhe Xuan, Qi Li Andy Eu-Jin Lim, Guo-Qiang Lo, Keren Bergman, Tom Baehr-Jones and Michael Hochberg “Silicon Mod-MUX-Ring transmitter with 4 channels at 40 Gb/s”, OPTICS EXPRESS, Vol. 22, No. 13, pages 16431-16438, published 25 Jun. 2014, which is incorporated herein by reference. 
     By connecting the cascaded PSR test structure to grating couplers that work at TE0 (or TM0) mode, the insertion loss at TE0 (or TM0) can be accurately extracted. Thus PDL can be calculated as the difference of losses between the two modes. One can also connect the PSR test structures to edge couplers with on-chip or off-chip polarizers to extract an accurate insertion loss and PDL. 
     Further Description 
     In some embodiments of the PSR  200 ,  600  or  700  the substrate is Si on insulator, and in other embodiments it can be III-V materials. In some embodiments the top material is SiO 2  but in other embodiments it can be other suitable topping materials, such as Air, silicon nitride, or other materials having a suitable optical index. 
       FIG. 12  is a schematic diagram of a PSR  1200  having a Y-junction, according to principles of the invention. The first part is a bi-layer taper rotator  1210  that rotates TM0 from a first port into TE1 but leaves TE0 undisturbed. The second part is a Y-junction splitter  1220  that splits both TE1 and TE0 into separate portions, and combines a first portion of the TE1 with a first portion of the TE0 for output a second port  1222 , and second portion of the TE1 with a second portion of the TE0 for output a third port  1223 , as hereinbefore defined. The PSR  1200  may be a passive reciprocal device, which also works in reverse to combine a pair of like polarized signals from the second and third ports  1222  and  1223  for launching as a mixed polarized signal onto an optical fiber from the first port  1202 . No directional-coupler-like structure is involved for mode conversion and separation. 
     A PSR  1200  may be constructed by connecting these two parts  1210  and  1220  with a PDL tuning section  1250 . By applying an optimization algorithm, such as the PSO, as defined in co-pending United States Patent Publication 2014/0178005 filed Nov. 29, 2013 in the name of Zhang et al, which is incorporated herein by reference, or the genetic algorithm, to the Y-junction  1220  geometry, the PDL can be highly controllable in design. By applying an optimization algorithm such as the PSO, or the genetic algorithm, to the bi-layer taper  1210 , the device length can be dramatically decreased. A linear adiabatic taper also works if the footprint is not a constraint for a given application. 
     Typically, the shape of the TE0 and TE1 modes may be deformed, i.e. expanded and/or compressed, by the shape of the PDL tuning section  1250 , e.g., gradual narrowing to widths less than the wide end of the tapered rotator  1210  and the splitter  1220  and/or broadening to widths greater than the wide end of the tapered rotator  1210  and the splitter  1220 , whereby the phase may be delayed between the portions of the TE0 and TE1 modes during splitting. The PDL tuning second  1250  enables the PSR  1200  to generate a specific PDL, a minimum PDL, a higher splitting efficiency, or a minimum PDL with highest achievable splitting efficiency. Ideally, the PDL tuning section  1250  is symmetrical, about a longitudinal axis along the direction of light propagation, to provide equal splitting for the TE0 and TE1 modes. 
     Optimization Example 
     We now explain how one may optimize the PSR  1200  and show an example of its geometry (TE=0.4 dB, TM=0.3 dB). 
       FIG. 12  a schematic showing that the Y-junction geometry is segmented (which can be thought of as being digitized) into several segments. By engineering the widths (indicated in the embodiment shown in  FIG. 12  as W 1 , W 2 , W 3 , . . . , W 9 ), the splitting efficiency of TE1 and TE0 and thus the PDL can be controlled. The multimode PDL tuning region  1250 , with a predetermined length, is divided into several equal segments, each having an independent width (W 1  to Wn) perpendicular to and symmetrical about the longitudinal axis thereof. One or more segments W 1  to Wn may have widths larger than the wide end of the tapered rotator  1210  and the splitter  1220  for expanding the intermediate TE0 and TE1 modes. One or more segments W 1  to Wn may have widths smaller than the wide end of the tapered rotator  1210  and the splitter  1220  for contracting the intermediate TE0 and TE1 modes. Different width combinations have different efficiency for the TE0 and TE1 modes. A smoothing algorithm, such as interpolating spline, can be used to smooth the outline of the PDL tuning region  1250  to provide a gradual expansion and contraction between widths W 1  to Wn. 
     As an example, for the geometry given in Table 2, the loss of PSR  1200  for TE0 and TM0 is 0.35 dB and 0.25 dB, respectively. The PDL can therefore be calculated 0.1 dB. Note that TM0 has lower loss than TE0. In other embodiments, one can use more or fewer than 9 segments to do this analysis. 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Y-junction geometry 
               
             
          
           
               
                   
                 W1 
                 W2 
                 W3 
                 W4 
                 W5 
                 W6 
                 W7 
                 W8 
                 W9 
               
               
                   
                   
               
             
          
           
               
                 Width 
                 1.25 
                 1.1 
                 1.018 
                 1.108 
                 1.257 
                 1.47 
                 1.534 
                 1.513 
                 1.6 
               
               
                 (μm) 
               
               
                   
               
             
          
         
       
     
       FIG. 13  is a graph of insertion loss as a function of wavelength for the TE mode and the TM mode. 
     Applications 
     The PSR that are constructed according to principles of the invention can be used in a variety of applications, such as by way of example, WDM systems, receiver systems, polarization controllers, combinations of such applications, and other applications, such as, by way of example, reconfigurable optical add-drop multiplexers (ROADMs) and variable optical attenuators (VOAs). 
     In another embodiment, illustrated in  FIG. 14 , an on-chip polarization controller comprises a PSR  1400   a  followed by a phase and/or power tuning element  1450 , e.g. by a 2×2 MMI and phase tuners. In the prior art, for example as described in Wesley D. Sacher, Tymon Barwicz, Benjamin J. F. Taylor, and Joyce K. S. Poon, “Polarization rotator-splitters in standard active silicon photonics platforms,” OPTICS EXPRESS, Vol. 22, No. 4, 3777-3786, published 10 Feb. 2014, which is incorporated herein by reference, the PSR is about 500 μm which is about the same size as the thermal tuner. By reducing the device length of the PSR to 9 μm, which is much shorter than the 500 μm long thermal tuner, we can almost reduce the controller footprint by half. See also Wesley D. Sacher, Ying Huang, Liang Ding, Tymon Barwicz, Jared C. Mikkelsen, Benjamin J. F. Taylor, Guo-Qiang Lo, and Joyce K. S. Poon, “Polarization rotator-splitters and controllers in a Si3N4-on-SOI integrated photonics platform,” OPTICS EXPRESS, Vol. 22, No. 9, 1167-11174, published 1 May 2014, which is incorporated herein by reference. 
       FIG. 14  is a schematic of an on-chip polarization controller that includes 2 PSR devices  1401   a  and  1401   b  and an interposed phase or power tuning element  1450  therebetween. An on-chip polarization controller  1400  can be constructed by connecting two butt-coupled PSRs  1401   a  and  1401   b  with the phase tuning and/or power tuning  1450  in between. The tuning can be single stage or multiple stages cascaded with 2×2 3 dB couplers. The first PSR  1401   a  receives light of mixed polarization at input port  1402 , and outputs one or two combined signals at the same predetermined polarization at the second and third ports  1422  and  1423 . The phase and/or power of each of the combined signals are adjusted in the phase and/or power tuner  1450 , whereby when the combined signals are input the second PSR  1401   b , via second and third ports  1442  and  1443 , the second PSR  1401   b  can output an output signal of a desired polarization via first port  1441 . 
       FIG. 15  is a schematic diagram of an on-chip polarization diversity transmitter  1500 , comprising a laser  1501  for generating an input signal, which is launched into a first PSR  1505 , as hereinbefore described, for rotating and splitting the input signal into two like-polarized output signals, and for outputting the two output signals via the second and third ports  1522  and  1523 . The two output signals are modulated by the modulator  1550 , and then output second and third ports of a second PSR  1510 . The second PSR  1510  then recombines and rotates the modulated output signals for output the first port  1541  of the second PSR  1510 . 
       FIG. 16  is a schematic diagram of an on-chip polarization diversity MUX/DEMUX  1600 . For multiplexing signals, the MUX/DEMUX  1600  comprises a plurality of light sources, e.g., lasers,  1601   a  and  1601   b  for generating input signals, which are launched into respective PSRs  1605   a  and  1605   b , as hereinbefore described, for rotating and splitting the input signals into pairs of like-polarized output signals, and for outputting the pairs of output signals via the respective second and third ports  1622   a / 1622   b  and  1623   a / 1623   b . The output signals from the second ports  1622   a  and  1622   b  are combined in a suitable first multiplexing device, e.g., AWG, while the output signals from the third ports  1623   a  and  1623   b  are combined in a suitable second multiplexing device, e.g., AWG. Then the two combined signals are combined and rotated in an input/output PSR  1610  for output as a combined WDM signal. 
     For demultiplexing, the MUX/DEMUX  1600  works in reverse. An input combined WDM signal is input the first port  1641  of the input/output PSR  1610  rotates the polarization of the TM0 and splits the input signal into two like-polarized combined signals. The first and second multiplexing devices separate each of the combined signals into constituent wavelengths, and direct each corresponding pair of constituent wavelengths to the second and third ports of one of the PSRs  1605   a  and  1605   b . The PSRs  1605   a  and  1605   b  combine and rotate the polarization of the pairs of constituent wavelengths, and output each combined wavelength signal to one of the first ports  1602   a  and  1602   b . The devices  1601   a  and  1601   b  may be a photodetector for converting the combined wavelength signal into an electrical signal or some other optical device for further transmitting or adjusting the individual wavelength signals. 
       FIG. 17  illustrates a schematic of a polarization diversity switch  1700  including a plurality of first PSR&#39;s  1705   a  and  1705   b , and a plurality of second PSR&#39;s  1710   a  and  1710   b  representing input/output ports for a switch core  1750 . Individual wavelength or WDM signals may be input the first or second PSR&#39;s, in which each signal has the TM0 mode rotated to TE0, and then both TE0 modes separated into a pair of like-polarized signals for output separately at the second and third ports  1722   a / 1722   b / 1742   a / 1742   b  and  1723   a / 1723   b / 1743   a / 1743   b , respectively, which are optically coupled to the switch core  1750 . Within the switch core  1750 , each pair of like-polarized signals may be separated further into pairs of individual wavelengths signals by a suitable DEMUX, as hereinbefore described. If necessary, the individual pairs of wavelength signals may then be directed to one of a plurality of suitable MUX devices corresponding to the desired input/output port for combination into a pair of combined WDM output signals. The pair of combined WDM output signals or a pair of individual wavelength signals is then directed by the switch core  1750  to the desired input/output port, i.e., PSR  1705   a ,  1705   b ,  1710   a ,  1710   b , for combining and rotating into a single output signal for outputting the corresponding first port  1702   a ,  1702   b ,  1741   a  and  1741   b.    
     Design and Fabrication 
     Methods of designing and fabricating devices having elements similar to those described herein, including high index contrast silicon waveguides, are described in one or more of U.S. Pat. Nos. 7,200,308, 7,339,724, 7,424,192, 7,480,434, 7,643,714, 7,760,970, 7,894,696, 8,031,985, 8,067,724, 8,098,965, 8,203,115, 8,237,102, 8,258,476, 8,270,778, 8,280,211, 8,311,374, 8,340,486, 8,380,016, 8,390,922, 8,798,406, and 8,818,141, each of which documents is hereby incorporated by reference herein in its entirety. 
     DEFINITIONS 
     As used herein, the term “optical communication channel” is intended to denote a single optical channel, such as light that can carry information using a specific carrier wavelength in a wavelength division multiplexed (WDM) system. 
     As used herein, the term “optical carrier” is intended to denote a medium or a structure through which any number of optical signals including WDM signals can propagate, which by way of example can include gases such as air, a void such as a vacuum or extraterrestrial space, and structures such as optical fibers and optical waveguides. 
     Theoretical Discussion 
     Although the theoretical description given herein is thought to be correct, the operation of the devices described and claimed herein does not depend upon the accuracy or validity of the theoretical description. That is, later theoretical developments that may explain the observed results on a basis different from the theory presented herein will not detract from the inventions described herein. 
     Any patent, patent application, patent application publication, journal article, book, published paper, or other publicly available material identified in the specification is hereby incorporated by reference herein in its entirety. Any material, or portion thereof, that is said to be incorporated by reference herein, but which conflicts with existing definitions, statements, or other disclosure material explicitly set forth herein is only incorporated to the extent that no conflict arises between that incorporated material and the present disclosure material. In the event of a conflict, the conflict is to be resolved in favor of the present disclosure as the preferred disclosure. 
     While the present invention has been particularly shown and described with reference to the various embodiments illustrated in the drawings, it will be understood by one skilled in the art that various changes in detail may be affected therein without departing from the spirit and scope of the invention, and it is not intended that the present teachings be limited to such embodiments.