Patent Publication Number: US-2023161106-A1

Title: Optical Input Polarization Management Device and Associated Methods

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation application under 35 U.S.C. 120 of prior U.S. application Ser. No. 17/353,782, filed Jun. 21, 2021, which claims priority under 35 U.S.C. 119(e) to U.S. Provisional Patent Application No. 63/043,774, filed on Jun. 24, 2020. The disclosure of each above-identified application is incorporated herein by reference in its entirety for all purposes. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to optical data communication. 
     2. Description of the Related Art 
     Optical data communication systems operate by modulating laser light to encode digital data patterns. The modulated laser light is transmitted through an optical data network from a sending node to a receiving node. The modulated laser light having arrived at the receiving node is de-modulated to obtain the original digital data patterns. Therefore, implementation and operation of optical data communication systems is dependent upon having reliable and efficient devices for modulating optical signals and for receiving optical signals. It is within this context that the present invention arises. 
     SUMMARY OF THE INVENTION 
     In an example embodiment, an electro-optic receiver is disclosed. The electro-optic receiver includes a polarization splitter and rotator that has an optical input optically connected to receive incoming light. The polarization splitter and rotator has a first optical output and a second optical output. The polarization splitter and rotator is configured to direct a first portion of the incoming light having a first polarization through the first optical output. The polarization splitter and rotator is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The polarization splitter and rotator is configured to direct the polarization-rotated second portion of the incoming light through the second optical output. The electro-optic receiver also includes an optical waveguide having a first end optically to the first optical output of the polarization splitter and rotator. The optical waveguide has a second end optically connected to the second optical output of the polarization splitter and rotator, such that the first portion of the incoming light travels from the first optical output of the polarization splitter and rotator through the optical waveguide in a first direction, and such that the polarization-rotated second portion of the incoming light travels from the second optical output of the polarization splitter and rotator through the optical waveguide in a second direction opposite the first direction. The electro-optic receiver also includes a plurality of ring resonator photodetectors positioned alongside the optical waveguide and within an evanescent optical coupling distance of the optical waveguide. Each of the plurality of ring resonator photodetectors is configured to operate at a respective resonant wavelength, such that the first portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of a given one of the plurality of ring resonator photodetectors optically couples into the given one of the plurality of ring resonator photodetectors in a first propagation direction, and such that the polarization-rotated second portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of the given one of the plurality of ring resonator photodetectors optically couples into the given one of the plurality of ring resonator photodetectors in a second propagation direction opposite the first propagation direction. 
     In an example embodiment, an electro-optic receiver is disclosed. The electro-optic receiver includes a polarization splitter and rotator that has an optical input optically connected to receive incoming light. The polarization splitter and rotator has a first optical output and a second optical output. The polarization splitter and rotator is configured to direct a first portion of the incoming light having a first polarization through the first optical output. The polarization splitter and rotator is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The polarization splitter and rotator is configured to direct the polarization-rotated second portion of the incoming light through the second optical output. The electro-optic receiver also includes an optical waveguide that has a first end optically to the first optical output of the polarization splitter and rotator. The optical waveguide has a second end optically connected to the second optical output of the polarization splitter and rotator, such that the first portion of the incoming light travels from the first optical output of the polarization splitter and rotator through the optical waveguide in a first direction, and such that the polarization-rotated second portion of the incoming light travels from the second optical output of the polarization splitter and rotator through the optical waveguide in a second direction opposite the first direction. The electro-optic receiver also includes a plurality of ring resonators positioned alongside the optical waveguide and within an evanescent optical coupling distance of the optical waveguide. Each of the plurality of ring resonators is configured to operate at a respective resonant wavelength, such that the first portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of a given one of the plurality of ring resonators optically couples into the given one of the plurality of ring resonators in a first propagation direction, and such that the polarization-rotated second portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of the given one of the plurality of ring resonators optically couples into the given one of the plurality of ring resonators in a second propagation direction opposite the first propagation direction. The electro-optic receiver also includes a plurality of photodetectors respectively associated with the plurality of ring resonators. The electro-optic receiver also includes a plurality of output optical waveguides respectively optically coupled to the plurality of ring resonators. Each of the plurality of output optical waveguides includes a coupling section, a short section, and a long section. The coupling section is positioned to evanescently couple light from a corresponding one of the plurality of ring resonators. The short section extends from a first end of the coupling section to a corresponding one of the plurality of photodetectors. The long section extends from a second end of the coupling section to the corresponding one of the plurality of photodetectors. 
     In an example embodiment, a method is disclosed for operating a photonic integrated circuit. The method includes receiving incoming light through an optical input port. A first portion of the incoming light has a first polarization, and a second portion of the incoming light has a second polarization. The method also includes splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes directing the first portion of the incoming light through a first end of an optical waveguide. The method also includes rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes directing the polarization-rotated second portion of the incoming light through a second end of the optical waveguide. The optical waveguide extends in a continuous manner from the first end to the second end. The method also includes operating a plurality of ring resonators to evanescently in-couple light from the optical waveguide. Each of the plurality of ring resonators is operated at a respective resonant wavelength to in-couple both the first portion of the incoming light having the respective resonant wavelength and the polarization-rotated second portion of the incoming light having the respective resonant wavelength. 
     In an example embodiment, an electro-optic receiver is disclosed. The electro-optic receiver includes a polarization splitter and rotator that has an optical input optically connected to receive incoming light. The polarization splitter and rotator has a first optical output and a second optical output. The polarization splitter and rotator is configured to direct a first portion of the incoming light having a first polarization through the first optical output. The polarization splitter and rotator is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The polarization splitter and rotator is configured to direct the polarization-rotated second portion of the incoming light through the second optical output. The electro-optic receiver also includes a first optical waveguide optically connected to the first optical output of the polarization splitter and rotator. The electro-optic receiver also includes a first plurality of ring resonators positioned within an evanescent optical coupling distance of the first optical waveguide. Each of the first plurality of ring resonators is configured to operate at a respective resonant wavelength, such that the first portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of a given one of the first plurality of ring resonators optically couples into the given one of the first plurality of ring resonators. The electro-optic receiver also includes a first plurality of output optical waveguides respectively positioned within an evanescent optical coupling distance of the first plurality of ring resonators. The electro-optic receiver also includes a second optical waveguide optically connected to the second optical output of the polarization splitter and rotator. The electro-optic receiver also includes a second plurality of ring resonators positioned within an evanescent optical coupling distance of the second optical waveguide. Each of the second plurality of ring resonators is configured to operate at a respective resonant wavelength, such that the polarization-rotated second portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of a given one of the second plurality of ring resonators optically couples into the given one of the second plurality of ring resonators. The electro-optic receiver also includes a second plurality of output optical waveguides respectively positioned within an evanescent optical coupling distance of the second plurality of ring resonators. The electro-optic receiver also includes a plurality of photodetectors. Each of the plurality of photodetectors is optically connected to receive light from a respective one of the first plurality of output optical waveguides and from a respective one of the second plurality of output optical waveguides, where the respective one of the first plurality of output optical waveguides is optically coupled to one of the first plurality of ring resonators having a given resonant wavelength, and where the respective one of the second plurality of output optical waveguides is optically coupled to one of the second plurality of ring resonators having substantially the same given resonant wavelength. 
     In an example embodiment, a method is disclosed for operating a photonic integrated circuit. The method includes receiving incoming light through an optical input port. A first portion of the incoming light has a first polarization, and a second portion of the incoming light has a second polarization. The method also includes splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes directing the first portion of the incoming light into a first optical waveguide. The method also includes rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes directing the polarization-rotated second portion of the incoming light into a second optical waveguide. The method also includes operating a first plurality of ring resonators to evanescently in-couple light from the first optical waveguide. Each of the first plurality of ring resonators is operated at a respective resonant wavelength to in-couple light having the respective resonant wavelength from the first optical waveguide. The method also includes optically coupling light from the first plurality of ring resonators into respective ones of a first plurality of output optical waveguides. The method also includes directing light within the first plurality of output optical waveguides into respective ones of a plurality of photodetectors. The method also includes operating a second plurality of ring resonators to evanescently in-couple light from the second optical waveguide. Each of the second plurality of ring resonators is operated at a respective resonant wavelength to in-couple light having the respective resonant wavelength from the second optical waveguide. The method also includes optically coupling light from the second plurality of ring resonators into respective ones of a second plurality of output optical waveguides. The method also includes directing light within the second plurality of output optical waveguides into respective ones of the plurality of photodetectors. 
     In an example embodiment, an electro-optic receiver is disclosed. The electro-optic receiver includes a polarization splitter and rotator that has an optical input optically connected to receive incoming light. The polarization splitter and rotator has a first optical output and a second optical output. The polarization splitter and rotator is configured to direct a first portion of the incoming light having a first polarization through the first optical output. The polarization splitter and rotator is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The polarization splitter and rotator is configured to direct a polarization-rotated second portion of the incoming light through the second optical output. The electro-optic receiver also includes a first optical waveguide that has a first end and second end. The first end of the first optical waveguide is optically connected to the first optical output of the polarization splitter and rotator. The electro-optic receiver also includes a second optical waveguide that has a first end and second end. The first end of the second optical waveguide is optically connected to the second optical output of the polarization splitter and rotator. The electro-optic receiver also includes a two-by-two optical splitter that has a first optical input optically connected to the second end of the first optical waveguide. The two-by-two optical splitter has a second optical input optically connected to the second end of the second optical waveguide. The two-by-two optical splitter has a first optical output and a second optical output. The two-by-two optical splitter is configured to output some of the first portion of the incoming light and some of the polarization-rotated second portion of the incoming light through each of the first optical output and the second optical output of the two-by-two optical splitter. The electro-optic receiver also includes a third optical waveguide optically connected to the first optical output of the two-by-two optical splitter. The electro-optic receiver also includes a first plurality of ring resonators positioned within an evanescent optical coupling distance of the third optical waveguide. Each of the first plurality of ring resonators is configured to operate at a respective resonant wavelength, such that light having a wavelength substantially equal to the respective resonant wavelength of a given one of the first plurality of ring resonators optically couples from the third optical waveguide into the given one of the first plurality of ring resonators. The electro-optic receiver also includes a first plurality of output optical waveguides respectively positioned within an evanescent optical coupling distance of the first plurality of ring resonators. The electro-optic receiver also includes a fourth optical waveguide optically connected to the second optical output of the two-by-two optical splitter. The electro-optic receiver also includes a second plurality of ring resonators positioned within an evanescent optical coupling distance of the fourth optical waveguide. Each of the second plurality of ring resonators is configured to operate at a respective resonant wavelength, such that light having a wavelength substantially equal to the respective resonant wavelength of a given one of the second plurality of ring resonators optically couples from the fourth optical waveguide into the given one of the second plurality of ring resonators. The electro-optic receiver also includes a second plurality of output optical waveguides respectively positioned within an evanescent optical coupling distance of the second plurality of ring resonators. The electro-optic receiver also includes a plurality of photodetectors. Each of the plurality of photodetectors is optically connected to receive light from a respective one of the first plurality of output optical waveguides and from a respective one of the second plurality of output optical waveguides, where the respective one of the first plurality of output optical waveguides is optically coupled to one of the first plurality of ring resonators having a given resonant wavelength, and wherein the respective one of the second plurality of output optical waveguides is optically coupled to one of the second plurality of ring resonators having the same given resonant wavelength. 
     In an example embodiment, a method is disclosed for operating a photonic integrated circuit. The method includes receiving incoming light through an optical input port. A first portion of the incoming light has a first polarization, and a second portion of the incoming light has a second polarization. The method also includes splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes directing the first portion of the incoming light through a first optical waveguide and into a first optical input of a two-by-two splitter. The method also includes rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes directing the polarization-rotated second portion of the incoming light through a second optical waveguide and into a second optical input of the two-by-two splitter. The method also includes directing some of the first portion of the incoming light through a first optical output of the two-by-two optical splitter and into a third optical waveguide. The method also includes directing some of the first portion of the incoming light through a second optical output of the two-by-two optical splitter and into a fourth optical waveguide. The method also includes directing some of the polarization-rotated second portion of the incoming light through the first optical output of the two-by-two optical splitter and into the third optical waveguide. The method also includes directing some of the polarization-rotated second portion of the incoming light through the second optical output of the two-by-two optical splitter and into the fourth optical waveguide. The method also includes operating a first plurality of ring resonators to evanescently in-couple light from the third optical waveguide. Each of the first plurality of ring resonators is operated at a respective resonant wavelength to in-couple light having the respective resonant wavelength from the third optical waveguide. The method also includes optically coupling light from the first plurality of ring resonators into respective ones of a first plurality of output optical waveguides. The method also includes directing light within the first plurality of output optical waveguides into respective ones of a plurality of photodetectors. The method also includes operating a second plurality of ring resonators to evanescently in-couple light from the fourth optical waveguide. Each of the second plurality of ring resonators is operated at a respective resonant wavelength to in-couple light having the respective resonant wavelength from the fourth optical waveguide. The method also includes optically coupling light from the second plurality of ring resonators into respective ones of a second plurality of output optical waveguides. The method also includes directing light within the second plurality of output optical waveguides into respective ones of the plurality of photodetectors. 
     In an example embodiment, an optical input polarization management device is disclosed. The optical input polarization management device includes a polarization splitter and rotator that has an optical input optically connected to receive incoming light. The polarization splitter and rotator has a first optical output and a second optical output. The polarization splitter and rotator is configured to direct a first portion of the incoming light that has a first polarization through the first optical output. The polarization splitter and rotator is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The polarization splitter and rotator is configured to direct the polarization-rotated second portion of the incoming light through the second optical output. The optical input polarization management device also includes a first optical waveguide that has a first end and second end. The first end of the first optical waveguide is optically connected to the first optical output of the polarization splitter and rotator. The optical input polarization management device also includes a second optical waveguide that has a first end and second end. The first end of the second optical waveguide is optically connected to the second optical output of the polarization splitter and rotator. The optical input polarization management device also includes a first phase shifter interfaced with either the first optical waveguide or the second optical waveguide. The optical input polarization management device also includes a first two-by-two optical splitter that has a first optical input optically connected to the second end of the first optical waveguide. The first two-by-two optical splitter has a second optical input optically connected to the second end of the second optical waveguide. The first two-by-two optical splitter has a first optical output and a second optical output. The optical input polarization management device also includes a third optical waveguide that has a first end and second end. The first end of the third optical waveguide is optically connected to the first optical output of the first two-by-two optical splitter. The optical input polarization management device also includes a fourth optical waveguide that has a first end and second end. The first end of the fourth optical waveguide is optically connected to the second optical output of the first two-by-two optical splitter. The optical input polarization management device also includes a second two-by-two optical splitter that has a first optical input optically connected to the second end of the third optical waveguide. The second two-by-two optical splitter has a second optical input optically connected to the second end of the fourth optical waveguide. The second two-by-two optical splitter has a first optical output and a second optical output. The optical input polarization management device also includes a second phase shifter interfaced with either the third optical waveguide or the fourth optical waveguide. The optical input polarization management device also includes a fifth optical waveguide optically connected to either the first optical output of the second two-by-two optical splitter or the second optical output of the second two-by-two optical splitter. 
     In an example embodiment, a method is disclosed for optical input polarization management. The method includes receiving incoming light through an optical input port. A first portion of the incoming light has a first polarization, and a second portion of the incoming light has a second polarization. The method also includes splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes directing the first portion of the incoming light through a first optical waveguide and into a first optical input of a first two-by-two splitter. The method also includes rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes directing the polarization-rotated second portion of the incoming light through a second optical waveguide and into a second optical input of the first two-by-two splitter. The method also includes operating a first phase shifter interfaced with either the first optical waveguide or the second optical waveguide to apply a controlled amount of shift to a phase of light traveling through either the first optical waveguide or the second optical waveguide to which the phase shifter is interfaced. The method also includes directing some of the first portion of the incoming light through a first optical output of the first two-by-two optical splitter and into a third optical waveguide. The method also includes directing some of the first portion of the incoming light through a second optical output of the first two-by-two optical splitter and into a fourth optical waveguide. The method also includes directing some of the polarization-rotated second portion of the incoming light through the first optical output of the first two-by-two optical splitter and into the third optical waveguide. The method also includes directing some of the polarization-rotated second portion of the incoming light through the second optical output of the first two-by-two optical splitter and into the fourth optical waveguide. The method also includes operating a second phase shifter interfaced with either the third optical waveguide or the fourth optical waveguide to apply a controlled amount of shift to a phase of light traveling through either the third optical waveguide or the fourth optical waveguide to which the phase shifter is interfaced. The method also includes directing said some of the first portion of the incoming light and said some of the polarization-rotated second portion of the incoming light from the third optical waveguide into a first optical input of a second two-by-two splitter. The method also includes directing said some of the first portion of the incoming light and said some of the polarization-rotated second portion of the incoming light from the fourth optical waveguide into a second optical input of the second two-by-two splitter. The method also includes directing part of said some of the first portion of the incoming light and part of said some of the polarization-rotated second portion of the incoming light through an optical output of the second two-by-two splitter and into a fifth optical waveguide. 
     In an example embodiment, an electro-optic transmitter is disclosed. The electro-optic transmitter includes a plurality of optical input ports. The electro-optic transmitter also includes a plurality of polarization controllers. Each of the plurality of polarization controllers has an optical input optically connected to a respective one of the plurality of optical input ports. Each of the plurality of polarization controllers is configured to convert two polarizations of incoming light as received through the respective one of the plurality of optical input ports into light having a single polarization, and output the light having the single polarization through an output optical waveguide of the polarization controller. The electro-optic transmitter also includes an optical multiplexer that has a plurality of optical inputs respectively optically connected to the output optical waveguides of the plurality of polarization controllers. The optical multiplexer has a plurality of optical outputs. The electro-optic transmitter also includes a plurality of optical waveguides. Each of the plurality of optical waveguides has a first end and second end. The first end of each of the plurality of optical waveguides is respectively optically connected to the plurality of optical outputs of the optical multiplexer. The electro-optic transmitter also includes a plurality of ring resonator modulators positioned along each of the plurality of optical waveguides. The electro-optic transmitter also includes a plurality of optical output ports. The second end of each of the plurality of optical waveguides is respectively optically connected to the plurality of optical output ports. 
     In an example embodiment, a method is disclosed for operating an electro-optic transmitter. The method includes receiving incoming light through a plurality of optical input ports. The method also includes operating a plurality of polarization controllers. Each of the plurality of polarization controllers has an optical input respectively optically connected to the plurality of optical input ports. Each of the plurality of polarization controllers is operated to convert light having two polarizations as received through a corresponding one of the plurality of optical input ports into light having a single polarization. Each of the plurality of polarization controllers is operated to direct the light having the single polarization through an output optical waveguide of the polarization controller. The method also includes operating an optical multiplexer that has a plurality of optical inputs respectively optically connected to the output optical waveguides of the plurality of polarization controllers. The optical multiplexer has a plurality of optical outputs. The optical multiplexer is operated to direct a portion of light received at each of the plurality of optical inputs of the optical multiplexer to each of the plurality of optical outputs of the optical multiplexer. The method also includes directing light from each of the plurality of optical outputs of the optical multiplexer through respective ones of a plurality of optical waveguides. Each of the plurality of optical waveguides has a first end and second end. The first end of each of the plurality of optical waveguides is respectively optically connected to the plurality of optical outputs of the optical multiplexer. The second end of each of the plurality of optical waveguides is respectively optically connected to a plurality of optical output ports. The method also includes operating a plurality of ring resonator modulators positioned along a given one of the plurality of optical waveguides to modulate light with the given one of the plurality of optical waveguides in accordance with a digital bit pattern. 
     In an example embodiment, an electro-optic transmitter is disclosed. The electro-optic transmitter includes a first polarization splitter and rotator having an optical input optically connected to receive incoming light. The first polarization splitter and rotator has a first optical output and a second optical output. The first polarization splitter and rotator is configured to direct a first portion of the incoming light having a first polarization through the first optical output. The first polarization splitter and rotator is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The first polarization splitter and rotator is configured to direct the polarization-rotated second portion of the incoming light through the second optical output. The electro-optic transmitter also includes a first optical waveguide that has a first end and a second end. The first end of the first optical waveguide is optically connected to the first optical output of the first polarization splitter and rotator. The electro-optic transmitter also includes a second optical waveguide that has a first end and a second end. The first end of the second optical waveguide is optically connected to the second optical output of the first polarization splitter and rotator. The electro-optic transmitter also includes a second polarization splitter and rotator that has a first reverse-connected optical output optically connected to the second end of the first optical waveguide. The second polarization splitter and rotator has a second reverse-connected optical output optically connected to the second end of the second optical waveguide. The second polarization splitter and rotator has a reverse-connected optical input. The second polarization splitter and rotator is connected in a reversed manner with respect to light propagation through the second polarization splitter and rotator. The second polarization splitter and rotator is connected to direct light having the first polarization as received from the first optical waveguide through the first reverse-connected optical output to the reverse-connected optical input of the second polarization splitter and rotator. The second polarization splitter and rotator is configured to derotate a polarization of the polarization-rotated second portion of the incoming light as received from the second optical waveguide through the second reverse-connected optical output from the first polarization back to the second polarization, so as to produce a polarization-derotated second portion of the incoming light. The polarization splitter and rotator is configured to direct the polarization-derotated second portion of the incoming light to the reverse-connected optical input of the second polarization splitter and rotator. The electro-optic transmitter also includes a plurality of ring resonator modulator pairs positioned along the first optical waveguide and the second optical waveguide. Each ring resonator modulator pair of the plurality of ring resonator modulator pairs includes one ring resonator modulator positioned within an evanescent optical coupling distance of the first optical waveguide and one ring resonator modulator positioned within an evanescent optical coupling distance of the second optical waveguide. 
     In an example embodiment, a method is disclosed for optical modulation. The method includes receiving incoming light through an optical input port. A first portion of the incoming light has a first polarization, and a second portion of the incoming light has a second polarization. The method also includes splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes directing the first portion of the incoming light through a first optical waveguide. The method also includes rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes directing the polarization-rotated second portion of the incoming light through a second optical waveguide. The method also includes operating a plurality of ring resonator modulator pairs positioned along the first optical waveguide and the second optical waveguide. Each ring resonator modulator pair of the plurality of ring resonator modulator pairs includes one ring resonator modulator positioned within an evanescent optical coupling distance of the first optical waveguide and one ring resonator modulator positioned within an evanescent optical coupling distance of the second optical waveguide. Each of the plurality of ring resonator modulator pairs is configured to operate at a specified resonant wavelength to modulate a same bit pattern onto light traveling through the first and second optical waveguides to create a first portion of modulated light having the first polarization within the first optical waveguide and to create a second portion of modulated light having the first polarization within the second optical waveguide. The method also includes rotating a polarization of the second portion of modulated light within the second optical waveguide back from the first polarization to the second polarization. The method also includes directing both the first portion of modulated light having the first polarization and the second portion of modulated light having the second polarization through a same optical output port. 
     In an example embodiment, an electro-optic transmitter is disclosed. The electro-optic transmitter includes a first polarization splitter and rotator that has an optical input optically connected to receive incoming light. The first polarization splitter and rotator has a first optical output and a second optical output. The first polarization splitter and rotator is configured to direct a first portion of the incoming light that has a first polarization through the first optical output. The first polarization splitter and rotator is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The first polarization splitter and rotator is configured to direct the polarization-rotated second portion of the incoming light through the second optical output. The electro-optic transmitter also includes a first optical waveguide that has a first end and second end. The first end of the first optical waveguide is optically connected to the first optical output of the first polarization splitter and rotator. The electro-optic transmitter also includes a second optical waveguide that has a first end and second end. The first end of the second optical waveguide is optically connected to the second optical output of the first polarization splitter and rotator. The electro-optic transmitter also includes a two-by-two optical splitter that has a first optical input optically connected to the second end of the first optical waveguide. The two-by-two optical splitter has a second optical input optically connected to the second end of the second optical waveguide. The two-by-two optical splitter has a first optical output and a second optical output. The two-by-two optical splitter is configured to output some of the first portion of the incoming light and some of the polarization-rotated second portion of the incoming light through each of the first optical output and the second optical output of the two-by-two optical splitter. The electro-optic transmitter also includes a third optical waveguide that has a first end and second end. The first end of the third optical waveguide is optically connected to the first optical output of the two-by-two optical splitter. The electro-optic transmitter also includes a fourth optical waveguide that has a first end and second end. The first end of the fourth optical waveguide is optically connected to the second optical output of the two-by-two optical splitter. The electro-optic transmitter also includes a second polarization splitter and rotator that has a first reverse-connected optical output optically connected to the second end of the third optical waveguide. The second polarization splitter and rotator has a second reverse-connected optical output optically connected to the second end of the fourth optical waveguide. The second polarization splitter and rotator has a reverse-connected optical input. The second polarization splitter and rotator is connected in a reversed manner with respect to light propagation through the second polarization splitter and rotator. The second polarization splitter and rotator is connected to direct light received through the first reverse-connected optical output of the second polarization splitter and rotator to the reverse-connected optical input of the second polarization splitter and rotator. The second polarization splitter and rotator is configured to derotate a polarization of light received through the second reverse-connected optical output of the second polarization splitter and rotator from the first polarization the second polarization so as to produce polarization-derotated light. The polarization splitter and rotator is configured to direct the polarization-derotated light to the reverse-connected optical input of the second polarization splitter and rotator. The electro-optic transmitter also includes a plurality of ring resonator modulator pairs positioned along the third optical waveguide and the fourth optical waveguide. Each ring resonator modulator pair of the plurality of ring resonator modulator pairs includes one ring resonator modulator positioned within an evanescent optical coupling distance of the third optical waveguide and one ring resonator modulator positioned within an evanescent optical coupling distance of the fourth optical waveguide. 
     In an example embodiment, a method is disclosed for optical modulation. The method includes receiving incoming light through an optical input port. A first portion of the incoming light has a first polarization, and a second portion of the incoming light has a second polarization. The method also includes splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes directing the first portion of the incoming light through a first optical waveguide and into a first optical input of a two-by-two splitter. The method also includes rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes directing the polarization-rotated second portion of the incoming light through a second optical waveguide and into a second optical input of the two-by-two splitter. The method also includes directing some of the first portion of the incoming light through a first optical output of the two-by-two optical splitter and into a third optical waveguide. The method also includes directing some of the first portion of the incoming light through a second optical output of the two-by-two optical splitter and into a fourth optical waveguide. The method also includes directing some of the polarization-rotated second portion of the incoming light through the first optical output of the two-by-two optical splitter and into the third optical waveguide. The method also includes directing some of the polarization-rotated second portion of the incoming light through the second optical output of the two-by-two optical splitter and into the fourth optical waveguide. The method also includes operating a plurality of ring resonator modulator pairs positioned along the third optical waveguide and the fourth optical waveguide. Each ring resonator modulator pair of the plurality of ring resonator modulator pairs includes one ring resonator modulator positioned within an evanescent optical coupling distance of the third optical waveguide and one ring resonator modulator positioned within an evanescent optical coupling distance of the fourth optical waveguide. Each of the plurality of ring resonator modulator pairs is configured to operate at a specified resonant wavelength to modulate a same bit pattern onto light traveling through the third optical waveguide and the fourth optical waveguide. The method also includes rotating a polarization of modulated light within either the third optical waveguide or the fourth optical waveguide from the first polarization to the second polarization. The method also includes directing both modulated light that has the first polarization and modulated light that has the second polarization through a same optical output port. 
     In an example embodiment, an electro-optic combiner is disclosed. The electro-optic combiner includes a polarization splitter and rotator that has an optical input optically connected to receive incoming light. The polarization splitter and rotator has a first optical output and a second optical output. The polarization splitter and rotator is configured to direct a first portion of the incoming light that has a first polarization through the first optical output. The polarization splitter and rotator is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The polarization splitter and rotator is configured to direct the polarization-rotated second portion of the incoming light through the second optical output. The electro-optic combiner also includes a first optical waveguide that has a first end and a second end. The first end of the first optical waveguide is optically connected to the first optical output of the polarization splitter and rotator. The electro-optic combiner also includes a second optical waveguide that has a first end and a second end. The first end of the second optical waveguide is optically connected to the second optical output of the polarization splitter and rotator. The electro-optic combiner also includes a plurality of ring resonators disposed between a combiner section of the first optical waveguide and a combiner section of the second optical waveguide. Each of the plurality of ring resonators is positioned within an evanescent optically coupling distance of both the first optical waveguide and the second optical waveguide. A light propagation direction through the combiner section of the first optical waveguide is opposite of a light propagation direction through the combiner section of the second optical waveguide. Each of the plurality of ring resonators is configured to operate at a respective resonant wavelength, such that light having a wavelength substantially equal to the respective resonant wavelength of a given one of the plurality of ring resonators optically couples light from the combiner section of the first optical waveguide into the given one of the plurality of ring resonators, and from the given one of the plurality of ring resonators into the second optical waveguide. 
     In an example embodiment, a method is disclosed for combination of optical signals. The method includes receiving incoming light through an optical input port. A first portion of the incoming light has a first polarization, and a second portion of the incoming light has a second polarization. The method also includes splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes directing the first portion of the incoming light through a first optical waveguide. The method also includes rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes directing the polarization-rotated second portion of the incoming light through a second optical waveguide. The method also includes operating a plurality of ring resonators disposed between the first optical waveguide and the second optical waveguide. Each of the plurality of ring resonators is operated to evanescently in-couple light from the first optical waveguide and out-couple light into the second optical waveguide. Each of the plurality of ring resonators is configured to operate at a respective resonant wavelength, such that light having a wavelength substantially equal to the respective resonant wavelength of a given one of the plurality of ring resonators optically couples light from the first optical waveguide into the given one of the plurality of ring resonators, and from the given one of the plurality of ring resonators into the second optical waveguide. 
     In an example embodiment, an electro-optic combiner is disclosed. The electro-optic combiner includes a polarization splitter and rotator that has an optical input optically connected to receive incoming light. The polarization splitter and rotator has a first optical output and a second optical output. The polarization splitter and rotator is configured to direct a first portion of the incoming light that has a first polarization through the first optical output. The polarization splitter and rotator is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The polarization splitter and rotator is configured to direct the polarization-rotated second portion of the incoming light through the second optical output. The electro-optic combiner also includes a first optical waveguide optically connected to the first optical output of the polarization splitter and rotator. The electro-optic combiner also includes a first plurality of ring resonators positioned along the first optical waveguide, such that the phase shifter is positioned alongside the first optical waveguide before the first plurality of ring resonators relative to a direction of light propagation through the first optical waveguide. Each of the first plurality of ring resonators is positioned within an evanescent optical coupling distance of the first optical waveguide. The electro-optic combiner also includes a second optical waveguide optically connected to the second optical output of the polarization splitter and rotator. The electro-optic combiner also includes a second plurality of ring resonators positioned along the second optical waveguide and within an evanescent optical coupling distance of the second optical waveguide. Each of the second plurality of ring resonators is positioned to optically in-couple light from a respective one of the first plurality of ring resonators and optically out-couple light into the second optical waveguide. 
     In an example embodiment, a method is disclosed for combination of optical signals. The method includes receiving incoming light through an optical input port. A first portion of the incoming light has a first polarization, and a second portion of the incoming light has a second polarization. The method also includes splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes directing the first portion of the incoming light through a first optical waveguide. The method also includes rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes directing the polarization-rotated second portion of the incoming light through a second optical waveguide. The method also includes operating a first plurality of ring resonators disposed between the first optical waveguide and the second optical waveguide. Each of the first plurality of ring resonators is operated to evanescently in-couple light from the first optical waveguide. The method also includes operating a second plurality of ring resonators disposed between the first optical waveguide and the second optical waveguide. Each of the second plurality of ring resonators is operated to evanescently in-couple light from a respective one of the first plurality of ring resonators. Each of the second plurality of ring resonators is operated to evanescently out-couple light to the second optical waveguide. Each optically coupled pair of ring resonators within the first and second pluralities of ring resonators is operated at a substantially same resonant wavelength. Each optically coupled pair of ring resonators within the first and second pluralities of ring resonators has opposite light propagation directions. 
     In an example embodiment, an electro-optic combiner is disclosed. The electro-optic combiner includes a polarization splitter and rotator that has an optical input optically connected to receive incoming light. The polarization splitter and rotator has a first optical output and a second optical output. The polarization splitter and rotator is configured to direct a first portion of the incoming light that has a first polarization through the first optical output. The polarization splitter and rotator configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The polarization splitter and rotator is configured to direct the polarization-rotated second portion of the incoming light through the second optical output. The electro-optic combiner also includes a first optical waveguide optically connected to the first optical output of the polarization splitter and rotator. The electro-optic combiner also includes a first plurality of ring resonators positioned along the first optical waveguide such that the phase shifter is positioned alongside the first optical waveguide before the first plurality of ring resonators relative to a direction of light propagation through the first optical waveguide. Each of the first plurality of ring resonators is positioned within an evanescent optical coupling distance of the first optical waveguide. The electro-optic combiner also includes a second optical waveguide optically connected to the second optical output of the polarization splitter and rotator. The electro-optic combiner also includes a second plurality of ring resonators positioned along the second optical waveguide and within an evanescent optical coupling distance of the second optical waveguide. The electro-optic combiner also includes a plurality of intermediate optical waveguides. Each of the plurality of intermediate optical waveguides is positioned between a corresponding one of the first plurality of ring resonators and a corresponding one of the second plurality of ring resonators, such that light optically couples from the first optical waveguide to the corresponding one of the first plurality of ring resonators, and from the corresponding one of the first plurality of ring resonators to said intermediate optical waveguide, and from said intermediate optical waveguide to the corresponding one of the second plurality of ring resonators, and from the corresponding one of the second plurality of ring resonators to the second optical waveguide. The electro-optic combiner also includes a plurality of photodetectors respectively optically connected to the plurality of intermediate optical waveguides, such that some of the light that optically couples into a given one of the plurality of intermediate optical waveguides from the corresponding one of the first plurality of ring resonators is conveyed into one of the plurality of photodetectors that is optically connected to the given one of the plurality of intermediate optical waveguides. 
     In an example embodiment, a method is disclosed for combination of optical signals. The method includes receiving incoming light through an optical input port. A first portion of the incoming light has a first polarization, and a second portion of the incoming light has a second polarization. The method also includes splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes directing the first portion of the incoming light through a first optical waveguide. The method also includes rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes directing the polarization-rotated second portion of the incoming light through a second optical waveguide. The method also includes operating a first plurality of ring resonators disposed between the first optical waveguide and the second optical waveguide. Each of the first plurality of ring resonators is operated to evanescently in-couple light from the first optical waveguide and evanescently out-couple light to a corresponding one of a plurality of intermediate optical waveguides. The method also includes operating a second plurality of ring resonators disposed between the first optical waveguide and the second optical waveguide. Each of the second plurality of ring resonators is operated to evanescently in-couple light from a corresponding one of the plurality of intermediate optical waveguides. Each of the second plurality of ring resonators is operated to evanescently out-couple light to the second optical waveguide. Each pair of ring resonators within the first and second pluralities of ring resonators that are optically coupled to a same one of the plurality of intermediate optical waveguides is operated at a substantially same resonant wavelength. Each pair of ring resonators within the first and second pluralities of ring resonators that are optically coupled to the same one of the plurality of intermediate optical waveguides has opposite light propagation directions. 
     Other aspects and advantages of the invention will become more apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating by way of example the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1 A  shows an example configuration of an electro-optic receiver, in accordance with some embodiments. 
         FIG.  1 B  shows an example configuration of an electro-optic receiver implemented within a PIC, in accordance with some embodiments. 
         FIG.  1 C  shows an example configuration of a PSR, in accordance with some embodiments. 
         FIG.  1 D  shows a vertical cross-section view through the example PSR, referenced as View A-A in  FIG.  1 C , in accordance with some embodiments. 
         FIG.  1 E  shows an example configuration of a PSR, in accordance with some embodiments. 
         FIG.  1 F  shows a vertical cross-section view through the example PSR, referenced as View A-A in  FIG.  1 E , in accordance with some embodiments. 
         FIG.  1 G  shows a vertical cross-section view through the example PSR, referenced as View B-B in  FIG.  1 E , in accordance with some embodiments. 
         FIG.  2 A  shows an example of a WDM optical receiver that includes multiple ring resonator photodetectors positioned along an optical waveguide that is configured to extend in a continuous, loop-like configuration, in accordance with some embodiments. 
         FIG.  2 B  shows a WDM optical receiver that is modified version of the WDM optical receiver of  FIG.  2 A , in accordance with some embodiments. 
         FIG.  2 C  shows a WDM optical receiver that is modified version of the WDM optical receiver of  FIG.  2 B , in accordance with some embodiments. 
         FIG.  3    shows an example configuration of an electro-optic receiver implemented within a PIC, in accordance with some embodiments. 
         FIG.  4    shows a diagram of an example linear photodetector, in accordance with some embodiments. 
         FIG.  5    shows a flowchart of a method for operating a photonic circuit, in accordance with some embodiments. 
         FIG.  6    shows an example configuration of an electro-optic receiver implemented within a PIC, in accordance with some embodiments. 
         FIG.  7    shows a flowchart of a method for operating a photonic circuit, in accordance with some embodiments. 
         FIG.  8    shows an example configuration of an electro-optic receiver implemented within a PIC, in accordance with some embodiments. 
         FIG.  9    shows a flowchart of a method for operating a photonic integrated circuit, in accordance with some embodiments. 
         FIG.  10 A  shows an example configuration of an optical input polarization management device implemented within a PIC, in accordance with some embodiments. 
         FIG.  10 B  shows the optical input polarization management device of  FIG.  10 A , with an example implementation of the polarization controller, in accordance with some embodiments. 
         FIG.  10 C  shows an example implementation of the optical input polarization management device in which the first phase shifter is implemented as a first plurality of ring resonator phase shifters and the second phase shifter is implemented as a second plurality of ring resonator phase shifters, in accordance with some embodiments. 
         FIG.  11    shows a flowchart of a method for optical input polarization management, in accordance with some embodiments. 
         FIG.  12    shows an example configuration of an electro-optic transmitter implemented within a PIC, in accordance with some embodiments. 
         FIG.  13    shows a flowchart of a method for operating an electro-optic transmitter, in accordance with some embodiments. 
         FIG.  14    shows an example configuration of an electro-optic transmitter implemented within a PIC, in accordance with some embodiments. 
         FIG.  15    shows a flowchart of a method for optical modulation, in accordance with some embodiments. 
         FIG.  16    shows an example configuration of an electro-optic transmitter implemented within a PIC, in accordance with some embodiments. 
         FIG.  17    shows a flowchart of a method for optical modulation, in accordance with some embodiments. 
         FIG.  18    shows an example configuration of an electro-optic combiner implemented within a PIC, in accordance with some embodiments. 
         FIG.  19    shows a flowchart of a method for combination of optical signals, in accordance with some embodiments. 
         FIG.  20    shows an example configuration of an electro-optic combiner implemented within a PIC, in accordance with some embodiments. 
         FIG.  21    shows a flowchart of a method for combination of optical signals, in accordance with some embodiments. 
         FIG.  22    shows an example configuration of an electro-optic combiner implemented within a PIC, in accordance with some embodiments. 
         FIG.  23    shows a flowchart of a method for combination of optical signals, in accordance with some embodiments. 
         FIG.  24 A  shows a diagram of an electro-optic receiver that is configured to tolerate polarization-dependent timing-skew, in accordance with some embodiments. 
         FIG.  24 B  shows a modification of the electro-optic receiver of  FIG.  24 A , in accordance with some embodiments. 
         FIG.  24 C  shows a modification of the electro-optic receiver of  FIG.  24 B , in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the following description, numerous specific details are set forth in order to provide an understanding of the disclosed embodiments. It will be apparent, however, to one skilled in the art that the present invention may be practiced without some or all of these specific details. In other instances, well known process operations have not been described in detail in order not to unnecessarily obscure the disclosed embodiments. 
     Optical data communication systems operate by modulating laser light to encode digital data patterns within the electrical domain as modulated light signals within the optical domain. The modulated light signals are transmitted through optical fibers to an electro-optic receiver where the modulated light signals are detected and decoded to obtain the original encoded digital data patterns back in the electrical domain. In many optical data communication systems, a polarization state of the light within the optical fiber is not controlled, and may be perturbed by small movements of the optical fiber and/or changes in ambient temperature while the system is operating. In these systems, the electro-optic receiver has to handle incoming light signals that have an arbitrary polarization that varies over time. 
     Electro-optic receiver systems are often built into photonic integrated circuits (PIC&#39;s), enabling compact and high-performance detection of modulated light signals received as input from optical fibers. Optical coupling of light from an optical fiber into a PIC requires an optical coupling configuration that can accept input light from either polarization (transverse electric (TE) or transverse magnetic (TM)) of an optical fiber and output it to one or more optical waveguides on the PIC, and often into a preferred polarization state. In some embodiments disclosed herein, an optical coupling configuration is provided in which incoming light is received through either a dual-polarization vertical grating coupler or an edge coupler and is conveyed into a PIC polarization splitter, which splits the incoming light from the two input optical fiber polarizations (TE and TM) and outputs the incoming light of a first polarization and a second polarization into two separate optical waveguides on the PIC, respectively. Also, in some embodiments, either the first polarization or the second polarization is rotated to the other polarization in route to the two separate optical waveguides on the PIC, such that light having the same polarization is conveyed into each of the two separate optical waveguides on the PIC. In some implementations, a significant advantage is gained by using optical devices that can efficiently detect optical signals that are split in this way based on polarization. Also, in some implementations, there are further advantages obtained by using one photodiode (such as in a photodetector) for both polarization mode components of the incoming light rather than duplicating the number of photodiodes to provide for separate detection of the two polarization mode components of the incoming light, where such further advantages include decreased complexity of the optical circuitry, reduced detector capacitance per channel, and reduced dark current, which results in increased photodiode/photodetector sensitivity. 
     Various embodiments are disclosed herein for an electro-optic receiver. The electro-optic receiver enables the detection of optical signals of arbitrary input polarization with a single photodetector or set of photodetectors. The electro-optic receiver includes an input optical fiber carrying incoming light (modulated light) with arbitrary (uncontrolled) polarization that conveys a signal that is decodable to a digital data pattern. The electro-optic receiver also includes an optical coupling device that transfers the incoming light from the input fiber to a PIC. The electro-optic receiver also includes a polarization beam splitter that receives an arbitrary input polarization state and splits it into two separate optical waveguides of the PIC, where each optical waveguide contains one of the orthogonal components of the input polarization state of the incoming light, possibly converted into a different polarization state. In some embodiments of the electro-optic receiver, the functionality of the polarization beam splitter is combined with the optical coupling device in the form of a dual-polarization grating coupler. In some embodiments of the electro-optic receiver, the two optical waveguides of the PIC support a single polarization mode that is well isolated in propagation constant from other spatial modes, including the other polarization state, making it operationally single-mode, single-polarization. The electro-optic receiver also includes an optical routing system in which the two optical waveguides of the PIC are routed to the same photodetector or set of photodetectors. The electro-optic receiver also includes a timing-skew management system that corrects for degradation in the signal arising from time delay mismatch between the two optical waveguides of the PIC and the photodetector or set of photodetectors. 
     The electro-optic receiver disclosed herein is particularly useful in applications where electro-optic receivers implemented within a PIC detect light from an input optical fiber in which the polarization is not controlled. The electro-optic receiver is especially advantageous in applications that encode multiple data channels on the input optical fiber on different wavelengths, for example using wavelength division multiplexing (WDM), and in cases where polarization-diversity WDM electro-optic receiver architectures have a timing-skew. This timing-skew may vary from one channel to the next, typically in a known way. Some existing electro-optic receivers that are capable of handling uncontrolled input polarization require two separate electro-optic receivers, one for each orthogonal polarization state, together with extensive digital signal processing to combine the signals. It should be appreciated that the electro-optic receiver embodiments disclosed herein provide a single, compact, and power-efficient electro-optic receiver to combine and detect signals from the two polarization states of any wavelength channel. 
     Some embodiments of the electro-optic receiver disclosed herein are particularly useful in situations in which the polarization states of the incoming light of the different wavelength channels are roughly the same from one wavelength channel to the next, and where the polarization states of the incoming light of the different wavelength channels are unknown. Some embodiments of the electro-optic receiver disclosed herein are particularly useful in situations in which the polarization state of the incoming light of a given wavelength channel is unknown, and where the polarization state of the incoming light of the given wavelength channel varies in a slow and controlled manner (such as monotonically) as compared to other wavelength channels of the incoming light. For example, these situations may occur when the WDM signal wavelength channels all originate at the same source, traverse the same optical fiber, and are received together, as is the case in a WDM point-to-point link. Some embodiments of the electro-optic receiver disclosed herein are useful in a more generalized situation in which each wavelength channel of the incoming light has a completely different unknown polarization, and where the polarization states of the different wavelength channels of the incoming light are uncorrelated. For example, these situations may occur when different WDM channels originate in different locations and may not share the same optical fiber(s) over the entire propagation path from the respective sources of the incoming light to the electro-optic receiver. The electro-optic receiver embodiments disclosed herein are configured to handle incoming light signals whose polarization state is unknown and is either static in time or dynamically changing in time. Various embodiments of the electro-optic receiver disclosed herein provide for reception of incoming light signals having unknown polarization states, even if the polarization states changes at high speeds, e.g., into the gigaHertz (GHz) regime, but more typically in the kiloHertz (kHz) (or millisecond) regime. 
       FIG.  1 A  shows an example configuration of an electro-optic receiver  100 , in accordance with some embodiments. The electro-optic receiver  100  includes a PIC  101  into which incoming light is received from an optical fiber  103 . The PIC includes an optical coupler  105  configured to receive the incoming light from the optical fiber  103  and direct the incoming light into an optical waveguide  107  within the PIC  101 . The incoming light conveys one or more optical signals. For example, the incoming light is modulated light that optically conveys a digital bit pattern. The incoming light also does not have polarization control. Therefore, the polarization of the incoming light received from the optical fiber  103  is unknown when it enters into the optical coupler  105 . In the example electro-optic receiver  100 , the optical coupler  105  is a vertical grating coupler. In some embodiments, the optical coupler  105  is configured as a dual-polarization grating coupler (either as an edge grating coupler or as a vertical grating coupler) that splits the two polarizations (TE and TM) of incoming light. The dual-polarization grating coupler is configured to direct a first portion of the incoming light having a first polarization (either TE or TM) into a first end  107 A of the optical waveguide  107 . The dual-polarization grating coupler is also configured to rotate a polarization of a second portion of the incoming light from a second polarization that is opposite of the first polarization (e.g., the second polarization is TM, if the first polarization is TE, and vice-versa) to the first polarization so as to provide a polarization-rotated second portion of the incoming light that has the first polarization. The dual-polarization grating coupler is also configured to direct the polarization-rotated second portion of the incoming light into a second end  107 B of the optical waveguide  107 . The optical waveguide  107  is configured to extend in a continuous, loop-like configuration from the first end  107 A to the second end  107 B. In this manner, the first portion of the incoming light having the first polarization travels in a first light propagation direction through the optical waveguide  107  from the first end  107 A toward the second end  107 B, and the polarization-rotated second portion of the incoming light (also having the first polarization) travels in a second light propagation direction through the optical waveguide  107  from the second end  107 B toward the first end  107 A. Therefore, the first portion of the incoming light and the polarization-rotated second portion of the incoming light travel in opposite light propagation directions through the optical waveguide  107 . In some embodiments, each of the first end  107 A and the second end  107 B of the optical waveguide  107  is configured as a respective tapered region of the optical waveguide  107  to facilitate optical coupling of light from the dual-polarization grating coupler into the optical waveguide  107 . 
     The electro-optic receiver  100  also includes multiple ring resonator photodetectors  109 - 1  to  109 - n , where n is an integer value greater than 1. The ring resonator photodetectors  109 - 1  to  109 - n  are positioned alongside the optical waveguide  107  and within an evanescent optical coupling distance of the optical waveguide  107 . Each of the ring resonator photodetectors  109 - 1  to  109 - n  is configured to operate at a respective resonant wavelength. In some embodiments, the respective resonant wavelength at which any one of the ring resonator photodetectors  109 - 1  to  109 - n  operates is a narrow wavelength range. For ease of description, any ring resonator disclosed herein is described as operating a respective resonant wavelength, with the understanding that the respective resonant wavelength is actually a narrow wavelength range that is distinguishable from other different resonant wavelength ranges. In this manner, each of the ring resonator photodetectors  109 - 1  to  109 - n  is configured to detect light at the respective resonant wavelength (within the narrow wavelength range about the respective resonant wavelength). In some embodiments, each of the ring resonator photodetectors  109 - 1  to  109 - n  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonator photodetectors  109 - 1  to  109 - n  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     Each of the ring resonator photodetectors  109 - 1  to  109 - n  is configured to operate at a respective resonant wavelength, such that the first portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of a given one of the ring resonator photodetectors  109 - x  optically couples into the given one of the ring resonator photodetectors  109 - x  in a first propagation direction, and such that the polarization-rotated second portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of the given one of the ring resonator photodetectors  109 - x  also optically couples into the given one of the ring resonator photodetectors  109 - x  in a second propagation direction opposite the first propagation direction. For example, a particular wavelength of the first portion of the incoming light traveling from the first end  107 A of the optical waveguide  107  toward the second end  107 B of the optical waveguide  107  will optically couple into one or more of the ring resonator photodetectors  109 - 1  to  109 - n  operating at a resonant wavelength substantially equal to the particular wavelength, such that the particular wavelength of the first portion of the incoming light propagates in a counter-clockwise direction within the one or more ring resonator photodetectors  109 - 1  to  109 - n  into which it optically couples. Conversely, a particular wavelength of the polarization-rotated second portion of the incoming light traveling from the second end  107 B of the optical waveguide  107  toward the first end  107 A of the optical waveguide  107  will optically couple into one or more of the ring resonator photodetectors  109 - 1  to  109 - n  operating at a resonant wavelength substantially equal to the particular wavelength, such that the particular wavelength of the polarization-rotated portion of the incoming light propagates in a clockwise direction within the one or more ring resonator photodetectors  109 - 1  to  109 - n  into which it optically couples. 
     Because the first portion of the incoming light and the corresponding polarization-rotated second portion of the incoming light may not arrive at a given one of the ring resonator photodetectors  109 - x  at the same time, the electro-optic receiver  100  also includes a timing-skew management system  111  that is configured to identify and compensate for the temporal differences in arrival time of the first portion of the incoming light and the corresponding polarization-rotated second portion of the incoming light at a given one of the ring resonator photodetectors  109 - x  in order to provide for recovery of the optical signal as conveyed within the incoming light. The difference in arrival time of the first portion of the incoming light and the corresponding polarization-rotated second portion of the incoming light at a given one of the ring resonator photodetectors  109 - x  can be caused by differences in optical path length through the optical waveguide  107  to the given one of the ring resonator photodetectors  109 - x  and/or by delay in outputting the polarization-rotated second portion of the incoming light relative to the first portion of the incoming light from the optical coupler  105  (from the dual-polarization grating coupler). 
       FIG.  1 B  shows an example configuration of an electro-optic receiver  150  implemented within a PIC  151 , in accordance with some embodiments. The electro-optic receiver  150  receives the incoming optical signal from an optical fiber/waveguide  152  through an optical coupler  153 , as indicated by arrow  154 . In some embodiments, the optical coupler  153  is implemented as an edge coupler. However, in other embodiments, the optical coupler  153  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the PIC  151  to the optical fiber/waveguide  152 . The incoming optical signal is conveyed from the optical coupler  153  through an optical waveguide  155  to an optical input of a polarization splitter and rotator (PSR)  156  of the electro-optic receiver  150 . In this manner, the PSR  156  has an optical input  156 A optically connected to receive incoming light. In some embodiments, the optical input  156 A of the PSR  156  is directly optically coupled to the optical coupler  153 , such that the optical waveguide  155  is not required. The PSR  156  has a first optical output  156 B and a second optical output  156 C. The PSR  156  is configured to direct a first portion of the incoming light having a first polarization through the first optical output  156 B. The PSR  156  is configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization. In this manner, the PSR  156  turns the second portion of the incoming light into a polarization-rotated second portion of the incoming light. The PSR  156  is configured to direct the polarization-rotated second portion of the incoming light through the second optical output  156 C. 
     The electro-optic receiver  150  includes an optical waveguide  157  formed within the PIC  151 . The optical waveguide  157  has a first end  157 A optically to the first optical output  156 B of the PSR  156 . The optical waveguide  157  also has a second end  157 B optically connected to the second optical output  156 C of the PSR  156 . In this manner, the first portion of the incoming light travels from the first optical output  156 A of the PSR  156  through the optical waveguide  157  in a first direction, as indicated by arrows  158 . Also, the polarization-rotated second portion of the incoming light travels from the second optical output  156 C of the PSR  156  through the optical waveguide  157  in a second direction, as indicated by arrows  159 , that is opposite the first direction. The optical waveguide  157  is formed of a material through which light can be in-coupled, out-coupled, and guided. The optical waveguide  157  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the optical waveguide  157  to enable guiding of light within the optical waveguide  157 . 
     The electro-optic receiver  150  also includes a plurality of ring resonator photodetectors  161 - 1  to  161 - 6  positioned alongside the optical waveguide  157  and within an evanescent optical coupling distance of the optical waveguide  157 . It should be understood that the number of the ring resonator photodetectors  161 - 1  to  161 - 6  is provided by way of example. In some embodiments, the electro-optic receiver  150  includes less than six ring resonator photodetectors. In some embodiments, the electro-optic receiver  150  includes more than six ring resonator photodetectors. It should be understood that there is no limit on the number of the ring resonator photodetectors (e.g.,  161 - 1  to  161 - 6 ) that can be positioned along the optical waveguide  157 , so long as the ring resonator photodetectors and associated signal processing circuitry can be spatially and electrically accommodated on the chip. In some embodiments, the ring resonator photodetectors  161 - 1  to  161 - 6  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonator photodetectors  161 - 1  to  161 - 6  are implemented as circular discs. The ring resonator photodetectors  161 - 1  to  161 - 6  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonator photodetectors  161 - 1  to  161 - 6  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonator photodetectors  161 - 1  to  161 - 6  to enable guiding of light within the ring resonator photodetectors  161 - 1  to  161 - 6  and around the circuitous path defined by each of the ring resonator photodetectors  161 - 1  to  161 - 6 . In some embodiments, each of the ring resonator photodetectors  161 - 1  to  161 - 6  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonator photodetectors  161 - 1  to  161 - 6  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     Each of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  is configured to operate at a respective resonant wavelength λ 1  to λ 6 , respectively, such that the first portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of a given one of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  optically couples into the given one of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  in a first propagation direction, and such that the polarization-rotated second portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of the given one of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  optically couples into the given one of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  in a second propagation direction opposite the first propagation direction. For example, if the incoming light has a wavelength substantially equal to the wavelength λ 2 , then the first portion of the incoming light having the wavelength λ 2  will optically couple into the ring resonator  161 - 2  and propagate in a counter-clockwise direction within the ring resonator  161 - 2 , and the polarization-rotated second portion of the incoming light having the wavelength λ 2  will also optically couple into the ring resonator  161 - 2  and propagate in a clockwise direction within the ring resonator  161 - 2 . It should be understood that both the first portion of the incoming light and the polarization-rotated second portion of the incoming light have the same polarization state within the optical waveguide  157 . Therefore, any given one of the ring resonator photodetectors  161 - 1  to  161 - 6  operating at a particular resonant wavelength is able to optically in-couple and detect both the first portion of the incoming light and the polarization-rotated second portion of the incoming light having the particular resonant wavelength. 
     In some embodiments, such as shown in the example electro-optic receiver  150 , the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  includes a first set of ring resonator photodetectors  161 - 1  to  161 - 3  positioned between the first end  157 A of the optical waveguide  157  and a midpoint  157 C of the optical waveguide  157  located halfway between the first end  157 A and the second end  157 B of the optical waveguide  157 . Also, in these embodiments, the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  includes a second set of ring resonator photodetectors  161 - 4  to  161 - 6  positioned between the second end  157 B of the optical waveguide  157  and the midpoint  157 C of the optical waveguide  157 . It should be understood that in some embodiments, the number of ring resonator photodetectors in the first set of ring resonator photodetectors is either less than or more than the three ring resonator photodetectors  161 - 1  to  161 - 3 . Also, in some embodiments, the number of ring resonator photodetectors in the second set of ring resonator photodetectors is either less than or more than the three ring resonator photodetectors  161 - 4  to  161 - 6 . 
     In some embodiments, the electro-optic receiver  150  also includes a variable optical attenuator (VOA)  163  that is configured to attenuate the light propagated through the optical waveguide  157  in a controlled manner in accordance with an electrical control signal. In some embodiments, the VOA  163  is positioned to optically couple to the optical waveguide  157  near either the first end  157 A or the second end  157 B of the optical waveguide  157 . In the example electro-optic receiver  150 , the VOA  163  is optically coupled to the optical waveguide  157  near the first end  157 A of the optical waveguide  157 . The VOA  163  operates to limit the optical reflection/transmission of light from the optical waveguide  157  back into the optical fiber/waveguide  152  when the electro-optic receiver  150  is initially turned on, and before the ring resonator photodetectors  161 - 1  to  161 - 6  have been tuned to their respective resonant wavelengths λ 1  to λ 6  to in-couple light of the various wavelength channels present in the incoming optical signal. During startup of the electro-optic receiver  150 , incoming light that does not couple into any of the ring resonator photodetectors  161 - 1  to  161 - 6  will pass through the optical waveguide  157  and back out through the optical fiber/waveguide  152 , which could possibly damage the source from which the incoming light was transmitted. For example, if the source of the incoming light is a laser source, reverse transmission of the incoming laser light back into the laser source could damage the laser source or degrade its performance. To prevent this from happening, during startup of the electro-optic receiver  150 , the VOA  163  operates to attenuate the light propagating within the optical waveguide  157  to a level where light returning to the optical fiber/waveguide  152  will not damage and/or disrupt operation of the source from which the incoming light was transmitted, e.g., the laser source, while also keeping the optical power within the optical waveguide  157  just high enough to allow the ring resonator photodetectors  161 - 1  to  161 - 6  to be tuned and locked to their respective resonant wavelengths λ 1  to λ 6  corresponding to the various wavelength channels present in the incoming optical signal. Then, after the ring resonator photodetectors  161 - 1  to  161 - 6  are tuned and locked to their respective resonant wavelengths λ 1  to λ 6  corresponding to the various wavelength channels present in the incoming optical signal, operation of the VOA  163  is adjusted to reduce or stop attenuation of the light propagating within the optical waveguide  157 . 
     In some embodiments, the VOA  163  is implemented as an optical waveguide (or portion of the optical waveguide  157 ) having a built-in PN or PIN diode that when forward-biased creates an electrical current within the optical waveguide of the VOA  163  that increases optical absorption within the optical waveguide of the VOA  163  through free-carrier absorption. In these embodiments, the optical absorption within the optical waveguide of the VOA  163  is increased by increasing the forward-bias voltage (and thus by increasing the electrical current) within the optical waveguide of the VOA  163 . Also, in these embodiments, the optical absorption within the optical waveguide of the VOA  163  is reduced by reducing the forward bias-voltage (and thus by reducing the electrical current) within the optical waveguide of the VOA  163 . Also, in these embodiments, the optical absorption within the optical waveguide of the VOA  163  is stopped by reverse-biasing of the PN or PIN diode within the optical waveguide of the VOA  163 . In some embodiments, the PN or PIN diode of the VOA  163  is actually formed within the optical waveguide  157 . In some embodiments, the VOA  163  includes its own optical waveguide separate from the optical waveguide  157 , where the optical waveguide of the VOA  163  is evanescently optically coupled to a section of the optical waveguide  157 , with the PN or PIN diode built into the optical waveguide of the VOA  163 . 
     In some embodiments, the electro-optic receiver  150  also includes a timing-skew management system  165  configured to electronically compensate for a temporal difference in photocurrent generation by any given one of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  caused by a difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at said any given one of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6 . After the timing-skew management system  165  operates to electronically compensate for the temporal difference in photocurrent generation by each of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6 , the photocurrents generated by each of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  are transmitted to photocurrent processing circuitry  167  to decode the photocurrents into digital data patterns as conveyed by the incoming optical signal. In some embodiments where light from different polarizations is made to have a same polarization and is combined into a single waveguide, or where light from different polarizations is made to have a same polarization and is combined into a single photodetector or set of photodetectors, there may be a time delay difference (timing-skew) between the optical signals from each polarization state. After converting the combined optical signal into an electronic signal with a photodetector or set of photodetectors, the timing-skew manifests itself as a notch filter around an electrical radiofrequency component of the baseband signal. The center frequency of the notch filter is dependent on the magnitude of the timing-skew, and the depth of the notch filter is determined by the relative split in optical power between the two polarization states. For a digital communications application, this notch filter results in increased inter-symbol interference (ISI). The timing-skew management system  165  is configured to detect the presence of the timing-skew, determine the magnitude of the timing-skew, and compensate for the timing-skew in the photocurrent-based signals that are transmitted to the photocurrent processing circuitry  167 . 
     In some embodiments, the temporal difference (timing-skew) in photocurrent generation by a given one of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  caused by a difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the given one of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  is reduced by reducing a difference in optical travel distance to the given one of the plurality of ring resonator photodetectors  161 - 1  to  161 - 6  that is traveled by the first portion of the incoming light and the polarization-rotated second portion of the incoming light.  FIGS.  2 A,  2 B, and  2 C  illustrate examples of how to reduce the difference in optical travel distance through a same optical waveguide to a given one of a plurality of photodetectors that is traveled by the first portion of the incoming light and the polarization-rotated second portion of the incoming light, where the first portion of the incoming light and the polarization-rotated second portion of the incoming light travel in opposite directions through the same optical waveguide, such as in the electro-optic receiver  150  of  FIG.  1 B . 
     In various embodiments, the PSR  156 , and any of the PSR&#39;s referred to herein, is configured in a manner that provides for: 1) reception of two polarizations of incoming light (TE and TM), 2) rotation of one of the polarizations of the incoming light to the other polarization (either rotation of TE to TM, or rotation of TM to TE), 3) outputting of the portion of the incoming light having the polarization that was not rotated to a first output optical waveguide, and 4) outputting of the portion of the incoming light having the polarization that was rotated to a second output optical waveguide. In it should be understood that in various embodiments, the polarization rotation and original-polarization-based splitting of the incoming light performed by the PSR  156 , and any of the PSR&#39;s referred to herein, can be done simultaneously or sequentially within the PSR (e.g., with the polarization rotation happening either before, after, or in conjunction with the original-polarization-based splitting of the incoming light). 
       FIG.  1 C  shows an example configuration of a PSR  171 , in accordance with some embodiments. It should be understood that the example PSR  171  can be used for the PSR  156  and/or any of the PSR&#39;s referred to herein. Also, it should be understood that the PSR  171  is provided by way of example and in no way limits how the PSR  156  and/or any of PSR&#39;s referred to herein can be configured in various embodiments. The PSR  171  includes a first optical waveguide  172  and a second optical waveguide  173 .  FIG.  1 D  shows a vertical cross-section view through the example PSR  171 , referenced as View A-A in  FIG.  1 C , in accordance with some embodiments. In some embodiments, the first optical waveguide  172  is a silicon nitride optical waveguide, and the second optical waveguide  173  is a silicon optical waveguide. In some embodiments, the PSR  171  is formed on a buried oxide (BOX) layer  175  that is disposed over a substrate  174 . In some embodiments, the first optical waveguide  173  and the second optical waveguide  172  are formed within an optical cladding  176 . In some embodiments, the optical cladding  176  is silicon dioxide. The first optical waveguide  172  is vertical separated from the second optical waveguide  173  by a layer of the optical cladding, as indicated by arrow  177 . 
     The first optical waveguide  172  includes an input section  172 A connected to receive incoming light that includes both the TE and TM polarizations. In some embodiments, the input section  172 A is configured as an inverse taper to convert a spot size of the incoming light to the optical mode of the first optical waveguide  172 . After the input section  172 A (with respect to the light propagation direction) the first optical waveguide  172  includes a rotation/splitting section  172 B. In some embodiments, the rotation/splitting section  172 B has a substantially linear shape. After the rotation/splitting section  172 B, the first optical waveguide  172  includes an output section  172 C that is optically connected to a first optical output  172 D of the PSR  171 . The first optical waveguide  172  is configured such that a portion of the incoming light having a first polarization (TE or TM) travels through the first optical waveguide  172  to the first optical output  172 D of the PSR  171  in a substantially unchanged manner. The example PSR  171  shows the TE polarization of the incoming light traveling through the first optical waveguide  172  to the first optical output  172 D of the PSR  171  in a substantially unchanged manner. 
     The second optical waveguide  173  includes a rotation/splitting section  173 A that is configured to evanescently in-couple the TM polarization of the incoming light from the rotation/splitting section  172 B of the first optical waveguide  172  and simultaneously rotate the in-coupled TM polarization to the TE polarization. To accomplish this, the rotation/splitting section  173 A of the second optical waveguide  173  has an inverse taper configuration that positioned off-center (having a lateral offset in a direction perpendicular to the light propagation direction) with respect to the rotation/splitting section  172 B of the first optical waveguide  172 . The lateral offset of the rotation/splitting section  173 A of the second optical waveguide  173  with respect to the rotation/splitting section  172 B of the first optical waveguide  172  serves to break horizontal and vertical symmetry so as to rotate the TM0 mode in the rotation/splitting section  172 B of the first optical waveguide  172  to a rotated TE0 mode and couple this rotated TE0 mode into the rotation/splitting section  173 A of the second optical waveguide  173 . The rotated TE0 mode is conveyed through an output section  173 B of the second optical waveguide  173  to a second optical output  173 C of the PSR  171 . While the example PSR  171  shows the TE polarization of the incoming light traveling through the first optical waveguide  172  to the first optical output  172 D of the PSR  171  in a substantially unchanged manner, and shows the TM polarization of the incoming light being rotated to the TE polarization in route to the second optical output  173 C of the PSR  171 , other embodiments of the PSR  171  are configured to have the TM polarization of the incoming light travel through the first optical waveguide  172  to the first optical output  172 D of the PSR  171  in a substantially unchanged manner, with the TE polarization of the incoming light rotated to the TM polarization in route to the second optical output  173 C of the PSR  171 . 
       FIG.  1 E  shows an example configuration of a PSR  181 , in accordance with some embodiments. It should be understood that the example PSR  181  can be used for the PSR  156  and/or any of the PSR&#39;s referred to herein. Also, it should be understood that the PSR  181  is provided by way of example and in no way limits how the PSR  156  and/or any of PSR&#39;s referred to herein can be configured in various embodiments. The PSR  181  is a broadband PSR that implements rib-type optical waveguides. The PSR  181  includes a first branch  183  and a second branch  185 . The PSR  181  is configured as an optical waveguide system that includes a first branch slab waveguide  187 , a first branch rib waveguide  189 , a second branch slab waveguide  188 , and a second branch rib waveguide  190 .  FIG.  1 F  shows a vertical cross-section view through the example PSR  181 , referenced as View A-A in  FIG.  1 E , in accordance with some embodiments.  FIG.  1 G  shows a vertical cross-section view through the example PSR  181 , referenced as View B-B in  FIG.  1 E , in accordance with some embodiments. In some embodiments, the first branch slab waveguide  187 , the second branch slab waveguide  188 , the first branch rib waveguide  189 , and the second branch rib waveguide  190  are integrally formed as a monolithic optical waveguide structure, in which the first branch slab waveguide  187 , the second branch slab waveguide  188 , the first branch rib waveguide  189 , and the second branch rib waveguide  190  form different parts of the monolithic optical waveguide structure. In some embodiments, the monolithic optical waveguide structure is formed as a silicon optical waveguide. In some embodiments, the monolithic optical waveguide structure is formed as a silicon nitride optical waveguide. In some embodiments, the PSR  181  is formed on a BOX layer  191  that is disposed over a substrate  192 . In some embodiments, the monolithic optical waveguide structure that includes the first slab waveguide  187 , the second branch slab waveguide  188 , the first branch rib waveguide  189 , and the second branch rib waveguide  190  is formed within an optical cladding  193 . In some embodiments, the optical cladding  193  is silicon dioxide. 
     The first branch rib waveguide  189  includes an input section  189 A that has a substantially linear shape, followed by a tapered section  189 B, followed by an output section  189 C (with respect to a light propagation direction through the PSR  181 ). The first branch slab waveguide  187  includes tapered input section  187 A, followed by a tapered section  187 B (corresponding to the rib tapered section  189 B), followed by an output section  187 C (corresponding to the rib output section  189 C). The second branch rib waveguide  190  includes a tapered section  190 A, followed by an output section  190 B (with respect to a light propagation direction through the PSR  181 ). The second branch slab waveguide  188  includes tapered section  188 A (corresponding to the rib tapered section  190 A, followed by an output section  188 B (corresponding to the rib output section  190 B). In some embodiments, a portion of the output section  188 B of the second branch slab waveguide  188  located between the first branch rib waveguide  189  and the second branch rib waveguide  190  has an increasing width along the light propagation direction to provide for easier optical routing of the outputs of the first branch  183  and the second branch  185  to separate output optical waveguides. 
     The input section  189 A and the tapered section  189 B of the first branch rib waveguide  189 , and the tapered input section  187 A and the tapered section  187 B of the first branch slab waveguide  187 , collectively function as a polarization rotator. The output section  189 C of the first branch rib waveguide  189  and the output section  187 C of the first branch slab waveguide  187 , and the tapered section  190 A of the second branch rib waveguide  190  and the tapered section  188 A of the second branch slab waveguide  188 , collectively function as a polarization splitter. In this manner, the TE0 polarization of the incoming light is transmitted in a substantially unchanged manner through the first branch  183  to a first optical output  195  of the PSR  181 . The TM0 polarization of the incoming light is rotated to a TE1 polarization and then to a TE0 polarization as this portion of the incoming light is transmitted through the first branch  183  and is optically coupled into the second branch  185  in route to a second optical output  197  of the PSR  181 . Alternatively, in some other embodiments, the PSR  181  is configured to pass through the TM polarization of the incoming light in a substantially unchanged manner and rotate/split the TE polarization of the incoming light to outgoing TM polarized light. 
     It should be understood that the PSR  171  and the PSR  181  are provided as examples of how the PSR&#39;s described herein may be implemented in some example embodiments. It should also be understood that in some embodiments, any of the PSR&#39;s described herein can be implemented as a dual-polarization grating coupler, such as described with regard to  FIG.  1 A . It should be understood that the example PSR  171  and the example PSR  181  do not limit in any way how the various PSR&#39;s described herein can be implemented in various embodiments. Any of the PSR&#39;s described herein can be implemented in different ways so long as one of the two input polarizations (TE or TM) of incoming light received by the PSR is rotated to the other polarization and is directed to one of two outputs of the PSR, with the non-rotated polarization of the incoming light being directed to another of the two outputs of the PSR. 
       FIG.  2 A  shows an example of a WDM optical receiver  201  that includes multiple ring resonator photodetectors  203 - 1  to  203 - 6  (one for each wavelength channel) positioned along an optical waveguide  205  that is configured to extend in a continuous, loop-like configuration from a first end  205 A to a second end  205 B, in accordance with some embodiments. Each of the multiple ring resonator photodetectors  203 - 1  to  203 - 6  is electrically connected to transmit detected photocurrent to a corresponding one of multiple receiver circuits  207 - 1  to  207 - 6 . Each of the multiple ring resonator photodetectors  203 - 1  to  203 - 6  is positioned to evanescently in-couple light from the optical waveguide  205  that has a substantially same wavelength as the operating resonant wavelength of the particular ring resonator photodetector. In some embodiments, each of the ring resonator photodetectors  203 - 1  to  203 - 6  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonator photodetectors  203 - 1  to  203 - 6  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. The optical waveguide  205  has a center location  205 C that is about halfway between the first end  205 A and the second end  205 B of the optical waveguide  205 . In the example of  FIG.  2 A , all of the multiple ring resonator photodetectors  203 - 1  to  203 - 6  are positioned along a same half of the optical waveguide  205 , which causes an increased optical path length mismatch between the different ring resonator photodetectors  203 - 1  to  203 - 6 . Therefore, in the example of  FIG.  2 A , there is a large temporal difference (timing-skew) in photocurrent generation by a given one of the multiple ring resonator photodetectors  203 - 1  to  203 - 6  that is caused by a difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the given one of the multiple ring resonator photodetectors  203 - 1  to  203 - 6 . 
       FIG.  2 B  shows a WDM optical receiver  201 A that is modified version of the WDM optical receiver  201  of  FIG.  2 A , in accordance with some embodiments. In the WDM optical receiver  201 A, a first half of the multiple ring resonator photodetectors  203 - 1  to  203 - 3  are positioned along a first half of the optical waveguide  205  extending from the first end  205 A to the center location  205 C of the optical waveguide. The first half of the ring resonator photodetectors  203 - 1  to  203 - 3  are also positioned close to the center location  205 C of the optical waveguide  205 . Similarly, in the WDM optical receiver  201 A, a second half of the multiple ring resonator photodetectors  203 - 4  to  203 - 6  are positioned along a second half of the optical waveguide  205  extending from the second end  205 B to the center location  205 C of the optical waveguide  205 . The second half of the ring resonator photodetectors  203 - 1  to  203 - 3  are also positioned close to the center location  205 C of the optical waveguide  205 . In the optical receiver  201 A, the ring resonator photodetectors  203 - 1  to  203 - 6  are distributed evenly about the center location  205 C of the optical waveguide  205  and as close as possible to the center location  205 C of the optical waveguide  205 . It should be understood that centering the multiple ring resonator photodetectors  203 - 1  to  203 - 6  on the center location  205 C of the optical waveguide  205  minimizes a difference in optical travel distance to a given one of the multiple ring resonator photodetectors  203 - 1  to  203 - 6  that is traveled by the first portion of the incoming light and the polarization-rotated second portion of the incoming light, which in turn minimizes the timing-skew between the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the given one of the multiple ring resonator photodetectors  203 - 1  to  203 - 6 . The optical receiver  201 A minimizes the residual path length difference between each polarization of each of the wavelength channel signals in the incoming optical signal. 
       FIG.  2 C  shows a WDM optical receiver  201 B that is modified version of the WDM optical receiver  201 A of  FIG.  2 B , in accordance with some embodiments. In the WDM optical receiver  201 B, the optical waveguide  205  is replaced by an optical waveguide  209  that has a first end  209 A, a second end  209 B, and a center location  209 C. The optical waveguide  209  also includes an extra waveguide section  209 D that is configured so that the center location  209 C of the optical waveguide  209  is positioned along a linear stretch of the optical waveguide  209  that is long enough to accommodate a linear positioning of the multiple ring resonator photodetectors  203 - 1  to  203 - 6  along the linear stretch of the optical waveguide  209 , with the multiple ring resonator photodetectors  203 - 1  to  203 - 6  centered on the center location  205 C of the optical waveguide  205 . Having the multiple ring resonator photodetectors  203 - 1  to  203 - 6  centered on the center location  209 C of the optical waveguide  205  provides for minimization of the difference in optical travel distance to a given one of the multiple ring resonator photodetectors  203 - 1  to  203 - 6  that is traveled by the first portion of the incoming light and the polarization-rotated second portion of the incoming light, which in turn minimizes the timing-skew between the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the given one of the multiple ring resonator photodetectors  203 - 1  to  203 - 6 . It should be appreciated that having the multiple ring resonator photodetectors  203 - 1  to  203 - 6  positioned in the linear arrangement within the WDM optical receiver  201 B provides for placement of the receiver circuits  207 - 1  to  207 - 6  next to each other on the chip, which opens up other areas of the chip for implementation of other photonic and/or electronic circuitry. The optical receiver  201 B also minimizes the residual path length difference between each of the signals of each polarization. 
       FIG.  3    shows an example configuration of an electro-optic receiver  300  implemented within a PIC  302 , in accordance with some embodiments. Like the electro-optic receiver  150  of  FIG.  1 B , the electro-optic receiver  300  receives the incoming optical signal from the optical fiber/waveguide  152  through the optical coupler  153 , as indicated by arrow  154 . The incoming optical signal is conveyed from the optical coupler  153  through the optical waveguide  155  to the optical input of the PSR  156 . As with the electro-optic receiver  150  of  FIG.  1 B , the PSR  156  is configured to direct a first portion of the incoming light having a first polarization through the first optical output  156 B of the PSR  156 . The PSR  156  is also configured to rotate a polarization of a second portion of the incoming light from a second polarization to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The PSR  156  is configured to direct the polarization-rotated second portion of the incoming light through the second optical output  156 C of the PSR  156 . The first end  157 A of the optical waveguide  157  is optically connected to the first optical output  156 B of the PSR  156 . The second end  157 B of the optical waveguide  157  is optically connected to the second optical output  156 C of the PSR  156 . The optical waveguide  157  of the electro-optic receiver  300  is like that of the electro-optic receiver  150  of  FIG.  1 B . The optical waveguide  157  has the continuous, loop-like structure. In this manner, the first portion of the incoming light travels from the first optical output  156 A of the PSR  156  through the optical waveguide  157  in a first direction, as indicated by arrows  158 . Also, the polarization-rotated second portion of the incoming light travels from the second optical output  156 C of the PSR  156  through the optical waveguide  157  in a second direction, as indicated by arrows  159 , that is opposite the first direction. 
     The electro-optic receiver  300  includes a plurality of ring resonators  301 - 1  to  301 - 3  positioned alongside the optical waveguide  157  and within an evanescent optical coupling distance of the optical waveguide  157 . The example configuration of the electro-optic receiver  300  includes three ring resonators  301 - 1  to  301 - 3  for description purposes. It should be understood that in various embodiments, the electro-optic receiver  300  includes either less than three or more than three ring resonators positioned alongside the optical waveguide  157  and within an evanescent optical coupling distance of the optical waveguide  157 . There is no limit on the number of ring resonators that (e.g.,  301 - 1  to  301 - 3 ) that can be positioned along the optical waveguide  157 , so long as the ring resonators and associated signal processing circuitry can be spatially and electrically accommodated on the chip. In some embodiments, the ring resonators  301 - 1  to  301 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonators  301 - 1  to  301 - 3  are implemented as circular discs. The ring resonators  301 - 1  to  301 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonators  301 - 1  to  301 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonators  301 - 1  to  301 - 3  to enable guiding of light within the ring resonators  301 - 1  to  301 - 3  and around the circuitous path defined by each of the ring resonators  301 - 1  to  301 - 3 . In some embodiments, each of the ring resonators  301 - 1  to  301 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonators  301 - 1  to  301 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     Each of the plurality of ring resonators  301 - 1  to  301 - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 . In this manner, the first portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of a given one of the plurality of ring resonators  301 - 1  to  301 - 3  optically couples into the given one of the plurality of ring resonators  301 - 1  to  301 - 3  in a first propagation direction, and the polarization-rotated second portion of the incoming light having a wavelength substantially equal to the respective resonant wavelength of the given one of the plurality of ring resonators  301 - 1  to  301 - 3  optically couples into the given one of the plurality of ring resonators  301 - 1  to  301 - 3  in a second propagation direction opposite the first propagation direction. For example, the first portion of the incoming light having a particular wavelength optically couples into the ring resonator  301 - x  operating at the particular wavelength and propagates in a counter-clockwise direction within the ring resonator  301 - x . The polarization-rotated second portion of the incoming light having a particular wavelength optically couples into the ring resonator  301 - x  operating at the particular wavelength and propagates in a clockwise direction within the ring resonator  301 - x.    
     The electro-optic receiver  300  includes a plurality of output optical waveguides  303 - 1  to  303 - 3  positioned within an evanescent optical coupling distance of the plurality of ring resonators  301 - 1  to  301 - 3 , respectively. Each of the plurality of output optical waveguides  303 - 1  to  303 - 3  includes a coupling section  303 A- 1  to  303 A- 3 , respectively. Each of the plurality of output optical waveguides  303 - 1  to  303 - 3  includes a short section  303 B- 1  to  303 B- 3 , respectively. Each of the plurality of output optical waveguides  303 - 1  to  303 - 3  includes a long section  303 C- 1  to  303 C- 3 , respectively. The number of output optical waveguides  303 - 1  to  303 - 3  is equal to the number of ring resonators  301 - 1  to  301 - 3 . Therefore, as the number of ring resonators changes in various embodiments, so does the number of output optical waveguides. The coupling section  303 A- 1  to  303 A- 3  is positioned to evanescently in-couple light from a corresponding one of the plurality of ring resonators  301 - 1  to  301 - 3 . In this manner, each of the ring resonators  301 - 1  to  301 - 3  operates to transfer a particular wavelength of the first portion of the incoming light and the polarization-rotated second portion of the incoming light from the optical waveguide  157  to the corresponding one of the output optical waveguides  303 - 1  to  303 - 3 . The first portion of the incoming light that propagates in the counter-clockwise direction within the ring resonators  301 - 1  to  301 - 3  is optically coupled through the coupling section  303 A- 1  to  303 A- 3 , respectively, and into the long section  303 C- 1  to  303 C- 3 , respectively, as indicated by arrows  307 - 1  to  307 - 3 , respectively. The polarization-rotated second portion of the incoming light that propagates in the clockwise direction within the ring resonators  301 - 1  to  301 - 3  is optically coupled through the coupling section  303 A- 1  to  303 A- 3 , respectively, and into the short section  303 B- 1  to  303 B- 3 , respectively, as indicated by arrows  309 - 1  to  309 - 3 , respectively. 
     The output optical waveguides  303 - 1  to  303 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the output optical waveguides  303 - 1  to  303 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the output optical waveguides  303 - 1  to  303 - 3 , respectively, to enable guiding of light within the output optical waveguides  303 - 1  to  303 - 3 . In some embodiments, the output optical waveguides  303 - 1  to  303 - 3  are implemented to have a rack-track type shape. However, it should be understood that in other embodiments, the output optical waveguides  303 - 1  to  303 - 3  can be implemented to have an arbitrary shape, so long as they include the coupling section  303 A- 1  to  303 A- 3 , respectively, and the short section  303 B- 1  to  303 B- 3 , respectively, and the long section  303 C- 1  to  303 C- 3 , respectively. 
     The electro-optic receiver  300  includes a plurality of photodetectors  305 - 1  to  305 - 3  respectively associated with the plurality of ring resonators  301 - 1  to  301 - 3 . Therefore, as the number of ring resonators changes in various embodiments, so does the number of photodetectors. The short section  303 B- 1  to  303 B- 3  of the output optical waveguides  303 - 1  to  303 - 3  extends from a first end of the corresponding coupling section  303 A- 1  to  303 A- 3  to the corresponding one of the plurality of photodetectors  305 - 1  to  305 - 3 . The long section  303 C- 1  to  303 C- 3  of the output optical waveguides  303 - 1  to  303 - 3  extends from a second end of the corresponding coupling section  303 A- 1  to  303 A- 3  to the corresponding one of the plurality of photodetectors  305 - 1  to  305 - 3 . A length of the long section  303 C- 1  to  303 C- 3  and a length of the short section  303 B- 1  to  303 B- 3  within a given one of the output optical waveguides  303 - 1  to  303 - 3  are defined to reduce a difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the corresponding one of the photodetectors  305 - 1  to  305 - 3  to which the long section  303 C- 1  to  303 C- 3  and the short section  303 B- 1  to  303 B- 3  are optically connected. Because the distance along the optical waveguide  157  from the second end  157 B of the optical waveguide  157  to each of the ring resonators  301 - 1  to  301 - 3  is different, the length of the long section  303 C- 1  to  303 C- 3  is different for each of the output optical waveguides  303 - 1  to  303 - 3 . In some embodiments, the length of the long section  303 C- 1  to  303 C- 3  decreases as a distance between the corresponding one of the plurality of ring resonators  301 - 1  to  301 - 3  and the midpoint of the optical waveguide  157  decreases, where the midpoint of the optical waveguide  157  is about halfway between the first end  157 A and the second end  157 B of the optical waveguide  157 . 
     The electro-optic receiver  300  also includes the timing-skew management system  165  configured to electronically compensate for a temporal difference in photocurrent generation by a given one of the plurality of photodetectors  305 - 1  to  305 - 3  caused by the difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the given one of the plurality of photodetectors  305 - 1  to  305 - 3 . In some embodiments, each of the photodetectors  305 - 1  to  305 - 3  is a linear photodetector, with the short section  303 B- 1  to  303 B- 3  of the corresponding one of the output optical waveguides  303 - 1  to  303 - 3  optically connected to a first end of the linear photodetector, and with the long section  303 C- 1  to  303 C- 3  of the corresponding one of the output optical waveguides  303 - 1  to  303 - 3  optically connected to a second end of the linear photodetector. 
       FIG.  4    shows a diagram of an example linear photodetector  400 , in accordance with some embodiments. In some embodiments, a separate instance of the linear photodetector  400  is used for each of the photodetectors  305 - 1  to  305 - 3  in the electro-optic receiver  300 . The linear photodetector  400  is shown as a PIN type of photodetector that includes a P doped region  401 , an intrinsic region  403 , and an N doped region  405 . The intrinsic region  403  is positioned between the P doped region  401  and the N doped region  405 . In some embodiments, the P doped region  401  and the N doped region  405  are switched. In some embodiments, the intrinsic region  403  is an optical waveguide through which light that is to be detected is directed. In some embodiments, at least a portion of the P doped region  401  and at least a portion of the N doped region  405  is formed within the optical waveguide. During operation the photodetector  400  is reverse-biased so that charge carriers generated by photo-absorption within the intrinsic region  403  are swept into electrical contacts  407  connected along the length of the photodetector  400 . 
     The linear photodetector  400  enables the incoming light from each polarization to be detected independently. More specifically, the first portion of the incoming light having the first polarization is input through a first end of the photodetector  400 , and the polarization-rotated second portion of the incoming light having the first polarization (but corresponding to the incoming light that had the second polarization) is input through a second end of the photodetector  400 . Due to photo-absorption along the length of the linear photodetector  400 , the intensity of the first portion of the incoming light having the first polarization as input through the first end of the photodetector  400  decays exponentially in accordance with the photo-absorption coefficient as the light travels along the length of the photodetector  400  in the first direction, as indicated by arrow  409 . Similarly, the intensity of the polarization-rotated second portion of the incoming light having the first polarization as input through the second end of the photodetector  400  decays exponentially in accordance with the photo-absorption coefficient as the light travels along the length of the photodetector  400  in the second direction, as indicated by arrow  411 . Therefore, a majority of the first portion of the incoming light having the first polarization is absorbed within a first half  413  of the linear photodetector  400 , and a majority of polarization-rotated second portion of the incoming light having the first polarization is absorbed within a second half  415  of the linear photodetector  400 . In some embodiments, the electrical contacts  407  along the first half  413  of the photodetector  400  are segmented and connected to a first reverse-biasing circuit and a first receive circuit, and the electrical contacts  407  along the second half  415  of the photodetector  400  are segmented and connected to a second reverse-biasing circuit and a second receive circuit. In these embodiments, comparison of the photocurrent measured by the first receive circuit to the photocurrent measured by the second receive circuit provides for determination of the relative optical power split between different polarizations within the incoming optical signal, given that the polarization-rotated second portion of the incoming signal actually corresponds to the second polarization within the incoming optical signal. 
     The electro-optic receiver  300  of  FIG.  3    represents an embodiment in which the input optical fiber/waveguide  152  transmits an input optical signal with no polarization control into the PIC  302 . The optical coupler  153  couples the incoming light of the input optical signal onto the waveguide  155  on the chip. In some embodiments, the PSR  156  splits the input optical signal polarizations and transmits the two polarizations into two separate waveguides within the PSR  156 . One of these two waveguides within the PSR  156  passes through a polarization rotator, so that its polarization is rotated into the same state as the other waveguide within the PSR  156 . The two waveguides within the PSR  156  are optically connected to the first end  157 A and the second end  157 B, respectively, of the optical waveguide  157  (loop) which is evanescently coupled to the ring resonators  301 - 1  to  301 - 3 . In some embodiments, the ring resonators  301 - 1  to  301 - 3  are respectively replaced by passive ring filters. Each of the ring resonators  301 - 1  to  301 - 3  (or passive ring filters) is designed to route the light from a single wavelength channel, within a narrow wavelength range, to the corresponding output optical waveguide  303 - 1  to  303 - 3  that is optically connected to the corresponding photodetector  305 - 1  to  305 - 3  (e.g., linear photodetector  400 ). 
     In the electro-optic receiver  300  of  FIG.  3   , light that is coupled from the optical waveguide  157  into the ring resonator  301 - 1  to  301 - 3  (or passive ring filter) from the right (light traveling from the second end  157 B toward the first end  157 A of the optical waveguide  157 ) is routed clockwise through the ring resonator  301 - 1  to  301 - 3  (or passive ring filter) and is coupled into the coupling section  303 A- 1  to  303 A- 3  of the corresponding output optical waveguide  303 - 1  to  303 - 3 , where it passes through the short section  303 B- 1  to  303 B- 3  of the corresponding output optical waveguide  303 - 1  to  303 - 3  and into the second end of the photodetector  305 - 1  to  305 - 3 . Conversely, light that is coupled from the optical waveguide  157  into the ring resonator  301 - 1  to  301 - 3  (or passive ring filter) from the left (light traveling from the first end  157 A toward the second end  157 B of the optical waveguide  157 ) is routed counter-clockwise through the ring resonator  301 - 1  to  301 - 3  (or passive ring filter) and is coupled into the coupling section  303 A- 1  to  303 A- 3  of the corresponding output optical waveguide  303 - 1  to  303 - 3 , where it passes through the long section  303 C- 1  to  303 C- 3  of the corresponding output optical waveguide  303 - 1  to  303 - 3  and into the first end of the photodetector  305 - 1  to  305 - 3 . The long section  303 C- 1  to  303 C- 3  of the output optical waveguide  303 - 1  to  303 - 3  functions as an optical delay line. The long section  303 C- 1  to  303 C- 3  of the output optical waveguide  303 - 1  to  303 - 3  is defined so that the two polarizations of the incoming optical signal from a given wavelength channel in the optical fiber/waveguide  152  (after splitting, polarization rotation, and waveguide routing), enter a given photodetector  305 - 1  to  305 - 3  (defined as the linear photodetector  400 ) from opposite directions at about the same time, which reduces timing-skew between the two polarizations of the incoming optical signal at the given photodetector  305 - 1  to  305 - 3  and correspondingly makes electronic timing-skew management possible (or easier) to implement, and may eliminate the need for timing-skew management altogether. 
     Additionally, in some embodiments of the electro-optic receiver  300  of  FIG.  3   , the photocurrent from a given photodetector  305 - 1  to  305 - 3  is used as a feedback signal to control alignment between the resonant wavelength of the corresponding ring resonator  301 - 1  to  301 - 3  and the wavelength of a given data channel in the incoming optical signal. For example, in some embodiments, the electro-optic receiver  300  includes a control circuit that tunes the ring resonance wavelength of the ring resonator  301 - 1  to  301 - 3  using a thermal tuner and/or a diode built into the ring resonator  301 - 1  to  301 - 3 , in order to optimize the optical power reaching the photodetector  305 - 1  to  305 - 3 . Also, in some embodiments, the electro-optic receiver  300  includes the VOA  163 , as described with regard to the electro-optic receiver  150  of  FIG.  1 B , for use at startup of the electro-optic receiver  300 . 
       FIG.  5    shows a flowchart of a method for operating a photonic circuit, in accordance with some embodiments. In some embodiments, the method of  FIG.  5    is practiced using the electro-optic receivers  150  and/or  300 . The method includes an operation  501  for receiving incoming light through an optical input port of the photonic circuit. A first portion of the incoming light has a first polarization and a second portion of the incoming light has a second polarization. The method also includes an operation  503  for splitting the first portion of the incoming light from the second portion of the incoming light, such as by using the PSR  156 . The method also includes an operation  505  for directing the first portion of the incoming light through a first end of an optical waveguide, such as the through the first end  157 A of the optical waveguide  157 . The method also includes an operation  507  for rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light, such as done by the PSR  156 . The method also includes an operation  509  for directing the polarization-rotated second portion of the incoming light through a second end of the optical waveguide, such as the through the second end  157 B of the optical waveguide  157 , where the optical waveguide  157  extends in a continuous manner from the first end  157 A to the second end  157 B. In some embodiments, the operations  503 ,  505 ,  507 , and  509  are done is an essentially simultaneous manner. The method also includes an operation  511  for operating a plurality of ring resonators, e.g.,  161 - 1  to  161 - 6  and  301 - 1  to  301 - 3 , to evanescently in-couple light from the optical waveguide  157 , wherein each of the plurality of ring resonators is operated at a respective resonant wavelength to in-couple both the first portion of the incoming light having the respective resonant wavelength and the polarization-rotated second portion of the incoming light having the respective resonant wavelength. 
     In some embodiments, the method also includes transmitting the first portion of the incoming light and the second portion of the incoming light through a variable optical attenuator, such as the VOA  163 , and controlling the variable optical attenuator to attenuate an optical power of first portion of the incoming light and the second portion of the incoming light during a time when the plurality of ring resonators, e.g.,  161 - 1  to  161 - 6  and  301 - 1  to  301 - 3 , are being tuned to their respective resonant wavelengths. In these embodiments, the method also includes controlling the variable optical attenuator to not attenuate the optical power of first portion of the incoming light and the second portion of the incoming light during a time when the plurality of ring resonators are operating at their respective resonant wavelengths, e.g., during normal operation. 
     In some embodiments, each of the plurality of ring resonators, e.g.,  161 - 1  to  161 - 6 , includes a respective photodetector. In some embodiments, the method includes optically coupling light from each of the plurality of ring resonators, e.g.,  301 - 1  to  301 - 3 , into a corresponding one of a plurality of output optical waveguides, e.g.,  303 - 1  to  303 - 3 , such that the first portion of the incoming light is transmitted through a long section, e.g.,  303 C- 1  to  3030 C- 3 , of the corresponding one of the plurality of output optical waveguides, and such that the polarization-rotated second portion of the incoming light is transmitted through a short section, e.g.,  303 B- 1  to  303 B- 3 , of the corresponding one of the plurality of output optical waveguides. In these embodiments, the method also includes operating a photodetector, e.g.,  305 - 1  to  305 - 3 , to detect the first portion of the incoming light at an output end of the long section of the corresponding one of the plurality of output optical waveguides, and to detect the polarization-rotated second portion of the incoming light at an output end of the short section of the corresponding one of the plurality of output optical waveguides. 
       FIG.  6    shows an example configuration of an electro-optic receiver  600  implemented within a PIC  601 , in accordance with some embodiments. The electro-optic receiver  600  includes a PSR  613  that has an optical input  613 A optically connected to receive incoming light from an optical coupler  615 , by way of an optical waveguide  614 . In some embodiments, the optical input  613 A of the PSR  156  is directly optically coupled to the optical coupler  615 , such that the optical waveguide  155  is not required. In some embodiments, the optical coupler  615  is implemented as an edge coupler. However, in other embodiments, the optical coupler  615  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the PIC  601  to an optical fiber/waveguide  617 . Incoming light is transmitted from the optical fiber/waveguide  617  into the optical coupler  615 , as indicated by arrow  616 . The PSR  613  has a first optical output  613 B and a second optical output  613 C. The PSR  613  is configured to direct a first portion of the incoming light having a first polarization (TE or TM) through the first optical output  613 B. The PSR  613  is also configured to rotate a polarization of a second portion of the incoming light from a second polarization (opposite of the first polarization) to the first polarization. In this manner, the PSR  613  turns the second portion of the incoming light into a polarization-rotated second portion of the incoming light. The PSR  613  is configured to direct the polarization-rotated second portion of the incoming light through the second optical output  613 C. 
     The electro-optic receiver  600  includes a first optical waveguide  603  optically connected to the first optical output  613 B of the PSR  613 . The electro-optic receiver  600  also includes a second optical waveguide  605  optically connected to the second optical output  613 C of the PSR  613 . In the electro-optic receiver  600 , the first optical waveguide  603  and the second optical waveguide  605  are not optically connected/coupled to each other. The first optical waveguide  603  and the second optical waveguide  605  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the first optical waveguide  603  and the second optical waveguide  605  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the first optical waveguide  603  and the second optical waveguide  605 , respectively, to enable guiding of light within the first optical waveguide  603  and the second optical waveguide  605 . In some embodiments, first optical waveguide  603  and the second optical waveguide  605  are formed of a same material. The first portion of the incoming light is transmitted through the first optical output  613 B of the PSR  613  and into the first optical waveguide  603 , and travels along the first optical waveguide  603 , as indicated by arrows  604 . The polarization-rotated second portion of the incoming light is transmitted through the second optical output  613 C of the PSR  613  and into the second optical waveguide  605 , and travels along the second optical waveguide  605 , as indicated by arrows  606 . 
     The electro-optic receiver  600  includes a first plurality of ring resonators  607 - 1  to  607 - 3  positioned along the first optical waveguide  603  and within an evanescent optical coupling distance of the first optical waveguide  603 . While the example electro-optic receiver  600  shows three ring resonators  607 - 1  to  607 - 3  for purposes of description, it should be understood that there is no limit on the number of the first plurality of ring resonators that can be positioned along the first optical waveguide  603 , so long as the first plurality of ring resonators and associated signal processing circuitry can be spatially and electrically accommodated on the chip. Each of the ring resonators  607 - 1  to  607 - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 , such that the first portion of the incoming light having a wavelength (λ 1 , λ 2 , or λ 3 ) substantially equal to the respective resonant wavelength (λ 1 , λ 2 , or λ 3 ) of a given one of the ring resonators  607 - 1  to  607 - 3  optically couples into the given one of the ring resonators  607 - 1  to  607 - 3 . In some embodiments, the ring resonators  607 - 1  to  607 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonators  607 - 1  to  607 - 3  are implemented as circular discs. The ring resonators  607 - 1  to  607 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonators  607 - 1  to  607 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonators  607 - 1  to  607 - 3  to enable guiding of light within the ring resonators  607 - 1  to  607 - 3  and around the circuitous path defined by each of the ring resonators  607 - 1  to  607 - 3 . In some embodiments, each of the ring resonators  607 - 1  to  607 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonators  607 - 1  to  607 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     The electro-optic receiver  600  includes a second plurality of ring resonators  609 - 1  to  609 - 3  positioned along the second optical waveguide  605  and within an evanescent optical coupling distance of the second optical waveguide  605 . While the example electro-optic receiver  600  shows three ring resonators  609 - 1  to  609 - 3  for purposes of description, it should be understood that there is no limit on the number of the second plurality of ring resonators that can be positioned along the second optical waveguide  605 , so long as the second plurality of ring resonators and associated signal processing circuitry can be spatially and electrically accommodated on the chip. Each of the ring resonators  609 - 1  to  609 - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 , such that the polarization-rotated second portion of the incoming light having a wavelength (λ 1 , λ 2 , or λ 3 ) substantially equal to the respective resonant wavelength (λ 1 , λ 2 , or λ 3 ) of a given one of the ring resonators  609 - 1  to  609 - 3  optically couples into the given one of the ring resonators  609 - 1  to  609 - 3 . The number of the second plurality of ring resonators  609 - 1  to  609 - 3  is equal to the number of the first plurality of ring resonators  607 - 1  to  607 - 3 . Also, the respective resonant wavelengths (λ 1 , λ 2 , λ 3 ) of the ring resonators  609 - 1  to  609 - 3  substantially match the respective resonant wavelengths (λ 1 , λ 2 , λ 3 ) of the ring resonators  607 - 1  to  607 - 3 . In some embodiments, the ring resonators  609 - 1  to  609 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonators  609 - 1  to  609 - 3  are implemented as circular discs. In some embodiments, each of the second plurality of ring resonators  609 - 1  to  609 - 3  is formed to have a same shape and size as the corresponding one (with respect to resonant wavelength (λ 1 , λ 2 , λ 3 )) of the first plurality of ring resonators  607 - 1  to  607 - 3 . The ring resonators  609 - 1  to  609 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonators  609 - 1  to  609 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonators  609 - 1  to  609 - 3  to enable guiding of light within the ring resonators  609 - 1  to  609 - 3  and around the circuitous path defined by each of the ring resonators  609 - 1  to  609 - 3 . In some embodiments, each of the second plurality of ring resonators  609 - 1  to  609 - 3  is formed of a same material as the corresponding one (with respect to resonant wavelength (λ 1 , λ 2 , λ 3 )) of the first plurality of ring resonators  607 - 1  to  607 - 3 . In some embodiments, each of the ring resonators  609 - 1  to  609 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonator resonators  609 - 1  to  609 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     The electro-optic receiver  600  includes a first plurality of output optical waveguides  608 - 1  to  608 - 3  respectively positioned within an evanescent optical coupling distance of the first plurality of ring resonators  607 - 1  to  607 - 3 . The electro-optic receiver  600  also includes a second plurality of output optical waveguides  610 - 1  to  610 - 3  respectively positioned within an evanescent optical coupling distance of the second plurality of ring resonators  609 - 1  to  609 - 3 . The electro-optic receiver  600  also includes a plurality of photodetectors  611 - 1  to  611 - 3 . Each of the photodetectors  611 - 1  to  611 - 3  is optically connected to receive light from a respective one of the first plurality of output optical waveguides  608 - 1  to  608 - 3  and from a respective one of the second plurality of output optical waveguides  610 - 1  to  610 - 3 , where the respective one of the first plurality of output optical waveguides  608 - 1  to  608 - 3  is optically coupled to one of the first plurality of ring resonators  607 - 1  to  607 - 3  having a given resonant wavelength (λ 1 , λ 2 , or λ 3 ), and where the respective one of the second plurality of output optical waveguides  610 - 1  to  610 - 3  is optically coupled to one of the second plurality of ring resonators  609 - 1  to  609 - 3  having the given resonant wavelength (λ 1 , λ 2 , or λ 3 ). In this manner, each of the photodetectors  611 - 1  to  611 - 3  receives incoming light of the substantially same wavelength from a corresponding one of the first plurality of output optical waveguides  608 - 1  to  608 - 3  and from a corresponding one of the second plurality of output optical waveguides  610 - 1  to  610 - 3 . 
     In some embodiments, each of the photodetectors  611 - 1  to  611 - 3  is configured like the linear photodetector described with regard to  FIG.  4   , such that the corresponding one of the first plurality of output optical waveguides  608 - 1  to  608 - 3  is connected to one end of the photodetector  611 - 1  to  611 - 3 , and the corresponding one of the second plurality of output optical waveguides  610 - 1  to  610 - 3  is connected to the other end of the photodetector  611 - 1  to  611 - 3 . In this manner, the photodetector  611 - 1  to  611 - 3  is configured to absorb a majority of the first portion of the incoming light (having the first polarization) in a first linear half of the photodetector  611 - 1  to  611 - 3 , and absorb a majority of the polarization-rotated second portion of the incoming light (also having the first polarization) in a second linear half of the photodetector  611 - 1  to  611 - 3 . In some embodiments, one or more electrical contacts (e.g.,  407 ) positioned along the first linear half of the photodetector  611 - 1  to  611 - 3  are electrically connected to a first photocurrent detection circuit within the photocurrent processing circuitry  167 , and one or more electrical contacts (e.g.,  407 ) positioned along the second linear half of the photodetector  611 - 1  to  611 - 3  are electrically connected to a second photocurrent detection circuit within the photocurrent processing circuitry  167 . 
     In some embodiments, the first optical waveguide  603  includes a first section  603 A extending from the first optical output  613 B of the PSR  613  to a nearest one ( 607 - 1 ) of the first plurality of ring resonators  607 - 1  to  607 - 3  to the PSR  613 . Also, the second optical waveguide  605  includes a first section  605 A extending from the second optical output  613 C of the PSR  613  to a nearest one ( 609 - 1 ) of the second plurality of ring resonators  609 - 1  to  609 - 3  to the PSR  613 . In these embodiments, either the first section  603 A of the first optical waveguide  603  is longer than the first section  605 A of the second optical waveguide  605 , or the first section  605 A of the second optical waveguide  605  is longer than the first section  603 A of the first optical waveguide  603 , in order to compensate for a timing delay between the first portion of the incoming light exiting the PSR  613  and the polarization-rotated second portion of the incoming light exiting the PSR  613 , so as to minimize a timing-skew (timing difference) between optical coupling of the first portion of the incoming light into the first plurality of ring resonators  607 - 1  to  607 - 3  and optical coupling of the polarization-rotated second portion of the incoming light into corresponding ones (by wavelength) of the second plurality of ring resonators  609 - 1  to  609 - 3 . In the example electro-optic receiver  600 , the first section  603 A of the first optical waveguide  603  includes a delay section  603 B configured so that the optical path length through the first section  603 A of the first optical waveguide  603  is longer than the optical path length through the first section  605 A of the second optical waveguide  605 . The delay section  603 B is configured to compensate for the timing delay between the first portion of the incoming light exiting the PSR  613  and the polarization-rotated second portion of the incoming light exiting the PSR  613 . The length of the first section  603 A of the first optical waveguide  603  and the length of the first section  605 A of the second optical waveguide  605  are defined to reduce a difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at a closest one ( 611 - 1 ) of the plurality of photodetectors  611 - 1  to  611 - 3  to the PSR  613 . Also, in some embodiments, the electro-optic receiver  600  includes the timing-skew management system  165  to electronically compensate for a temporal difference in photocurrent generation by a given one of the plurality of photodetectors  611 - 1  to  611 - 3  caused by a difference between the arrival time of the first portion of the incoming light at the corresponding one of the plurality of photodetectors  607 - 1  to  607 - 3 , respectively, and the arrival time of the polarization-rotated second portion of the incoming light at the corresponding one of the plurality of photodetectors  609 - 1  to  609 - 3 , respectively. 
     In some embodiments of the electro-optic receiver  600 , the two optical waveguides ( 603  and  605 ) are separately coupled to an array of passive ring filters ( 607 - 1  to  607 - 3  and  609 - 1  to  609 - 3 , respectively). Each passive ring filter ( 607 - 1  to  607 - 3  and  609 - 1  to  609 - 3 ) is designed to route the light from a single wavelength channel (λ 1 , λ 2 , λ 3 ), within a narrow wavelength range, to a corresponding output waveguide ( 608 - 1  to  608 - 3 , respectively, and  610 - 1  to  610 - 3 , respectively) that is connected to a linear photodetector ( 611 - 1  to  611 - 3 , respectively). The light routing within the electro-optic receiver  600  is designed so that the two polarizations of incoming light in a given wavelength channel as received through the optical coupler  615  are routed separately, through separate ring filters ( 607 - 1  to  607 - 3  and  609 - 1  to  609 - 3 ), into the same linear detector ( 611 - 1  to  611 - 3 ) from opposite directions. In some embodiments, an optical delay line ( 603 B) may be added (for example, in the form of a longer section of waveguide) to one of the two optical waveguides ( 603 ,  605 ) in order to compensate for asymmetric delay between the first portion of the incoming light and the polarization-rotated second portion of the incoming light introduced by the PSR  613 . The electronic timing-skew management system  165  can be implemented and operated to correct for any remaining timing-skew between the first portion of the incoming light and the polarization-rotated second portion of the incoming light introduced by the PSR  613 . Also, because the first optical waveguide  603  is not optically connected to the second optical waveguide  605 , the electro-optic receiver  600  does not require a VOA, such as previously described with regard to the VOA  163  in the electro-optic receiver  150  of  FIG.  1 B . 
     In some embodiments of the electro-optic receiver  600 , the photocurrent from a given photodetector  611 - 1  to  611 - 3  is used as a feedback signal to control the alignment between the resonance wavelength (λ 1 , λ 2 , λ 3 ) of the pair of ring resonators ( 607 - 1  to  607 - 3  and  609 - 1  to  609 - 3 ) corresponding to the given photodetector  611 - 1  to  611 - 3  and the wavelength of the corresponding data wavelength channel of the incoming light as received through the optical coupler  615 . For example, in some embodiments, a control circuit is used to tune the two the resonance wavelengths of the pair of ring resonators ( 607 - 1  to  607 - 3  and  609 - 1  to  609 - 3 ) corresponding to the given photodetector  611 - 1  to  611 - 3  to optimize optical power reaching the given photodetector  611 - 1  to  611 - 3 . In some embodiments, the control circuit operates to control a thermal tuner (e.g., heater) implemented to control a temperature of the pair of ring resonators ( 607 - 1  to  607 - 3  and  609 - 1  to  609 - 3 ) corresponding to the given photodetector  611 - 1  to  611 - 3  to optimize optical power reaching the given photodetector  611 - 1  to  611 - 3 . In some embodiments, the control circuit operates to control a diode built into the pair of ring resonators ( 607 - 1  to  607 - 3  and  609 - 1  to  609 - 3 ) corresponding to the given photodetector  611 - 1  to  611 - 3  to optimize optical power reaching the given photodetector  611 - 1  to  611 - 3 . 
       FIG.  7    shows a flowchart of a method for operating a photonic circuit, in accordance with some embodiments. In some embodiments, the method of  FIG.  7    is practiced using the electro-optic receiver  600 . The method includes an operation  701  for receiving incoming light through an optical input port (e.g., optical coupler  615 ) of the photonic circuit (e.g., PIC  601 ). A first portion of the incoming light has a first polarization and a second portion of the incoming light having a second polarization. The method also includes an operation  703  for splitting the first portion of the incoming light from the second portion of the incoming light. In some embodiments, the operation  703  is performed by the PSR  613 . The method also includes an operation  705  for directing the first portion of the incoming light into a first optical waveguide (e.g., optical waveguide  603 ). The method also includes an operation  707  for rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. In some embodiments, the operation  703  is performed by the PSR  613 . The method also includes an operation  709  for directing the polarization-rotated second portion of the incoming light into a second optical waveguide (e.g., optical waveguide  605 ). The method also includes an operation  711  for operating a first plurality of ring resonators (e.g., ring resonators  607 - 1  to  607 - 3 ) to evanescently in-couple light from the first optical waveguide, where each of the first plurality of ring resonators is operated at a respective resonant wavelength to in-couple light having the respective resonant wavelength from the first optical waveguide. The method also includes an operation  713  for optically coupling light from the first plurality of ring resonators into respective ones of a first plurality of output optical waveguides (e.g., optical waveguides  608 - 1  to  608 - 3 ). The method also includes an operation  715  for directing light within the first plurality of output optical waveguides into respective ones of a plurality of photodetectors (e.g., photodetectors  611 - 1  to  611 - 3 ). The method also includes an operation  717  for operating a second plurality of ring resonators (e.g., ring resonators  609 - 1  to  609 - 3 ) to evanescently in-couple light from the second optical waveguide, where each of the second plurality of ring resonators is operated at a respective resonant wavelength to in-couple light having the respective resonant wavelength from the second optical waveguide. The method also includes an operation  719  for optically coupling light from the second plurality of ring resonators into respective ones of a second plurality of output optical waveguides (e.g., optical waveguides  610 - 1  to  610 - 3 ). The method also includes an operation  721  for directing light within the second plurality of output optical waveguides into respective ones of the plurality of photodetectors. 
     In some embodiments, the first optical waveguide includes an input section (e.g.,  603 A), and the second optical waveguide includes an input section (e.g.,  605 A), where either the input section of the first optical waveguide is longer than the input section of the second optical waveguide, or the input section of the second optical waveguide is longer than the input section of the first optical waveguide. In these embodiments, the method includes defining a length of the input section of the first optical waveguide and a length of the input section of the second optical waveguide to reduce a difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at a given one of the plurality of photodetectors. In some embodiments, the method includes electronically compensating for a temporal difference in photocurrent generation by a given one of the plurality of photodetectors caused by a difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the given one of the plurality of photodetectors. In some embodiments, the length of the input section of the first optical waveguide and the length of the input section of the second optical waveguide are defined to compensate for a temporal difference between directing the first portion of the incoming light into the first optical waveguide and directing the polarization-rotated second portion of the incoming light into the second optical waveguide. 
     In some embodiments, the each of the plurality of photodetectors used in the method is a linear photodetector (e.g., linear photodetector  400 ) that has a first end optically connected to a respective one of the first plurality of output optical waveguides and a second end optically connected to a respective one of the second plurality of output optical waveguides. In some of these embodiments, the method includes operating the linear photodetector to absorb a majority of the first portion of the incoming light in a first half of the linear photodetector, and absorb a majority of the polarization-rotated second portion of the incoming light in a second half of the linear photodetector. In some of these embodiments, the method includes operating a first photocurrent detection circuit to detect photocurrent generated within the first half of the linear photodetector, and operating a second photocurrent detection circuit to detect photocurrent generated within the second half of the linear photodetector. In this manner, the method provides for determination of how much optical power is conveyed into the linear photodetector from each of the first polarization and the second polarization of the original incoming optical signal. Correspondingly, in this manner, the method provides for determination of how much optical power was received in the original incoming optical signal in each of the first polarization and the second polarization. 
       FIG.  8    shows an example configuration of an electro-optic receiver  800  implemented within a PIC  801 , in accordance with some embodiments. The electro-optic receiver  800  includes a PSR  821  that has an optical input  821 A optically connected to receive incoming light from an optical coupler  823 , by way of an optical waveguide  824 . In some embodiments, the optical input  821 A of the PSR  821  is directly optically coupled to the optical coupler  823 , such that the optical waveguide  824  is not required. In some embodiments, the optical coupler  823  is implemented as an edge coupler. However, in other embodiments, the optical coupler  823  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the PIC  801  to an optical fiber/waveguide  825 . Incoming light is transmitted from the optical fiber/waveguide  825  into the optical coupler  823 , as indicated by arrow  826 . The PSR  821  has a first optical output  821 B and a second optical output  821 C. The PSR  821  is configured to direct a first portion of the incoming light having a first polarization (TE or TM) through the first optical output  821 B. The PSR  821  is also configured to rotate a polarization of a second portion of the incoming light from a second polarization (opposite of the first polarization) to the first polarization. In this manner, the PSR  821  turns the second portion of the incoming light into a polarization-rotated second portion of the incoming light. The PSR  821  is configured to direct the polarization-rotated second portion of the incoming light through the second optical output  821 C. In some embodiments, the first portion of the incoming light having a first polarization is transmitted through the second optical output  821 C, and the polarization-rotated second portion of the incoming light is transmitted through the first optical output  821 B. 
     The electro-optic receiver  800  includes a first optical waveguide  803  optically connected to the first optical output  821 B of the PSR  821 . The electro-optic receiver  800  also includes a second optical waveguide  805  optically connected to the second optical output  821 C of the PSR  821 . The first optical waveguide  803  and the second optical waveguide  805  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the first optical waveguide  803  and the second optical waveguide  805  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the first optical waveguide  803  and the second optical waveguide  805 , respectively, to enable guiding of light within the first optical waveguide  803  and the second optical waveguide  805 . In some embodiments, first optical waveguide  803  and the second optical waveguide  805  are formed of a same material. In some embodiments, the first portion of the incoming light is transmitted through the first optical output  821 B of the PSR  821  and into the first optical waveguide  803 , and travels along the first optical waveguide  803 , as indicated by arrow  804 . Also, in these embodiments, the polarization-rotated second portion of the incoming light is transmitted through the second optical output  821 C of the PSR  821  and into the second optical waveguide  805 , and travels along the second optical waveguide  805 , as indicated by arrow  806 . Alternatively, in some embodiments, the first portion of the incoming light is transmitted through the second optical output  821 C of the PSR  821  and into the second optical waveguide  805 , and travels along the second optical waveguide  805 , as indicated by arrow  806 . Also, in these alternative embodiments, the polarization-rotated second portion of the incoming light is transmitted through the first optical output  821 B of the PSR  821  and into the first optical waveguide  803 , and travels along the first optical waveguide  803 , as indicated by arrow  804 . 
     The electro-optic receiver  800  also includes a two-by-two optical splitter  809  that has a first optical input  809 A optically connected to the second end of the first optical waveguide  803 . The two-by-two optical splitter  809  has a second optical input  809 B optically connected to the second end of the second optical waveguide  805 . The two-by-two optical splitter  809  has a first optical output  809 C and a second optical output  809 D. The two-by-two optical splitter  809  is configured to output some of the first portion of the incoming light and some of the polarization-rotated second portion of the incoming light through each of the first optical output  809 C and the second optical output  809 D of the two-by-two optical splitter  809 . In some embodiments, the two-by-two optical splitter  809  is an even 50-50 optical splitter. However, in other embodiments, the two-by-two optical splitter  809  is not an even 50-50 optical splitter. The optical splitting ratio of the two-by-two optical splitter  809  defines how much optical power is transmitted to each of the first optical output  809 C and the second optical output  809 D from each of the first optical input  809 A and the second optical input  809 B. The optical splitting ratio provided by the two-by-two optical splitter  809  is set and/or controlled to ensure that very low optical power transmission through either the first optical output  809 C or the second optical output  809 D is avoided for any of the wavelength channels of the incoming light received through the first optical input  809 A and the second optical input  809 B. Also, in some embodiments, the two-by-two optical splitter  809  is a non-broadband optical splitter. 
     In some embodiments, a phase shifter  807  is optically coupled to either the first optical waveguide  803  or the second optical waveguide  805 . The example electro-optic receiver  800  has the phase shifter  807  optically coupled to the second optical waveguide  805 . In some embodiments, the phase shifter  807  is implemented as a thermal tuner (e.g., heating device) positioned over the second optical waveguide  805 , which operates by exploiting the thermo-optic effect of the second optical waveguide  805  material. In some embodiments, the phase shifter  807  is implemented as an electro-optic device (e.g., diode) built into the second optical waveguide  805 , which operates by exploiting electro-optic effects within the second optical waveguide  805 . In some embodiments, the phase shifter  807  is implemented as one or more ring resonator phase shifters. 
     In these embodiments, either the first optical waveguide  803  is longer than the second optical waveguide  805 , or the second optical waveguide  805  is longer than the first optical waveguide  803 , in order to compensate for a timing delay between the first portion of the incoming light exiting the PSR  821  and the polarization-rotated second portion of the incoming light exiting the PSR  821 , so as to minimize a timing-skew (timing difference) between arrival of the first portion of the incoming light into the two-by-two optical splitter  809  and arrival of the polarization-rotated second portion of the incoming light into the two-by-two optical splitter  809 . In the example electro-optic receiver  800 , the first optical waveguide  803  includes a delay section  803 A configured so that the optical path length through the first optical waveguide  803  is longer than the optical path length through the second optical waveguide  805 . The delay section  803 A is configured to compensate for the timing delay between the first portion of the incoming light exiting the PSR  821  and the polarization-rotated second portion of the incoming light exiting the PSR  821 . In some embodiments, the phase shifter  807  is optically coupled to a shorter one of the first optical waveguide  803  and the second optical waveguide  805 . 
     In some embodiments, the delay section  803 A is defined to compensate/minimize the timing-skew between arrival of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the two-by-two optical splitter  809  when the electro-optic receiver  800  is implemented to operate over a broad range of optical wavelengths, rather than just at a single optical wavelength. If a group delay difference between the two polarizations is not sufficiently compensated/minimized, a phase difference between the first portion of the incoming light in the first optical waveguide  803  and the polarization-rotated second portion of the incoming light in the second optical waveguide  805  will depend on the wavelength of the light, such that the single phase shifter  807  may not be able to set an appropriate phase for all wavelengths of interest. The delay section  803 A is defined to ensure that the group delay difference between the two polarizations is sufficiently compensated/minimized so that the phase difference between the first portion of the incoming light in the first optical waveguide  803  and the polarization-rotated second portion of the incoming light in the second optical waveguide  805  does not vary as a function of the wavelength of the light, which allows the single phase shifter  807  to set an appropriate phase for all channel wavelengths of interest within the incoming optical signal received through the optical coupler  823 . The combination of the PSR  821 , the first optical waveguide  803  with the delay section  803 A, the second optical waveguide  805 , the two-by-two optical splitter  809 , the phase shifter  807  constitutes a polarization equalizer  812 . 
     The electro-optic receiver  800  includes a third optical waveguide  811  optically connected to the first optical output  809 C of the two-by-two optical splitter  809 . The electro-optic receiver  800  also includes a fourth optical waveguide  813  optically connected to the second optical output  809 D of the two-by-two optical splitter  809 . In the electro-optic receiver  800 , the third optical waveguide  811  and the fourth optical waveguide  813  are not optically connected/coupled to each other. The third optical waveguide  811  and the fourth optical waveguide  813  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the third optical waveguide  811  and the fourth optical waveguide  813  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the third optical waveguide  811  and the fourth optical waveguide  813 , respectively, to enable guiding of light within the third optical waveguide  811  and the fourth optical waveguide  813 . In some embodiments, third optical waveguide  811  and the fourth optical waveguide  813  are formed of a same material. Some of the first portion of the incoming light (having the first polarization) is directed/conveyed through the first optical output  809 C of the two-by-two optical splitter  809  and into a third optical waveguide  811 . Also, some of the first portion of the incoming light (having the first polarization) is directed/conveyed through the second optical output  809 D of the two-by-two optical splitter  809  and into a fourth optical waveguide  813 . Some of the polarization-rotated second portion of the incoming light (having the first polarization) is directed/conveyed through the first optical output  809 C of the two-by-two optical splitter  809  and into the third optical waveguide  811 . Also, some of the polarization-rotated second portion of the incoming light (having the first polarization) is directed/conveyed through the second optical output  809 D of the two-by-two optical splitter  809  and into the fourth optical waveguide  813 . 
     The electro-optic receiver  800  includes a first plurality of ring resonators  815 - 1  to  815 - 3  positioned along the third optical waveguide  811  and within an evanescent optical coupling distance of the third optical waveguide  811 . While the example electro-optic receiver  800  shows three ring resonators  815 - 1  to  815 - 3  for purposes of description, it should be understood that there is no limit on the number of the first plurality of ring resonators that can be positioned along the third optical waveguide  811 , so long as the first plurality of ring resonators and associated signal processing circuitry can be spatially and electrically accommodated on the chip. Each of the ring resonators  815 - 1  to  815 - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 , such that the first portion of the incoming light and the polarization-rotated second portion of the incoming light having a wavelength (λ 1 , λ 2 , or λ 3 ) substantially equal to the respective resonant wavelength (λ 1 , λ 2 , or λ 3 ) of a given one of the ring resonators  815 - 1  to  815 - 3  optically couples into the given one of the ring resonators  815 - 1  to  815 - 3  from the third optical waveguide  811 . In some embodiments, the ring resonators  815 - 1  to  815 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonators  815 - 1  to  815 - 3  are implemented as circular discs. The ring resonators  815 - 1  to  815 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonators  815 - 1  to  815 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonators  815 - 1  to  815 - 3  to enable guiding of light within the ring resonators  815 - 1  to  815 - 3  and around the circuitous path defined by each of the ring resonators  815 - 1  to  815 - 3 . In some embodiments, each of the ring resonators  815 - 1  to  815 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonators  815 - 1  to  815 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     The electro-optic receiver  800  includes a second plurality of ring resonators  817 - 1  to  817 - 3  positioned along the fourth optical waveguide  813  and within an evanescent optical coupling distance of the fourth optical waveguide  813 . While the example electro-optic receiver  800  shows three ring resonators  817 - 1  to  817 - 3  for purposes of description, it should be understood that there is no limit on the number of the second plurality of ring resonators that can be positioned along the second optical waveguide  813 , so long as the second plurality of ring resonators and associated signal processing circuitry can be spatially and electrically accommodated on the chip. Each of the ring resonators  817 - 1  to  817 - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 , such that the polarization-rotated second portion of the incoming light having a wavelength (λ 1 , λ 2 , or λ 3 ) substantially equal to the respective resonant wavelength (λ 1 , λ 2 , or λ 3 ) of a given one of the ring resonators  609 - 1  to  609 - 3  optically couples into the given one of the ring resonators  817 - 1  to  817 - 3  from the fourth optical waveguide  813 . The number of the second plurality of ring resonators  817 - 1  to  817 - 3  is equal to the number of the first plurality of ring resonators  815 - 1  to  815 - 3 . Also, the respective resonant wavelengths (λ 1 , λ 2 , λ 3 ) of the ring resonators  817 - 1  to  817 - 3  substantially match the respective resonant wavelengths (λ 1 , λ 2 , λ 3 ) of the ring resonators  815 - 1  to  815 - 3 . In some embodiments, the ring resonators  817 - 1  to  817 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonators  817 - 1  to  817 - 3  are implemented as circular discs. In some embodiments, each of the second plurality of ring resonators  817 - 1  to  817 - 3  is formed to have a same shape and size as the corresponding one (with respect to resonant wavelength (λ 1 , λ 2 , λ 3 )) of the first plurality of ring resonators  815 - 1  to  815 - 3 . The ring resonators  817 - 1  to  817 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonators  817 - 1  to  817 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonators  817 - 1  to  817 - 3  to enable guiding of light within the ring resonators  817 - 1  to  817 - 3  and around the circuitous path defined by each of the ring resonators  817 - 1  to  817 - 3 . In some embodiments, each of the second plurality of ring resonators  817 - 1  to  817 - 3  is formed of a same material as the corresponding one (with respect to resonant wavelength (λ 1 , λ 2 , λ 3 )) of the first plurality of ring resonators  815 - 1  to  815 - 3 . In some embodiments, each of the ring resonators  817 - 1  to  817 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonators  817 - 1  to  817 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     The electro-optic receiver  800  includes a first plurality of output optical waveguides  816 - 1  to  816 - 3  respectively positioned within an evanescent optical coupling distance of the first plurality of ring resonators  815 - 1  to  815 - 3 . The electro-optic receiver  800  also includes a second plurality of output optical waveguides  818 - 1  to  818 - 3  respectively positioned within an evanescent optical coupling distance of the second plurality of ring resonators  817 - 1  to  817 - 3 . The electro-optic receiver  800  also includes a plurality of photodetectors  819 - 1  to  819 - 3 . Each of the photodetectors  819 - 1  to  819 - 3  is optically connected to receive light from a respective one of the first plurality of output optical waveguides  816 - 1  to  816 - 3  and from a respective one of the second plurality of output optical waveguides  818 - 1  to  818 - 3 , where the respective one of the first plurality of output optical waveguides  816 - 1  to  816 - 3  is optically coupled to one of the first plurality of ring resonators  815 - 1  to  815 - 3  having a given resonant wavelength (λ 1 , λ 2 , or λ 3 ), and where the respective one of the second plurality of output optical waveguides  818 - 1  to  818 - 3  is optically coupled to one of the second plurality of ring resonators  817 - 1  to  817 - 3  having the same given resonant wavelength (λ 1 , λ 2 , or λ 3 ). In this manner, each of the photodetectors  819 - 1  to  819 - 3  receives incoming light of the substantially same wavelength from a corresponding one of the first plurality of output optical waveguides  816 - 1  to  816 - 3  and from a corresponding one of the second plurality of output optical waveguides  818 - 1  to  818 - 3 . 
     In some embodiments, each of the photodetectors  819 - 1  to  819 - 3  is configured like the linear photodetector described with regard to  FIG.  4   , such that the corresponding one of the first plurality of output optical waveguides  816 - 1  to  816 - 3  is connected to one end of the photodetector  819 - 1  to  819 - 3 , and the corresponding one of the second plurality of output optical waveguides  818 - 1  to  818 - 3  is connected to the other end of the photodetector  819 - 1  to  819 - 3 . In this manner, the photodetector  819 - 1  to  819 - 3  is configured to absorb a majority of the first portion of the incoming light (having the first polarization) in a first linear half of the photodetector  819 - 1  to  819 - 3 , and absorb a majority of the polarization-rotated second portion of the incoming light (also having the first polarization) in a second linear half of the photodetector  819 - 1  to  819 - 3 . In some embodiments, one or more electrical contacts (e.g.,  407 ) positioned along the first linear half of the photodetector  819 - 1  to  819 - 3  are electrically connected to a first photocurrent detection circuit within the photocurrent processing circuitry  167 , and one or more electrical contacts (e.g.,  407 ) positioned along the second linear half of the photodetector  819 - 1  to  819 - 3  are electrically connected to a second photocurrent detection circuit within the photocurrent processing circuitry  167 . Also, in some embodiments, the electro-optic receiver  800  includes the timing-skew management system  165  to electronically compensate for a temporal difference in photocurrent generation by a given one of the plurality of photodetectors  819 - 1  to  819 - 3  caused by a difference between the arrival time of the first portion of the incoming light at the corresponding one of the plurality of photodetectors  819 - 1  to  819 - 3 , respectively, and the arrival time of the polarization-rotated second portion of the incoming light at the corresponding one of the plurality of photodetectors  819 - 1  to  819 - 3 , respectively. 
     The electro-optic receiver  800  addresses a possible problematic situation in which either the first optical waveguide  803  or the second optical waveguide  805  conveys very little light due to most or all of the incoming light, as received through the optical coupler  823 , having one polarization (either mostly TE or mostly TM). In this situation, if the two-by-two optical splitter  809  were not implemented, it would be very difficult for any ring tuning algorithm to keep the operating resonant wavelengths of the ring resonators  815 - 1  to  815 - 3  and  817 - 1  to  817 - 3  aligned with the corresponding channel wavelengths, respectively, in the incoming light signal, as received through the optical coupler  823 . Also, the above-mentioned situation is even more problematic when the polarization in the optical fiber/waveguide  825  evolves over time, because the ring resonators  815 - 1  to  815 - 3  and  817 - 1  to  817 - 3  will have to re-lock to the channel wavelengths as the optical power ramps up. If the ring resonators  815 - 1  to  815 - 3  and  817 - 1  to  817 - 3  have to re-lock to changing channel wavelengths, an interruption will occur in the data signal output by the electro-optic receiver  800 . To address the above-mentioned situation, the electro-optic receiver  800  implements the two-by-two optical splitter  809  and the phase shifter  807  to ensure non-negligible optical power in each of the third optical waveguide  811  and the fourth optical waveguide  813  before the light reaches the ring resonators  815 - 1  to  815 - 3  and  817 - 1  to  817 - 3 . The two-by-two optical splitter  809  ensures that each of the third optical waveguide  811  and the fourth optical waveguide  813  conveys enough light of the first polarization to ensure that the ring resonators  815 - 1  to  815 - 3  and  817 - 1  to  817 - 3  can lock onto and maintain respective resonant wavelengths that substantially align with the channel wavelengths in the incoming light signal. In some embodiments, the phase shifter  807  uses active control as the polarization in the optical fiber/waveguide  825  drifts over time. The active control of the phase shifter  807  is implemented by active control circuitry (feedback circuitry  1015 ). For example, in some embodiments, active control of the phase shifter  807  is implemented by active control circuitry that measures optical power in the ring resonators  815 - 1  to  815 - 3  and  817 - 1  to  817 - 3 , and uses that measured optical power as feedback signals to adjust the operation of the phase shifter  807  as needed to track with the polarization in the optical fiber/waveguide  825 . 
       FIG.  9    shows a flowchart of a method for operating a photonic integrated circuit, in accordance with some embodiments. In some embodiments, the method of  FIG.  9    is practiced using the electro-optic receiver  800 . The method includes an operation  901  for receiving incoming light through an optical input port (e.g., optical coupler  823 ) of the photonic circuit (e.g., PIC  801 ). A first portion of the incoming light has a first polarization and a second portion of the incoming light has a second polarization. The method also includes an operation  903  for splitting the first portion of the incoming light from the second portion of the incoming light. In some embodiments, the operation  903  is performed by the PSR  821 . The method also includes an operation  905  for directing the first portion of the incoming light through a first optical waveguide (e.g., optical waveguide  803 ) and into a first optical input (e.g.,  809 A) of a two-by-two splitter (e.g.,  809 ). In some embodiments, the operation  905  is performed by the PSR  821 . The method also includes an operation  907  for rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. In some embodiments, the operation  907  is performed by the PSR  821 . The method also includes an operation  909  for directing the polarization-rotated second portion of the incoming light through a second optical waveguide (e.g., optical waveguide  805 ) and into a second optical input (e.g.,  809 B) of the two-by-two splitter. In some embodiments, the operation  909  is performed by the PSR  821 . The method also includes an operation  911  for directing some of the first portion of the incoming light through a first optical output (e.g.,  809 C) of the two-by-two optical splitter and into a third optical waveguide (e.g., optical waveguide  811 ). The method also includes an operation  913  for directing some of the first portion of the incoming light through a second optical output (e.g.,  809 D) of the two-by-two optical splitter and into a fourth optical waveguide (e.g., optical waveguide  813 ). The method also includes an operation  915  for directing some of the polarization-rotated second portion of the incoming light through the first optical output of the two-by-two optical splitter and into the third optical waveguide. The method also includes an operation  917  for directing some of the polarization-rotated second portion of the incoming light through the second optical output of the two-by-two optical splitter and into the fourth optical waveguide. In some embodiments, the operations  911  through  917  are performed by the two-by-two optical splitter  809 . 
     The method of  FIG.  9    also includes an operation  919  for operating a first plurality of ring resonators (e.g., ring resonators  815 - 1  to  815 - 3 ) to evanescently in-couple light from the third optical waveguide, where each of the first plurality of ring resonators is operated at a respective resonant wavelength to in-couple light having the respective resonant wavelength from the third optical waveguide. The method also includes an operation  921  for optically coupling light from the first plurality of ring resonators into respective ones of a first plurality of output optical waveguides (e.g., optical waveguides  816 - 1  to  816 - 3 ). The method also includes an operation  923  for directing light within the first plurality of output optical waveguides into respective ones of a plurality of photodetectors (e.g., photodetectors  819 - 1  to  819 - 3 ). The method also includes an operation  925  for operating a second plurality of ring resonators (e.g., ring resonators  817 - 1  to  817 - 3 ) to evanescently in-couple light from the fourth optical waveguide, where each of the second plurality of ring resonators is operated at a respective resonant wavelength to in-couple light having the respective resonant wavelength from the fourth optical waveguide. The method also includes an operation  927  for optically coupling light from the second plurality of ring resonators into respective ones of a second plurality of output optical waveguides (e.g., optical waveguides  818 - 1  to  818 - 3 ). The method also includes an operation  929  for directing light within the second plurality of output optical waveguides into respective ones of the plurality of photodetectors. 
     In some embodiments, the method of  FIG.  9    also includes operating a phase shifter in optical coupling with either the first optical waveguide or the second optical waveguide to apply a controlled amount of shift to a phase of light traveling through either the first optical waveguide or the second optical waveguide to which the phase shifter is optically coupled. In some embodiments, the first optical waveguide is longer than the second optical waveguide, or the second optical waveguide is longer than the first optical waveguide. In these embodiments, the method of  FIG.  9    includes defining a length of the first optical waveguide and a length of the second optical waveguide to reduce a difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the two-by-two optical splitter. In some embodiments, the method includes electronically compensating for a temporal difference in photocurrent generation by a given one of the plurality of photodetectors caused by a difference in arrival time of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the given one of the plurality of photodetectors. In some embodiments, the length of the first optical waveguide and the length of the second optical waveguide are defined to compensate for a temporal difference between directing the first portion of the incoming light into the first optical waveguide and directing the polarization-rotated second portion of the incoming light into the second optical waveguide. 
     In some embodiments, the each of the plurality of photodetectors used in the method of  FIG.  9    is a linear photodetector (e.g., linear photodetector  400 ) that has a first end optically connected to a respective one of the first plurality of output optical waveguides and a second end optically connected to a respective one of the second plurality of output optical waveguides. In some of these embodiments, the method of  FIG.  9    includes operating the linear photodetector to absorb a majority of the first portion of the incoming light in a first half of the linear photodetector, and absorb a majority of the polarization-rotated second portion of the incoming light in a second half of the linear photodetector. In some of these embodiments, the method of  FIG.  9    includes operating a first photocurrent detection circuit to detect photocurrent generated within the first half of the linear photodetector, and operating a second photocurrent detection circuit to detect photocurrent generated within the second half of the linear photodetector. In this manner, the method of  FIG.  9    provides for determination of how much optical power is conveyed into the linear photodetector from each of the first polarization and the second polarization of the original incoming optical signal. Correspondingly, in this manner, the method provides for determination of how much optical power was received in the incoming optical signal in each of the first polarization and the second polarization. 
       FIG.  10 A  shows an example configuration of an optical input polarization management device  1000  implemented within a PIC  1001 , in accordance with some embodiments. The optical input polarization management device  1000  includes a polarization controller  1003  that has an optical input  1003 A optically connected to receive incoming light from an optical coupler  1005 , by way of an optical waveguide  1006 . In some embodiments, the optical input  1003 A of the polarization controller  1003  is directly optically coupled to the optical coupler  1005 , such that the optical waveguide  1006  is not required. In some embodiments, the optical coupler  1005  is implemented as an edge coupler. However, in other embodiments, the optical coupler  1005  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the polarization controller  1003  to an optical fiber/waveguide  1007 . Incoming light is transmitted from the optical fiber/waveguide  1007  into the optical coupler  1005 , as indicated by arrow  1008 . The optical fiber/waveguide  1007  is optically connected to receive and convey light from a multi-wavelength light source  1009 . In some embodiments, the multi-wavelength light source  1009  is configured to transmit multiple wavelengths of continuous wave laser light through the optical fiber/waveguide  1007 . In some embodiments, a polarization of the light transmitted by the multi-wavelength light source  1009  through the optical fiber/waveguide  1007  is uncontrolled and possibly varies over time. 
     The on-chip polarization controller  1003  is configured to combine the two polarizations of the incoming light as received through the optical input  1003 A as a single polarization of light and output the single polarization of light through an optical output  1003 B of the polarization controller  1003  in a low loss manner. For example, in some embodiments, the polarization controller  1003  is configured to receive both TE and TM polarizations of light through the optical input  1003 A, rotate the TE polarized light to TM polarized light, and transmit essentially all of the light received through the optical input  1003 A as TM polarized light through the optical output  1003 B. Conversely, in some embodiments, the polarization controller  1003  is configured to receive both TE and TM polarizations of light through the optical input  1003 A, rotate the TM polarized light to TE polarized light, and transmit essentially all of the light received through the optical input  1003 A as TE polarized light through the optical output  1003 B. In some embodiments, the polarization controller  1003  is electronically tunable to accommodate a power difference and a phase difference between the two polarizations (TE and TM) within the incoming light that are unknown and possibly varying with time. 
     The optical input polarization management device  1000  includes an output optical waveguide  1011  optically connected to the optical output of the polarization controller  1003 . In some embodiments, feedback circuitry  1015  is configured to control the polarization controller  1003  based on the light transmitted through the optical output waveguide  1011 . A small fraction of the optical power in the output waveguide  1011  is optically tapped and measured to serve as an input signal to the feedback circuitry  1015 . In some embodiments, a directional optical coupler is implemented as an optical tap to transfer a small fraction of the optical power in the optical waveguide  1011  to a tap-off waveguide  1017 , which is then incident on a photodetector  1019 , e.g., linear photodetector. In some embodiments, the photodetector  1019  is configured to detect a fraction of the optical power in all wavelength channels. In some embodiments, a series of ring resonator filters  1013 - 1  to  1013 - 1  are designed to tap a small fraction of optical power from a single wavelength channel in the output waveguide  1011  and detect it, either by a photodetector placed within the ring resonator filter  1013 - 1  to  1013 - 3  itself, or by sending the optical signal to an output waveguide connected to a linear detector, such as previously described with regard to the ring resonators  815 - 1  to  815 - 3 , output optical waveguides  816 - 1  to  816 - 3 , and photodetectors  819 - 1  to  819 - 3  in the electro-optic receiver  800 . In this embodiment, the optical power in each wavelength channel (λ 1 , λ 2 , λ 3 ) can be measured separately, which enables the feedback circuitry  1015  to separately and independently optimize the operation of the polarization controller  1003  for each wavelength channel in the incoming optical signal as received through the optical input  1003 A of the polarization controller  1003 . 
     While the example optical input polarization management device  1000  shows three ring resonator filters  1013 - 1  to  1013 - 3  for purposes of description, it should be understood that there is no limit on the number of the ring resonator filters that can be positioned along the output waveguide  1011 , so long as the ring resonator filters  1013 - 1  to  1013 - 3  and associated signal processing circuitry can be spatially and electrically accommodated on the chip. Each of the ring resonator filters  1013 - 1  to  1013 - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 , such that light within the output waveguide  1011  having a wavelength (λ 1 , λ 2 , or λ 3 ) substantially equal to the respective resonant wavelength (λ 1 , λ 2 , or λ 3 ) of a given one of the ring resonator filters  1013 - 1  to  1013 - 3  optically couples into the given one of the ring resonator filters  1013 - 1  to  1013 - 3  from the output waveguide  1011 . In some embodiments, the ring resonator filters  1013 - 1  to  1013 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonator filters  1013 - 1  to  1013 - 3  are implemented as circular discs. The ring resonator filters  1013 - 1  to  1013 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonator filters  1013 - 1  to  1013 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonator filters  1013 - 1  to  1013 - 3  to enable guiding of light within the ring resonator filters  1013 - 1  to  1013 - 3  and around the circuitous path defined by each of the ring resonator filters  1013 - 1  to  1013 - 3 . In some embodiments, each of the ring resonator filters  1013 - 1  to  1013 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonator filters  1013 - 1  to  1013 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
       FIG.  10 B  shows the optical input polarization management device  1000  of  FIG.  10 A , with an example implementation of the polarization controller  1003 , in accordance with some embodiments. The polarization controller  1003  includes a PSR  1021  that has an optical input  1021 A optically connected to receive incoming light from the optical input  1003 A of the polarization controller  1003 . In some embodiments, the optical input  1021 A of the PSR  1021  is the optical input  1003 A of the polarization controller  1003 . The PSR  1021  has a first optical output  1021 B and a second optical output  1021 C. The PSR  1021  is configured to direct a first portion of the incoming light having a first polarization (TE or TM) through the first optical output  1021 B. The PSR  1021  is also configured to rotate a polarization of a second portion of the incoming light from a second polarization (opposite of the first polarization) to the first polarization. In this manner, the PSR  1021  turns the second portion of the incoming light into a polarization-rotated second portion of the incoming light. The PSR  1021  is configured to direct the polarization-rotated second portion of the incoming light through the second optical output  1021 C. In some alternative embodiments, the first portion of the incoming light having a first polarization is transmitted through the second optical output  1021 C, and the polarization-rotated second portion of the incoming light is transmitted through the first optical output  1021 B. 
     The polarization controller  1003  includes a first optical waveguide  1023  optically connected to the first optical output  1021 B of the PSR  1021 . The polarization controller  1021  also includes a second optical waveguide  1025  optically connected to the second optical output  1021 C of the PSR  1021 . The first optical waveguide  1023  and the second optical waveguide  1025  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the first optical waveguide  1023  and the second optical waveguide  1025  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the first optical waveguide  1023  and the second optical waveguide  1025 , respectively, to enable guiding of light within the first optical waveguide  1023  and the second optical waveguide  1025 . In some embodiments, first optical waveguide  1023  and the second optical waveguide  1025  are formed of a same material. In some embodiments, the first portion of the incoming light is transmitted through the first optical output  1021 B of the PSR  1021  and into the first optical waveguide  1023 , and travels along the first optical waveguide  1023 , as indicated by arrow  1024 . Also, in these embodiments, the polarization-rotated second portion of the incoming light is transmitted through the second optical output  1021 C of the PSR  1021  and into the second optical waveguide  1025 , and travels along the second optical waveguide  1025 , as indicated by arrow  1026 . Conversely, in some alternative embodiments, the first portion of the incoming light is transmitted through the second optical output  1021 C of the PSR  1021  and into the second optical waveguide  1025 , and travels along the second optical waveguide  1025 , as indicated by arrow  1026 . Also, in these alternative embodiments, the polarization-rotated second portion of the incoming light is transmitted through the first optical output  1021 B of the PSR  1021  and into the first optical waveguide  1023 , and travels along the first optical waveguide  1023 , as indicated by arrow  1024 . 
     The polarization controller  1003  also includes a first two-by-two optical splitter  1029  that has a first optical input  1029 A optically connected to the second end of the first optical waveguide  1023 . The first two-by-two optical splitter  1029  has a second optical input  1029 B optically connected to the second end of the second optical waveguide  1025 . The first two-by-two optical splitter  1029  has a first optical output  1029 C and a second optical output  1029 D. The first two-by-two optical splitter  1029  is configured to output some of the first portion of the incoming light and some of the polarization-rotated second portion of the incoming light through each of the first optical output  1029 C and the second optical output  1029 D of the first two-by-two optical splitter  1029 . In some embodiments, the first two-by-two optical splitter  1029  is an even 50-50 optical splitter. However, in other embodiments, the first two-by-two optical splitter  1029  is not an even 50-50 optical splitter. The optical splitting ratio of the first two-by-two optical splitter  1029  defines how much optical power is transmitted to each of the first optical output  1029 C and the second optical output  1029 D from each of the first optical input  1029 A and the second optical input  1029 B. The optical splitting ratio provided by the first two-by-two optical splitter  1029  is set and/or controlled to ensure that very low optical power transmission through either the first optical output  1029 C or the second optical output  1029 D is avoided for any of the wavelength channels of the incoming light received through the first optical input  1029 A and the second optical input  1029 B. Also, in some embodiments, the first two-by-two optical splitter  1029  is a non-broadband optical splitter. In some embodiments, the first two-by-two optical splitter  1029  is implemented using a multi-mode interference device (MMI) or a directional waveguide coupler, e.g., an adiabatic directional coupler. 
     In some embodiments, a first phase shifter  1027  is optically coupled to either the first optical waveguide  1023  or the second optical waveguide  1025 . The example polarization controller  1003  has the first phase shifter  1027  optically coupled to the second optical waveguide  1025 . In some embodiments, the first phase shifter  1027  is implemented as a thermal tuner (e.g., heating device) positioned over the second optical waveguide  1025 , which operates by exploiting the thermo-optic effect of the second optical waveguide  1025  material. In some embodiments, the first phase shifter  1027  is implemented as an electro-optic device (e.g., diode) built into the second optical waveguide  1025 , which operates by exploiting electro-optic effects within the second optical waveguide  1025 . In some embodiments, the first phase shifter  1027  is implemented as one or more ring resonators, in which each of these ring resonators operates at a particular wavelength to shift the phase of light at the particular wavelength within the optical waveguide to which the first phase shifter  1027  is optically coupled. 
     In these embodiments, either the first optical waveguide  1023  is longer than the second optical waveguide  1025 , or the second optical waveguide  1025  is longer than the first optical waveguide  1023 , in order to compensate for a timing delay between the first portion of the incoming light exiting the PSR  1021  and the polarization-rotated second portion of the incoming light exiting the PSR  1021 , so as to minimize a timing-skew (timing difference) between arrival of the first portion of the incoming light into the first two-by-two optical splitter  1029  and arrival of the polarization-rotated second portion of the incoming light into the first two-by-two optical splitter  1029 . In the example polarization controller  1003 , the first optical waveguide  1023  includes a delay section  1023 A configured so that the optical path length through the first optical waveguide  1023  is longer than the optical path length through the second optical waveguide  1025 . The delay section  1023 A is configured to compensate for the timing delay between the first portion of the incoming light exiting the PSR  1021  and the polarization-rotated second portion of the incoming light exiting the PSR  1021 . In some embodiments, the phase shifter  1027  is optically coupled to a shorter one of the first optical waveguide  1023  and the second optical waveguide  1025 . 
     In some embodiments, the delay section  1023 A is defined to compensate/minimize the timing-skew between arrival of the first portion of the incoming light and the polarization-rotated second portion of the incoming light at the first two-by-two optical splitter  1029  when the polarization controller  1003  is implemented to operate over a broad range of optical wavelengths, rather than just at a single optical wavelength. If a group delay difference between the two polarizations is not sufficiently compensated/minimized, a phase difference between the first portion of the incoming light in the first optical waveguide  1023  and the polarization-rotated second portion of the incoming light in the second optical waveguide  1025  will depend on the wavelength of the light, such that the single phase shifter  1027  may not be able to set an appropriate phase for all wavelengths of interest. The delay section  1023 A is defined to ensure that the group delay difference between the two polarizations is sufficiently compensated/minimized so that the phase difference between the first portion of the incoming light in the first optical waveguide  1023  and the polarization-rotated second portion of the incoming light in the second optical waveguide  1025  does not vary as a function of the wavelength of the light, which allows the phase shifter  1027  to set an appropriate phase for all channel wavelengths of interest within the incoming optical signal received through the optical coupler  1005 . 
     The polarization controller  1003  includes a third optical waveguide  1031  optically connected to the first optical output  1029 C of the first two-by-two optical splitter  1029 . The polarization controller  1003  also includes a fourth optical waveguide  1033  optically connected to the second optical output  1029 D of the first two-by-two optical splitter  1029 . The third optical waveguide  1031  and the fourth optical waveguide  1033  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the third optical waveguide  1031  and the fourth optical waveguide  1033  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the third optical waveguide  1031  and the fourth optical waveguide  1033 , respectively, to enable guiding of light within the third optical waveguide  1031  and the fourth optical waveguide  1033 . In some embodiments, third optical waveguide  1031  and the fourth optical waveguide  1033  are formed of a same material. Some of the first portion of the incoming light (having the first polarization) is directed/conveyed through the first optical output  1029 C of the first two-by-two optical splitter  1029  and into a third optical waveguide  1031 . Also, some of the first portion of the incoming light (having the first polarization) is directed/conveyed through the second optical output  1029 D of the first two-by-two optical splitter  1029  and into a fourth optical waveguide  1033 . Some of the polarization-rotated second portion of the incoming light (having the first polarization) is directed/conveyed through the first optical output  1029 C of the first two-by-two optical splitter  1029  and into the third optical waveguide  1031 . Also, some of the polarization-rotated second portion of the incoming light (having the first polarization) is directed/conveyed through the second optical output  1029 D of the first two-by-two optical splitter  1029  and into the fourth optical waveguide  1033 . 
     The polarization controller  1003  also includes a second two-by-two optical splitter  1037  that has a first optical input  1037 A optically connected to the second end of the third optical waveguide  1031 . The second two-by-two optical splitter  1037  has a second optical input  1037 B optically connected to the second end of the fourth optical waveguide  1033 . The second two-by-two optical splitter  1037  has at least one optical output  1037 C optically connected to the optical output  1003 B of the polarization controller  1003 . In some embodiments, the at least one optical output  1037 C of the second two-by-two optical splitter  1037  is the optical output  1003 B of the polarization controller  1003 . The second two-by-two optical splitter  1037  is configured to output some of the first portion of the incoming light and some of the polarization-rotated second portion of the incoming light through the optical output  1037 C. The second two-by-two optical splitter  1037  is not required to be an even 50-50 optical splitter. The optical splitting ratio of the second two-by-two optical splitter  1037  defines how much optical power is transmitted to the optical output  1037 C from each of the first optical input  1037 A and the second optical input  1037 B. The optical splitting ratio provided by the second two-by-two optical splitter  1037  is set and/or controlled to ensure that optical power transmission through the optical output  1037 C is optimized for the wavelength channels of the incoming light received through the first optical input  1037 A and the second optical input  1037 B. Also, in some embodiments, the second two-by-two optical splitter  1037  is a non-broadband optical splitter. In some embodiments, the second two-by-two optical splitter  1037  is implemented using an MMI device or a directional waveguide coupler, e.g., an adiabatic directional coupler. 
     In some embodiments, a second phase shifter  1035  is optically coupled to either the third optical waveguide  1031  or the fourth optical waveguide  1033 . The example polarization controller  1003  has the second phase shifter  1035  optically coupled to the second optical waveguide  1033 . In some embodiments, the second phase shifter  1035  is implemented as a thermal tuner (e.g., heating device) positioned over the fourth optical waveguide  1033 , which operates by exploiting the thermo-optic effect of the fourth optical waveguide  1033  material. In some embodiments, the second phase shifter  1035  is implemented as an electro-optic device (e.g., diode) built into the fourth optical waveguide  1033 , which operates by exploiting electro-optic effects within the fourth optical waveguide  1033 . In some embodiments, the second phase shifter  1035  is implemented as one or more ring resonators, in which each of these ring resonators operates at a particular wavelength to shift the phase of light at the particular wavelength within the optical waveguide to which the second phase shifter  1033  is optically coupled. In some embodiments, the relative phase between the two phase shifters  1027  and  1035  is controlled by placing phase shifters on the two optical waveguides  1025  and  1033 , respectively, instead of on just one of the optical waveguides. This provides for faster tuning of the relative phase, especially for thermal phase shifters. 
     In some embodiments, the polarization controller  1003  functions as an effective electro-optic combiner by using the PSR  1021  and the cascaded configuration of the first two-by-two optical splitter  1029  and the second two-by-two optical splitter  1037 , with the first phase shifter  1027  on one of the two waveguides  1023 ,  1025  entering the first two-by-two optical splitter  1029 , and with the second phase shifter  1035  on one of the two waveguides  1031 ,  1033  entering the second two-by-two optical splitter  1037 . The first phase shifter  1027  and the second phase shifter  1035  are tuned to account for the phase and intensity imbalance of the two respective optical waveguides over time. The first phase shifter  1027  and the second phase shifter  1035  are used to optimize the optical power in the output waveguide  1011  as the input fiber/waveguide  1007  polarization changes over time. In some embodiments, the first phase shifter  1027  and/or the second phase shifter  1035  are/is implement as a heater placed near the respective optical waveguide or as a diode built into the respective optical waveguide. Also, in some embodiments, the first phase shifter  1027  and/or the second phase shifter  1035  are/is implemented as a ring resonator phase shifter, in which each of a plurality of ring resonators is operated to shift the phase of a single respective wavelength channel of the light within the optical waveguide. 
     Implementation of the first phase shifter  1027  and the second phase shifter  1035  as ring resonator phase shifters provides for higher optical power transmission to the output waveguide  1011  over a wide range of wavelength channels. In some situations, as the input fiber/waveguide  1007  polarization drifts enough over time, the first phase shifter  1027  and the second phase shifter  1035  may have to “reset” by abruptly changing the phase by a 2π amount to avoid reaching the end of its range. Such a “reset” would take time and cause an interruption in signal. In some embodiments, to avoid having a “reset” of the phase shifters  1027 ,  1035 , the polarization controller  1003  includes more than two cascaded two-by-two optical splitters with corresponding preceding phase shifters. Also, in some embodiments, the feedback circuitry  1015  is configured to control the first phase shifter  1027  and the second phase shifter  1035 , and any other phase shifters in the polarization controller  1003 , based on the light transmitted through the optical output waveguide  1011 . 
     The optical input polarization management device  1000  functions to convert an incoming light signal that has unknown polarization characteristics (and possibly uncontrolled polarization states that vary over time) into a corresponding input light signal of known polarization. Because the optical outputs of the PSR  1021  are combined into the single output waveguide  1011 , with the same polarization, it is possible to simplify optical circuits and electrical circuits for detection and/or modulation of the light within the output waveguide  1011 . In some embodiments, the optical input polarization management device  1000  is implemented as an electro-optic combiner to combine two optical signals having relative phase and relative intensities that are unknown and that may vary over time, with low loss, over a range of wavelength channels. In some embodiments, when the optical input polarization management device  1000  is used to combine modulated light signals for output to a detection system, optical timing-skew management and/or electrical timing-skew management can be implemented in conjunction with the optical input polarization management device  1000  to support receipt of the incoming optical signal. 
       FIG.  10 C  shows an example implementation of the optical input polarization management device  1000  in which the first phase shifter  1027  is implemented as a first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second phase shifter  1035  is implemented as a second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3 , in accordance with some embodiments. Each of the first plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  is positioned along the optical waveguide  1025  and within an evanescent optical coupling distance of the optical waveguide  1025 . Each of the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  is positioned along the optical waveguide  1033  and within an evanescent optical coupling distance of the optical waveguide  1033 . Each of the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  is operated to provide a controlled amount of shift in the phase of a single, respective wavelength channel of the light within the optical waveguide  1025 . Each of the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  is operated to provide a controlled amount of shift in the phase of a single, respective wavelength channel of the light within the optical waveguide  1033 . A number of ring resonators within the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  is equal to a number of ring resonators within the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3 . Also, for feedback control purposes, the number of ring resonator filters (photodetectors)  1013 - 1  to  1013 - 3  is equal to the number of first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3 , and the number of ring resonator filters (photodetectors)  1013 - 1  to  1013 - 3  is also equal to the number of the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3 . 
     In some embodiments, the ring resonators within the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonators within the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  are implemented as circular discs. The ring resonators within the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonators within the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonators to enable guiding of light within the ring resonators and around the circuitous path defined by each of the ring resonators. In some embodiments, each of the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     While the example of  FIG.  10 C  shows three ring resonators within each of the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  for purposes of description, it should be understood that there is no limit on the number of ring resonators within each of the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3 , so long as the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  and associated signal processing circuitry can be spatially and electrically accommodated on the chip. Each ring resonator within the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3  and the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 , such that light having a wavelength (λ 1 , λ 2 , or λ 3 ) substantially equal to the respective resonant wavelength (λ 1 , λ 2 , or λ 3 ) of a given one of the ring resonators optically couples into the given one of the ring resonators from the optical waveguide  1025 ,  1033 . Each of the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3 , the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3 , and the ring resonator filters  1013 - 1  to  1013 - 3  includes at least one ring resonator configured to operate at a same resonant wavelength (λ 1 , λ 2 , or λ 3 ) corresponding to a channel wavelength within the incoming light signal. Also, each of the first plurality of ring resonator phase shifters  1041 - 1  to  1041 - 3 , the second plurality of ring resonator phase shifters  1043 - 1  to  1043 - 3 , and the ring resonator filters  1013 - 1  to  1013 - 3  includes at least one ring resonator configured to operate at each of multiple different resonant wavelengths (λ 1 , λ 2 , or λ 3 ) corresponding to the channel wavelengths within the incoming light signal. It should be appreciated that first plurality of ring resonators  1041 - 1  to  1041 - 3  and the second plurality of ring resonators  1043 - 1  to  1043 - 3  enables different wavelength channels to be phase shifted separately to accommodate unique phase and intensity imbalances among the different wavelength channels of the incoming light signal. 
       FIG.  11    shows a flowchart of a method for optical input polarization management, in accordance with some embodiments. In some embodiments, the method of  FIG.  11    is practiced using the optical input polarization management device  1000  of  FIGS.  10 A to  10 C . The method includes an operation  1101  for receiving incoming light through an optical input port (e.g.,  1003 A) of a PIC (e.g.,  1001 ). A first portion of the incoming light has a first polarization and a second portion of the incoming light has a second polarization. The method also includes an operation  1103  for splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes an operation  1105  for directing the first portion of the incoming light through a first optical waveguide (e.g.,  1023 ) and into a first optical input (e.g.,  1029 A) of a first two-by-two splitter (e.g.,  1029 ). The method also includes an operation  1107  for rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes an operation  1109  for directing the polarization-rotated second portion of the incoming light through a second optical waveguide (e.g.,  1025 ) and into a second optical input (e.g.,  1029 B) of the first two-by-two splitter. The method also includes an operation  1111  for operating a first phase shifter (e.g.,  1027 ) in optical coupling with either the first optical waveguide or the second optical waveguide to apply a controlled amount of shift to a phase of light traveling through either the first optical waveguide or the second optical waveguide to which the phase shifter is optically coupled. 
     The method also includes an operation  1113  for directing some of the first portion of the incoming light through a first optical output (e.g.,  1029 C) of the first two-by-two optical splitter and into a third optical waveguide (e.g.,  1031 ). The method also includes an operation  1115  for directing some of the first portion of the incoming light through a second optical output (e.g.,  1029 D) of the first two-by-two optical splitter and into a fourth optical waveguide (e.g.,  1033 ). The method also includes an operation  1117  for directing some of the polarization-rotated second portion of the incoming light through the first optical output of the first two-by-two optical splitter and into the third optical waveguide. The method also includes an operation  1119  for directing some of the polarization-rotated second portion of the incoming light through the second optical output of the first two-by-two optical splitter and into the fourth optical waveguide. The method also includes an operation  1121  for operating a second phase shifter (e.g.,  1035 ) in optical coupling with either the third optical waveguide or the fourth optical waveguide to apply a controlled amount of shift to a phase of light traveling through either the third optical waveguide or the fourth optical waveguide to which the phase shifter is optically coupled. 
     The method also includes an operation  1123  for directing some of the first portion of the incoming light and some of the polarization-rotated second portion of the incoming light from the third optical waveguide into a first optical input (e.g.,  1037 A) of a second two-by-two splitter (e.g.,  1037 ). The method also includes an operation  1125  for directing some of the first portion of the incoming light and some of the polarization-rotated second portion of the incoming light from the fourth optical waveguide into a second optical input (e.g.,  1037 B) of the second two-by-two splitter. The method also includes an operation  1127  for directing some of the first portion of the incoming light and some of the polarization-rotated second portion of the incoming light through an optical output (e.g.,  1037 C) of the second two-by-two splitter and into a fifth optical waveguide (e.g., into the output optical waveguide  1011 ). 
     In some embodiments, the method of  FIG.  11    includes operating a plurality of ring resonator photodetectors (e.g.,  1013 - 1  to  1013 - 3 ) to evanescently in-couple light from the fifth optical waveguide, where each of the plurality of ring resonator photodetectors is operated at a respective resonant wavelength to in-couple a fraction of the first portion of the incoming light having the respective resonant wavelength and a fraction of the polarization-rotated second portion of the incoming light having the respective resonant wavelength. In some embodiments of the method of  FIG.  11   , the first phase shifter includes a first plurality of ring resonator phase shifters (e.g.,  1041 - 1  to  1041 - 3 ), and the second phase shifter includes a second plurality of ring resonator phase shifters (e.g.,  1043 - 1  to  1043 - 3 ). In these embodiments, the ring resonator photodetectors are used to generate feedback signals to control respective ones of the ring resonator phase shifters in the first phase shifter and the second phase shifter. 
       FIG.  12    shows an example configuration of an electro-optic transmitter  1200  implemented within a PIC  1201 , in accordance with some embodiments. The electro-optic transmitter  1200  implements multiple (N) instances of the polarization controller  1003  as previously described with regard to  FIGS.  10 A- 10 C and  11   . Each instance of the polarization controller  1003 - x , where x is 1 to N, has the optical input  1003 A optically connected to receive incoming light from a respective optical coupler  1203 - x , where x is 1 to N, by way of an optical waveguide  1204 - x , where x is 1 to N. In some embodiments, the optical input  1003 A of each instance of the polarization controller  1003 - x  is directly optically coupled to the respective optical coupler  1203 - x , such that the optical waveguide  1204 - x  is not required. In some embodiments, the optical coupler  1203 - x  is implemented as an edge coupler. However, in other embodiments, the optical coupler  1203 - x  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the polarization controller  1003 - x  to a respective optical fiber/waveguide  1205 - x , where x is 1 to N. Incoming light is transmitted from the optical fiber/waveguide  1205 - x  into the optical coupler  1203 - x , as indicated by arrow  1206 - x , where x is 1 to N. Each of the optical fiber/waveguides  1205 - 1  to  1205 -N is optically connected to receive and convey light from a respective single-wavelength light source  1207 - 1  to  1207 -N. In some embodiments, the different single-wavelength light sources  1207 - 1  to  1207 -N are configured to supply respectively different wavelengths of continuous wave laser light. In some embodiments, a polarization of the light transmitted by the single-wavelength light sources  1207 - 1  to  1207 -N through the respective optical fibers/waveguides  1205 - 1  to  1205 -N is uncontrolled. 
     Each of the on-chip polarization controllers  1003 - 1  to  1003 -N is configured to combine the two polarizations (TE and TM) of the incoming light as received through the respective optical coupler  1203 - 1  to  1203 -N as a single polarization of light and output the single polarization of light through a respective optical waveguide  1209 - 1  to  1209 -N in a low loss manner. For example, in some embodiments, a given instance of the polarization controller  1003 - x  is configured to receive both TE and TM polarizations of light through the optical coupler  1203 - x , rotate the TE polarized light to TM polarized light, and transmit essentially all of the light received through the optical coupler  1203 - x  as TM polarized light through the optical waveguide  1209 - x . Alternatively, in some embodiments, a given instance of the polarization controller  1003 - x  is configured to receive both TE and TM polarizations of light through the optical coupler  1203 - x , rotate the TM polarized light to TE polarized light, and transmit essentially all of the light received through the optical coupler  1203 - x  as TE polarized light through the optical waveguide  1209 - x . In some embodiments, each instance of the polarization controller  1003 - x  is electronically tunable to accommodate a power difference and a phase difference between the two polarizations (TE and TM) within the incoming light that are unknown and possibly varying with time. It should be appreciated that because each of the polarization controllers  1003 - 1  to  1003 -N can be optimized for a single wavelength, the configuration of the electro-optic transmitter  1200  advantageously overcomes any limitation associated with individual ones of the polarization controllers  1003 - 1  to  1003 -N having a finite optical bandwidth. 
     The electro-optic transmitter  1200  also includes an optical multiplexer  1211  having a plurality of optical inputs  1211 A- 1  to  1211 A-N respectively optically connected to the optical waveguides  1209 - 1  to  1209 -N corresponding to the plurality of polarization controllers  1003 - 1  to  1003 -N. The optical multiplexer  1211  also has a plurality of optical outputs  1211 B- 1  to  1211 B-N. The optical multiplexer  1211  is configured to convey a portion of the light received through any given one of the optical inputs  1211 A- 1  to  1211 A-N to each of the optical outputs  1211 B- 1  to  1211 B-N. In this manner, a portion of the light received through each of the optical inputs  1211 A- 1  to  1211 A-N is conveyed to each of the optical outputs  1211 B- 1  to  1211 B-N. Therefore, with the single-wavelength light sources  1207 - 1  to  1207 -N respectively supplying N different wavelengths (λ 1  to λ N ) of light, each of the optical inputs  1211 A- 1  to  1211 A-N receives a different one of the N different wavelengths (λ 1  to λ N ) of light (having a single, controlled polarization (either TE or TM)), and the optical multiplexer  1211  functions to convey a portion of each of the N different wavelengths (λ 1  to λ N ) of light from each of the optical inputs  1211 A- 1  to  1211 A-N to each of the optical outputs  1211 B- 1  to  1211 B-N, such that all of the N different wavelengths (λ 1  to λ N ) of light (having the single, controlled polarization (either TE or TM)) are conveyed through each of the optical outputs  1211 B- 1  to  1211 B-N. In some embodiments, the optical multiplexer  1211  is implemented as a star coupler. In some embodiments, the optical multiplexer  1211  is implemented as a series of cascaded two-by-two optical splitters. It should be understood, however, that in other embodiments, the optical multiplexer  1211  can be implemented in other ways so long as the above-mentioned functionality of the optical multiplexer  1211  is achieved. 
     The electro-optic transmitter  1200  also includes a plurality of optical waveguides  1213 - 1  to  1213 -N, where each of the optical waveguides  1213 - 1  to  1213 -N has a first end optically connected to a respective one of the plurality of optical outputs  1211 B- 1  to  1211 B-N of the optical multiplexer  1211 , and where each of the optical waveguides  1213 - 1  to  1213 -N has a second end optically connected to a respective optical output port of the electro-optic transmitter  1200 . In some embodiments, the optical output ports of the electro-optic transmitter  1200  are implemented as optical couplers  1219 - 1  to  1219 -N. In some embodiments, each instance of the optical coupler  1219 - x , where x is 1 to N, is implemented as an edge coupler. However, in other embodiments, the optical coupler  1219 - x  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the corresponding optical waveguide  1213 - 1  to  1213 -N to a respective output optical fiber/waveguide connected/couple to the electro-optic transmitter  1200 . 
     In some embodiments, the electro-optic transmitter  1200  includes a plurality of ring resonator modulators  1215 - x - y  positioned along and within an evanescent optical coupling distance of each of the plurality of optical waveguides  1213 - 1  to  1213 -N, where x is 1 to N, and y is 1 to Y. While the example electro-optic transmitter  1200  shows three ring resonator modulators  1215 - x - 1  to  1215 - x - 3  along each of the optical waveguides  1213 - 1  to  1213 -N for purposes of description, it should be understood that there is no limit on the number of ring resonator modulators that can be positioned along each of the optical waveguides  1213 - 1  to  1213 -N, so long as the ring resonator modulators and associated signal processing circuitry can be spatially and electrically accommodated on the chip. In some embodiments, the ring resonator modulators  1215 - x - y  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonator modulators  1215 - x - y  are implemented as circular discs. The ring resonator modulators  1215 - x - y  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonator modulators  1215 - x - y  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonator modulators  1215 - x - y  to enable guiding of light within the ring resonator modulators  1215 - x - y  and around the circuitous path defined by each of the ring resonator modulators  1215 - x - y . In some embodiments, each of the ring resonator modulators  1215 - x - y  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonator modulators  1215 - x - y  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     Each of the ring resonator modulators  1215 - x - 1  to  1215 - x - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 , such that the first portion of the incoming light and the polarization-rotated second portion of the incoming light having a wavelength (λ 1 , λ 2 , or λ 3 ) substantially equal to the respective resonant wavelength (λ 1 , λ 2 , or λ 3 ) of a given one of the ring resonator modulators  1215 - x - 1  to  1215 - x - 3  optically couples into the given one of the ring resonator modulators  1215 - x - 1  to  1215 - x - 3  from the corresponding optical waveguide  1213 - x . Each of the ring resonator modulators  1215 - x - y  operates to modulate light of a particular wavelength within the corresponding optical waveguide  1213 - x  to convey a digital data. In some embodiments, the ring resonator modulators  1215 - x - y  include photodetector devices to enable monitoring of the optical power coupled into each of the ring resonator modulators  1215 - x - y . In some embodiments, the optical power measured by photodetectors within the ring resonator modulators  1215 - x - y  is by the feedback circuitry  1015  to control the polarization controllers  1003 - 1  to  1003 -N. 
       FIG.  13    shows a flowchart of a method for operating an electro-optic transmitter, in accordance with some embodiments. In some embodiments, the method of  FIG.  13    is practiced using the electro-optic transmitter  1200  of  FIG.  12   . The method includes an operation  1301  for receiving incoming light through a plurality of optical input ports (e.g., optical couplers  1203 - 1  to  1203 -N). In some embodiments, the incoming light received through any given one of the plurality of optical input ports is continuous wave laser light of a single wavelength (e.g., any one of wavelengths λ 1  to λ N ). Also, the incoming light received through different ones of the plurality of optical input ports has different wavelengths. In this manner, each of the different optical input ports receives a different wavelength of continuous wave laser light. The method also includes an operation  1303  for operating a plurality of polarization controllers (e.g., polarization controllers  1003 - 1  to  1003 -N). Each of the plurality of polarization controllers has an optical input respectively optically connected to the plurality of optical input ports. Each of the plurality of polarization controllers operates to convert light having two polarizations (TE and TM) as received through a corresponding one of the plurality of optical input ports into a light having a single polarization (TE or TM). Each of the plurality of polarization controllers operates to direct the light having the single polarization through an output optical waveguide (e.g.,  1209 - 1  to  1209 -N) of the polarization controller. In some embodiments, each of the plurality of polarization controllers is operated in accordance with the method of  FIG.  11   . 
     The method also includes an operation  1305  for operating an optical multiplexer (e.g.,  1211 ) having a plurality of optical inputs (e.g.,  1211 A- 1  to  1211 A-N) respectively optically connected to the output optical waveguides of the plurality of polarization controllers. The optical multiplexer has a plurality of optical outputs (e.g.,  1211 B- 1  to  1211 B-N). The optical multiplexer operates to direct a portion of light received at each of the plurality of optical inputs of the optical multiplexer to each of the plurality of optical outputs of the optical multiplexer. The method also includes an operation  1307  for directing light from each of the plurality of optical outputs of the optical multiplexer through respective ones of a plurality of optical waveguides (e.g., optical waveguides  1213 - 1  to  1213 -N). Each of the plurality of optical waveguides has a first end and second end. The first end of each of the plurality of optical waveguides is respectively optically connected to the plurality of optical outputs of the optical multiplexer. The second end of each of the plurality of optical waveguides is respectively optically connected to a plurality of optical output ports (e.g.,  1219 - 1  to  1219 -N). The method also includes an operation  1309  for operating a plurality of ring resonator modulators (e.g.,  1215 - x - y ) positioned along a given one of the plurality of optical waveguides to modulate light within the given one of the plurality of optical waveguides in accordance with digital data. In some embodiments, a separate plurality of ring resonator modulators is positioned along each of the plurality of optical waveguides, where each of the separate pluralities of ring resonator modulators are operated to modulate light within the corresponding optical waveguide in accordance with digital data. 
       FIG.  14    shows an example configuration of an electro-optic transmitter  1400  implemented within a PIC  1401 , in accordance with some embodiments. The electro-optic transmitter  1400  includes a first PSR  1403  that has an optical input  1403 A optically connected to receive incoming light from an optical coupler  1405  through an optical waveguide  1406 . In some embodiments, the optical input  1403 A of the PSR  1403  is directly optically coupled to the optical coupler  1405 , such that the optical waveguide  1406  is not required. In some embodiments, the optical coupler  1405  is implemented as an edge coupler. However, in other embodiments, the optical coupler  1405  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the PIC  1401  to an optical fiber/waveguide  1407 . Incoming light is transmitted from the optical fiber/waveguide  1407  into the optical coupler  1405 , as indicated by arrow  1408 . The optical fiber/waveguide  1407  is optically connected to receive and convey light from a multi-wavelength light source  1409 . In some embodiments, the multi-wavelength light source  1409  is configured to transmit multiple wavelengths of continuous wave laser light through the optical fiber/waveguide  1407 . In some embodiments, a polarization of the light transmitted by the multi-wavelength light source  1409  through the optical fiber/waveguide  1407  is uncontrolled and possibly varies over time. 
     The PSR  1403  has a first optical output  1403 B and a second optical output  1403 C. The PSR  1403  is configured to direct a first portion of the incoming light having a first polarization (TE or TM) through the first optical output  1403 B. The PSR  1403  is also configured to rotate a polarization of a second portion of the incoming light from a second polarization (opposite of the first polarization) to the first polarization. In this manner, the PSR  1403  turns the second portion of the incoming light into a polarization-rotated second portion of the incoming light. The PSR  1403  is configured to direct the polarization-rotated second portion of the incoming light through the second optical output  1403 C. 
     The electro-optic transmitter  1400  includes a first optical waveguide  1411  optically connected to the first optical output  1403 B of the PSR  1403 . The electro-optic transmitter  1400  also includes a second optical waveguide  1413  optically connected to the second optical output  1403 C of the PSR  1403 . The first optical waveguide  1411  and the second optical waveguide  1413  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the first optical waveguide  1411  and the second optical waveguide  1413  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the first optical waveguide  1411  and the second optical waveguide  1413 , respectively, to enable guiding of light within the first optical waveguide  1411  and the second optical waveguide  1413 . In some embodiments, first optical waveguide  1411  and the second optical waveguide  1413  are formed of a same material. In some embodiments, the first portion of the incoming light is transmitted through the first optical output  1403 B of the PSR  1403  and into the first optical waveguide  1411 , and travels along the first optical waveguide  1411 , as indicated by arrows  1412 . Also, in these embodiments, the polarization-rotated second portion of the incoming light is transmitted through the second optical output  1403 C of the PSR  1403  and into the second optical waveguide  1413 , and travels along the second optical waveguide  1413 , as indicated by arrows  1414 . Alternatively, in some embodiments, the first portion of the incoming light is transmitted through the second optical output  1403 C of the PSR  1403  and into the second optical waveguide  1413 , and travels along the second optical waveguide  1413 , as indicated by arrows  1414 . Also, in these alternative embodiments, the polarization-rotated second portion of the incoming light is transmitted through the first optical output  1403 B of the PSR  1403  and into the first optical waveguide  1411 , and travels along the first optical waveguide  1411 , as indicated by arrows  1412 . 
     The electro-optic transmitter  1400  includes a first plurality (array) of ring resonator modulators  1415 - 1  to  1415 - 3  positioned along the first optical waveguide  1411  and within an evanescent optical coupling distance of the first optical waveguide  1411 . While the example electro-optic transmitter  1400  shows three ring resonator modulators  1415 - 1  to  1415 - 3  for purposes of description, it should be understood that there is no limit on the number of ring resonator modulators in the first plurality of ring resonator modulators  1415 - 1  to  1415 - 3  that can be positioned along the first optical waveguide  1411 , so long as the first plurality of ring resonator modulators  1415 - 1  to  1415 - 3  and associated signal processing circuitry can be spatially and electrically accommodated on the chip. Each of the ring resonator modulators  1415 - 1  to  1415 - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 , such that the first portion of the incoming light having a wavelength (λ 1 , λ 2 , or λ 3 ) substantially equal to the respective resonant wavelength (λ 1 , λ 2 , or λ 3 ) of a given one of the ring resonator modulators  1415 - 1  to  1415 - 3  optically couples into the given one of the ring resonator modulators  1415 - 1  to  1415 - 3  from the first optical waveguide  1411 . In some embodiments, the ring resonator modulators  1415 - 1  to  1415 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonator modulators  1415 - 1  to  1415 - 3  are implemented as circular discs. The ring resonator modulators  1415 - 1  to  1415 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonator modulators  1415 - 1  to  1415 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonator modulators  1415 - 1  to  1415 - 3  to enable guiding of light within the ring resonator modulators  1415 - 1  to  1415 - 3  and around the circuitous path defined by each of the ring resonators resonator modulators  1415 - 1  to  1415 - 3 . In some embodiments, each of the ring resonator modulators  1415 - 1  to  1415 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonator modulators  1415 - 1  to  1415 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     The electro-optic transmitter  1400  also includes a second plurality (array) of ring resonator modulators  1417 - 1  to  1417 - 3  positioned along the second optical waveguide  1413  and within an evanescent optical coupling distance of the second optical waveguide  1413 . While the example electro-optic transmitter  1400  shows three ring resonator modulators  1417 - 1  to  1417 - 3  for purposes of description, it should be understood that there is no limit on the number of ring resonator modulators in the second plurality of ring resonator modulators  1417 - 1  to  1417 - 3  that can be positioned along the second optical waveguide  1413 , so long as the second plurality of ring resonator modulators  1417 - 1  to  1417 - 3  and associated signal processing circuitry can be spatially and electrically accommodated on the chip. Each of the ring resonator modulators  1417 - 1  to  1417 - 3  is configured to operate at a respective resonant wavelength λ 1  to λ 3 , such that the polarization-rotated second portion of the incoming light having a wavelength (λ 1 , λ 2 , or λ 3 ) substantially equal to the respective resonant wavelength (λ 1 , λ 2 , or λ 3 ) of a given one of the ring resonator modulators  1417 - 1  to  1417 - 3  optically couples into the given one of the ring resonator modulators  1417 - 1  to  1417 - 3  from the second optical waveguide  1413 . In some embodiments, the ring resonator modulators  1417 - 1  to  1417 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonator modulators  1417 - 1  to  1417 - 3  are implemented as circular discs. The ring resonator modulators  1417 - 1  to  1417 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonator modulators  1417 - 1  to  1417 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonator modulators  1417 - 1  to  1417 - 3  to enable guiding of light within the ring resonator modulators  1417 - 1  to  1417 - 3  and around the circuitous path defined by each of the ring resonators resonator modulators  1417 - 1  to  1417 - 3 . In some embodiments, each of the ring resonator modulators  1417 - 1  to  1417 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonator modulators  1417 - 1  to  1417 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     The first plurality of ring resonator modulators  1415 - 1  to  1415 - 3  and the second plurality of ring resonator modulators  1417 - 1  to  1417 - 3  form a plurality of ring resonator modulator pairs positioned along the first optical waveguide  1411  and the second optical waveguide  1413 . Each ring resonator modulator pair of the plurality of ring resonator modulator pairs includes one ring resonator modulator (one of  1415 - 1  to  1415 - 3 ) positioned within an evanescent optical coupling distance of the first optical waveguide  1411  and one ring resonator modulator (one of  1417 - 1  to  1417 - 3 ) positioned within an evanescent optical coupling distance of the second optical waveguide  1413 , where each of the plurality of ring resonator modulator pairs is configured to operate at a specified resonant wavelength (one of λ 1  to λ 3 ). Each ring resonator modulator within a given one of the plurality of ring resonator modulator pairs is configured to modulate a same bit pattern. For example, the pair of ring resonator modulators  1415 - 1  and  1417 - 1  is configured to modulate a same bit pattern. The pair of ring resonator modulators  1415 - 2  and  1417 - 2  is configured to modulate a same bit pattern. And, the pair of ring resonator modulators  1415 - 3  and  1417 - 3  is configured to modulate a same bit pattern, and so on. 
     The electro-optic transmitter  1400  includes a second PSR  1419  that has a reverse-connected optical input  1419 A, a first reverse-connected optical output  1419 B, and a second reverse-connected optical output  1419 C. The second PSR  1419  is connected in a reversed manner in the electro-optic transmitter  1400 , such that the first reverse-connected optical output  1419 B and the second reverse-connected optical output  1419 C are connected to function as respective optical inputs, and such that the reverse-connected optical input  1419 A is connected to function as an optical output. In this manner, the second PSR  1419  functions as a polarization rotator and optical combiner. Specifically, the first reverse-connected optical output  1419 B of the second PSR  1419  is optically connected to a second end of the first optical waveguide  1411 , such that light conveyed through the first optical waveguide  1411  is received as input light into the first reverse-connected optical output  1419 B. Also, the second reverse-connected optical output  1419 C of the second PSR  1419  is optically connected to a second end of the second optical waveguide  1413 , such that light conveyed through the second optical waveguide  1413  is received as input light into the second reverse-connected optical output  1419 C. The reverse-connected optical input  1419 A of the PSR  1419  is optically connected to output coupler  1421  of the electro-optic transmitter  1400  through an optical waveguide  1423 . In this manner, the reverse-connected optical input  1419 A actually operates as an optical output through which light is transmitted from the PSR  1419  through the optical waveguide  1423  to the output coupler  1421 . Modulated output light is transmitted through the optical coupler  1421 , as indicated by arrow  1425 . In some embodiments, the reverse-connected optical input  1419 A of the PSR  1419  is directly optically coupled to the optical coupler  1421 , such that the optical waveguide  1423  is not required. In some embodiments, the optical coupler  1421  is implemented as an edge coupler. However, in other embodiments, the optical coupler  1421  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the PIC  1401  to an optical fiber/waveguide. 
     In a reverse functional manner, the PSR  1419  is configured to direct modulated light based on the first portion of the incoming light (having the first polarization) as received from the first optical waveguide  1411  through the first reverse-connected optical output  1419 B to the reverse-connected optical input  1419 A and on to the optical coupler  1421 . Also, in a reverse functional manner, the PSR  1419  is configured to rotate a polarization of modulated light based on the polarization-rotated second portion of the incoming light (having the first polarization), as received from the second optical waveguide  1413  through the second reverse-connected optical output  1419 C, from the first polarization back to the second polarization (opposite of the first polarization). In this manner, the PSR  1419  turns the modulated light based on the polarization-rotated second portion of the incoming light (having the first polarization) into a polarization-derotated modulated light (having the second polarization). The PSR  1419  is configured to direct the polarization-derotated modulated light through the reverse-connected optical input  1419 A and on to the optical coupler  1421 . The reverse-implemented PSR  1419  allows optical signals to be combined without active phase control, as each optical signal is in a different polarization state when it gets combined and transmitted through the reverse-connected optical input  1419 A of the PSR  1419  as a combined optical output signal which is then output through the optical coupler  1421  to an optical fiber/waveguide. 
       FIG.  15    shows a flowchart of a method for optical modulation, in accordance with some embodiments. In some embodiments, the method of  FIG.  15    is practiced using the electro-optic transmitter  1400  of  FIG.  14   . The method includes an operation  1501  for receiving incoming light through an optical input port, where a first portion of the incoming light has a first polarization and a second portion of the incoming light has a second polarization. In some embodiments, the method of  FIG.  15    is practiced using the electro-optic transmitter  1400  of  FIG.  14   . In some embodiments, the incoming light has an unknown polarization. In some embodiments, a polarization of the incoming light is uncontrolled and can possibly vary over time. The method includes an operation  1503  for splitting the first portion of the incoming light from the second portion of the incoming light. The method includes an operation  1505  for directing the first portion of the incoming light through a first optical waveguide (e.g., optical waveguide  1411 ). The method includes an operation  1507  for rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method includes an operation  1509  for directing the polarization-rotated second portion of the incoming light through a second optical waveguide (e.g., optical waveguide  1413 ). In some embodiments, the operations  1501  through  1509  are performed by the PSR  1403 . 
     The method includes an operation  1511  for operating a plurality of ring resonator modulator pairs (e.g., pairs of ring resonator modulators  1415 - 1  to  1415 - 3  and  1417 - 1  to  1417 - 3 ) positioned along the first optical waveguide and the second optical waveguide. Each ring resonator modulator pair of the plurality of ring resonator modulator pairs includes one ring resonator modulator positioned within an evanescent optical coupling distance of the first optical waveguide and one ring resonator modulator positioned within an evanescent optical coupling distance of the second optical waveguide. Each of the plurality of ring resonator modulator pairs is configured to operate at a specified resonant wavelength to modulate a same bit pattern onto light traveling through the first optical waveguide and the second optical waveguide to create a first portion of modulated light having the first polarization within the first optical waveguide and to create a second portion of modulated light having the first polarization within the second optical waveguide. The method includes an operation  1513  for rotating a polarization of the second portion of modulated light within the second optical waveguide back to the second polarization from the first polarization. The method also includes an operation  1515  for directing both the first portion of modulated light having the first polarization and the second portion of modulated light having the second polarization through a same optical output port (e.g., optical coupler  1421 ). In some embodiments, the operations  1513  and  1515  are performed by the reverse-implemented PSR  1419 . 
       FIG.  16    shows an example configuration of an electro-optic transmitter  1600  implemented within a PIC  1601 , in accordance with some embodiments. The electro-optic transmitter  1600  is a variation of the electro-optic transmitter  1400  of  FIG.  14   . Specifically, in the electro-optic transmitter  1600 , the PSR  1403  of the electro-optic transmitter  1400  is replaced by the polarization equalizer  812  as previously described with regard to electro-optic receiver  800  of  FIG.  8   . The optical input  821 A of the PSR  821  is optically connected to receive the incoming light from the optical coupler  1405 , either through the optical waveguide  1406  or through direct optical coupling of the optical input  821 A with the optical coupler  1405 . The first optical output  809 C of the two-by-two optical splitter  809  is optically connected to the first end of the first optical waveguide  1411 . The second optical output  809 D of the two-by-two optical splitter  809  is optically connected to the first end of the second optical waveguide  1413 . 
     The electro-optic transmitter  1600  addresses a possible problematic situation in which either the first optical waveguide  803  or the second optical waveguide  805  conveys very little light due to most or all of the incoming light, as received through the optical coupler  1405 , having one polarization (either mostly TE or mostly TM). In this situation, if the two-by-two optical splitter  809  were not implemented, it would be very difficult for any ring tuning algorithm to keep the operating resonant wavelengths of the ring resonator modulators  1415 - 1  to  1415 - 3  and  1417 - 1  to  1417 - 3  aligned with the corresponding channel wavelengths, respectively, in the incoming light signal, as received through the optical coupler  1405 . Also, the above-mentioned situation is even more problematic when the polarization in the optical fiber/waveguide  1407  evolves over time, because the ring resonator modulators  1415 - 1  to  1415 - 3  and  1417 - 1  to  1417 - 3  will have to re-lock to the channel wavelengths as the optical power ramps up. If the ring resonator modulators  1415 - 1  to  1415 - 3  and  1417 - 1  to  1417 - 3  have to re-lock to changing channel wavelengths, an interruption will occur in the signal output by the electro-optic transmitter  1600 . To address the above-mentioned situation, the electro-optic transmitter  1600  implements the polarization equalizer  812  that includes the two-by-two optical splitter  809  and the phase shifter  807  to ensure non-negligible optical power in each of the first optical waveguide  1411  and the second optical waveguide  1413  before the light reaches the ring resonator modulators  1415 - 1  to  1415 - 3  and  1417 - 1  to  1417 - 3 . The two-by-two optical splitter  809  ensures that each of the first optical waveguide  1411  and the second optical waveguide  1413  conveys enough light of the first polarization to ensure that the ring resonators  1415 - 1  to  1415 - 3  and  1417 - 1  to  1417 - 3  can lock onto and maintain respective resonant wavelengths that substantially align with the channel wavelengths in the incoming light signal. In some embodiments, the phase shifter  807  uses active control as the polarization in the optical fiber/waveguide  1407  drifts over time. The active control of the phase shifter  807  is implemented by active control circuitry (feedback circuitry  1015 ). For example, in some embodiments, active control of the phase shifter  807  is implemented by active control circuitry that measures optical power in the ring resonator modulators  1415 - 1  to  1415 - 3  and  1417 - 1  to  1417 - 3 , and uses that measured optical power as feedback signals to adjust the operation of the phase shifter  807  as needed to track with the polarization in the optical fiber/waveguide  1407 . 
       FIG.  17    shows a flowchart of a method for optical modulation, in accordance with some embodiments. In some embodiments, the method of  FIG.  17    is practiced using the electro-optic transmitter  1600  of  FIG.  16   . The method includes an operation  1701  for receiving incoming light through an optical input port (e.g., optical coupler  1405 ), where a first portion of the incoming light has a first polarization and a second portion of the incoming light has a second polarization. The method also includes an operation  1703  for splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes an operation  1705  for directing the first portion of the incoming light through a first optical waveguide (e.g., optical waveguide  1411 ) and into a first optical input (e.g.,  809 A) of a two-by-two splitter (e.g.,  809 ). The method also includes an operation  1707  for rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes an operation  1709  for directing the polarization-rotated second portion of the incoming light through a second optical waveguide (e.g., optical waveguide  805 ) and into a second optical input (e.g.,  809 B) of the two-by-two splitter. In some embodiments, the operations  1701  through  1709  are performed by the PSR  821 . 
     The method also includes an operation  1711  for directing some of the first portion of the incoming light through a first optical output (e.g.,  809 C) of the two-by-two optical splitter and into a third optical waveguide (e.g., the optical waveguide  1411 ). The method also includes an operation  1713  for directing some of the first portion of the incoming light through a second optical output (e.g.,  809 D) of the two-by-two optical splitter and into a fourth optical waveguide (e.g., the optical waveguide  1413 ). The method also includes an operation  1715  for directing some of the polarization-rotated second portion of the incoming light through the first optical output (e.g.,  809 C) of the two-by-two optical splitter and into the third optical waveguide (e.g.,  1411 ). The method also includes an operation  1717  for directing some of the polarization-rotated second portion of the incoming light through the second optical output (e.g.,  809 D) of the two-by-two optical splitter and into the fourth optical waveguide (e.g.,  1413 ). 
     The method also includes an operation  1719  for operating a plurality of ring resonator modulator pairs (e.g., ring resonator modulators  1415 - 1  to  1415 - 3  and  1417 - 1  to  1417 - 3 ) positioned along the third optical waveguide (e.g.,  1411 ) and the fourth optical waveguide (e.g.,  1413 ), where each ring resonator modulator pair of the plurality of ring resonator modulator pairs includes one ring resonator modulator positioned within an evanescent optical coupling distance of the third optical waveguide (e.g.,  1411 ) and one ring resonator modulator positioned within an evanescent optical coupling distance of the fourth optical waveguide (e.g.,  1413 ). Each of the plurality of ring resonator modulator pairs is configured to operate at a specified resonant wavelength to modulate a same bit pattern onto light traveling through the third optical waveguide (e.g.,  1411 ) and the fourth optical waveguide (e.g.,  1413 ). The method also includes an operation  1721  for rotating a polarization of modulated light in either the third optical waveguide (e.g.,  1411 ) or the fourth optical waveguide (e.g.,  1413 ) from the first polarization back to the second polarization. The method also includes an operation  1723  for directing both modulated light having the first polarization and modulated light having the second polarization from the third and fourth optical waveguides through a same optical output port (e.g., optical coupler  1421 ). In some embodiments, the operations  1721  through  1723  are performed by the reverse-implemented PSR  1419 . 
       FIG.  18    shows an example configuration of an electro-optic combiner  1800  implemented within a PIC  1801 , in accordance with some embodiments. The electro-optic combiner  1800  includes a PSR  1803  that has an optical input  1803 A optically connected to receive incoming light from an optical coupler  1805 , by way of an optical waveguide  1806 . In some embodiments, the optical input  1803 A of the PSR  1803  is directly optically coupled to the optical coupler  1805 , such that the optical waveguide  1806  is not required. In some embodiments, the optical coupler  1805  is implemented as an edge coupler. However, in other embodiments, the optical coupler  1805  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the PIC  1801  to an optical fiber/waveguide  1807 . Incoming light is transmitted from the optical fiber/waveguide  1807  into the optical coupler  1805 , as indicated by arrow  1808 . The PSR  1803  has a first optical output  1803 B and a second optical output  1803 C. The PSR  1803  is configured to direct a first portion of the incoming light having a first polarization (TE or TM) through the first optical output  1803 B. The PSR  1803  is also configured to rotate a polarization of a second portion of the incoming light from a second polarization (opposite of the first polarization) to the first polarization. In this manner, the PSR  1803  turns the second portion of the incoming light into a polarization-rotated second portion of the incoming light. The PSR  1803  is configured to direct the polarization-rotated second portion of the incoming light through the second optical output  1803 C. Alternatively, in some embodiments, the first portion of the incoming light having a first polarization is transmitted through the second optical output  1803 C, and the polarization-rotated second portion of the incoming light is transmitted through the first optical output  1803 B. 
     The electro-optic combiner  1800  includes a first optical waveguide  1809  optically connected to the first optical output  1803 B of the PSR  1803 . The electro-optic combiner  1800  also includes a second optical waveguide  1811  optically connected to the second optical output  1803 C of the PSR  1803 . The first optical waveguide  1809  and the second optical waveguide  1811  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the first optical waveguide  1809  and the second optical waveguide  1811  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the first optical waveguide  1809  and the second optical waveguide  1811 , respectively, to enable guiding of light within the first optical waveguide  1809  and the second optical waveguide  1811 . In some embodiments, first optical waveguide  1809  and the second optical waveguide  1811  are formed of a same material. In some embodiments, the first portion of the incoming light is transmitted through the first optical output  1803 B of the PSR  1803  and into the first optical waveguide  1809 , and travels along the first optical waveguide  1809 , as indicated by arrow  1810 . Also, the first polarization-rotated second portion of the incoming light is transmitted through the second optical output  1803 C of the PSR  1803  and into the second optical waveguide  1811 , and travels along the second optical waveguide  1811 , as indicated by arrow  1812 . The first optical waveguide  1809  is configured to reverse its direction into a combiner section  1809 A of the first optical waveguide  1809 . In this manner, light travels through the combiner section  1809 A of the first optical waveguide  1809  in a direction, as indicated by arrow  1810 A, that is opposite of the direction (arrow  1812 ) that light travels through the second optical waveguide  1811 . Alternatively, in some embodiments, the first portion of the incoming light is transmitted through the second optical output  1803 C of the PSR  1803  and into the second optical waveguide  1811 , and travels along the second optical waveguide  1811 , as indicated by arrow  1812 . Also, in these alternative embodiments, the polarization-rotated second portion of the incoming light is transmitted through the first optical output  1803 B of the PSR  1803  and into the first optical waveguide  1809 , and travels along the first optical waveguide  1809  as indicated by arrow  1810 , and back through the combiner section  1809 A of the first optical waveguide  1809  as indicated by arrow  1810 A. 
     The electro-optic combiner  1800  also includes a plurality of ring resonators  1813 - 1  to  1813 - 3  disposed between the combiner section  1809 A of the first optical waveguide  1809  and a combiner section  1811 A of the second optical waveguide  1811 . While the example electro-optic combiner  1800  shows three ring resonators  815 - 1  to  815 - 3  for purposes of description, it should be understood that there is no limit on the number of these ring resonators, so long as the ring resonators and associated signal processing circuitry can be spatially and electrically accommodated on the chip. In some embodiments, the ring resonators  1813 - 1  to  1813 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonators  1813 - 1  to  1813 - 3  are implemented as circular discs. The ring resonators  1813 - 1  to  1813 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonators  1813 - 1  to  1813 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonators  1813 - 1  to  1813 - 3  to enable guiding of light within the ring resonators  1813 - 1  to  1813 - 3  and around the circuitous path defined by each of the ring resonators  1813 - 1  to  1813 - 3 . In some embodiments, each of the ring resonators  1813 - 1  to  1813 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonators  1813 - 1  to  1813 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     Each of the plurality of ring resonators  1813 - 1  to  1813 - 3  is positioned within an evanescent optically coupling distance of both the combiner section  1809 A of the first optical waveguide  1809  and the combiner section  1811 A of the second optical waveguide  1811 . A light propagation direction through the combiner section  1809 A of the first optical waveguide  1809  is opposite of a light propagation direction through the combiner section  1811 A of the second optical waveguide  1811 . Each of the plurality of ring resonators  1813 - 1  to  1813 - 3  is configured to operate at a respective resonant wavelength (λ 1  to λ 3 ), such that light having a wavelength substantially equal to the respective resonant wavelength of a given one of the plurality of ring resonators  1813 - 1  to  1813 - 3  optically couples from the combiner section  1811 A of the optical waveguide  1811  into the given one of the plurality of ring resonators  1813 - 1  to  1813 - 3 . The light that is coupled into the ring resonators  1813 - 1  to  1813 - 3  travels around the ring resonators  1813 - 1  to  1813 - 3  in a clockwise direction and couples into the combiner section  1811 A of the second optical waveguide  1811 , as indicated by arrows  1814 . In this manner, the light output from the PSR  1803  into the first optical waveguide  1809  is combined with the light output by the PSR  1803  into the second optical waveguide  1811 . The combined light within the second optical waveguide  1811  after the combiner section  1811 A of the second optical waveguide  1811  (with respect to the light propagations directions  1812  and  1814 ) is output from the electro-optic combiner  1800 . In some embodiments, the combined light is output from the electro-optic combiner  1800  to photodetectors. However, in other embodiments, the combined light is output from the electro-optic combiner  1800  to essentially any type of photonic device, as needed. The ring resonators  1813 - 1  to  1813 - 3  function as passive filters to combine the light signals output by the PSR  1803 . 
     Also, the electro-optic combiner  1800  includes a plurality of phase shifters  1815 - 1  to  1815 - 3  optically coupled to the first optical waveguide  1809 . Each of the plurality of phase shifters  1815 - 1  to  1815 - 3  is positioned before a respective one of the plurality of ring resonators  1813 - 1  to  1813 - 3  with respect to the light propagation direction  1810 A through the combiner section  1809 A of the second optical waveguide  1809 . In this manner, in some embodiments, a number of the plurality of phase shifters  1815 - 1  to  1815 - 3  is equal to a number of the plurality of ring resonators  1813 - 1  to  1813 - 3 . In some embodiments, each of the phase shifters  1815 - 1  to  1815 - 3  is implemented as a thermal tuner (e.g., heating device) positioned over the combiner section  1809 A of the first optical waveguide  1809 , which operates by exploiting the thermo-optic effect of the first optical waveguide  1809  material. In some embodiments, each of the phase shifters  1815 - 1  to  1815 - 3  is implemented as an electro-optic device (e.g., diode) built into the combiner section  1809 A of the first optical waveguide  1809 , which operates by exploiting electro-optic effects within the first optical waveguide  1809 . In some embodiments, each of the phase shifters  1815 - 1  to  1815 - 3  is implemented as a set of ring resonators. Each of the plurality of phase shifters  1815 - 1  to  1815 - 3  is configured to apply a controlled amount of shift to a phase of light traveling through the first optical waveguide  1809 . The phase shifters  1815 - 1  to  1815 - 3  are controlled/operated to ensure proper phase matching between the light signals within the first optical waveguide  1809  and the second optical waveguide  1811 . The phase shifters  1815 - 1  to  1815 - 3  are tuned along with the resonance wavelengths of the ring resonators  1813 - 1  to  1813 - 3  to account for phase and intensity imbalances over time within the first optical waveguide  1809  and the second optical waveguide  1811 . In some embodiments, the electro-optic combiner  1800  does not require a timing-skew management system. 
       FIG.  19    shows a flowchart of a method for combination of optical signals, in accordance with some embodiments. In some embodiments, the method of  FIG.  19    is practiced using the electro-optic combiner  1800  of  FIG.  18   . The method includes an operation  1901  for receiving incoming light through an optical input port (e.g., optical coupler  1805 ) of the photonic circuit (e.g., PIC  1801 ), where a first portion of the incoming light has a first polarization and a second portion of the incoming light has a second polarization. The method also includes an operation  1903  for splitting the first portion of the incoming light from the second portion of the incoming light. The method also includes an operation  1905  for directing the first portion of the incoming light through a first optical waveguide (e.g., optical waveguide  1809 ). The method also includes an operation  1907  for rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method also includes an operation  1909  for directing the polarization-rotated second portion of the incoming light through a second optical waveguide (e.g., optical waveguide  1811 ). In some embodiments, the operations  1903  through  1909  are performed by the PSR  1803 . The method also includes an operation  1911  for operating a plurality of ring resonators (e.g.,  1813 - 1  to  1813 - 3 ) disposed between the first optical waveguide and the second optical waveguide, where each of the plurality of ring resonators is operated to evanescently in-couple light from the first optical waveguide and out-couple light into the second optical waveguide. Each of the plurality of ring resonators is configured to operate at a respective resonant wavelength, such that light having a wavelength substantially equal to the respective resonant wavelength of a given one of the plurality of ring resonators optically couples from the first optical waveguide into the given one of the plurality of ring resonators. The method also includes an operation  1913  for operating a plurality of phase shifters (e.g.,  1815 - 1  to  1815 - 3 ) in optical coupling with the first optical waveguide to apply a controlled amount of shift to a phase of light traveling through the first optical waveguide. Each of the plurality of phase shifters is disposed before a respective one of the plurality of ring resonators with respect to a light propagation direction through the first optical waveguide. In some embodiments, the method includes directing light from an output portion of the second optical waveguide to one or more photodetectors, where the output portion of the second optical waveguide is located after the plurality of ring resonators with respect to the light propagation direction through the second optical waveguide. 
       FIG.  20    shows an example configuration of an electro-optic combiner  2000  implemented within a PIC  2001 , in accordance with some embodiments. The electro-optic combiner  2000  includes a PSR  2003  that has an optical input  2003 A optically connected to receive incoming light from an optical coupler  2005 , by way of an optical waveguide  2006 . In some embodiments, the optical input  2003 A of the PSR  2003  is directly optically coupled to the optical coupler  2005 , such that the optical waveguide  2006  is not required. In some embodiments, the optical coupler  2005  is implemented as an edge coupler. However, in other embodiments, the optical coupler  2005  is implemented as a vertical grating coupler, or as another type of optical coupling device that provides for optical coupling of the PIC  2001  to an optical fiber/waveguide  2007 . Incoming light is transmitted from the optical fiber/waveguide  2007  into the optical coupler  2005 , as indicated by arrow  2008 . The PSR  2003  has a first optical output  2003 B and a second optical output  2003 C. The PSR  2003  is configured to direct a first portion of the incoming light having a first polarization (TE or TM) through the first optical output  2003 B. The PSR  2003  is also configured to rotate a polarization of a second portion of the incoming light from a second polarization (opposite of the first polarization) to the first polarization. In this manner, the PSR  2003  turns the second portion of the incoming light into a polarization-rotated second portion of the incoming light. The PSR  2003  is configured to direct the polarization-rotated second portion of the incoming light through the second optical output  2003 C. Alternatively, in some embodiments, the first portion of the incoming light having a first polarization is transmitted through the second optical output  2003 C, and the polarization-rotated second portion of the incoming light is transmitted through the first optical output  2003 B. 
     The electro-optic combiner  2000  includes a first optical waveguide  2009  optically connected to the first optical output  2003 B of the PSR  2003 . The electro-optic combiner  2000  also includes a second optical waveguide  2011  optically connected to the second optical output  2003 C of the PSR  2003 . The first optical waveguide  2009  and the second optical waveguide  2011  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the first optical waveguide  2009  and the second optical waveguide  2011  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the first optical waveguide  2009  and the second optical waveguide  2011 , respectively, to enable guiding of light within the first optical waveguide  2009  and the second optical waveguide  2011 . In some embodiments, first optical waveguide  2009  and the second optical waveguide  2011  are formed of a same material. In some embodiments, the first portion of the incoming light is transmitted through the first optical output  2003 B of the PSR  2003  and into the first optical waveguide  2009 , and travels along the first optical waveguide  2009 , as indicated by arrow  2010 . Also, the polarization-rotated second portion of the incoming light is transmitted through the second optical output  2003 C of the PSR  2003  and into the second optical waveguide  2011 , and travels along the second optical waveguide  2011 , as indicated by arrow  2012 . Alternatively, in some embodiments, the first portion of the incoming light is transmitted through the second optical output  2003 C of the PSR  2003  and into the second optical waveguide  2011 , and travels along the second optical waveguide  2011 , as indicated by arrow  2012 . Also, in these alternative embodiments, the polarization-rotated second portion of the incoming light is transmitted through the first optical output  2003 B of the PSR  2003  and into the first optical waveguide  2009 , and travels along the first optical waveguide  2009  as indicated by arrow  2010 . 
     The electro-optic combiner  2000  includes a first plurality of ring resonators  2013 - 1  to  2013 - 3  positioned along the first optical waveguide  2010  and within an evanescent optical coupling distance of the first optical waveguide  2010 . The electro-optic combiner  2000  also includes a second plurality of ring resonators  2017 - 1  to  2017 - 3  positioned along the second optical waveguide  2011  and within an evanescent optical coupling distance of the second optical waveguide  2011 . The first plurality of ring resonators  2013 - 1  to  2013 - 3  and the second plurality of ring resonators  2017 - 1  to  2017 - 3  are positioned between the first optical waveguide  2009  and the second optical waveguide  2011 . Each of the second plurality of ring resonators  2017 - 1  to  2017 - 3  is positioned to optically in-couple light from a respective one of the first plurality of ring resonators  2013 - 1  to  2013 - 3 . While the example electro-optic combiner  2000  shows three ring resonators  2013 - 1  to  2013 - 3  and three ring resonators  2017 - 1  to  2017 - 3  for purposes of description, it should be understood that there is no limit on the number of these ring resonators, so long as the ring resonators and associated signal processing circuitry can be spatially and electrically accommodated on the chip. Also, a number of the second plurality of ring resonators  2017 - 1  to  2017 - 3  is equal to a number of the first plurality of ring resonators  2013 - 1  to  2013 - 3 , such that the first plurality of ring resonators  2013 - 1  to  2013 - 3  and the second plurality of ring resonators  2017 - 1  to  2017 - 3  collectively form a plurality of pairs of ring resonators, where each ring resonator within a given pair of ring resonators is operated at a same resonant wavelength. Each pair of ring resonators  2013 - 1 / 2017 - 1  to  2013 - 3 / 2017 - 3  is functions as a double-ring filter. The ring resonance wavelength of the double ring filter can be tuned relative to the channel wavelength to account for the phase and intensity imbalance of the first optical waveguide  2009  and the second optical waveguide  2011  over time. 
     In some embodiments, the ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3  are implemented as annular-shaped waveguides having circuitous configuration, e.g., circular, oval, race-track, or another arbitrary circuitous shape. In some embodiments, the ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3  are implemented as circular discs. The ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3  are formed of a material through which light can be in-coupled, out-coupled, and guided. Each of the ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3  is formed within a surrounding material that has an optical index of refraction sufficiently different from that of the ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3  to enable guiding of light within the ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3  and around the circuitous path defined by each of the ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3 . In some embodiments, each of the ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 50 micrometers. In some embodiments, each of the ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3  is configured to have an annular-shape or disc-shape with an outer diameter of less than about 10 micrometers. 
     The first plurality of ring resonators  2013 - 1  to  2013 - 3  in-couples light from the first optical waveguide  2009  and out-couples light into respective ones of the second plurality of ring resonators  2017 - 1  to  2017 - 3 . The second plurality of ring resonators  2017 - 1  to  2017 - 3  in-couples light from respective ones of the first plurality of ring resonators  2013 - 1  to  2013 - 3  and out-couples light into the second optical waveguide  2011 . In this manner, the first plurality of ring resonators  2013 - 1  to  2013 - 3  and the second plurality of ring resonators  2017 - 1  to  2017 - 3  collectively operate to couple light from the first optical waveguide  2009  to the second optical waveguide  2011 , as indicated by arrows  2014 . A light propagation direction through the first plurality of ring resonators  2013 - 1  to  2013 - 3  is opposite of a light propagation direction through the second plurality of ring resonators  2017 - 1  to  2017 - 3 . In the example electro-optic combiner  2000 , light propagates in a counter-clockwise direction, as indicated by arrows  2016 - 1  to  2016 - 3 , within each of the first plurality of ring resonators  2013 - 1  to  2013 - 3 , and light propagates in a clockwise direction, as indicated by arrows  2018 - 1  to  2018 - 3 , within each of the second plurality of ring resonators  2017 - 1  to  2017 - 3 . 
     Each of the first plurality of ring resonators  2013 - 1  to  2013 - 3  is configured to operate at a respective resonant wavelength (λ 1  to λ 3 ), such that light having a wavelength substantially equal to the respective resonant wavelength of a given one of the first plurality of ring resonators  2013 - 1  to  2013 - 3  optically couples from the first optical waveguide  2009  into the given one of the plurality of ring resonators  2013 - 1  to  2013 - 3 . Each of the second plurality of ring resonators  2017 - 1  to  2017 - 3  is configured to operate at a respective resonant wavelength (λ 1  to λ 3 ), such that light having a wavelength substantially equal to the respective resonant wavelength of a given one of the second plurality of ring resonators  2017 - 1  to  2017 - 3  optically couples from the corresponding one of the first plurality of ring resonators  2013 - 1  to  2013 - 3  into the given one of the second plurality of ring resonators  2017 - 1  to  2017 - 3 . The light that is coupled into the second plurality of ring resonators  2017 - 1  to  2017 - 3  travels around the second plurality of ring resonators  2017 - 1  to  2017 - 3  in a clockwise direction and couples into the second optical waveguide  2011 , as indicated by arrows  2014 . In this manner, the light output from the PSR  2003  into the first optical waveguide  2009  is combined with the light output by the PSR  2003  into the second optical waveguide  2011 . The combined light within the second optical waveguide  2011  after the second plurality of ring resonators  2017 - 1  to  2017 - 3  (with respect to the light propagations directions  2012  and  2014 ) is output from the electro-optic combiner  2000 . In some embodiments, the combined light is output from the electro-optic combiner  2000  to photodetectors. However, in other embodiments, the combined light is output from the electro-optic combiner  2000  to essentially any type of photonic device, as needed. The ring resonators  2013 - 1  to  2013 - 3  and  2017 - 1  to  2017 - 3  function as passive filters to combine the light signals output by the PSR  2003 . 
     In some embodiments, the first optical waveguide  2009  includes a first section  2009 A extending from the first optical output  2003 B of the PSR  2003  to a nearest one ( 2013 - 1 ) of the first plurality of ring resonators  2013 - 1  to  2013 - 3  to the PSR  2003 . Also, the second optical waveguide  2011  includes a first section  2011 A extending from the second optical output  2003 C of the PSR  2003  to a nearest one ( 2017 - 1 ) of the second plurality of ring resonators  2017 - 1  to  2017 - 3  to the PSR  2003 . In these embodiments, either the first section  2009 A of the first optical waveguide  2009  is longer than the first section  2011 A of the second optical waveguide  2011 , or the first section  2011 A of the second optical waveguide  2011  is longer than the first section  2009 A of the first optical waveguide  2009 , in order to compensate for a timing delay between the first portion of the incoming light exiting the PSR  2003  and the polarization-rotated second portion of the incoming light exiting the PSR  2003 , so as to minimize a timing-skew (timing difference) between transmission of the first portion of the incoming light into the first optical waveguide  2009  and transmission of the polarization-rotated second portion of the incoming light into the second optical waveguide  2011 . In the example electro-optic combiner  2000 , the first section  2009 A of the first optical waveguide  2009  includes a delay section  2009 B configured so that the optical path length through the first section  2009 A of the first optical waveguide  2009  is longer than the optical path length through the first section  2011 A of the second optical waveguide  2011 . The delay section  2009 B is configured to compensate for the timing delay between the first portion of the incoming light exiting the PSR  2003  and the polarization-rotated second portion of the incoming light exiting the PSR  2003 . The delay section  2009 B is configured to ensure broadband operation of the electro-optic combiner  2000 . The delay section  2009 B is designed to compensate for the differential group delay between the two polarizations accumulated when propagating through PIC  2001  components such as the optical coupler  2005 , the PSR  2003 , and routing waveguides  2006 ,  2009 ,  2011 . In the absence of the delay section  2009 B, a plurality of independent phase shifters can be optically coupled to the first optical waveguide  2009 , such that one of the plurality of independent phase shifters is positioned before a respective one of the first plurality of ring resonators  2013 - 1  to  2013 - 3  (similar to the phase shifters  1815 - 1  to  1815 - 3  described with regard to  FIG.  18   ). 
     With the delay section  2009 B provided with the first section  2009 A of the first optical waveguide  2009 , the electro-optic combiner  2000  is able to implement a single phase shifter  2019  on either the first optical waveguide  2009  or the second optical waveguide  2011  at a position before the ring resonator pairs  2013 - 1 / 2017 - 1  to  2013 - 3 / 2017 - 3 . In the example electro-optic combiner  2000 , the phase shifter  2019  is implemented on the first optical waveguide  2009  before the first ring resonator  2013 - 1  of the first plurality of ring resonators  2013 - 1  to  2013 - 3 . The phase shifter  2019  is tuned along with the resonance wavelength of each of the ring resonator pairs  2013 - 1 / 2017 - 1  to  2013 - 3 / 2017 - 3 , relative to the wavelength of the channel of the incoming light signal to which the ring resonator pair couples, to ensure low-loss combining of the optical signals into the second optical waveguide  2011  (the output waveguide). In some embodiments, the phase shifter  2019  is implemented as a thermal tuner (e.g., heating device) positioned over the first optical waveguide  2009 , which operates by exploiting the thermo-optic effect of the first optical waveguide  2009  material. In some embodiments, the phase shifter  2019  is implemented as an electro-optic device (e.g., diode) built into the first optical waveguide  2009 , which operates by exploiting electro-optic effects within the first optical waveguide  2009 . In some embodiments, the phase shifter  2019  is implemented as a set of ring resonators. 
       FIG.  21    shows a flowchart of a method for combination of optical signals, in accordance with some embodiments. In some embodiments, the method of  FIG.  21    is practiced using the electro-optic combiner  2000  of  FIG.  20   . The method includes an operation  2101  for receiving incoming light through an optical input port (e.g., optical coupler  2005 ) of the photonic circuit (e.g., PIC  2001 ), where a first portion of the incoming light has a first polarization and a second portion of the incoming light has a second polarization. The method includes an operation  2103  for splitting the first portion of the incoming light from the second portion of the incoming light. The method includes an operation  2105  for directing the first portion of the incoming light through a first optical waveguide (e.g., optical waveguide  2009 ). The method includes an operation  2107  for rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method includes an operation  2109  for directing the polarization-rotated second portion of the incoming light through a second optical waveguide (e.g., optical waveguide  2011 ). In some embodiments, the operations  2103  through  2109  are performed by the PSR  2003 . The method includes an operation  2111  for operating a first plurality of ring resonators (e.g.,  2013 - 1  to  2013 - 3 ) disposed between the first optical waveguide and the second optical waveguide, where each of the first plurality of ring resonators is operated to evanescently in-couple light at a particular channel wavelength from the first optical waveguide. The method includes an operation  2113  for operating a second plurality of ring resonators (e.g.,  2017 - 1  to  2017 - 3 ) disposed between the first optical waveguide and the second optical waveguide, where each of the second plurality of ring resonators is operated to evanescently in-couple light at a particular channel wavelength from a respective one of the first plurality of ring resonators. Each of the second plurality of ring resonators is also operated to evanescently out-couple light to the second optical waveguide. Each optically coupled pair of ring resonators within the first plurality of ring resonators and the second plurality of ring resonators is operated at a substantially same resonant wavelength. Also, each optically coupled pair of ring resonators within the first plurality of ring resonators and the second plurality of ring resonators has an opposite light propagation direction. In some embodiments, the method includes operating a phase shifter (e.g., phase shifter  2019 ) in optical coupling with the first optical waveguide to apply a controlled amount of shift to a phase of light traveling through the first optical waveguide. Also, in some embodiments, the method also includes routing light from a output section of the second optical waveguide to one or more photodetectors, wherein the output section of the second optical waveguide is located after the second plurality of ring resonators with respect to a light propagation direction through the second optical waveguide. 
       FIG.  22    shows an example configuration of an electro-optic combiner  2200  implemented within a PIC  2201 , in accordance with some embodiments. The electro-optic combiner  2200  is a modification of the electro-optic combiner  2000  of  FIG.  20   . Specifically, the electro-optic combiner  2200  includes all of the components of the electro-optic combiner  2000 , and further includes a plurality of intermediate optical waveguides  2203 - 1  to  2203 - 3  respectively disposed between the first plurality of ring resonators  2013 - 1  to  2013 - 3  and the second plurality of ring resonators  2017 - 1  to  2017 - 3 . Each of the plurality of intermediate optical waveguides  2203 - 1  to  2203 - 3  is positioned between a corresponding one of the first plurality of ring resonators  2013 - 1  to  2013 - 3  configured to operate at a specified resonant wavelength and a corresponding one of the second plurality of ring resonators  2017 - 1  to  2017 - 3  configured to operate at the same specified resonant wavelength. Light having the specified resonant wavelength optically couples from the first optical waveguide  2009  to the corresponding one of the first plurality of ring resonators  2013 - 1  to  2013 - 3 , and from the corresponding one of the first plurality of ring resonators  2013 - 1  to  2013 - 3  to the corresponding one of the plurality of intermediate optical waveguide  2203 - 1 , and from the intermediate optical waveguide  2203 - 1  to  2203 - 3  to the corresponding one of the second plurality of ring resonators  2017 - 1  to  2017 - 3 , and from the corresponding one of the second plurality of ring resonators  2017 - 1  to  2017 - 3  to the second optical waveguide  2011 . In some embodiments, each of the plurality of intermediate optical waveguides  2203 - 1  to  2203 - 3  has a substantially linear shape and is oriented to have a substantially same lengthwise direction of extent. In some embodiments, such as shown in  FIG.  22   , the first plurality of ring resonators  2013 - 1  to  2013 - 3  and the second plurality of ring resonators  2017 - 1  to  2017 - 3  are offset with respect to each other in a direction substantially parallel to the lengthwise direction of extent of the plurality of intermediate optical waveguides  2203 - 1  to  2203 - 3 . 
     The electro-optic combiner  2200  also includes a plurality of photodetectors  2205 - 1  to  2205 - 3  respectively optically connected to the plurality of intermediate optical waveguides  2203 - 1  to  2203 - 3 , such that some of the light that optically couples into a given one of the plurality of intermediate optical waveguides  2203 - 1  to  2203 - 3  from the corresponding one of the first plurality of ring resonators  2013 - 1  to  2013 - 3  is conveyed into one of the plurality of photodetectors  2205 - 1  to  2205 - 3  that is optically connected to the given one of the plurality of intermediate optical waveguides  2203 - 1  to  2203 - 3 . In some embodiments, the electro-optic combiner  2200  includes feedback circuitry  2207  configured to control the resonant wavelengths of the first plurality of ring resonators  2013 - 1  to  2013 - 3  and the second plurality of ring resonators  2017 - 1  to  2017 - 3  using electrical signals (photocurrent signals) output from corresponding ones of the plurality of photodetectors  2205 - 1  to  2205 - 3 . Also, in some embodiments, the feedback circuitry  2207  is configured to control the phase shifter  2019  using electrical signals output from the plurality of photodetectors  2205 - 1  to  2205 - 3 . The plurality of intermediate optical waveguides  2203 - 1  to  2203 - 3  advantageously provide for better control over the evanescent optical coupling between the first plurality of ring resonators  2013 - 1  to  2013 - 3  and respective ones of the second plurality of ring resonators  2017 - 1  to  2017 - 3 . The plurality of intermediate optical waveguides  2203 - 1  to  2203 - 3  also advantageously provide a linear optical tap to feed into a feedback control system (feedback circuitry  2207 ) for the first plurality of ring resonators  2013 - 1  to  2013 - 3 , the second plurality of ring resonators  2017 - 1  to  2017 - 3 , and the phase shifter  2019 . In some embodiments, the optimal tuning of the first plurality of ring resonators  2013 - 1  to  2013 - 3  and the second plurality of ring resonators  2017 - 1  to  2017 - 3 , and the optimum phase shift in the first optical waveguide  2009  by the phase shifter  2019  will result in a minimum amount of optical power entering each of the plurality of photodetectors  2205 - 1  to  2205 - 3 , which allows a control system to separately and independently optimize the output transmission for each wavelength channel in the incoming light signal. 
       FIG.  23    shows a flowchart of a method for combination of optical signals, in accordance with some embodiments. In some embodiments, the method of  FIG.  23    is practiced using the electro-optic combiner  2200  of  FIG.  22   . The method includes an operation  2301  for receiving incoming light through an optical input port (e.g., optical coupler  2005 ) of the photonic circuit (e.g., PIC  2001 ), where a first portion of the incoming light has a first polarization and a second portion of the incoming light has a second polarization. The method includes an operation  2303  for splitting the first portion of the incoming light from the second portion of the incoming light. The method includes an operation  2305  for directing the first portion of the incoming light through a first optical waveguide (e.g., optical waveguide  2009 ). The method includes an operation  2307  for rotating the second polarization of the second portion of the incoming light to the first polarization so that the second portion of the incoming light is a polarization-rotated second portion of the incoming light. The method includes an operation  2309  for directing the polarization-rotated second portion of the incoming light through a second optical waveguide (e.g., optical waveguide  2011 ). In some embodiments, the operations  2303  through  2309  are performed by the PSR  2003 . The method includes an operation  2311  for operating a first plurality of ring resonators (e.g.,  2013 - 1  to  2013 - 3 ) disposed between the first optical waveguide and the second optical waveguide, where each of the first plurality of ring resonators is operated to evanescently in-couple light at a particular channel wavelength from the first optical waveguide. 
     The method also includes an operation  2313  for optically coupling light from each of the first plurality of ring resonators into a corresponding one of a plurality of intermediate optical waveguides (e.g., optical waveguides  2203 - 1  to  2203 - 3 ). The method includes an operation  2315  for operating a second plurality of ring resonators (e.g.,  2017 - 1  to  2017 - 3 ) disposed between the first optical waveguide and the second optical waveguide, where each of the second plurality of ring resonators is operated to evanescently in-couple light at a particular channel wavelength from a respective one of the plurality of intermediate optical waveguides. Each of the second plurality of ring resonators is also operated to evanescently out-couple light to the second optical waveguide. Each optically connected pair of ring resonators within the first plurality of ring resonators and the second plurality of ring resonators is operated at a substantially same resonant wavelength. Also, each optically connected pair of ring resonators within the first plurality of ring resonators and the second plurality of ring resonators has an opposite light propagation direction. In some embodiments, the method includes operating a phase shifter (e.g., phase shifter  2019 ) in optical coupling with the first optical waveguide to apply a controlled amount of shift to a phase of light traveling through the first optical waveguide. Also, in some embodiments, the method includes routing light from a output section of the second optical waveguide to one or more photodetectors, wherein the output section of the second optical waveguide is located after the second plurality of ring resonators with respect to a light propagation direction through the second optical waveguide. 
     In some embodiments, the method includes operating a plurality of photodetectors (e.g., photodetectors  2205 - 1  to  2205 - 3 ) to detect an amount light optically coupled into a respective ones of the plurality of intermediate optical waveguides. In some embodiments, the method includes controlling resonant wavelengths of the first plurality of ring resonators and the second plurality of ring resonators in accordance with photocurrents generated by corresponding ones of the plurality of photodetectors to optimize an amount of optical power conveyed from the first optical waveguide to the second optical waveguide by way of the first plurality of ring resonators, the plurality of intermediate waveguides, and the second plurality of ring resonators. In some embodiments, the method includes controlling operation of the phase shifter in accordance with photocurrents generated by the plurality of photodetectors. 
       FIG.  24 A  shows a diagram of an electro-optic receiver that is configured to tolerate polarization-dependent timing-skew, in accordance with some embodiments. The electro-optic receiver accepts photocurrent from a photodetector and performs amplification and linear equalization, as indicated by block  2401 . In some embodiments, the linear equalization is used to cancel added ISI due to polarization skew. Next, the filtered and amplified signal is sampled to extract the data, as indicated by block  2403 . Also, in some embodiments, the filtered and amplified signal undergoes non-linear equalization such as decision feedback equalization (DFE). Simultaneously, the precursor ISI, the postcursor ISI, and the main tap height are measured through a data level slicer (dLev). Also, a clock-data recovery (CDR) samples the filtered data and outputs data to extract the optimal sampling time, as indicated by block  2405 . Information about the ISI is sent to the equalization (EQ) adaptation block to analyze the residual ISI and adjust the filter weights accordingly, as indicated by block  2407 . 
       FIG.  24 B  shows a modification of the electro-optic receiver of  FIG.  24 A , in accordance with some embodiments. In this embodiment, information about the ISI is also sent to a polarization detector, as indicated by block  2409 . Based on the relative strength of the precursor ISI and the postcursor ISI, information about the polarization state is extracted and is then used to adjust the EQ adaptation and CDR to move to an ideal lock position. 
       FIG.  24 C  shows a modification of the electro-optic receiver of  FIG.  24 B , in accordance with some embodiments. In this embodiment, the linear photodetector  400  of  FIG.  4    is implemented to output photocurrents from each of the two polarizations (TE and TM) to separate outputs for measurement by the polarization detector, as indicated by block  2409 . The polarization detector provides a reverse bias to the linear photodetector  400 , and measures the amount of photocurrent flowing through each bias. By comparing the relative photocurrent of each bias, information about the polarization state is extracted. This information is then used to adjust the EQ adaptation and CDR to move to the ideal lock position. 
     In some embodiments, the electro-optic receiver includes equalization and timing recovery circuits to handle the combined effects of polarization-dependent timing-skew, bandwidth limitations, and clock timing jitter. In some embodiments, the electro-optic receiver includes amplifiers for the purpose of conditioning the signal for equalization and clock-data recovery. In some embodiments, the electro-optic receiver includes an adaptive equalization circuit which detects the presence of ISI, and corrects for it with linear filters or non-linear feedback control through DFE. In some embodiments, the amount of ISI is measured during operation by a monitor or dLev. Information about the relative ISI tap weights is used to adapt the equalization circuit to minimize the residual ISI. In some embodiments, the electro-optic receiver includes CDR circuitry which detects the optimal time to sample the incoming signal by extracting timing information from data transitions and adjusting the internal sampling clock accordingly. 
     In some embodiments, the input polarization may not be well controlled, and can vary over time. The presence of a time-varying input polarization results in time-varying ISI conditions. Time-varying input polarization can also dynamically shift the electro-optic receiver&#39;s optimal sampling time by up to the skew between the two polarizations during operation. In some embodiments, without further correction, the CDR and equalization circuitry may encounter conditions where it will not lock to the optimal settings. In some embodiments, the electro-optic receiver contains additional circuitry to detect the relative split in optical power between polarization states during operation. In some embodiments, the spatial distribution of photocurrent generation in the photodetector may be used to measure the polarization state of the input. In some embodiments, a linear photodetector (e.g.,  400 ) may be used where light is input from two different sides, where each side supplies light from one input polarization. In these embodiments, the intensity of light, and as a result the generated carriers, from one polarization decays exponentially across the length of the photodetector according to the photo-absorption coefficient. Due to this, a majority of light from one polarization is absorbed on one half of the photodetector, and a majority of light from the other polarization is absorbed on the other half of the photodetector. In these embodiments, the contacts to the photodetector may be segmented and connected to a plurality of different reverse biasing and receiver circuits. By comparing the relative photocurrent measured between different receivers, the relative power split between different polarizations can be determined. 
     In some embodiments changes to the relative amount of ISI can be used to detect the polarization state of the input. The impact of polarization timing-skew on ISI is minimized when the input polarization directly aligns with one of the linear polarizations of the receive chip. The impact of polarization timing-skew on ISI is maximized when the input polarization splits power evenly between the two linear polarizations of the receive chip. In some embodiments, dLev may be used to measure the magnitude of ISI during operation. Information about changes in the magnitude of ISI, and changes to the ratio of the precursor ISI and the postcursor ISI can be used to infer shifts in the polarization state. Also, in some embodiments, information about the polarization state can be used to dynamically adjust the CDR circuitry to cancel drift in the optimal sampling position. In some embodiments, information about the polarization state can be used to dynamically adjust the equalization circuitry to minimize residual ISI. In some embodiments, information about the polarization state can be used to detect and separate data streams that have been combined using polarization multiplexing. 
     In some embodiments, the optical coupler that couples light from the input optical fiber/waveguide into the PIC is a dual-polarization vertical grating coupler that routes light from different input polarizations directly into two output waveguides on the PIC, possibly with the same waveguide polarization. In some embodiments, the light from the two polarizations of the input optical fiber/waveguide is split into separate directions by a polarization beam splitter, and is coupled into two separate PIC waveguides through two separate vertical grating couplers, or through two separate edge couplers, or through any other coupling scheme. In various embodiments, the polarization beam-splitter is a separate device, or is built into the input optical fiber/waveguide itself by a suitable modification of the input optical fiber/waveguide termination. 
     In some embodiments, the light from the two polarizations are input into the same waveguide of the PIC, with different waveguide polarizations, either through edge-coupling or vertical grating coupling or some other method, and the splitting of the signal into two different waveguides is done by a polarization splitter built into the PIC. In such cases, the output of an integrated polarization splitter provides two output waveguides each carrying one polarization mode, and the polarization modes are different, such that one polarization mode is TE-like and the other polarization mode is TM-like. Hence, in some embodiments, a further integrated polarization rotator converts one of the output modes to match the same polarization state as the other, in a matching waveguide cross-section. In other embodiments, the two outputs of the polarization splitter device contain a combination of two input orthogonal polarization states. For example, the two outputs of the polarization splitter device contain the sum and the difference of the input TM and TE waves. 
     In some embodiments, the PIC is built on a semiconductor chip, such as a silicon or indium phosphide based chip. In some embodiments, the electronics of the electro-optic receiver are co-located with the optical devices on the chip. In some embodiments, the electrical signal from the photodetector is routed off-chip to an external receiver circuit. In some embodiments, the PIC is built out of glass, and the two waveguides in the glass PIC receiving the input optical fiber/waveguide signal are routed to a photodetector on a different chip, either through butt-coupling of two chips, or through a connecting external optical fiber/waveguide. 
     In some embodiments, WDM is used to receive information from different wavelength channels within the input optical fiber/waveguide. In these embodiments, the PIC will have a plurality of photodetectors, with each photodetector detecting a single wavelength channel within a narrow, distinct wavelength range. In some embodiments, all of a plurality of photodetectors are placed near a single bus optical waveguide that connects the two PIC waveguides receiving the split input signal. The photodetectors are designed to couple to the optical signal in the single bus optical waveguide, from either direction, only if the optical signal falls within the specified wavelength range of a given photodetector, which allows multiple photodetectors to operate independently on the single (shared) bus optical waveguide. In some embodiments, the plurality of photodetectors are built into ring resonators, or disk resonators, or other resonant photodetectors with wavelength selectivity control. In some embodiments, the plurality of photodetectors are linear detectors. In some embodiments, passive ring resonators are used as WDM filters, passing each wavelength channel of the incoming optical signal to a single linear photodetector that detects only data from a single wavelength channel. 
     In some embodiments in which the photodetector is a resonant device, such as a ring resonator or a Fabry-Perot resonator, or a non-resonant linear photodetector, a standing wave or partial standing wave will form within the photodetector if it receives light signals from two opposite directions. This standing wave pattern will manifest itself as an array of discrete positions within the photodetector where the optical power is high. In some configurations, the photodetector is built in such a way that the responsivity varies locally within the photodetector cavity. For example, in some embodiments, the photodetector includes a set of interleaved diodes formed by non-uniform dopant profiles throughout the photodetector cavity. In another example, in some embodiments, the photodetector includes a division of the photo-absorptive material into “islands” of discrete areas. In some embodiments, there is a chance that the standing wave will isolate the optical power density into discrete parts of the photodetector that do not have strong responsivity. In some embodiments, to address this issue, the photodetectors are configured so that the average responsivity over the length of the photodetector is not minimized. For example, in some embodiments, the photodetector is configured to have appropriate spacing or placement of the photodetector regions that show high responsivity, so as to spatially align with the peak amplitude locations of the standing wave within the photodetector cavity. 
     In some embodiments, a differential delay to the photodetector via the two PIC waveguides carrying the two components of the polarization state is compensated with an optical circuit. For example, in the electro-optic receiver  300  of  FIG.  3   , optical delay lines are implemented to equalize the waveguide path length for each wavelength channel of the two split signals, thereby reducing the time delay of the signals to the photodetector. In some cases, this eliminates the need for a receiver timing-skew management system. In other cases, the uncertainty in the timing delay still necessitates a receiver timing-skew management system, but the optical delay lines will enable the size of the system (such as the spacing between the detectors) to be much larger, which helps to accommodate the size of the receiver and other circuitry in embodiments where the photodetectors and receiver circuits are co-located on the same chip, and which helps to reduce packaging constraints for embodiments where the receiver circuits are located on a separate chip. 
     In some embodiments, an additional PIC optical skew compensator (OSC) is inserted between the inputs of the two PIC waveguides carrying the two components of the polarization state and the plurality of channel receivers. The OSC is designed to provide a group delay as a function of frequency (wavelength) to match the group delay mismatch imposed by the waveguide length for the wavelength channels. In some embodiments, the OSC provides a linear group delay with frequency, and the channel receivers are arranged along the receiver waveguide in order of monotonically increasing frequency. In some embodiments, two OSC&#39;s are provided, each providing half of the timing-skew delay compensation, with one OSC at each of the two PIC waveguide inputs. In some embodiments, the two OSC&#39;s provide linearly ramped group delay with frequency, with the first OSC having an increasing ramped group delay with frequency, and with the second OSC having a decreasing ramped group delay with frequency. In some embodiments, the OSC includes an all pass filter. In some embodiments, the OSC includes a set of ring (microring) resonator all-pass filters. In some embodiments, the OSC provides minimal insertion loss at all wavelengths corresponding to the WDM channels, and tailored group delays. In some embodiments, the OSC&#39;s slope of group delay ramp with increasing frequency is such that, over a single channel spacing, the group delay difference produced is approximately equal to the group delay difference produced by the difference in physical position of the channel receivers for two adjacent channels. 
     In some embodiments disclosed herein, a channel receiver circuit is provided that is capable of compensating for the two-path differential group delay. Also, in some embodiments disclosed herein, a WDM receiver architecture is provided as a wrap-around loop. Also, in some embodiments disclosed herein, a channel receiver photodiode is provided that avoids issues with arbitrarily distributed input light between two input ports (e.g., interdigitated photodetector with number of junctions different from number of wavelengths around at operating wavelength—to have constant responsivity versus detuning, with no nulls). Also, in some embodiments disclosed herein, a method and a system are provided for combining polarizations into a single mode with a feedback control, including use of an integrated delay line for timing-skew compensation to ensure broadband operation, which is generalized to WDM communication. Also, in some embodiments disclosed herein, a transmitter with modulation of orthogonal polarization components with the same bit pattern is provided. 
     In some embodiments disclosed herein, an electro-optic receiver configuration is provided in which an optical signal having arbitrary polarization is coupled from an input optical fiber/waveguide into a PIC and is detected by one or more optical detectors within the PIC, regardless of the polarization state of the light of the optical signal in the input optical fiber/waveguide. In some embodiments, the electro-optic receiver includes a polarization beam-splitting and rotating device that couples light having uncontrolled polarization from the input optical fiber/waveguide into two separate ends of a same loop-structured optical waveguide within the PIC, such that light from each linear polarization is coupled into a different end of the same loop-structured optical waveguide within the PIC, and such that light having one of the two linear polarizations is rotated to the other polarization before coupling into the loop-structured optical waveguide. In this manner, light propagating through the loop-structured optical waveguide from either the first end or the second end has the same polarization and can be detected by the same photodetector. This eliminates the need to have duplicate photodetector devices for detecting the two polarizations of light, respectively, thereby optimizing chip area usage and reducing cost. 
     Also, in some embodiments, the electro-optic receiver includes a polarization beam-splitting and rotating device that couples light having uncontrolled polarization from the input optical fiber/waveguide into two separate waveguides within the PIC, such that light from each linear polarization within the input optical fiber/waveguide is coupled into a separate waveguide within the PIC. Also, the polarization beam-splitting and rotating device is designed to rotate a polarization of light having one of the two linear polarizations to the other polarization before coupling of the light into the respective waveguide within the PIC. In this manner, light coupled into the two waveguides within the PIC have the same preferred waveguide polarization. The two waveguides within the PIC are routed to the same photodetector device (or set of photodetector devices), which allows any polarization of the input optical signal to be detected in the same photodetector device. This eliminates the need to have duplicate photodetector devices for detecting the two polarizations of light, respectively, thereby optimizing chip area usage and reducing cost. 
     In some embodiments, in the event that the optical signal from the input optical fiber/waveguide contains both polarizations, the light of the optical signal will be coupled into both waveguides of the PIC. Since the two waveguides within the PIC have different lengths to reach a given photodetector device, each polarization component of the optical signal may reach the given photodetector device at different times, so as to have a timing difference (timing-skew). In such cases, the timing-skew management system is implemented in the electro-optic receiver circuitry to enable the electro-optic receiver to faithfully recover the optical signal as received from the input optical fiber/waveguide even with the timing difference. In cases where the timing difference is too large to be handled by the timing-skew management system, an optical delay line is implemented within the PIC to either reduce the timing difference to a low enough level that can be handled by the timing-skew management system, or eliminate the timing difference. 
     It should be appreciated that the electro-optic receiver embodiments disclosed herein are useful in applications where electro-optic receivers detect light from an input optical fiber/waveguide in which the polarization is not controlled. A polarization beam-splitter and rotator, such as the dual-polarization grating coupler among others, is used in some embodiments to transmit incoming light of either polarization into a preferred polarization of the electro-optic receiver PIC. In some embodiments, with the input optical signal split into two separate optical waveguides within the PIC, the light from the two optical waveguides cannot be combined into a single waveguide in a low-loss, broadband way without complex phase control and optical power monitoring systems. To mitigate this issue, various embodiments of the electro-optic receiver disclosed herein provide for non-simultaneous detection of the polarization-split input optical signal by the same detector or set of detectors, thereby reducing cost and complexity of the electro-optic receiver. 
     The foregoing description of the embodiments has been provided for purposes of illustration and description, and is not intended to be exhaustive or limiting. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. In this manner, one or more features from one or more embodiments disclosed herein can be combined with one or more features from one or more other embodiments disclosed herein to form another embodiment that is not explicitly disclosed herein, but rather that is implicitly disclosed herein. This other embodiment may also be varied in many ways. Such embodiment variations are not to be regarded as a departure from the disclosure herein, and all such embodiment variations and modifications are intended to be included within the scope of the disclosure provided herein. 
     Although some method operations may be described in a specific order herein, it should be understood that other housekeeping operations may be performed in between method operations, and/or method operations may be adjusted so that they occur at slightly different times or simultaneously or may be distributed in a system which allows the occurrence of the processing operations at various intervals associated with the processing, as long as the processing of the method operations are performed in a manner that provides for successful implementation of the method. 
     Although the foregoing embodiments have been described in some detail for purposes of clarity of understanding, it will be apparent that certain changes and modifications can be practiced within the scope of the appended claims. Accordingly, the embodiments disclosed herein are to be considered as illustrative and not restrictive, and are therefore not to be limited to just the detail s given herein, but may be modified within the scope and equivalents of the appended claims.