Abstract:
An optical device may include a slab, a first waveguide extending from a first portion of the slab to supply multiple first optical signals to the first portion of the slab, multiple second waveguides coupled to a second portion and to a third portion of the slab. The optical device may include multiple third waveguides provided extending from a fourth portion of the slab to direct a corresponding one of the multiple first optical signals away from the slab, a fourth waveguide extending from the fourth portion of the slab to supply multiple second optical signals to the fourth portion of the slab, and multiple fifth waveguides extending from the first portion of the slab to direct a corresponding one of the multiple second optical signals away from the slab. The optical device may include circuits to receive the first optical signals, the second optical signals, and local oscillator signals.

Description:
BACKGROUND 
     Wavelength division multiplexed (WDM) optical communication systems (referred to as “WDM systems”) are systems in which multiple optical signals, each having a different wavelength, are combined onto a single optical fiber using an optical multiplexer circuit (referred to as a “multiplexer”). Such systems may include a transmitter circuit, such as a transmitter (Tx) photonic integrate circuit (PIC) having a transmitter component to provide a laser associated with each wavelength, a modulator configured to modulate the output of the laser, and a multiplexer to combine each of the modulated outputs (e.g., to form a combined output or WDM signal). 
     The multiplexer may include a first slab, a second slab, and/or one or more waveguides connected to the first slab and the second lab. The first slab may receive multiple inputs (e.g., the modulated outputs from the transmitter component), each having a different wavelength. The first slab may include a propagation region (e.g., a free space) to allow the received inputs to propagate into respective first ends of the waveguides connected to the first slab. Additionally, the waveguides may each have different lengths, such that each waveguide applies a different phase shift to the received inputs. Further, the waveguides may supply the received inputs (e.g., through respective second ends of the waveguides) to the second slab. The received inputs may propagate in the free space, associated with the second slab, in such a way that the second slab supplies a single combined output (e.g., a WDM signal) associated with the received inputs. 
     A PIC is a device that integrates multiple photonic functions on a single integrated device. PICs may be fabricated in a manner similar to electronic integrated circuits but, depending on the type of PIC, may be fabricated using one or more of a variety of types of materials, including silica on silicon, silicon on insulator, and various polymers and semiconductor materials which are used to make semiconductor lasers, such as GaAs, InP and their alloys. 
     A WDM system may also include a receiver circuit having a receiver (Rx) PIC and an optical demultiplexer circuit (referred to as a “demultiplexer”) configured to receive the combined output and demultiplex the combined output into individual optical signals. Additionally, the receiver circuit may include receiver components to convert the optical signals into electrical signals, and output the data carried by those electrical signals. 
     The demultiplexer may include a first slab, a second slab, and one or more waveguides connected to the first slab and the second lab. The first slab may receive an input (e.g., a WDM signal outputted by a multiplexer). The received input may include optical signals, each having a different wavelength. The first slab may include a propagation region (e.g., a free space) to allow multiple optical signals, associated with the received input, to propagate into respective first ends of the waveguides connected to the first slab. Additionally, the waveguides may each have different lengths, such that each waveguide is configured to apply a different phase shift to the multiple optical signals associated with the received input. Further, the waveguides may supply the multiple optical signals (e.g., through respective second ends of the waveguides) to the second slab. The multiple optical signals may propagate through the free space, associated with the second slab, in such a way that the second slab supplies the multiple optical signals associated with the received input. 
     The transmitter (Tx) and receiver (Rx) PICs, in an optical communication system, may support communications over a number of wavelength channels. For example, a pair of Tx/Rx PICs may support ten channels, each spaced by, for example, 200 GHz. The set of channels supported by the Tx and Rx PICs can be referred to as the channel “grid” for the PICs. Channel grids for Tx/Rx PICs may be aligned to standardized frequencies, such as those published by the Telecommunication Standardization Sector (ITU-T). The set of channels supported by the Tx and Rx PICs may be referred to as the ITU frequency grid for the Tx/Rx PICs. 
     SUMMARY 
     According to one example implementation, an optical device may include a substrate, a slab provided on the substrate, and a first waveguide provided on the substrate and extending from a first portion of the slab. The first waveguide may supply multiple first optical signals to the first portion of the slab. 
     The optical device may further include multiple second waveguides. Each of the multiple second waveguides may have a first end and a second end. The first ends of the multiple second waveguides may be optically coupled to a second portion of the slab, and the second ends of the multiple second waveguides may be optically coupled to a third portion of the slab. 
     The optical device may further include multiple third waveguides provided on the substrate and extending from a fourth portion of the slab. Each of the multiple third waveguides may direct a corresponding one of the multiple first optical signals away from the slab. 
     The optical device may further include a fourth waveguide extending from the fourth portion of the slab. The fourth waveguide may supply multiple second optical signals to the fourth portion of the slab. 
     The optical device may further include multiple fifth waveguides extending from the first portion of the slab. Each of the multiple fifth waveguides may direct a corresponding one of the multiple second optical signals away from the slab. 
     The optical device may further include a first optical hybrid circuit to receive one of the multiple first optical signals from one of the multiple third waveguides and a first local oscillator signal. The first optical hybrid circuit may process the one of the multiple first optical signals based on the first local oscillator signal. 
     The optical device may further include a second optical hybrid circuit to receive one of the multiple second optical signals from one of the multiple fifth waveguides and a second local oscillator signal. The second optical hybrid circuit may process the one of the multiple second optical signals based on the second local oscillator signal. 
     According to another example implementation, an optical device may include a substrate, a slab provided on the substrate, and a first waveguide provided on the substrate and extending from a first portion of the slab. The first waveguide may supply multiple first optical signals to the first portion of the slab. 
     The optical device may further include multiple second waveguides. Each of the multiple second waveguides may have a first end and a second end. The first ends of the multiple second waveguides may be optically coupled to a second portion of the slab, and the second ends of the multiple second waveguides may be optically coupled to a third portion of the slab. 
     The optical device may further include multiple third waveguides provided on the substrate and extending from a fourth portion of the slab. Each of the multiple third waveguides may direct a corresponding one of the multiple first optical signals away from the slab. 
     The optical device may further include a fourth waveguide extending from the fourth portion of the slab. The fourth waveguide may supply multiple second optical signals to the fourth portion of the slab. 
     The optical device may further include multiple fifth waveguides extending from the first portion of the slab. Each of the multiple fifth waveguides may direct a corresponding one of the multiple second optical signals away from the slab. 
     The optical device may further include multiple first coherent detector circuits. Each of the multiple first coherent detector circuits may receive a corresponding one of the multiple first optical signals from a respective one of the multiple third waveguides and a first local oscillator signal. Each of the multiple first coherent detector circuits may process the one of the multiple first optical signals based on the first local oscillator signal. 
     The optical device may further include multiple second coherent detector circuits. Each of the multiple second coherent detector circuits may receive a corresponding one of the multiple second optical signals from a respective one of the multiple fifth waveguides and a second local oscillator signal. Each of the multiple second coherent detector circuits may process the one of the multiple second optical signals based on the second local oscillator signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate one or more implementations described herein and, together with the description, explain these implementations. In the drawings: 
         FIG. 1  is a diagram of an example network in which systems and/or methods may be implemented; 
         FIG. 2A  is a diagram illustrating example components of a transmitter module as shown in  FIG. 1 ; 
         FIG. 2B  is a diagram illustrating example components of a receiver module as shown in  FIG. 1 ; 
         FIG. 3  is a diagram illustrating a top view of an example optical multiplexer or optical demultiplexer as shown in  FIG. 1 ; 
         FIG. 4  is a diagram illustrating a front view of a slab for a multiplexer or demultiplexer as shown in  FIG. 3 ; 
         FIG. 5  is a diagram illustrating an isometric view of a slab for the multiplexer or demultiplexer as shown in  FIG. 3 ; 
         FIGS. 6-7  are graphs illustrating transmission characteristics, associated with an optical signal, transmitted via the multiplexer or demultiplexer as shown in  FIG. 3 ; 
         FIG. 8  is a diagram illustrating a front view of a for a multiplexer or demultiplexer as shown in  FIG. 1 ; 
         FIG. 9  is a diagram illustrating an isometric view of a slab for a multiplexer or demultiplexer as shown in  FIG. 8 ; 
         FIGS. 10-11  are diagrams illustrating transmission characteristics associated with an optical signal transmitted via the multiplexer or the demultiplexer as shown in  FIG. 8 ; 
         FIG. 12A  is a diagram illustrating example elements of a transmitter module according to an implementation described herein; 
         FIG. 12B  is a diagram illustrating example elements of a receiver module according to an implementation described herein; 
         FIGS. 13-15  are diagrams illustrating a cross-section of slab for an optical demultiplexer shown in  FIG. 12B ; 
         FIG. 16A  is a diagram illustrating transmitter module according to an implementation described herein; and 
         FIG. 16B  is a diagram illustrating receiver module according to an implementation described herein. 
     
    
    
     DETAILED DESCRIPTION 
     The following detailed description refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements. Also, the following detailed description does not limit the disclosure. 
     Some implementations described herein may provide a WDM system with a polarizer (e.g., a Transverse Electric (TE) polarizer) and/or a Transverse Magnetic (TM) polarizer) provided on one or more slabs, associated with an optical multiplexer or an optical demultiplexer of the WDM system. In some implementations, the polarizer may include a material to absorb components of an optical signal having a particular polarization (e.g., a TE or TM polarization) when the slab receives and/or supplies the optical signal. Providing the polarizer on the slab of the multiplexer or demultiplexer may allow the multiplexer or demultiplexer to process optical signals with components having one polarization type. In some implementations, the construction of the optical multiplexer or optical demultiplexer may be simplified when the optical multiplexer or optical demultiplexer receives components having the same polarization type. Additionally, the optical demultiplexer may output signals with components having one polarization type based on receiving components with one polarization type. In some implementations, it may be desirable to output signals having the same polarization type in order to match the polarization type of a local oscillator, associated with the WDM system, thereby improving the performance of the local oscillator. 
     Further, providing the polarizer on the slab of the multiplexer or demultiplexer may reduce the size of the respective PIC, associated with the multiplexer or demultiplexer, in relation to an implementation in which a polarizer is provided as separate element from the multiplexer or demultiplexer. Additionally, providing the polarizer on the slab of the multiplexer or demultiplexer may provide a polarizer with relatively large dimensions, thereby simplifying the process of aligning an input optical signal with the polarizer in relation to aligning the input optical signal with a polarizer in the form of a separate module. 
     Some implementations described herein may provide a WDM system with a multiplexer or demultiplexer having a single slab functioning as two slabs with one or more waveguides connected to the slab. The slab may include a single propagation region (e.g., a free-space region) having a first propagation section and a section propagation section, such that a portion of the first propagation section and a portion of the second propagation section overlap each other to form a shared propagation section. The first propagation section and the second propagation section may each have a first end and a second end. The multiplexer or demultiplexer may also include one or more waveguides each having a first end and a second end. Respective first ends of the waveguides may connect to the second end of the first propagation section and respective second ends of the waveguides may connect to the second end of the second propagation section. 
     In some implementations, the slab having the shared propagation region may be associated with an optical multiplexer. For example, the first propagation section may receive multiple inputs having different wavelengths, (e.g., modulated outputs from transmitter components of a transmitter module), and the second propagation section may supply a combined output, associated with the received inputs. 
     In some implementations, the first propagation section may include a free space to allow the received inputs to propagate into respective first ends of the waveguides connected to the second end of the first propagation section. The waveguides may each have different lengths, such that each waveguide applies a different phase shift to the received inputs. The waveguides may supply the received inputs (e.g., through respective second ends of the waveguides) to the second propagation section having a free space. The received inputs may propagate in the free space, associated with the second propagation section, in such a way that the second propagation section supplies a single combined output (e.g., a WDM signal) associated with the received inputs. The second propagation section may also receive multiple inputs such that the first propagation section outputs a single combined input associated with the inputs received by the second propagation section. 
     Additionally, or alternatively, the slab having the shared propagation region may be associated with an optical demultiplexer. For example, the first propagation section may receive an input (e.g., a WDM signal outputted by an optical multiplexer, a signal supplied by a polarization beam splitter, a signal supplied by a rotator, and/or some other signal), and the second propagation section may supply multiple outputs (e.g., multiple modulated outputs and/or some other optical signals), associated with the received input. 
     In some implementations, the received input may include optical signals, each having a different wavelength. The first propagation section may include a free space to allow multiple optical signals, associated with the received input, to propagate into respective first ends of the waveguides connected to the first propagation section. The waveguides may each have different lengths, such that each waveguide applies a different phase shift to the multiple optical signals associated with the received input. Further, the waveguides may supply the multiple optical signals (e.g., through respective second ends of the waveguides) to the second propagation section having a free space. The multiple optical signals may propagate through the free space, associated with the second propagation section, in such a way that the second propagation section supplies the multiple optical signals associated with the received input. The second propagation section may also receive a combined input such that the first propagation section outputs multiple optical signals associated with the combined input received by the second propagation section. 
     In some implementations, the slab having the shared propagation region may include a material formed on the slab to function as a TE polarizer and/or a TM polarizer in a manner similar to that described above. For example, the first propagation section may include a material to absorb components of an optical signal having a particular polarization. Additionally, or alternatively, the second propagation section may include a material to absorb components of an optical signal having a particular polarization. 
     In some implementations, providing a multiplexer or demultiplexer with slab having a shared propagation region may reduce the size of the multiplexer or demultiplexer. As a result, additional multiplexers or demultiplexers may be provided in a WDM system to increase data rates and/or processing capacity, associated with the WDM system. 
       FIG. 1  is a diagram of an example network  100  in which systems and/or methods described herein may be implemented. In practice, network  100  may include additional, fewer, or differently arranged components than are shown in  FIG. 1 . 
     As illustrated in  FIG. 1 , network  100  may include transmitter (Tx) module  110  (e.g., a Tx PIC), and/or receiver (Rx) module  120  (e.g., an Rx PIC). In some implementations, transmitter module  110  may be optically connected to receiver module  120  via link  117 . Additionally, link  117  may include one or more optical amplifiers  118  that amplify an optical signal as the optical signal is transmitted over link  117 . 
     Transmitter module  110  may include a number of optical transmitters  112 - 1  through  112 -N (where N≧1), waveguides  113 , and/or optical multiplexer  114 . Each optical transmitter  112  may receive a data channel (TxCh1 through TxChM), modulate the data channel with an optical signal, and transmit the data channel as an optical signal. In one implementation, transmitter module  110  may include 5, 10, 20, 50, 100, or some other number of optical transmitters  112 . Each optical transmitter  112  may be tuned to use an optical carrier of a designated wavelength. It may be desirable that the grid of wavelengths emitted by optical transmitters  112  conform to a known standard, such as a standard published by the Telecommunication Standardization Sector (ITU-T). 
     In some implementations, each of optical transmitters  112  may include a laser, a modulator, a semiconductor optical amplifier (SOA), and/or some other components. The laser, modulator, and SOA may be coupled with a tuning element that can be used to tune the wavelength of the optical signal channel by the laser, modulator, and/or SOA. 
     Waveguides  113  may include an optical link or some other link to transmit modulated outputs (referred to as “signal channels”) of optical transmitters  112 . In some implementations each optical transmitter  112  may include one waveguide  113  or multiple waveguides  113  to transmit signal channels of optical transmitters  112  to optical multiplexer  114 . 
     Optical multiplexer  114  may include an AWG or some other multiplexer device. In some implementations, optical multiplexer  114  may combine multiple signal channels, associated with optical transmitters  112  into a single optical signal  115  (e.g., a WDM signal). In some implementations, a corresponding waveguide may transmit optical signal  115  (e.g., via link  117 ). For example, optical multiplexer  114  may include an input, (e.g., a first slab to receive input signal channels supplied by optical transmitters  112 ) and an output (e.g., a second slab to supply a single WDM signal, such as optical signal  115 , associated with the input signal channels). Optical multiplexer  114  may also include waveguides connected to the input and the output. In some implementations, the first slab and the second slab may each act as an input and an output. For example, the first slab and the second slab may each receive multiple signal channels (e.g., signal channels supplied by optical transmitters  112 ). Additionally, the first slab may supply a single WDM signal (e.g., optical signal  115 ) corresponding to the signal channels received by the second slab. Further, the second slab may supply a single WDM signal (e.g., optical signal  116 ) corresponding to the signal channels received by the first slab. In some implementations, a corresponding waveguide may transmit optical signal  116  (e.g., via link  117 ). 
     As shown in  FIG. 1 , optical multiplexer  114  may receive signal channels outputted by transmit modules  112 , and output optical signal  115  and/or optical signal  116 . Additionally, optical signal  115  and/or optical signal  116  may include one or more optical signals, such that each optical signal includes one or more wavelengths. In some implementations, optical signal  115  may include a first polarization (e.g., a TM polarization), and optical signal  116  may include a second polarization (e.g., a TE polarization). Alternatively, optical signal  115  and optical signal  116  may include the same polarization. 
     While implementations may be described in terms of the TM polarization as the first polarization and the TE polarization as the second polarization, it will be apparent that the first polarization may be the TE polarization and the second polarization may be the TM polarization. 
     As further shown in  FIG. 1 , receiver module  120  may include optical demultiplexer  121 , waveguides  122 , and/or optical receivers  123 - 1  through  123 -N (where N≧1). In some implementations, optical demultiplexer  121  may include an AWG or some other demultiplexer device. Additionally, optical demultiplexer  121  may supply multiple signal channels based on receiving one or more optical signals, such as WDM signals (e.g., optical signal  115  and/or optical  116 ), or components associated with the one or more optical signals. For example, optical demultiplexer  121  may include an input (e.g., a first slab to receive optical signal  115  and/or some other input signal), and an output (e.g., a second slab region to supply multiple signal channels associated with optical signal  115 ). Additionally, optical demultiplexer  121  may include waveguides connected to the first slab and the second slab. In some implementations, the first slab and the second slab may each act as an input and an output. For example, the first slab and the second slab may each receive an optical signal (e.g., a WDM signal supplied by optical multiplexer  114 , an optical signal provided by a rotator, and/or some other optical signal). Additionally, the first slab may supply signal channels corresponding to the optical signal received by the second slab. Further, the second slab my supply signal channels corresponding to the optical signal received by the first slab. As shown in  FIG. 1 , optical demultiplexer  121  may supply signal channels to optical receivers  123  via waveguides  122 . 
     Waveguides  122  may include an optical link or some other link to transmit outputs of optical demultiplexer  121  to optical receivers  123 . In some implementations, each optical receiver  123  may receive outputs via a single waveguide  122  or via multiple waveguides  122 . 
     Optical receivers  123  may each include one or more photodetectors and related devices to receive respective input optical signals outputted by optical demultiplexer  121  and a local oscillator, convert the input optical signals to a photocurrent, and provide voltage outputs corresponding to electrical signals of the input optical signals. Optical receivers  123  may each operate to convert the input optical signal to an electrical signal that represents the transmitted data. 
       FIG. 2A  is a diagram illustrating example components of transmitter module  110  as shown in  FIG. 1 . In practice, transmitter module  110  may include additional, fewer, or differently arranged elements than are shown in  FIG. 2A . 
     As shown in  FIG. 2A , transmitter module  110  may include optical transmitters  112 , waveguides  113 , and optical multiplexer  114 -A. As described above, optical transmitters  112  may include laser  270 , tuner  280 , modulator  290 , and/or SOA  295 . 
     Laser  270  may include a semiconductor laser, such as a distributed feedback (DFB) laser, or some other type of laser. Laser  270  may provide an output optical light beam to modulator  290 . Laser  270  may be an optical source for a corresponding optical transmitter  112 . 
     Tuner  280  may include a tuning device, or a collection of tuning devices. In some implementations, laser  270 , modulator  290 , and/or SOA  295  may be coupled with tuner  280  such that tuner  280  may tune a wavelength of an optical signal channel associated with laser  270 , modulator  290 , or SOA  295 . 
     Modulator  290  may include an optical modulator such as an electro-absorption modulator (EAM), or some other type of modulator. Modulator  290  may control (modulate) the intensity of an input optical light beam (e.g., supplied by laser  270 ), based on an input voltage signal (e.g., signals provided over TxCh1 through TxChM). Modulator  290  may be formed as a waveguide with electrodes for applying an electric field, based on the input voltage signal, in a direction perpendicular to the light beam. Alternatively, modulator  290  may be implemented based on other modulation technologies, such as electro-optic modulation. 
     SOA  295  may include an amplifying device, or a collection of amplifying devices. In some implementations, SOA  295  may include an amplifier that may directly amplify an input optical signal (e.g., a signal supplied by laser  270 ). In some implementations, SOA  295  may be replaced by a variable optical attenuator (VOA), or by an element that combines both an SOA and a VOA. Additionally, or alternatively, SOA  295  may function as an SOA and as a VOA. 
     Waveguides  113  may include individual waveguides associated with individual signal channels outputted by optical transmitters  112 . For example, waveguides  113  may include corresponding waveguides to transmit signal channels  116 - 1 ,  116 - 2 ,  116 - 3  . . .  116 -K (where K≧1) supplied by optical transmitters  112 - 1 ,  112 - 2 ,  112 - 3  . . .  112 -K, respectively. Further, waveguides  113  may include corresponding waveguides to transmit signal channels  115 - 1 ,  115 - 2 ,  115 - 3  . . .  115 -O (where O≧1) supplied by optical transmitters  112 -K+1,  112 -K+2,  112 -K+3 . . .  112 -M). 
     Optical multiplexer  114 -A may include slab  210 , slab  211 , and/or waveguides  220  connected to slabs  210  and  211 . In some implementations, slabs  210  and  211  may each include an input and an output. For example, slab  210  may receive one or more inputs (e.g., signal channels  116 - 1  through  116 -K), and slab  211  may receive one or more inputs (e.g., signal channels  115 - 1  through  115 -O. Waveguides  220  may supply slab  210  with a combined WDM signal (e.g., optical signal  115 ) associated with the inputs of slab  211 . Further, waveguides  220  may supply slab  211  with a combined WDM signal (e.g., optical signal  116 ) associated with the inputs of slab  210 . 
     For example, slabs  210  and  211  may each include a free-space region (e.g., a propagation region). The free-space regions of slabs  210  and  211  may allow the wavelengths, associated with input signals, to propagate freely. Slab  210  may receive signal channels  116 - 1  through  116 -K, thereby allowing the signal channels to propagate in the free-space region of slab  210 . Waveguides  220  may guide individual signal channels associated with the signal channels and supply a combined WDM signal (e.g., optical signal  116 ) to slab  211 . Slab  211  may receive signal channels from optical transmitters  115 - 1  through  115 -O, thereby allowing the received signal channels to propagate in the free-space region of slab  211 . Waveguides  220  may guide individual signal channels associated with the received signal channels and supply a combined WDM signal (e.g., optical signal  115 ) to slab  210 . In some implementations, optical multiplexer  114 -A may supply optical signals  115  and  116  to optical demultiplexer  121 -A (e.g., via link  117 ). 
     In some other implementation, slab  210  and/or slab  211  may include an input, but may not include an output. Alternatively, slab  210  and/or  211  may include an output, but may not include an input. For example, slab  210  may include an input to receive signal channels  116 - 1  through  116 -K. Slab  211  may include an output to supply a combined WDM signal (e.g., optical signal  116 ) associated with the inputs of slab  210 . Alternatively, slab  211  may include an input to receive signal channels  115 - 1  through  115 -O. Slab  210  may include an output to supply a combined WDM signal (e.g., optical signal  115 ) associated with the inputs of slab  211 . 
     In some implementations, slab  210  and/or slab  211  may include material  230  (e.g., to form a polarizer on the respective slab). Material  230  may include a metal, or a metal composite, such gold, titanium, and/or some other material. Material  230  may absorb components of a signal channel, WDM signal, and/or some other optical signal having a particular polarization (e.g., a TE or TM polarization) when the signal channel passes through the respective slab having material  230 . For example, as described above, slabs  210  and  211  may receive signal channels from optical transmitters  112 , and may supply combined optical signals  115  and  116  (e.g., WDM signals). Material  230  may absorb components of the received signal channels having a particular polarization (e.g., a TE or TM polarization). Further, material  230  may absorb components of optical signal  115  and/or optical signal  116  having a particular polarization. 
       FIG. 2B  is a diagram illustrating example components of receiver module  120  as shown in  FIG. 1 . In practice, receiver module  120  may include additional, fewer, or differently arranged elements than are shown in  FIG. 2B . 
     As shown in  FIG. 2B , receiver module  120  may include optical demultiplexer  121 -A, waveguides  122 , local oscillator  235 , and/or optical receivers  123 . Optical demultiplexer  121 -A may include slab  210 , slab  211 , and/or waveguides  220  connected to slabs  210  and  211 . In some implementations, slabs  210  and  211  may each include an input and an output. For example, slab  210  may receive an input (e.g., optical signal  115 ) and slab  211  may receive an input (e.g., optical signal  116 ). Waveguides  220  may supply slab  210  with output signal channels associated with the input of slab  211 . Further, waveguides  220  may supply slab  211  with output signal channels associated with the input of slab  210 . 
     In some other implementation, slab  210  and/or slab  211  may include an input, but may not include an output. Alternatively, slab  210  and/or  211  may include an output, but may not include an input. For example, slab  210  may include an input to receive optical signal  115  (e.g., from optical multiplexer  114 ). Slab  211  may include an output to supply signal channels associated with the input of slab  210 . Alternatively, slab  211  may include an input to receive optical signal  116  (e.g., from optical multiplexer  114 ). Slab  210  may include an output to supply a signal channels associated with the input of slab  211 . 
     While the implementations may be described as optical demultiplexer  121  receiving optical signals  115  and  116  provided by optical multiplexer  114  (e.g., WDM signals), in practice, it will be apparent that optical signals  115  and  116  may correspond to any type of optical signal. For example, optical signals  115  and  116  may refer to optical signals provided by a polarization beam splitter, a rotator, or some other optical device. 
     Slabs  210  and  211  may each include a free-space region (e.g., a propagation region). The free-space regions of slabs  210  and  211  may allow the wavelengths, associated with input signals, to propagate freely. Slab  210  may receive optical signal  115 , thereby allowing wavelengths of optical signal  115  to propagate in the free-space region of slab  210 . Waveguides  220  may guide individual signal channels associated with optical signal  115  and supply the individual signal channels to slab  211 . Slab  211  may receive optical signal  116 , thereby allowing wavelengths of optical signal  116  to propagate in the free-space region of slab  211 . Waveguides  220  may guide individual signal channels, associated with optical signal  116 , and supply the individual signal channels to slab  210 . 
     As shown in  FIG. 2B , slabs  210  and  211  may supply respective signal channels to optical receivers  123 , via waveguides  122 . Waveguides  122  may include individual waveguides associated with individual signal channels outputted by slabs  210  and  211 . For example, waveguides  122  may include corresponding waveguides to transmit signal channels  116 - 1 ,  116 - 2 ,  116 - 3  . . .  116 -L (where L≧1), associated with optical signal  116 , to optical receivers  123 - 1 ,  123 - 2 ,  123 - 3  . . .  123 -L, respectively. Additionally, waveguides  122  may include individual waveguides associated with individual signal channels associated with optical signal  115 . For example, waveguides  122  may include corresponding waveguides to transmit signal channels  115 - 1 ,  115 - 2 ,  115 - 3  . . .  115 -P (where P≧1), associated with optical signal  115 , to optical receivers  123 -L+1,  123 -L+2,  123 -L+3 . . .  123 -N (where N≧1), respectively. 
     In some implementations, slab  210  and/or slab  211  may include material  230  (e.g., to form a polarizer on the respective slab). As described above, material  230  may absorb components of a signal channel, WDM signal, and/or some other optical signal having a particular polarization when the optical signal passes through the respective slab having material  230 . For example, as described above, slabs  210  and  211  may receive optical signals  115  and  116  from optical multiplexer  114 -A, and may supply corresponding signal channels. Material  230  may absorb components of the received WDM signals having a particular polarization (e.g., a TE or TM polarization). Further, material  230  may absorb components of the supplied corresponding signal channels having a particular polarization. 
     Local oscillator  235  may include a laser, a collection of lasers, or some other device. In some implementations, local oscillator  235  may include a laser to provide an optical signal to optical receivers  153 . In some implementations, local oscillator  235  may include a single-sided laser to provide an optical signal to a coupler. In some other implementations, local oscillator  235  may include a double-sided laser to provide optical signals to respective optical receivers  123 . Receiver module  120  may include multiple local oscillators  235 , to provide optical signals to respective optical receivers  123 . 
     Local oscillator  235  may provide a coherent detection system for optical receivers  123 . (e.g., to allow optical receivers  123  to reconstruct a received optical signal having crosstalk or dispersion). For example, local oscillator may provide optical receiver  123 -L with a phase reference signal, such that optical receiver  123 -L may reconstruct a received signal (e.g., signal channel  116 -L supplied by optical demultiplexer  121 -A) that may include linear crosstalk and/or dispersion. 
     As further shown in  FIG. 2B , optical receivers  123  may each include multi-mode interference (MMI) coupler  240 , photodiodes  250 , and transimpedence amplifiers (TIAs)  260 . Additionally, or alternatively, optical receivers  123  may include additional, fewer, or differently arranged components than shown in  FIG. 2B . 
     MMI coupler  240  may include an optical device to receive a signal channel supplied by optical demultiplexer  151  and/or an optical signal from local oscillator  220 . In some implementations, MMI coupler  240  may supply multiple signals associated with the received signal channel and optical signal to photodiodes  250 . 
     Photodiodes  250  may receive optical outputs from MMI coupler  240  and convert the optical outputs to corresponding electrical signals. In some implementations, photodiodes  250  may be arranged in pairs and connected to one another in a balanced configuration. The output of each balanced pair may supply one of a quadrature (Q) or in-phase (I) electrical signal, which is amplified by one of TIAs  260 . 
     TIAs  260  may include an amplifier device, or some other device. In some implementations, TIAs  260  may receive electrical signals from photodiodes  250 . TIAs  260  may amplify quadrature (Q), in-phase (I), and/or some other type of electrical signal. 
       FIG. 3  is a diagram illustrating a top view of an example optical multiplexer  114  or optical demultiplexer  121  as shown in  FIG. 1 . As shown in  FIG. 3 , optical multiplexer  114  or optical demultiplexer  121  may include slabs  210  and  211 . In some implementations, slabs  210  and  211  may be constructed in a substantially rectangular form. In some other implementation, slabs  210  and  211  may be constructed as some other shape (e.g., a square, a triangle, etc.). Slabs  210  and  211  may each include material  230 , as described above (e.g., to provide a polarizer to absorb components having a particular polarization). Further, as shown in  FIG. 3 , slab  210  may receive an optical signal (e.g., optical signal  115 , optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , or some other optical signal). 
       FIG. 4  is a diagram illustrating a front view of slab  210  for optical multiplexer  114  or optical demultiplexer  121  as shown in  FIG. 3 . Slab  210  may include a layer of material  230  provided on the top surface of slab  210  and having a thickness. In some implementations, slab  210  may function as a TE polarizer and may absorb components having a TM polarization. 
     As shown in  FIG. 4 , slab  210  may receive optical signal  115 . Optical signal  115  may include first components having a first polarization (e.g., a TM polarization), and second components having a second polarization (e.g., a TE polarization). 
     As shown in  FIG. 4 , the direction of the electric field of components having the TM polarization may be substantially vertical as optical signal  115  passes through slab  210 . The direction of the electric field of components having the TE polarization may be substantially horizontal as optical signal  115  passes through slab  210 . The components of optical signal  115  having the TM polarization may contact material  230 , thereby causing material  230  to absorb components having the TM polarization. As a result, components having the TM polarization may be absorbed while components having the TE polarization pass through slab  210 . 
     While the example implementation of  FIG. 4  is described in terms of slab  210  receiving optical signal  115 , it will be apparent that the example implementation may apply to slab  210  receiving some other optical signal (e.g., optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , etc.) and may apply to slab  211  receiving an optical signal (e.g., optical signal  115 , optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , etc.). 
       FIG. 5  is a diagram illustrating an isometric view of slab  210  for optical multiplexer  114  or optical demultiplexer  121  as shown in  FIG. 3 . In some implementations, slab  210  may function as a TE polarizer. Slab  210  may include a layer of material  230  having a thickness. In some implementations material  230  may be formed on a top surface of slab  210 . 
     As shown in  FIG. 5 , slab  210  may receive optical signal  115 . In some other implementations, slab  210  may receive some other optical signal (e.g., optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , etc.). Optical signal  115  may include first components having a first polarization (e.g., a TM polarization), and second components having a second polarization (e.g., a TE polarization). 
     As further shown in  FIG. 5 , the direction of the electric field of components having the TM polarization may be substantially vertical as optical signal  115  passes through slab  210 . The direction of the electric field of components having the TE polarization may be substantially horizontal as optical signal  115  passes through slab  210 . The components of optical signal  115  having the TM polarization may contact material  230 , thereby causing material  230  to absorb components having the TM polarization. As a result, components having the TM polarization may be absorbed while components having the TE polarization pass through slab  210 . 
     While the example implementation of  FIG. 5  is described in terms of slab  210  receiving optical signal  115 , it will be apparent that the example implementation may apply to slab  210  receiving some other optical signal (e.g., optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , etc.) and may apply to slab  211  receiving an optical signal (e.g., optical signal  115 , optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , etc.). 
       FIGS. 6-7  are graphs illustrating transmission characteristics, associated with an optical signal, transmitted via optical multiplexer  114  or optical demultiplexer  121  as shown in  FIG. 3 . In some implementations, the graphs in  FIGS. 6-7  may describe transmission characteristics for components associated with slab  210  of optical multiplexer  114  and/or optical demultiplexer  121 , and/or slab  211  of optical multiplexer  114  and/or optical demultiplexer  121 . 
     In  FIG. 6 , assume that a slab (e.g., slab  210  or slab  211 ) receives an optical signal (e.g., signal channel  115 - 1 , optical signal  115 , and/or some other optical signal). Further assume that the slab includes a polarizer (e.g., a TE polarizer) in the form of material  230  provided on the slab. As shown in  FIG. 6 , components having the TE polarization may pass through the slab, as represented by a minimal transmission loss (e.g., in relation to a reference component) of components having the TE polarization. As further shown in  FIG. 6 , components having the TM polarization may be absorbed (e.g., by material  230  as described above), as represented by a substantial transmission loss (e.g., in relation to the reference component) of components having the TM polarization. 
     In  FIG. 7 , assume that a slab (e.g., slab  210  or slab  211 ) receives an optical signal (e.g., signal channel  115 - 1 , optical signal  115 , and/or some other optical signal). In graph  710 , further assume that the slab does not include a TE polarizer. As shown in graph  710 , first components of the optical signal having the TM polarization and second components of the optical signal having the TE polarization may pass through the slab, as represented by a substantial parabolic progression of the transmission of the first components and the second components through the slab. 
     In graph  720 , assume that a slab (e.g., slab  210  or slab  211 ) includes a polarizer (e.g., a TE polarizer) in the form of material  230  provided on the slab. As shown in graph  720 , components having the TE polarization may pass through the slab, as represented by a substantial parabolic progression of transmission of the components through the slab. As further shown in diagram  720 , components having the TM polarization may be absorbed (e.g., by material  230  as described above), as represented by a minimal progression of the transmission of components having the TM polarization. 
       FIG. 8  is a diagram illustrating a front view of a slab for optical multiplexer  114  or optical demultiplexer  121  as shown in  FIG. 3 . In some implementations, slab  210  may function as a TM polarizer and may absorb components having a TE polarization. For example, slab  210  may include a layer of material  230  having a thickness formed on a top surface and/or side surfaces of slab  210  to absorb components having a TE polarization. Slab  210  may also include material  810  having a thickness formed directly beneath material  230  on a top surface of slab  210 . In some implementations, material  810  may include a nitride and/or some other material, to prevent components having the TM polarization from contacting material  230 . 
     As shown in  FIG. 8 , slab  210  may receive optical signal  115 . Optical signal  115  may include first components having a first polarization (e.g., a TM polarization), and second components having a second polarization (e.g., a TE polarization). 
     As further shown in  FIG. 8 , the direction of the electric field of components having the TM polarization may be substantially vertical as optical signal  115  passes through slab  210 . The direction of the electric field of components having the TE polarization may be substantially horizontal as optical signal  115  passes through slab  210 . The components of optical signal  115  having the TE polarization may contact material  230 , thereby causing material  230  to absorb components having the TE polarization. The components of optical signal  115  having the TM polarization may contact material  810 , such that the components having the TM polarization may not contact material  230 . As a result, components having the TE polarization may be absorbed while components having the TM polarization may pass through slab  210 . 
     While the example implementation of  FIG. 8  is described in terms of slab  210  receiving optical signal  115 , it will be apparent that the example implementation may apply to slab  210  receiving some other optical signal (e.g., optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , etc.) and may apply to slab  211  receiving an optical signal (e.g., optical signal  115 , optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , etc.). 
       FIG. 9  is a diagram illustrating an isometric view of a slab  210  for optical multiplexer  114  or optical demultiplexer  121 . In some implementations slab  210  may function as a TM polarizer. Slab  210  may include a layer of material  230  having a thickness formed on a top surface and/or side surfaces of slab  210  to absorb components having a TE polarization. Slab  210  may also include material  810  having a thickness formed directly beneath material  230  on a top surface of slab  210 . 
     As shown in  FIG. 9 , slab  210  may receive optical signal  115 . Optical signal  115  may include first components having a first polarization (e.g., a TM polarization), and second components having a second polarization (e.g., a TE polarization). 
     As further shown in  FIG. 9 , the direction of the electric field of components having the TM polarization may be substantially vertical as optical signal  115  passes through slab  210 . The direction of the electric field of components having the TE polarization may be substantially horizontal as optical signal  115  passes through slab  210 . The components of optical signal  115  having the TE polarization may contact material  230 , thereby causing material  230  to absorb components having the TE polarization. The components of optical signal  115  having the TM polarization may contact material  810 , such that the components having the TM polarization may not contact material  230 . As a result, components having the TE polarization may be absorbed while components having the TM polarization may pass through slab  210 . 
     While the example implementation of  FIG. 9  is described in terms of slab  210  receiving optical signal  115 , it will be apparent that the example implementation may apply to slab  210  receiving some other optical signal (e.g., optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , etc.) and may apply to slab  211  receiving an optical signal (e.g., optical signal  115 , optical signal  116 , signal channel  115 - 1 , signal channel  116 - 1 , etc.). 
       FIGS. 10-11  are graphs illustrating transmission characteristics associated with an optical signal transmitted via the multiplexer or the demultiplexer as shown in  FIG. 8 . In some implementations, the graphs in  FIGS. 10-11  may describe transmission characteristics for components associated with slab  210  of optical multiplexer  114  and/or optical demultiplexer  121 , and/or slab  211  of optical multiplexer  114  and/or optical demultiplexer  121 . 
     In  FIG. 10 , assume that a slab (e.g., slab  210  or slab  211 ) receives an optical signal (e.g., signal channel  115 - 1 , optical signal  115 , and/or some other optical signal). Further assume that the slab includes a polarizer (e.g., a TM polarizer) in the form of material  230  and/or material  810  provided on the slab. As shown in  FIG. 10 , components having the TM polarization may pass through the slab, as represented by a minimal transmission loss (e.g., in relation to a reference component) of components having the TM polarization. As further shown in  FIG. 10 , components having the TE polarization may be absorbed (e.g., by material  230  as described above), as represented by a substantial transmission loss (e.g., in relation to the reference component) of components having the TE polarization. 
     In  FIG. 11 , assume that a slab (e.g., slab  210  or slab  211 ) receives an optical signal (e.g., signal channel  115 - 1 , optical signal  115 , and/or some other optical signal). In graph  1110 , further assume that the slab does not include a TM polarizer. As shown in graph  1110 , first components of the optical signal having the TM polarization and second components of the optical signal having the TE polarization may pass through the slab, as represented by a substantial parabolic progression of the transmission of the first components and the second components through the slab. 
     In graph  1120 , assume that a slab (e.g., slab  210  or slab  211 ) includes a polarizer (e.g., a TM polarizer) in the form of material  230  and material  810  provided on the slab, as described above. As shown in graph  1120 , components having the TM polarization may pass through the slab, as represented by a substantial parabolic progression of transmission of the components through the slab. As further shown in diagram  1120 , components having the TE polarization may be absorbed (e.g., by material  230  as described above), as represented by a minimal progression of the transmission of components having the TE polarization. 
     In some implementations, optical multiplexer  114  and/or optical demultiplexer  121  may include a shared propagation region (e.g., a single slab functioning as slabs  210  and  211 ). In an example implementation, the shared propagation region may include material  230  and/or material  810  (e.g., to form a polarizer on the slab, associated with the shared propagation region). In another example implementation, the shared propagation region may not include material  230  and/or material  810 . 
     In some implementations, providing a multiplexer or demultiplexer with slab having a shared propagation region may reduce the size of the multiplexer or demultiplexer. As a result, additional multiplexers or demultiplexers may be provided in a WDM system to increase data rates and/or processing capacity, associated with the WDM system. 
       FIG. 12A  is a diagram illustrating example elements of transmitter module  110  according to an implementation described herein. In practice, transmit module  110  may include additional, fewer, or differently arranged elements than are shown in  FIG. 12A . 
     Transmitter module  110  may include optical transmitters  112 , waveguides  113 , and/or optical multiplexer  114 -B. In some implementations, elements of transmitter module  110  may correspond to elements of transmitter module  110  as shown in  FIG. 2A . 
     Optical multiplexer  114 -B may include slab  1210  having a single propagation region (e.g., a free-space region). Slab  1210  may have a first propagation section and a section propagation section, such that a portion of the first propagation section and a portion of the second propagation section overlap each other to form a shared propagation section. The first propagation section and the second propagation section may each have a first end and a second end. Waveguides  220  may connect the second end of the first propagation section with the second end of the second propagation section. 
     In some implementations, and as shown in  FIG. 12A , the first propagation section may receive multiple inputs (e.g., signal channels via waveguides  116 - 1 ,  116 - 2 ,  116 - 3  . . .  116 -K from optical transmitters  112 ), with each input having a different wavelength. The first propagation section may include a free space to allow the received inputs to propagate into respective first ends of waveguides  220  connected to the first propagation section. Additionally, waveguides  220  may each have different lengths, such that each waveguide  220  applies a different phase shift to the received inputs. Further, waveguides  220  may supply the received inputs to the second propagation section having a free space. The received inputs may propagate in the free space, associated with the second propagation section, in such a way that the second propagation section supplies a single combined output (e.g., optical signal  116 ) associated with the received inputs. The second propagation section may also receive multiple inputs (e.g. signal channels via waveguides  115 - 1 ,  115 - 2 ,  115 - 3  . . .  115 -M) such that the first propagation section outputs a single combined output (e.g., optical signal  115 ) associated with the inputs received by the second propagation section. 
       FIG. 12B  is a diagram illustrating example elements of receiver module  120  according to an implementation described herein. In practice, receiver module  120  may include additional, fewer, or differently arranged elements than are shown in  FIG. 12B . In some implementations, elements of receiver module  120  may correspond to elements of receiver module  120  as shown in  FIG. 2B . 
     As shown in  FIG. 12B , receiver module  120  may include optical demultiplexer  121 -B, waveguides  122 , optical receivers  123 , rotator  1220  local oscillator  1225 , and/or coupler  1230 . 
     Rotator  1220  may include an optical device or a collection of optical devices. In some implementations, rotator  1220  may receive optical signal  115  with components having a first polarization (e.g., a TM polarization). Rotator  1220  may rotate the polarization, associated with components of optical signal  115 , and supply optical signal  115  such that optical signal  115  has components having a second polarization (e.g., a TE polarization). Rotator  1220  may supply optical signal  115  (e.g., an optical signal with components having the second polarization) to optical demultiplexer  121 -B. In some implementations, rotator  1220  may supply optical signal  115  having components of the same polarization as optical signal  116 . As a result, optical demultiplexer  121 -B may receive optical signals with components having one polarization (i.e., the second polarization). 
     In some implementations, rotator  1220  may be capable of receiving multiple optical signals  115 , rotating the first components associated with the multiple optical signals  115  and supplying multiple optical signals  115  having the second polarization. 
     Optical demultiplexer  121 -B may include one or more waveguides  220  similar to those as described above with respect to optical demultiplexer  121 -B. In some implementations, it may be desirable to reduce the number of waveguides  220  (e.g., to reduce the size of optical demultiplexer  121 -B). In some implementations, reducing the number of waveguides  220  may cause waveguides  220  to create linear crosstalk between output signals (e.g., signal channels supplied by optical demultiplexer  121 -B). 
     Optical demultiplexer  121 -B may include slab  1210  and waveguides  220  connected to slab  1210  in an arrangement as described above. In some implementations, and as shown in  FIG. 12B , the first propagation section of slab  1210  may receive an input (e.g., optical signal  115  supplied by rotator  1220 ) with components having a different wavelength. The first propagation section may include a free space to allow components of optical signal  115  to propagate into respective first ends of waveguides  220  connected to the first propagation section. Additionally, waveguides  220  may each have different lengths, such that each waveguide applies a different phase shift to components of optical signal  115 . Further, waveguides  220  may supply components of optical signal  115  to the second propagation section of slab  1210 . The components of optical signal  115  may propagate in the free space, associated with the second propagation section, in such a way that the second propagation section supplies multiple signal channels (e.g., signal channels corresponding to waveguides  115 - 1 ,  115 - 2 ,  115 - 3  . . .  115 -S), associated with the received inputs. The second propagation section may also receive an optical signal (e.g. optical signal  116 ) such that the first propagation section supplies multiple signal channels (e.g. via waveguides  116 - 1 ,  116 - 2 ,  116 - 3  . . .  116 -M) associated with optical signal  116  received by the first propagation section. 
     Local oscillator  1225  may include a laser, a collection of lasers, or some other device. In some implementations, local oscillator  1225  may include a laser to provide an optical signal (e.g., optical signal  1231  and/or optical signal  1232 ) to respective optical receivers  123 . In some implementations, local oscillator  1225  may include a single-sided laser to provide an optical signal to coupler  1230 . In some other implementations, local oscillator  1225  may include a double-sided laser to provide optical signals  1231  and  1232 . Each one of optical signals  1231  and  1232  may be received by respective optical receivers  123 . Receiver module  120  may include multiple local oscillators  1225 , to provide optical signals to respective optical receivers  123 . 
     Coupler  1230  may include a power splitter, a power coupler, a collection of power splitters or power couplers, or some other type of device. In some implementations, coupler  1230  may receive an optical signal from local oscillator  1225 . Coupler  1230  may supply multiple optical signals (e.g., optical signal  1231  and/or optical signal  1232 ), associated with the input optical signal supplied by local oscillator  1225 . 
     Local oscillator  1225  and/or coupler  1230  may provide a coherent detection system for optical receivers  123  (e.g., to allow optical receivers  123  to reconstruct a received optical signal having crosstalk or dispersion). For example, optical signal  1231  may provide optical receiver  123 -M with a phase reference signal, such that optical receiver  123 -M may reconstruct a received signal (e.g., signal channel  116 -M supplied by optical demultiplexer  121 -B) that may include linear crosstalk and/or dispersion. 
     Optical receivers  123  may include elements similar to those described above with respect to  FIG. 2B . Optical receivers  123  may additionally include analog-to-digital (A/D) converters  1240 . In some implementations, A/D converters  1240  may include a signal converting device, some other device, or a collection of devices. A/D converters  1240  may receive amplified electrical signals from TIAs  260 , and convert the received electrical signals into digital signals. A/D converters  1240  may include a digital signal processor (DSP) device to process the converted digital signals and to reconstruct an optical signal received by a respective optical receiver  123  (e.g., signal channel  116 -M). 
     Optical receivers  123  may each include an optical hybrid circuitry, a coherent detection circuitry, or some other circuitry, to allow optical receivers  123  to reconstruct received optical signals having linear crosstalk and/or dispersion. For example, assume that optical receiver  123 -M receives an optical signal (e.g., signal channel  116 -M). Further assume that signal channel  116 -M includes linear crosstalk and/or dispersion. MMI coupler  240  may receive optical signal  116 -M and a local oscillator signal (e.g., optical signal  1231 ) corresponding to a reference optical signal. MMI coupler  240  may supply multiple signals associated with the received optical signals (i.e., optical signal  116 -M and optical signal  1231 ) to photodiodes  250 . Photodiodes  250  may receive optical outputs from MMI coupler  240  and convert the optical outputs to corresponding electrical signals. TIAs  260  may amplify the electrical signals outputted by photodiodes  250 , and output the amplified electrical signals to A/D converters  1230 . A/D converters  1230  may supply and process digital signals, associated with the amplified electrical signals, and may reconstruct signal channel  116 -M, based on processing the digital signals, associated with signal channel  116 -M (i.e., a signal channel with crosstalk and/or dispersion), and with the reference signal (e.g., optical signal  1231 ). 
       FIGS. 13-15  are diagrams illustrating a cross-section of slab  1210  for optical demultiplexer  121 -B as shown in  FIG. 12B . While  FIGS. 13-15  are described in terms of slab  1210  being associated with optical demultiplexer  121  to receive optical signals  115  and  116  and supply signal channels associated with optical signal  115  and  116 , in practice, it will be apparent that slab  1210  may be associated with optical multiplexer  114  to receive signal channels (e.g., signal channels associated with waveguides  115 - 1 ,  115 - 2 ,  115 - 3 , etc.) and combined optical signals associated with the received signal channels. While a particular shape of slab  1210  is shown in  FIGS. 13-15 , in practice slab  1210  may have some other shape. 
     As shown in  FIG. 13 , slab  1210  may receive optical signal  115  via a first end of a first propagation section of slab  1210 . Optical signal  115  may propagate through the first propagation section such that individual signal channels, associated with optical signal  115 , may be received by respective first ends of waveguides  220  connected to a second end of the first propagation section. Additionally, slab  1210  may receive optical signal  116  via a first end of a second propagation section of slab  1210 . Optical signal  116  may propagate through the second propagation section such that individual signal channels, associated with optical signal  116 , may be received by respective second ends of waveguides  220  connected to a second end of the second propagation section. 
     As shown in  FIG. 14 , waveguides  220  may supply respective signal channels, associated with optical signal  115 , to the first end of the second propagation section. For clarity, one signal channel is shown (i.e., signal channel  115 -Q, where Q≧1). As described above, waveguides  220  may supply multiple signal channels associated with optical signal  116 . Waveguides  220  may also supply respective signal channels associated with optical signal  116 , to the first end of the first propagation section. For clarity, one signal channel is shown (i.e., signal channel  116 -R, where R≧1). As described above, waveguides  220  may supply multiple signal channels associated with optical signal  116 . 
     As shown in  FIG. 15 , slab  1210  may include a shared propagation region having a first propagation section  1505  and a second propagation section  1510 . In some implementations, the shared propagation region of slab  1210  may be substantially X-shaped, V-shaped, or some other shape. First propagation section  1505  may include first end  1515 , second end  1520 , and shared propagation section  1540 . Second propagation section  1510  may include first end  1525 , second end  1530 , and shared propagation section  1540 . First propagation section  1505  and second propagation section  1510  may overlap to form shared propagation section  1540  including a portion of first propagation section  1505  and a portion of second propagation section  1510 . Respective first ends of waveguides  220  may be connected to second end  1520  and respective second ends of waveguides  220  may be connected to second end  1530 . 
     In some implementations, first end  1515  may include inputs  1550 - 1  through  1550 -Z (where Z≧1) to receive respective optical signals (e.g., optical signal  115 , signal channel  115 - 1 , and/or some other optical signal). First end  1515  may also include outputs  1551 - 1  to  1551 -V (where V≧1) to supply respective outputs associated with inputs of first end  1525  (e.g., optical signal  116 , signal channel  116 - 1 , and/or some other optical signal). 
     In some implementations, first end  1525  may include inputs  1560 - 1  through  1560 -X (where X≧1) to receive respective optical signals (e.g., optical signal  116 , signal channel  116 - 1 , and/or some other optical signal). First end  1525  may also include outputs  1561 - 1  through  1561 -Y (where Y≧1) to supply respective outputs associated with inputs of first end  1515  (e.g., optical signal  115 , signal channel  115 - 1 , and/or some other optical signal). 
       FIG. 16A  is a diagram illustrating transmitter module  110  according to an implementation described herein. Transmitter module  110 , as shown in  FIG. 16A , may include similar elements as described above with respect to transmitter module  110  as shown in FIG.  12 A. As shown in  FIG. 16A , transmitter module  110  may include optical multiplexer  114 -C which may have similar elements as described above with respect to optical multiplexer  114 -B. Additionally, optical multiplexer  114 -C may include material  230  and/or material  810  formed on slab  1210  (e.g., to form a TE polarizer or TM polarizer on slab  1210 ). For example, optical multiplexer  114 -C may include material  230  and/or material  810  formed on slab  1210  in a similar manner as described above with respect to  FIG. 4  and  FIG. 8 . 
       FIG. 16B  is a diagram illustrating receiver module  120  according to an implementation described herein. Receiver module  120 , as shown in  FIG. 16B , may include similar elements as described above with respect to receiver module  120  as shown in  FIG. 12B . As shown in  FIG. 16B , receiver module  120  may include optical demultiplexer  121 -C which may have similar elements as described above with respect to optical demultiplexer  121 -B. Additionally, optical demultiplexer  121 -C may include material  230  and/or material  810  formed on slab  1210  (e.g., to form a TE polarizer or TM polarizer on slab  1210 ). For example, optical demultiplexer  121 -C may include material  230  and/or material  810  formed on slab  1210  in a similar manner as described above with respect to  FIG. 4  and  FIG. 8 . 
     The foregoing description provides illustration and description, but is not intended to be exhaustive or to limit the possible implementations to the precise form disclosed. Modifications and variations are possible in light of the above disclosure or may be acquired from practice of the implementations. 
     Even though particular combinations of features are recited in the claims and/or disclosed in the specification, these combinations are not intended to limit the disclosure of the possible implementations. In fact, many of these features may be combined in ways not specifically recited in the claims and/or disclosed in the specification. Although each dependent claim listed below may directly depend on only one other claim, the disclosure of the possible implementations includes each dependent claim in combination with every other claim in the claim set. 
     No element, act, or instruction used in the present application should be construed as critical or essential unless explicitly described as such. Also, as used herein, the article “a” is intended to include one or more items and may be used interchangeably with “one or more.” Where only one item is intended, the term “one” or similar language is used. Further, the phrase “based on” is intended to mean “based, at least in part, on” unless explicitly stated otherwise.