Abstract: In an optical transfer system, an optical transmission unit generates an optical signal in which respective polarization components are alternately present on a time axis, a time period during which the respective polarization components are simultaneously present on the time axis is substantially zero, and a symbol repetition cycle of optical signals of the respective polarization components becomes Ts, an optical reception unit causes an interference between local oscillation light and a received optical signal and converts an interfered optical signal to an electric signal, and a received electric-signal processing unit performs analog-digital conversion of an electric signal, elimination of a delay difference of Ts/2 between the respective polarized signal components, and adaptive equalization of a distortion other than the delay difference.

Abstract: A method and apparatus for suppressing pump-mode optical beat interference noise in a Raman amplified fiber link of an optical network, wherein a wavelength of a laser beam generated by a first pump laser and a wavelength of a laser beam generated by a second pump laser of a pair of polarization multiplexed pump lasers are detuned with respect to each other to suppress the optical beat interference, OBI, noise in the Raman amplified fiber link of said optical network.

Abstract: A system, e.g. for optical communication, includes an I-Q modulator and a transmission signal processor. The I-Q modulator is configured to modulate a first light source in response to first I and Q modulation signals. The transmission signal processor is configured to receive a data stream including data corresponding to a first data subchannel. The processor maps the data subchannel to an optical transmission subchannel and outputs the first I and Q modulation signals. The I and Q modulation signals modulate the light source to produce an optical transmission signal that includes wavelength components corresponding to the optical transmission subchannel.

Abstract: An optical receiving apparatus includes a variable dispersion compensation unit, a delay interference unit, a photoelectric converter, a polarization control unit for control the polarization state of an optical signal inputted to the photoelectric converter, a received data processing unit for monitoring the number of error occurrences, and a control unit for controlling the dispersion compensation amount at the variable dispersion compensation unit and the optical phase control amount at the delay interference unit, based on information on the number of error occurrences from the received data processing unit.

Abstract: An apparatus receives data encoded in a format where information bits for transmission are mapped into symbols each carrying a plurality of bits, some of which are encoded through a frequency-shift keyed (FSK) format and the rest of which are encoded through an additional modulation format on at least one FSK carrier. The receiver detects the signal through a dual-polarization coherent receiver front-end, and recovers polarization components of the signal by decoding a first non-zero portion of a plurality of bits carried by a symbol based on frequency slot position of at least one FSK carrier in the polarization components and a second non-zero portion of the plurality of bits carried by the symbol based on the additional modulation carried by at least one FSK carrier in the polarization components. Pilot-assisted orthogonal frequency-division de-multiplexing (PA-OFDM) may be used for spectrally-efficient signal reception, even in the presence of severe FSK errors.

Abstract: The invention relates to an apparatus and a method for modulation of an optical signal with a data signal, said apparatus (6) comprising a configurable digital encoding unit (8) encoding data of said data signal to provide an encoded modulation control signal (EMCS), and a signal modulation unit (9) modulating said optical signal with respect to its signal phase and/or signal amplitude in orthogonal polarization directions in response to said encoded modulation control signal (EMCS) to generate a multi-dimensional optical signal vector.

Abstract: An apparatus comprises a coherent optical transmitter. The coherent optical transmitter comprises a first modulator for generating a first polarization, a second modulator for generating a second polarization, and a symbol interleaver configured to receive a first symbol stream intended to be transmitted on a first polarization and a second symbol stream intended to be transmitted on a second polarization, to direct one portion of symbols of the first symbol stream to the first modulator for modulation onto the first polarization and another portion of the symbols of the first symbol stream to the second modulator for modulation onto the second polarization, and to direct one portion of symbols of the second symbol stream to the first modulator for modulation onto the first polarization and another portion of the symbols of the second symbol stream to the second modulator for modulation onto the second polarization.

Abstract: A system is configured to receive a block of symbols, associated with a phase-modulated signal that includes data symbols that correspond to a payload associated with the signal, and control symbols; process the control symbols to identify an amount of phase noise associated with the control symbols; reset a phase, associated with each of the data symbols, based on the amount of phase noise and a reference phase; interleave the respective data samples, of each of the data symbols with other data samples, where the interleaved respective data samples cause errors, associated with the respective data samples, to be spread out among the other data samples and reduces an error rate relative to a prior data rate that existed before the interleaving; and perform forward error correction on the interleaved respective data samples.

Abstract: A compensator device may include a selection switch to receive a first optical signal and provide first and second groups of channels associated with the first optical signal; a polarization beam splitter to receive the first channels, and provide first and second components; a photodiode that provides an electrical signal indicative of an intensity of the first group of channels; a first modulator to receive the electrical signal and the first components and to modulate the first components to form first modulated channels; a second modulator to receive the electrical signal and the second components to modulate the second components to form second modulated channels; a polarization beam combiner to receive the first and second modulated channels to form combined modulated channels; and a coupler to receive the combined modulated channels and the second group of channels to form a second optical signal.

Abstract: Method, transmitter, receiver, and system for communicating information carried by a polarization divided optical signal in an optical fiber, comprising: producing and transmitting a polarization divided optical signal OTApol comprising optical sideband pairs SBLA, SBHA each having one sideband SBLA at a first polarization and an other sideband SBHA at a second polarization that is orthogonal to the first polarization, the one sideband and the other sideband carry the same set of information A; and receiving and detecting the polarization divided optical signal OTApol to produce an electrical signal RFApol corresponding to the polarization divided optical signal; down converting the electrical signal to produce, for each sideband pair, a first converted signal BBLA corresponding to the one sideband SBLA and a second converted signal BBHA corresponding to the other sideband SBHA; and extracting the set of information A for each sideband pair using a polarization diversity scheme.

Abstract: A high data rate optical signal is inverse multiplexed into a multitude of lower-rate tributaries, each of which is coded by its unique OCDM code, and the combined coded tributaries are injected into a common phase scrambler. Coherent summation of these optically encoded tributaries pass through a shared phase or phase and frequency scrambler before exiting the secure location. The setting of the scrambler acts as the key. The authorized recipient with the correct key retrieves the ones and zeros of the several decoded signals.

Abstract: There is a need to prevent two receivers from converging on a state of receiving the same polarization state, fast start receivers, and ensure highly reliable operations. A polarization-multiplexed transmitter previously applies frequency shifts of frequencies +?f and ??f to X-polarization and Y-polarization digital information signals to be transmitted. Optical field modulators modulate and polarization-multiplex the signals. As a result, a frequency difference of 2?f is supplied to X-polarization and Y-polarization components. A polarization diversity coherent optical receiver 215 receives the signal. A frequency estimation portion in a digital signal processing circuit detects a frequency difference signal in both polarization components. This signal is used to a polarization splitting circuit in the digital signal processing circuit.

Abstract: An optical transmission system includes a polarization multiplexing optical transmitter for transmitting an optical signal, where an X-polarized signal and a Y-polarized signal each having a having predetermined frame structure are polarization-multiplexed, to an optical fiber transmission path, and a polarization multiplexing receiver for receiving the optical signal that has propagated through the optical transmission path. The polarization multiplexing optical transmitter delays a frame assignment signal (FAS) in the Y-polarized signal, by a predetermined delay time ?, relative to FAS in the X-polarized signal.

Abstract: A method of tap coefficient correction includes: obtaining a synchronization symbol difference between a first polarization and a second polarization orthogonal to the first polarization; obtaining a delay amount of each of the first polarization and the second polarization in an adaptive equalizer; calculating, in a case where a horizontal axis represents a tap number and a vertical axis represents a tap coefficient and a tap number or a nearest tap number with which an area of a drawn figure is halved is set as a gravity center of tap coefficients, a correction reference gravity center of the tap coefficients set in the adaptive equalizer, based on the synchronization symbol difference and the delay amount; and performing a correction of shifting an entire tap coefficients in units of symbol to cause the correction reference gravity center to be closest to a tap center.

Abstract: In a coherent optical receiver receiving a polarization multiplexed optical signal through an optical communications network, a method of compensating noise due to polarization dependent loss (PDL). A Least Mean Squares (LMS) compensation block processes sample streams of the received optical signal to generate symbol estimates of symbols modulated onto each transmitted polarization of the optical signal. A decorrelation block de-correlates noise in the respective symbol estimates of each transmitted polarization and generating a set of decorrelated coordinate signals. A maximum likelihood estimator soft decodes the de-correlated coordinate signals generated by the decorrelation block.

Abstract: A modulation unit for a quantum communication system, wherein said modulation unit comprises an optical component configured to cause a delay between photons with different polarisation modes and a phase modulator, the optical component comprising a birefringent optical material, wherein the birefringent optical material supports the transmission of photons with a first polarisation mode and a second polarisation mode, wherein the optical path length for photons propagating with the first polarisation mode is different to the optical path length of photons propagating with the second polarisation mode, photons with the first polarisation mode having an orthogonal polarisation to those with the second polarisation mode, the phase modulator being configured to apply a further phase difference between photons with the first and second polarisation mode which pass through said modulation unit.

Abstract: A polarization controller includes a first polarization controller, a demultiplexer, a second polarization controller, and a multiplexer. The first polarization controller controls the state of polarization of input light such that a part of the wavelength components of the input light is in a first state of polarization. The demultiplexer demultiplexes the light output from the first polarization controller into a plurality of wavelength components. The second polarization controller controls the plurality of wavelength components in a second state of polarization by using liquid crystal modulation devices. The multiplexer multiplexes the plurality of wavelength components output from the second polarization controller.

Abstract: Techniques, devices and applications are provided for monitoring a polarization mode dispersion (PMD) effect in an optical signal.

Abstract: A handheld device includes: a transmitter or receiver of a signal beam for quantum key distribution; and a source of alignment beams that diverge from each other in a pattern that matches sensors on a station containing a receiver or transmitter for the quantum key distribution. The alignment beams from the handheld device are of sufficient intensity to produce on the station visible spots that facilitate manual alignment of the handheld device. The station can measure a position and a direction of respective alignment beams and dynamically steer the signal beam according to the measurements.

Abstract: The first photon in single-photon state is divided into two components by the half beam splitter, and the first component is sent to the sender while the second component is sent to the receiver. The sender measures the first component of the first photon when he sends “1”. The sender doesn't measure the first component of the first photon when he sends “0”. The receiver makes the second component of the first photon enter into the Sagnac interferometer, and the receiver also makes the reference light enter into the Sagnac interferometer at the same time. The receiver makes the second component of the first photon interact with the reference light in the nonlinear optical medium arranged in the Sagnac interferometer. The receiver knows the signal from the phase modulation of the reference light caused by the interaction with the second component of the first photon.

Abstract: An optical signal transmission system comprises a transmitter that phase-modulates two optical signals of a same frequency by asymmetrically chirping the two optical signals, combines the two optical signals that have been phase-modulated as polarization components according to polarization multiplexing, and transmits an optical signal that has been combined and obtained; and a receiver that receives said optical signal from said transmitter, compresses pulses of at least one of the polarization components of the optical signal, and splits the optical signal into two polarization components.

Abstract: Systems and methods are disclosed to perform four-dimensional optical multiband OFDM communication by organizing an N-dimensional (ND) signal constellation points as a signal matrix; performing 2D-inverse FFT and 2D-FFT to perform modulation and demodulation, respectively; and applying both orthogonal polarizations in the OFDM communication to deal with chromatic dispersion, PMD and PDL effects, and multidimensional signal constellation to improve optical signal-to-noise ratio (OSNR) sensitivity.

Abstract: An optical system may have an optical transmitter including a digital signal processor to receive a signal channel, add data corresponding to a pilot tone, generate a digital signal associated with the signal channel and including the pilot tone, and output the digital signal. The optical system may further have a digital-to-analog converter to convert the digital signal to an analog signal, a laser to provide an optical signal, and a modulator to receive the optical signal and the analog signal, and modulate the optical signal based on the analog signal to form a modulated optical signal. The modulated optical signal may include the pilot tone. The optical system may also have an optical receiver to receive the modulated optical signal, process the modulated optical signal to determine a phase associated with the pilot tone, and apply the phase to the modulated optical signal to recover the signal channel.

Abstract: Systems and methods are disclosed to provide optical communication by using subcarriers as individual bases functions, obtaining signal constellation points of an N-dimensional pulse amplitude modulation (ND-PAM) constellation diagram as an N-dimensional Cartesian product of a one-dimensional PAM; and transmitting the N-dimensional signal constellation point over all N orthogonal subcarriers serving as individual bases functions.

Abstract: An optical system having an input surface configured to receive an input optical signal having a polarization, and a polarization changer comprising the input surface and configured to generate two orthogonal polarization components from the input optical signal. The polarization changer also changes a direction of the polarization of the input optical signal in a controlled manner as a function of time while maintaining coherence of the two orthogonal polarization components in order to reduce stimulated Brillion scattering.

Abstract: Polarization mode dispersion (PMD) in a dual-pole optical communications network is compensated for using an adaptive PMD equalizer. The PMD equalizer may include a number of substantially identical filter modules that provide partial outputs which may be combined to form a PMD compensated output. A constant modulus algorithm (CMA)-based equalizer may track PMD across both poles and generates an error signal. The CMA-based equalizer includes a filter bank, and uses an update algorithm and tap/output adjustments based on a difference between combined tap energies and an index, and feedback from a forward error correction code frame synchronizer.

Abstract: The sender and the receiver prepare two photons in the entangled state of polarization. The first photon of the two photons is sent to the sender and the second photon of the two photons is sent to the receiver. The sender measures the first photon after the first photon pass the polarizer in which the vertical polarized photon can pass, when the sender sends the signal “1”. The sender measures the first photon after the first photon pass the polarizer in which the 45 degrees polarized photon can pass, when the sender sends the signal “0”. The receiver measures the second photon by the balanced homodyne measurement. And, the receiver knows the signal from the absolute value of the result of the balanced homodyne measurement.

Abstract: In the optical transmitting system, the optical transmitter transmits a polarization combined signal light obtained by combining a pair of lights having different polarization orientation, and the optical receiver separates the combined signal light. In the optical transmitter, a polarization changer changes a state of polarization of the polarization combined signal light. In the optical receiver, a polarization reverse-changer changes the state of the polarization combined signal light in a reverse direction of the change that polarization changer applies.

Abstract: In general, a wavelength division multiplexed (WDM) communication system may use wavelength selective switching to simultaneously pre-filter and combine groups of channel wavelengths with orthogonal polarizations to provide a pre-filtered, pair-wise orthogonal aggregate WDM optical signal. An orthogonally-combining wavelength selective switch (WSS) multiplexer may route channel wavelengths individually from different sets of channels to a common output. The orthogonally-combining WSS multiplexer may also provide substantially orthogonal polarizations for the wavelengths in the different sets of channels. The different sets of channels may include odd channels and even channels.

Abstract: A polarization fluctuation compensation device, when WDM light received by, for example, an optical reception device includes a polarization scrambled optical signal and a non-polarization scrambled optical signal, collects information related to whether optical signals having respective wavelengths are polarization scrambled, obtains a target value of control parameters which are different from each other, according to the speed of polarization fluctuations in the non-polarization scrambled optical signal based on the collected information, and performs reception processing of the non-polarization scrambled optical signal by using a control parameter set as the target value. As a result, an influence of fast polarization fluctuations generated resulting from an interaction between optical signals having respective wavelengths can be reliably compensated for, thereby enabling to realize excellent reception characteristics.

Abstract: A method of transmitting a data signal using an optical transmitter of an optical communications system. The optical transmitter is configured to modulate an optical carrier in successive signalling intervals to generate an optical signal. A modulation scheme is provided which comprises a multi-dimensional symbol constellation. The modulation scheme is designed such that an average degree of polarization of a modulated optical signal output from the optical transmitter has a first value when averaged across a first signalling interval, and has a second value when averaged across more than one and fewer than 100 signalling intervals. The second value is less than 10 percent of the first value. During run-time, an encoder of the optical transmitter encoding a data signal to be transmitted as symbols of the constellation, and a modulator of the optical transmitter modulating available dimensions of the optical carrier in accordance with the symbols.

Abstract: An optical communication system includes a polarization multiplexed orthogonal frequency-division multiplexing POLMUX-OFDM transmitter for generating a POLMUX-OFDM double sideband signal, an optical processing path for processing the double sideband signal from the transmitter; an analog-to-digital convert ADC-OFDM receiver coupled to the optical processing path for receiving the double sideband signal processed by the optical path; and a block-diagonal multiple-input multiple-output MIMO equalizer responsive to the receiver for enabling correct operation for a completely random incoming signal polarization state without adaptive polarization control at said receiver, which enables complexity.

Abstract: An optical transmission system includes an optical transmitter, an optical receiver, and an optical transmission path connecting the optical transmitter and the optical receiver, wherein the optical transmitter has a first polarization scrambler to change a polarization state of an optical transmission signal in a first direction at a first polarization scrambling frequency synchronized with a transmission signal frequency, and the optical receiver has a second polarization scrambler to change a polarization state of an optical signal received from the optical transmission path at a second scrambling frequency synchronized with a received signal frequency in a second direction opposite to the first direction.

Abstract: A method and a device are provided for phase recovery of at least two channels comprising the steps of (i) a phase is estimated for each channel; (ii) the phase estimated of each channel is superimposed by a coupling factor with at least one other phase estimated. Further, a communication system is suggested comprising such a device.

Abstract: Methods, systems, and devices are described for tap adjustment and reseeding in a digital filter. Filter and signal characteristics are measured and tap adjustments and reseeding of tap values may be performed based on the filter and signal characteristics. Filter characteristics that may be measured include a filter center of mass which may provide an indication that filter taps for a filter may be drifting toward a filter edge and thus reducing the dynamic range of the filter. Signal characteristics may include a timing offset between received input signals, and characteristics related to which of a particular input signal is present at a filter output. Filter taps, according to various embodiments, may be adjusted, and/or re-initialized responsive to one or more of the signal or filter characteristics.

Abstract: The present disclosure provides a polarization multiplexed transceiver, including: a transmitter; a receiver; circuitry within the transmitter configured to insert pilot tones as a reference state of polarization for a polarization multiplexed signal; and circuitry within the receiver configured to de-multiplex the polarization multiplexed signal using the pilot tones. The transmitted signal is constructed in such a manner as to facilitate the division of the receiver processing between the analog and digital domains such that the implementation may be simultaneously both highly spectrally efficient and power efficient.

Abstract: Methods and apparatus for generating and processing a signal are disclosed. The signal may comprise a plurality of mutually orthogonal subcarriers constituting a plurality of bands. The signal may be either an optical or a radio frequency signal.

Abstract: A long haul transmission system uses a digital signal processor DSP instead of an additional optical phase conjugate copier because the optical phase conjugate copier requires high quality optical carrier regeneration to recover the pump and optical PLL to maintain phase matching between signal and pump. Therefore, the use of DSP to process the signal and idler at receiver end greatly simplifies the system setup, increases the system stability and decreases the system cost.

Abstract: The invention is directed to a novel computer implemented method for finding a modulation format that has better receiver sensitivity than modulation formats that are currently being used, with a correlated symbol modulation in which neighboring symbols are coded and decoded together to increase receiver sensitivity.

Abstract: In an optical multilevel transmitter (210), a polar representation of an optical multilevel signal (r, ?) is generated by a polar coordinate multilevel signal generation circuit (212), input to an optical amplitude modulator (211) and a polar coordinate type optical phase modulator (201), and output as an optical multilevel modulated signal (213). The polar coordinate type optical phase modulator (201) generates an optical phase rotation proportional to an input voltage, so the modulation distortion of the electric signal is transferred in a linear form to the optical phases of the optical multilevel modulated signal (213). In an optical multilevel receiver (219), a received signal is input to two sets of optical delay detectors (133) and balance receivers (134) and directly demodulated, and a differential phase ?? for the received signal is calculated by arctangent computation from the output signal.

Abstract: An optoelectronic transmission system has a photoemitter semiconductor component and a photodetector semiconductor component. The photoemitter semiconductor component has a radiation source for converting a first electrical signal into a first electromagnetic radiation and a first polarization filter having a first polarization direction for filtering the first electromagnetic radiation. The photodetector semiconductor component has a second polarization filter having a second polarization direction for filtering a second electromagnetic radiation and a sensor element for converting a second electromagnetic radiation which has been polarized by the polarization filter into a second electrical signal. In this case, the first polarization direction of the first polarization filter is identical to the second polarization direction of the second polarization filter.

Abstract: An apparatus receives data encoded in a format where information bits for transmission are mapped into symbols each carrying a plurality of bits, some being encoded through a pulse position modulation (PPM) format and some being encoded through an additional modulation format on at least one PPM pulse. A receiver detects the signal through a dual-polarization coherent receiver front-end, recovering polarization components of the signal by decoding a first non-zero portion of a plurality of bits carried by a symbol based on slot position of at least one PPM pulse in the polarization components and a second non-zero portion of the plurality of bits carried by the symbol based on the additional modulation carried by at least one PPM pulse in the polarization components. Pilot-assisted single-carrier frequency-division equalization (PA-SC-FDE) may be used for reliable signal reception in the presence of severe PPM errors.

Abstract: An optical receiver according to the invention includes a polarization diversity unit receiving a polarization multiplexed optical signal obtained by multiplexing two optical signals having a same frequency band of carrier waves and polarization states orthogonal to each other, and a frequency domain equalization unit receiving signal components parallel to mutually orthogonal polarization axes from the polarization diversity unit, wherein the frequency domain equalization unit includes filters for which filter coefficients thereof are set for compensating degradation of transmission characteristics in one optical signal without polarization multiplexing by means of the frequency domain equalization.

Abstract: Embodiments of the present invention provide a coefficient determining apparatus, equalizer, receiver and transmitter. The coefficient determining apparatus comprises: a synchronizer configured to find a position of a training sequence from signals containing the training sequence received by a transmitter; and a first processor configured to set an initial tap coefficient of an equalizer according to the received signals and the training sequence; wherein in each polarization state, the training sequence comprises n pairs of training symbols, in the n pairs of training symbols, the training symbols of the same pair being identical, the training symbols of the different pair being different, a cyclic prefix and a cyclic postfix being respectively inserted before and after each pair of training symbols, and n being an integer greater than 1.

Abstract: A method of transmitting data using electromagnetic waves, comprising the steps of providing (101) a first electromagnetic signal (S1) having a first wavelength (?1) and a second electromagnetic signal (S2) having a second wavelength (?2) different from the first wavelength; dividing (102) each of the first (S1) and second (S2) electromagnetic signals into a first polarization component (S1x; S2x) having a first polarization direction and a second polarization component (S1y; S2y) having a second polarization direction orthogonal to the first polarization direction; modulating (103) the first polarization component (S1x) of the first electromagnetic signal (S1) to encode a first data stream (DS1); modulating (104) the second polarization component (S2y) of the second electromagnetic signal (S2) to encode a second data stream (DS2); and transmitting (105) a combined electromagnetic signal (Scomb) comprising the first and second polarization components of the first electromagnetic signal (S1) and the first and

Abstract: In one embodiment, an optical transmission system transmits data using a format according to which a data frame has two or more pilot-symbol blocks, each having a guard interval, and two or more payload-symbol blocks that are concatenated without a guard interval between them. The use of guard intervals in the pilot-symbol blocks helps the synchronization and channel-estimation procedures performed at a receiver of the optical transmission system to be robust in the presence of certain transmission impairments. The absence of guard intervals in the payload-symbol blocks helps to minimize the transmission overhead and thus achieve relatively high payload-data throughput.

Abstract: There is provided an optical transmitting device including a detector to detect a transmission rate of a transmission signal, a transmission method selector to determine a transmission method of the transmission signal, based on the transmission rate detected by the detector, a modulation signal generator circuit to generate a modulation signal from the transmission signal, based on the transmission method determined by the transmission method selector, and an optical modulator to generate a modulated optical signal from the modulation signal generated by the modulation signal generator circuit.

Abstract: An optical node disposed along a transmission line that uses optical fiber. The optical node includes a first signal generator and a monitor. The first signal generator generates a first measurement signal for measuring polarization mode dispersion values and transmits the first measurement signal along the transmission line. The monitor detects a second measurement signal from the transmission line and measures polarization mode dispersion values by performing signal processing with respect to the second measurement signal.

Abstract: The present invention provides a system, apparatus and method to maintain the polarization state of an optical signal propagating within a photonic integrated circuit, or from a first photonic integrated circuit to a second photonic integrated circuit. According to various embodiments of the invention, an optical circuit is provided which includes an optical coupler configured to accept a first optical signal on a first input and a second optical signal on a second input, the second optical signal having a polarization state. The optical coupler may combine the first and second optical signals into an optical output signal. A principle axis of a first end of an optical fiber is may be configured to align with the polarization state of the second optical signal, such that a polarization maintaining connection is established. The polarization state may be a TM polarization state, a TE polarization state, or another polarization state.

Abstract: Digital timing error detection systems and techniques are described. The described techniques are independent of polarization and differential-group-delay and are used to perform timing recovery of polarization-multiplexed coherent optical systems.