Coherent and partially coherent optical detection with photonic-analog processing

Abstract

A method for reconstructing a first information stream and a second information stream, the method includes receiving, by an optical receiver, a received multiplexed optical signal that is a transmitted optical signal that passed through a polarization and phase rotating medium, the transmitted multiplexed optical signal being generated by using at least one transmitter phase-modulated periodical pilot signal, and by allocating a first polarization to the first information stream and a second polarization that differs from the first polarization to the second information stream; and processing the received multiplexed optical signal to provide a first reconstructed information stream and a second reconstructed information stream, wherein the processing comprises using at least one receiver phase-modulated periodical pilot signal that is associated with the at least one transmitter phase-modulated periodical pilot signal.

Description

[0001]COHERENT AND PARTIALLY COHERENT OPTICAL DETECTION WITH PHOTONIC-ANALOG PROCESSING CROSS REFERENCE This application claims priority from US provisional patent 63 / 645,766 filing date May 10, 2024, which is incorporated herein in its entirety. FIELD OF THE INVENTION This application refers to Coherent and Partially Coherent Optical Detection with Photonic-Analog Processing BACKGROUND This invention addresses improved structures and methods for optical interconnect links, in particular optical Transceivers (TRX) for bi-directional optical links, as well as Transmitter (Tx) to Receiver (Rx) unidirectional (simplex) optical links. As data networks tasked with massive data traffic transport evolve, the challenges facing their underlying photonic infrastructure pose bottlenecks impeding the information-centric societal evolution. The upcoming generations of hyperscale datacentres, hosting High-Performance-Computing (HPC) fabric comprising GPU clusters spanning hundreds of racks, especially in support of AI workloads, will be required to operate at improved energy-efficiencies, sustaining exponential rate upscaling of their data transport capacities. The bottleneck is also apparent in 6G fronthaul and backhaul networks data transport. Prior art optical transmitters drive a pair of two MZMs by high-speed Pulse Amplitude Modulation (PAM) electrical signals denoted X-PAM and Y-PAM. Pilot tones at much slower rates (say in the ~MHz range) are additively injected along with the two PAM electrical signals as shown. The additively injected sinusoidal pilot tones (aka ‘marker’ or ‘label’ or ‘probe’ tonesin prior-art), referred to as the Xpilot (^^^^^^^ ൌ ^^ ^^^^^^ 2^^^^^^^) and Ypilot (^^^^^^^ ൌ^^ ^^^^^^ 2 ^^^^^^^), have different frequencies, superpose onto the optically transmitteddata, ‘dithering’ the two modulators in the X and Y paths, to induce small periodic fluctuations of the optical field amplitudes, enabling distinguishing between the two X,Y POL tributaries at the Rx, in order to facilitate POL-DEMUX, effectively contributing to precise ‘undoing’ of the linear mixing of POL components in the optical fiber. SUMMARY An optical receiver and / or an optical transmitter and / or a method as illustrated in the application. BRIEF DESCRIPTION OF THE DRAWINGS The subject matter regarded as the embodiments of the disclosure is particularly pointed out and distinctly claimed in the concluding portion of the specification. The embodiments of the disclosure, however, both as to organization and method of operation, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description when read with the accompanying drawings in which: Figure.1A illustrates a prior art circuit; Figure.1B illustrates an example of a receiver and a transmitter; Figures.2, 3, 4, 5, 6, 7, 9, 10, 11, 12 and 13 illustrates signals and / or spectrums and / or test results and / or measurements; Figures.8, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33 and 36 illustrate example of receivers and / or transmitter and / or portions of receivers and / or portions of transmitters; Figures.34 and 35 are examples of methods. DETAILED DESCRIPTION OF THE DRAWINGS There are provided designs for optical transmitters (Tx), receivers (Rx), and transceivers (TRX) that offer much better performance than current direct-detection (DD) optical interconnects and also outperform prior-art AM-pilot (marker)-tones- aided techniques for polarization multiplexing (also known as dual-polarization) to increase the transmitted data rates. Our improvement is achieved by jointly monitoring and controlling the polarization, optical phase, and frequency of the light signals. Unlike previous methods that used amplitude-modulated pilot tones, our designs use phase-modulated pilot tones. These tones allow the receiver to more accurately separate and identify data from different signal paths, accurately estimating the cross-talk between orthogonal polarizations and / or orthogonal quadratures. This leads to more reliable data transmission and to improved link loss budget. At the receiver end, we have developed new techniques for analysing the incoming phase- modulated pilot tones. These techniques, based on matched-phase-modulation cross-correlation, enhance the receiver ability to detect these tones accurately and robustly. This improvement enables the design of advanced optical phase-locked loops (oPLL) and state-of- polarization-locked loops (SoPL) operating jointly. These loops are crucial for reducing errors caused by frequency shifts, phase noise, and polarization crosstalk, making the system more stable and efficient. The application also extends to a new detection method called partially-coherent detection (pCOHD). This method offers a balance between the simplicity of DD receivers and the high performance of fully-coherent receivers. By implementing our advanced oPLL and SoPLL, along with expanding the technology to include pCOHD and fully-coherent detection, we can significantly enhance the capabilities of short- reach photonic interconnects. These improvements could double or quadruple the data rates achievable with current ultra-high-speed DD links, extend the range of optical connections, and reduce energy consumption by shifting some processing tasks from digital signal processors to the optical domain. Figure 34 illustrates an example of method 340 for reconstructing a first information stream and a second information stream. According to an embodiment, method 340 includes step 341 of receiving, by an optical receiver, a received multiplexed optical signal that is a transmitted optical signal that passed through a polarization and phase rotating medium, the transmitted multiplexed optical signal being generated by using at least one transmitter phase-modulated periodical pilot signal (for example one or more outputs of one or more PM units of a receiver), and by allocating a first polarization to the first information stream (for example X-PAM) and a second polarization that differs from the first polarization to the second information stream (for example Y-APM). Method 340 also includes step 342 of processing the received multiplexed optical signal to provide a first reconstructed information stream (for example X-Rx) and a second reconstructed information stream (for example Y-Rx), wherein the processing includes using at least one receiver phase-modulated periodical pilot signal (for example one or more outputs of one or more PM units of a transmitter) that is associated with the at least one transmitter phase-modulated periodical pilot signal. According to an embodiment, the at least one receiver phase-modulated periodical pilot signal is generated from a non-sinusoidal pilot signal (for example Xpilot and Ypilot). According to an embodiment, the at least one receiver phase-modulated periodical pilot signal is generated from a sinusoidal pilot signal (for example Xpilot and Ypilot). According to an embodiment, the at least one receiver phase-modulated periodical pilot signal is multiple receiver phase-modulated sinusoidal pilot signals having non- overlapping harmonics. According to an embodiment, the multiple information streams further include a third information stream allocated with the first polarization and a fourth information stream allocated with the second polarization. According to an embodiment, the processing includes providing a third reconstructed information stream and a fourth reconstructed information stream. See for example figures 17, 21 and 22. According to an embodiment, a specified transmitter phase-modulated periodical pilot signal is allocated to the first and third information streams and another specified transmitter phase-modulated periodical pilot signal is allocated to the second and fourth information streams. According to an embodiment, the at least one receiver phase-modulated periodical pilot signal includes a first information stream phase-modulated periodical pilot signal and a second information stream phase-modulated periodical pilot signal. According to an embodiment, the using of the at least one receiver phase-modulated periodical pilot signal is made in an optical domain. Most receivers illustrated in this application include using at least one receiver phase-modulated periodical pilot signal is made in an optical domain. According to an embodiment, the using of the at least one receiver phase-modulated periodical pilot signal is made in an electrical domain. See, for example, figure 14. According to an embodiment, the processing of the received signal includes at least partially compensating for a polarization and phase rotation introduced by the polarization and phase rotating medium to provide polarization and phase compensated optical signals (for example X" and Y"). According to an embodiment, the processing further includes analyzing the polarization and phase compensated optical signals to determine a state of polarization related to the polarization and phase compensated optical signal; determining, based on the analyzing, whether to further compensate for the polarization and phase rotation; and selectively further compensating for the phase polarization rotation based on the determining. According to an embodiment, the at least partially compensating includes reducing a cross-talk between one or more polarization and phase compensated optical signals associated with the first polarization and one or more other polarization and phase compensated optical signals associated with the second polarization. According to an embodiment, the processing of the received multiplexed optical signal further includes performing an initial split of polarization components of the received multiplexed optical signal to provide a first intermediate polarization optical signal (for example X') and a second intermediate polarization optical signal (for example Y'). According to an embodiment, the processing of the received multiplexed optical signal further includes analyzing the polarization and phase compensated optical signals (for example X" and Y") by multiple circuits to provide frequency and phase information regarding the received multiplexed optical signal. According to an embodiment, the processing further includes analyzing the polarization and phase compensated optical signals by a single analysis unit. According to an embodiment, the processing further includes analyzing the polarization and phase compensated optical signals by a first analysis unit and a second analysis unit that operated at a lower operation frequency than the first analysis unit. According to an embodiment, the second analysis unit includes optical hybrid circuits (see, for example optical hybrids X-IA-H-HYB and Y-IQ-HYB of figure 1B), and wherein the second analysis unit is a direct detection optical unit (see, for example the ROSA backend and the digital portion that follows the ROAS backend of figure 1B). According to an embodiment, the processing of the received multiplexed optical signal further includes generating at least one phase modulated local oscillator signal. According to an embodiment, the processing of the received multiplexed optical signal further includes estimating at least one phase difference between the at least one phase modulated local oscillator signal and the at least one transmitter phase- modulated periodical pilot signal. According to an embodiment there is provided an optical receiver that includes an input (for example FIBER IN of figure 1B) configured to receive a received multiplexed optical signal that is a transmitted optical signal that passed through a polarization and phase rotating medium (for example OPTICAL LINK of figure 1B), the transmitted multiplexed optical signal being generated by using at least one transmitter phase-modulated periodical pilot signal, and by allocating a first polarization to a first information stream and a second polarization that differs from the first polarization to a second information stream; and at least one processing circuit (optical and / or electrical processing circuits such as PSR, POLtrk, ROSE-BE - DD, DIGITAL, X-IQ-HYB, Y-IQ-HYB, eFABRIC of figure 1B), an example of eFABRIC is illustrated in figure 8) that is configured to process the received multiplexed optical signal to provide a first reconstructed information stream and a second reconstructed information stream, wherein the processing includes using at least one receiver phase-modulated periodical pilot signal that is associated with the at least one transmitter phase-modulated periodical pilot signal. According to an embodiment, the at least one receiver phase-modulated periodical pilot signal is generated from a non-sinusoidal pilot signal (Xpilot or Ypilot). According to an embodiment, the at least one receiver phase-modulated periodical pilot signal is generated from a sinusoidal pilot signal (Xpilot or Ypilot). According to an embodiment, the at least one receiver phase-modulated periodical pilot signal is multiple receiver phase-modulated sinusoidal pilot signals having non- overlapping harmonics (see, for example figure 5). According to an embodiment, the multiple information streams further include a third information stream allocated with the first polarization and a fourth information stream allocated with the second polarization. According to an embodiment, the processing includes providing a third reconstructed information stream and a fourth reconstructed information stream. According to an embodiment, a specified transmitter phase-modulated periodical pilot signal is allocated to the first and third information streams and another specified transmitter phase-modulated periodical pilot signal is allocated to the second and fourth information streams. According to an embodiment, the at least one receiver phase-modulated periodical pilot signal includes a first information stream phase-modulated periodical pilot signal and a second information stream phase-modulated periodical pilot signal. According to an embodiment, the using of the at least one receiver phase-modulated periodical pilot signal is made in an optical domain. According to an embodiment, the using of the at least one receiver phase-modulated periodical pilot signal is made in an electrical domain. According to an embodiment, the processing of the received signal includes at least partially compensating for a polarization and phase rotation introduced by the polarization and phase rotating medium to provide polarization and phase compensated optical signals. According to an embodiment, the processing further includes analyzing the polarization and phase compensated optical signals to determine a state of polarization related to the polarization and phase compensated optical signal; determining, based on the analyzing, whether to further compensate for the polarization and phase rotation; and selectively further compensating for the phase polarization rotation based on the determining. According to an embodiment, the at least partially compensating includes reducing a cross-talk between one or more polarization and phase compensated optical signals associated with the first polarization and one or more other polarization and phase compensated optical signals associated with the second polarization. According to an embodiment, the processing of the received multiplexed optical signal further includes performing an initial split of polarization components of the received multiplexed optical signal to provide a first intermediate polarization optical signal and a second intermediate polarization optical signal. According to an embodiment, the processing of the received multiplexed optical signal further includes analyzing the polarization and phase compensated optical signals by multiple circuits to provide frequency and phase information regarding the received multiplexed optical signal. According to an embodiment, the processing further includes analyzing the polarization and phase compensated optical signals by a single analysis unit. According to an embodiment, the processing further includes analyzing the polarization and phase compensated optical signals by a first analysis unit and a second analysis unit that operated at a lower operation frequency than the first analysis unit. According to an embodiment, second analysis unit includes optical hybrid circuits, and wherein the second analysis unit is a direct detection optical unit. According to an embodiment, the processing of the received multiplexed optical signal further includes generating at least one phase modulated local oscillator signal. According to an embodiment, the processing of the received multiplexed optical signal further includes estimating at least one phase difference between the at least one phase modulated local oscillator signal and the at least one transmitter phase- modulated periodical pilot signal. Figure 35 illustrates an example of a method 350 for optically processing a first information stream and a second information stream, the method includes step 351 of receiving, by an optical transmitter, the first information stream and the second information stream (see for example X-PAM and Y-PAM of figure 1B), step 352 of generating at least one transmitter phase-modulated periodical pilot signal; step 353 of optically processing the first information stream and the second information stream, using the at least one transmitter phase-modulated periodical pilot signal to provide a transmitted multiplexed optical signal; wherein the optically processing includes allocating a first polarization to the first information stream and a second polarization that differs from the first polarization to the second information stream; and step 354 of transmitting the transmitted multiplexed optical signal to a polarization and phase rotating medium. According to an embodiment, the generating of the at least one transmitter phase- modulated periodical pilot signal includes phase modulating at least one non- sinusoidal pilot signal. According to an embodiment, the generating of the at least one transmitter phase- modulated periodical pilot signal includes phase modulating at least one sinusoidal pilot signal According to an embodiment, the at least one transmitter phase-modulated periodical pilot signal is multiple transmitter phase-modulated sinusoidal pilot signals having non-overlapping harmonics. According to an embodiment the method includes receiving, by an optical transmitter, a third information stream and a fourth information stream; and wherein the processing further includes optically processing the third information stream and the fourth information stream, using the at least one transmitter phase-modulated periodical pilot signal to provide the transmitted multiplexed optical signal; wherein the optically processing further includes allocating the first polarization to the third information stream and the second polarization to the fourth information stream. See, for example figure 17 and figure 21. According to an embodiment there is provided an optical transmitter that includes an input (the input for receiving X-PAM and Y-PAM) configured to receive a first information stream and a second information stream; a pilot circuit (see for example phase modulators PM, laser source LSM and signal sources that provide Xpilot and Ypilot of figure 1B) that is configured to generate at least one transmitter phase- modulated periodical pilot signal; at least one processor (see, for example, modulators MOD and PCR of figure 1B) configured to optically process the first information stream and the second information stream, using the at least one transmitter phase-modulated periodical pilot signal to provide a transmitted multiplexed optical signal; wherein the optically processing includes allocating a first polarization to the first information stream and a second polarization that differs from the first polarization to the second information stream; and an output (see FIBER OUR of figure 1B) that is configured to transmit the transmitted multiplexed optical signal to a polarization and phase rotating medium. According to an embodiment the pilot circuit is configured to generate the at least one transmitter phase-modulated periodical pilot signal using at least one non- sinusoidal pilot signal. According to an embodiment the pilot circuit is configured to generate the at least one transmitter phase-modulated periodical pilot signal using at least one sinusoidal pilot signal. According to an embodiment, the at least one transmitter phase-modulated periodical pilot signal is multiple transmitter phase-modulated sinusoidal pilot signals having non-overlapping harmonics. According to an embodiment the input (see DATA IN for receiving XI, XQ, YI, YA data streams of figure 17) is further configured to receive a third information stream and a fourth information stream; and wherein the at least one processor is further configured to optically process the third information stream and the fourth information stream, using the at least one transmitter phase-modulated periodical pilot signal to provide the transmitted multiplexed optical signal, and to allocate the first polarization to the third information stream and the second polarization to the fourth information stream. Figure 2 illustrates an example of mean values of the sine and cosine of the phase- domain Tx-side PAM4 constellation, both plotted vs. the modulation backoff factor, including transmitted PAM4 constellation and its unity mean (the normalized carrier value), and the mean of the cosine yields the pilot attenuation factor induced by the random fluctuation of the PAM4 modulation among its four levels. Figure 3 illustrates an example of a tradeoff between the pilots and the datapath - stronger pilots tend to reduce the PAM4 transmission loss budget; the monotonically increasing curve is the pilot normalized intensity; the decreasing curve is the transmitted data-modulation normalized intensity, both plotted vs. the Optical Modulation index; the inset zooms onto several operating points of interest, allowing various levels of degradation for the datapath, in order to benefit from stronger pilots, which improve the estimation of the State of Polarization at the Rx. Figure 4 illustrates an example of the Fourier series coefficients for sinusoidal-PM are given by the successive orders of Bessel Functions of the first kind.Figure 5 illustrates an example of selected pilot frequencies, ^^^ ≡ 9^^௨, ^^^ ≡ 14^^௨forming a pair of interspersed spectral grids. Figures 6A-6C illustrates an example of the transmitted Line spectra induced by the X&Y-pilots: 6A- line spectrum of Xpilot; 6B - line spectrum of Ypilot, and 6C - the plots of the Xpilot and Ypilot overlaid two plots overlayed. Figure 7 illustrates an example of the received line spectra in the X,Y POLs (contributions of the pilots only) assuming the Xpilot and Ypilot fields are superposed by the end-to-end 2x2 MIMO POL channel in the ratio 12 / 13:5 / 13. Figure 8 illustrates an example of the algorithmic Intelligence Controller (AIC)– block diagram of the sub-algorithms used in the POL-Locked-Loop (SoPLL) and optical-PLL (oPLL). Figure 9 illustrates an example of an autocorrelation (ACOR) of the Bessel functions sequence of Fourier coefficients of sinusoidal phase modulation signals such as the PM-pilots, the fact that the ACOR is ‘perfect’ (has zero sidelobes) is a new mathematical property of the three centuries old Bessel functions of the first kind. Figure 10 illustrates an example of Auto|Cross-correlations of the spectra of the X|Y- PM-pilots. (top-left) and (bot-right): Autocorrelations of the spectra of the respective X|Y-PM-pilots. (top-right) and (bot-left): Crosscorrelations of the spectra of the X- PM-pilot and Y-PM-pilot and vice versa. Figure 11 illustrates an example of a 2D Array of the sidelobe levels of the XCOR (see equation 91). Figure 12 illustrates an example of Peak X,Y pilots cross-correlation sidelobe modulus vs. the modulation index. Figure 13A and Figure 13B illustrates an example of the spectra at the two X|Y-IQ- hybrid outputs – evaluated as spectral domain XCORs.13A: XCOR of the spectrum of optical field at the X-IQ-HYB input with the spectrum of the X-PM-pilot.13B: XCOR of the spectrum of optical field at the Y-IQ-HYB input with the spectrum of the Y-PM-pilot. Figure 14 illustrates an example of a variant of the ROSA-FE (disclosed in figure 1) with the physical PMs in the ROSA removed, replaced by digital complex multipliers with the X|Y-pilot-PM-transfer factors. (the other elements within the POLest sub- module and the AIC are not explicitly depicted). Figure 15A and Figure 15B illustrate an example of Embodiments of PAM4-driven MZMs for the X|Y-I|Q tributaries of a COH 16QAM optical Tx with PM-pilot-tones insertion enabled by optical carrier generation using one of these two methods: 15A: bias-point-shifted MZM with interferometric differential-phase-balancing.15B: MZM in parallel to a reference waveguide of matched DGD, forming an asymmetric interferometric CW combiner. Figures 16A and Figure 16B illustrates an example of optical DACs comprising OOK&NRZ-driven MZM pairs, used in the X|Y tributaries of a COH 16QAM optical Tx, with PM-pilot-tones insertion enabled by optical carrier generation within the oDACs due to inherently asymmetric BIP-PAM4 constellation generation.16A: oDAC with interferometric 0o-phase-balancing using slow Thermo-Optic (TO) PMs. An external PM is used for pilot injection.16B: oDAC with a pair of internal PMs, used for both pilots' injection and interferometric 0o-phase-balancing. Figure 17 illustrates an example of the Tx of a PM-pilots aided COH POLMUX 16QAM link based on replicating in the four I|Q-X|Y lanes the ASYM-BIP-PAM4 oDAC structure of figure 16A. The four PM-pilots generate orthogonal signals. Substantial optical carriers are present in the X|Y-I|Q signals. Figures 18A-18C illustrates an example of 18A: Prior-art IQ-hybrid.18B: Disclosed PMs-Correlated (PMC) IQ-hybrid (PMC-IQ-HYB).18C: Using a pair of PMC-IQ- HYBs in the ROSA Monitor for a PM-pilots aided COH link (the internals of the Y- PMC-IQ-HYB and X-PMC-IQ-HYB in figure 20B). Figures 19A-19D illustrate an example of TOSA options for PM-pilots insertion in our disclosed PM-pilots aided POL-MUX links.19A: Two PM-pilots (XI, YI), one in each of the X,Y-POL-tributaries.19B: Four PM-pilots (XI,XQ,YI,YQ).19C: Single PM-pilot (YQ).19D. Two PM-pilots in the same (X) POL tributary (XI,XQ). Figures 20A-20D illustrate an example of ROSA-FE disclosed embodiments for a PM-pilots aided POLMUX COH link. The block diagrams correspond to the set of PM-pilots injected at the Tx (various options comprising 1|2|4 PM-pilots are assumed).20A: Two PM-pilots (XI, YI).20B: Four PM-pilots (XI, XQ, YI, YQ). 20C: Single PM-pilot (YQ).20D: Two PM-pilots (XI, XQ). Note that the ROSA options 20A-20D respectively correspond to the TOSA (20A-20D). Options of 20B and 20D require the PMC-IQ-HYB version(s) of hybrid, in order to distinguish between I|Q pilots in the same X|Y POL (see figure 18C for the hybrid internal structure). Figure 21A and Figure 21B illustrate an example of Two disclosed end-to-end embodiments of the PM-pilots aided POLMUX COH link. Note: link options 20A and 20B correspond to the respective TOSAs in figure 19A and Figure 19B and ROSA-FEs figure 20A and Figure 20B. Figure 22 illustrates an example of Two more disclosed end-to-end embodiments of the PM-pilots aided POLMUX COH link. Note: link options (A, B) here correspond to the respective TOSAs in figure 19c and figure 19d) and ROSA-FEs figure 20c and figure 20d. Figure 23 illustrates an example of PM-pilots-aided POLMUX-IMDD link with partially-Coherent-Detection (pCOHD), based on Phase-Diversity (ΦDIV) combining by means of sum-of-squares broadband RF circuits. Figure 24 illustrates an example of Sum-of-squares analog circuit. Each of the two broadband mixers (driven by broadband amplifiers) is fed by two identical copies I(t),Q(t) of the same quadrature signals. The sum of squares, ^^ଶ^^^^ is generatedupon summing up the mixer outputs. Figure 25 illustrates an example of ROSA-Back-End (BE) options: (A) for Direct- Detection (DD). (B): For Partially-Coherent-Detection (pCOHD). (C). For full- Coherent-Detection. Figure 26 illustrates an example of The least complex IMDD POLMUX link uses a single PM in the Tx and in the Rx (A) a single-PM-pilot-aided POLMUX IMDD link – requiring a single IQ-hybrid. (B) the two-PM-pilots-aided link of @ reproduced for ready comparison. Figure 27 illustrates an example of Phase-diversity POLMUX partially-coherent (pCOHD) link with a single PM pilot injected in the X-tributary. In the ROSA-FE a single X|Y-IQ-hybrid monitors the received SoP (the accuracy of IQ alignments is not critical here). The ROSA-BE pCOHD phase-diversity detects the POLMUX IMDD data using a pair of high-speed X|Y-IQ-hybrids each followed by a sum-of- squares RFIC. Figure 28 illustrates an example of ROSA-FE embodiments injecting a sole-PM- pilot, say, into the X-POL at the Tx, yet using both an X-IQ-HYB and Y-IQ-HYB for monitoring. (A): for IMDD. (B): For COHD or pCOHD. Figure 29 illustrates an example of Transceiver (TRX) Digital Back-End (BE) embodiments. Figure 30 illustrates an example of PM-pilots-aided POLMUX IMDD TRX. Figure A: using a pair of PM-pilots transmitted over X- and Y- POLs and a pair of IQ-HYBs for monitoring. Figure B: using sole PM-pilot and a sole IQ-HYB. Figure 31 illustrates an example of PM-pilots-aided TRX using POLMUX Intensity- Modulation-partially-coherent-detection (IM-pCOHD) also known as Phase- Diversity (aka Φ-Div) detection, implemented here using a sum-of-squares RFIC. The transmission is conventional POLMUX IMDD one, but the coherent detection of the data is much more sensitive. (A) with X, Y-pilots and X, Y-IQ-hybrids. (B): with a single (Y-) pilot and a single IQ-hybrid, monitoring the received Y-POL. Figure 32 illustrates an example of PM-pilots-aided POLMUX TRX using full- coherent-detection (COHD) based on IQ-HYBs for the data-path as well as for pilots monitoring. (A): with X, Y-pilots and X, Y-IQ-hybrids. (B): with a single (Y-) pilot and a single IQ-hybrid, monitoring the received Y-POL. Figure 33 illustrates an example of PM-pilots-aided POLMUX fully-coherent TRX with PM-pilot(s) monitoring based on the innovative PMC-IQ-hybrid(s). (A): with X,Y-pilots and X,Y-IQ-hybrids. (B): with a single (Y-) pilot and a single IQ-hybrid, monitoring the received Y-POL. POL-MUX DD link with phase-modulated pilots and LOs Our first disclosure in this subsection, depicted in figure 1B pertains to a polarization-multiplexed (POLMUX) optical link, over an optical channel with randomly varying SoP, to be compensated at the Rx in order to demultiplex (DEMUX) the two independent orthogonal X- and Y- transmitted POL tributaries, such as utilize both orthogonal POL DOFs for POLMUX IMDD transmission. Such functionality is provided in the prior art (figure 1A), however our disclosure will enable modified links of improved performance, specifically, improved receiver sensitivity, larger link budget, and improved resilience to impairments relative to the prior-art, and in some of our embodiments further improvement of the spectral efficiency. The advantages of the suggested solution are attained by modifications of the conventional Tx and Rx block diagrams, and also by enabling improved POLMUX not only for IMDD but also for Coherent Detection (COHD) and for a new form of optical detection referred to as partially-Coherent Detection (pCOHD). The first embodiment as depicted in our embodiment of figure 1B. It is going to become apparent that our modifications of the prior-art AM-pilots-aided POLMUX IMDD link are going to provide much improved performance in terms of several criteria. Our invention may be referred to as ‘PM-pilots-aided POLMUX links’ where PM stands for Phase-Modulator or Phase Modulation (whereas in the context of the POLMUX links, the prior-art AM, stands for Amplitude-Modulator or Amplitude Modulation). Commencing with the IMDD case, comparing our Tx figure 1B with the prior-art Tx in figure 1A, critical inventive element apparent in our disclosed Tx and Rx of are: (i) a pair of Phase Modulators (PM) are now used in series with the two amplitude modulators (the MOD devices). These two new PMs are driven by the two pilot tones (aka marker, label or probe tones), denoted Xpilot and Ypilot, modulating the waveforms denoted ^^^^^^^ and ^^^^^^^ onto the optical phases of the two transmitted data-carrying X- and Y- tributaries. As in prior art, these pilot tones are sinusoidal, attwo distinct pilot frequencies ^^^ ് ^^^, with relatively low distinct frequencies (say inthe MHz range), repeated here: ^^^|^^^^^ ≡ ^^ ^^^^^^ 2^^^^^|^^^.We also disclose usage of more general waveforms for the PM-pilots, namely periodic but non-sinusoidal PM-pilots with periods We justify in the sequel why our embodiments may be made to function with such pilot waveforms as well. However, in the bulk of this disclosure we assume, for simplicity of exposition, the use of a pair of a pair of distinct sinusoidal tones. We further disclose that it is possible to operate with a single pilot tone inserted at the Tx into one of the two POL tributary be it X|Y, say added to the Y-POL, rather than having two distinct pilot tones. This is going to be elaborated in the sequel. As an alternative to inserting PM-pilot(s) at the Tx in our embodiment, in case the two AM-MODs are realized as Mach-Zehnder Modulators (MZM), it is possible to use the MZMs for both AM-data and PM-pilot generation, by having the drivers of the modulating electrodes on the two parallel WGs of the MZM driven by two electrical signals that are not antipodal (push-pull) but are given by the sum anddifference of two signals, േ^^AM^^^^ ^ ^^PM^^^^. The advantage is that the separate optical PMs are eliminated, the disadvantage is that now low-frequency signals ^^PM^^^^ must be added up to the two wideband voltages േ^^AM^^^^ in for each of the two top and bottom electrodes.For now, we consider a pair of sinusoidal tones at frequencies ^^^, ^^^, respectivelyapplied as phase modulations (rather than amplitude modulations in prior-art) to the X, Y POL tributaries. Inspecting our Tx structure in figure 1B, it is apparent that the two disclosed PMs are directly fed by split CW signals derived from the Laser Source (LS). Therefore, ideally assuming that the LS is monochromatic, the complex-envelopes (CE) at the outputs of the two PMs, are proportional to the corresponding PM Transfer Factor (TF) which is developed into a Fourier Series, with the Fourier coefficients^^^^^^^ given by the successive Bessel Functions of the first kind: In the range of phase index values, ^^, of interest the Bessel coefficients becomenegligible for orders |n|>6. In particular we prefer selecting ^^ ൌ 2.405 whereat thezeroth order coefficient nulls out, ^^^^^^^ ൌ 0, at which phase index, the relevantBessel coefficients in the integer range [-6,6] are depicted in figure 4. At this point we disclose that our preferred sub-embodiment for selection of pilottone frequencies ^^^ , ^^^is to have those frequencies commensurate, i.e., belonging toan equi-spaced spectral grid, such that ^^^ ൌ ^^^^௨, ^^^ ൌ ^^^^௨where the common divisor ^^௨of the commensurate pilot frequencies, ^^^ , ^^^, is calledhere the ‘unary-frequency’ (^^௨is the common unit of the two regular spectral grids), and ^^,^^are relative prime (aka co-prime) integers (at least one of the two integers is prime, as special case). In our exemplary design we take ^^:ൌ 9,   ^^:ൌ 14,  ^^௨:ൌ 1 MHz       ^^^:ൌ ^^^^௨ ൌ 9^^௨ ൌ 9 MHz,     ^^^ ൌ ^^^^௨ ൌ14^^௨ ൌ 14 MHz. The frequency grid for this selection of pilot tone frequencies is plotted in figure 5. The rationale is to enable structured spectra, exhibiting multiple orders of intermodulation products of the two tones at mutually distinct frequencies around the pilot tones. As k=9, l=14 are co-prime numbers, the two spectral grids intersect (i.e., have common points) at the frequency origin and again at ±kl =±9*14 MHz = ±126 MHz Inspecting the frequency range (0,126) in Error! Reference source not found.figure 5, it is apparent that the two grids are disjoint in this range but there is a couple of spots where a point from the first grid and a point from the second grid get as close as ^^௨from each other (the pairs (27,28) and (98,99)). Spectral plots for the transmitted X|Y-pilots are depicted in figure 6, readily obtained from figure 4 by scaling the abscissa axis of such that the step no longer be unity but rather be ^^^|^^^. The Rx DSP could use 256 MHz sampling rate, i.e., the Nyquist frequency is 128 MHz. The Free-Spectral-Range (FSR) of [-128,128] MHz wouldinclude 2*13 distinct grid spectral locations ^^^ ⋅ and2*8 distinct spectral locations ^^^ ⋅ ^^^^ ଼^ୀି଼ ൌ ^^^ ⋅ ^^^^௨^଼^ୀି଼of the ^^^^^௨^on both sides of the frequency origin (‘distinct’ spectral locations in the sense that none of the points of the two grids overlap), as may be seen in figure 5. Since, as explained above, just 6 Bessel harmonics, either side of the origin are non-negligible in the Fourier series of the two sinusoidal- PM transfer factors (see figure 4) then it is apparent that that those non-negligible harmonics are entirely contained within the FSR of [-128,128] MHz (see , figure 6) and there should be aliasing in the DSP spectrum if such analog spectra were to be digitized. Note: the disclosed tone frequencies policy would also benefit prior-art AM-pilots- aided POLMUX links. A distinct aspect in our first embodiment the suggested solution has two sinusoidal pilot tones modulate optical phases, rather than optical amplitudes in prior art. Unlike the prior-art AM-pilots-based method, our POL-MUX method is rather based on PM- pilots inserted in the two POLs at the Tx. This calls, at the Rx side, for a substantial modification in the opto-electronic processing of the received PM-pilots. Evidently, phase modulations are essentially undetectable using optical Direct-Detect receivers, which erase the phase of the optical field, only responding to the optical intensity. In addition, a modified Rx-side scheme for detecting the pilots based on slow-speed Coherent Detection used in the Monitoring (MON) optical Rx (as well as detecting the PAM data transmitted over the X and Y tributaries). Inspecting our disclosed ROSA-FE (figure 1B). Moreover, our structure of the ROSA-BE and the DIGITAL stage (the ADC) is quite conventional for ultra-high- speed Rx-s. The benefit of our disclosure is in the ability to efficiently multiplex two such DD transmission lanes only a common optical bandwidth, that would conventionally be dedicated to a single link – the POLMUX action, and do while the ADC and DSP requirements, complexity and power consumption are minimized, by virtue of a substantial portion of the signal processing functionality allocated to the DSP being moved ‘upfront’ in the Analog-Optical-Domain (AOD). In particular, the phase-and-frequency recovery and the 2x2 MIMO POL-demultiplexing are performed in the AOD, and if the AOSP optical filters are included then also the CD and PDM (DGD) equalization may also be performed in the AOD. The performance of our disclosed link of figure 1B is expected to much exceed that of the prior-art link given much stronger PM pilots and much more sensitive COH - detection pilots monitoring. However, we also use some elements present in the prior-art: a PSR is used to separate the two orthogonal POL tributaries, feeding the POLtrk 2x2 optical MIMO module performing POL derotation, for the purpose of demodulating the original transmitted X and Y tributaries out of the received linear combinations of the orthogonal transmitted polarization components, which are received in the two X’,Y’ polarization components at the inputs of the POLtrk module. In our disclosed system, the Direct-Detection of pilots by means of MON DD Rx-s is not feasible. Instead, we adopt relatively slow optically coherent detection in a pair of auxiliary (aux) optical IQ-Hybrids (IQ-HYB, aka 90o-HYB) operating at relatively slow rate WRT the baud rate, as depicted in the ROSA-FE of figure 1B, used as POL Monitors (MON), operating at relatively low bandwidths (say, sub-GHz) compatible with the adopted pilot frequencies and their relevant harmonics. A first IQ-hybrid, denoted X-IQ-HYB, is assigned to photo-detecting the ^^^Rx^^^^ pilot and a second IQ-hybrid, denoted Y- IQ-HYB, is assigned to photo-detecting the ^^^Rx^^^^ pilot. The four hybrid output signals XImon, XQmon, YImon, YQmon are fed to the eFabric for digitization and signal processing as detailed below. These signals are formally denoted in the sequel PIL ^ (with X|Y the POL components and I|Q the Quadrature components), and are compactly represented in complex-valued form as follows: The fact thatwe have switched from MON-DD Rx-s to MON-COHD Rx-s is evident (given that phase modulations are ‘invisible’ to MON DD Rx-s), but what is not evident is that this added means in the Rx is in itself insufficient for attaining a working solution, but it requires augmentation by other inventive elements aboard our ROSA-FE, as disclosed in figure 1B, namely our adoption in the Rx of a pair phase-modulations synchronized with the transmitted PM-pilots. The two matched-pilots-driven-PMs are inserted into the Local Oscillator feeds of the two X|Y-IQ-HYBs, and driven by tones at the same nominal frequencies ^^^|^as our disclosed PM-pilots injected at the Tx, and optimally delayed to account for the latency between the Tx and the Rx such that the arrival delay of the transmitted PM-pilots is matched by a delay applied to the driving sinusoidal waveforms applied to the PMs in the LO paths at the receiver. In practice the frequency and timing synchronizations of the Rx-PM-pilots with the respective Tx-PM-pilots may be performed by one of a multitude of available slow- speed clock|timing-recovery subsystems as available in the vast literature on prior-art wireline or wireless electrical links. E.g., electrical Phase-Locked-Loops (PLL) slightly adjusting the pilot oscillators may be used to synchronize the Tx and Rx frequencies, whereas a Delay-Locked-Loop (DLL) may be used to match the timing phases of the Rx and Rx pilot clocks). Note: the necessity of clock|timing recovery for synchronizing the pilot injections at the Tx and at the Rx also arises in the prior-art system of figure 1A. Both systems require Tx-Rx synchronization. Let us now explain the requirement of synchronized pilot PMs at the Tx and the Rx. Generally, fiber propagation generates ‘cross-talk’ between the X- and Y- polarization components. Thus, in the X”|Y”-output of the POLtrk module, besides the desired X|Y-POL transmitted data-signals (and X|Y-pilots), there also arises cross-talk from the transmitted Y|X-POL (both data-signal and pilot), respectively. It is then necessary to adjust the parameters of the POLtrk module such as to have the cross-POL contributions cancelled. The first step is providing the means for sensing the cross-talk contributions between the two received POLs at the POLtrk module output, as per our disclosed pilots-aided POLMUX IMDD scheme of figure 1B, based on synchronized pilot PMs at the Tx and the Rx. Prior to disclosing the signal processing at the Rx-side, let us exemplify how without additional measures (such as the synchronized PMs inserted, at the Rx-side, in the two POL paths as we disclosed, and / or special signal processing in the eFABRIC AIC) the resulting Rx scheme would be generally unusable. Assume that we have the two PMs aboard the ROSA-FE removed (or we still have them in place, but their driving pilot tones are turned off). The resulting spectra at the hybrid outputs in this hypothetical case (for a particular SoP special case outlined below) are depicted in figure 7, which may now be interpreted the signals at the IQ-hybrid outputs (since we have assumed the LO references of the hybrids are not actually PM modulated; then the hybrids simply measure the received optical fields in the X,Y POLs, up to complex proportionality constant). Actually, figure 7 shows the received contribution of both additively superposed transmitted PM-pilots, assuming an instance of the matrix product of the Jones matrix of the optical channel and the 2x2 MIMO matrix of the POLtrk module (referred to so-called end-to-end MIMO matrix) featuring real- valued matrix elements, in particular diagonal elements ^ଶ ^ଷ and off-diagonal elements േ ହ The underlying math for this figure is going to be elaborated in the following text in terms of Fourier series with Bessel functions coefficients, accounting the multitude of spectral lines consists of the intermodulations ^^^^^^^^^^^of the twopilot tones at frequencies^^^, ^^^ and their relative amplitudes, as determined by theFourier orders, n, m, as well as by the elements of the end-to-end 2x2 MIMO matrix. Figure 7 suggests that ‘sorting out’ the multitude of tones and their inter-modulations^^^^^ ^ ^^^^^at the Rx seemingly poses a daunting task for any signal processingsystem to separate the contributions of the X- and Y- transmitted tones in the received superposition of the received POLs. Our invention teaches how to address this issue. One preferred embodiment teaches the adoption of PMs inserted on the paths from the LO to the reference inputs of the two IQ-hybrids. This will be shown to have the remarkable effect of providing ‘pattern-recognition’ (in the opto- electronic domain, all-analog) of the particular pilots (Xpilot or Ypilots) participating in the displayed superpositions in figure 7 Each of the spectral lines induced by each of the two transmitted pilots will be seen to be collapsing into a single spectral line, the amplitude of which is indicative of the superposition diagonal coefficients (^ଶ ^ଷin our example). This may be previewed ahead in figure 13 A prerequisite to grasping the functionality of our invention is the end-to-end link modelling derived in the following subsection. It should be noted that the phases measured at the two output ports of the hybrids in our scheme figure 1B may be utilized in an optical Phase-Locked-Loop (oPLL), (acting to cancel out phase and frequency random variations in the end-to-end system) operating jointly alongside the State-of-Polarization-Locked-Loop (SoPLL), acting to bring the M-matrix is approximated by a unity matrix. Thus, the hybrid outputs are usable not only for POL estimation but they also enable oPLL feedback, i.e., real-time tuning the LO laser based on the sensed instantaneous frequency and phase, leveraging the capability of the X|Y-IQ-hybrid to effectively acts as a ‘phase- frequency-detector’. The emerging unexpected benefit of our invention of figure 1B is that it enables joint realization of SoPLL and oPLL, having the two feedback loops operate concurrently. In fact, as soon as the oPLL starts converging, then the convergence of the SoPLL is accelerated, and vice versa. The concurrent operation of the oPLL with the SoPLL enables aligning the received IQ quadrature signals in each of the X|Y POLs, in frequency and in phase with respect to the IQ quadratures generated in each of the two orthogonal X, Y POLs at the Tx side. To establish this joint capability, we proceed describe the signal processing to be applied onto the X|Y-IQ-HYB outputs in order to enable theextraction of the three five parameters This is carried out in the remainder of this section, addressing the signal processing onto the ^̰^HYB^|^^^^^ MON-signals, required to accurately estimate the five parameters listed above, despite the presence of the cross-terms interference (the terms cross-term^^|^^). Note 1: Sensing ^^CFO^^^^ in the AIC enables the oPLL to cancel out the Carrier Frequency Offset (CFO) (as perceived at the hybrid outputs, reflecting the differences of the CFOs in the Tx+Ch and the LO) by tuning the LO frequency by means of applying control voltages to the SoPLL-actuation (SoPLL act) inputs.Note 2: Sensing the moduli is evidently the enabler of the SoPLL closed-loop operation, in order to cancel the POL-cross-talk in the received IQ quadratures. Note 3: Additional information may be extracted re the phase arguments of the M-matrix off-diagonal elements, by subtracting out the two sensed phases ^^ST^^^^ ^∠^^^^^|^^^^^^ , yielding: Algorithmic Intelligence Controller (AIC) in the eFABRIC and its joint SoPLL & oPLL role As shown heretofore, the IQ-hybrid outputs convey valuable sensing optical frequency and phase information, usable in an optical-Phase-Locked-Loop (oPLL), or more generally in an optical-Phase-Locked-Loop (oPLL). Our disclosure of the functionality of the link disclosed in figure 1B is extended to encompass Joint sensing (monitoring) of the State-of-Polarization (SoP) as well as to optical Frequency-and- Phase-Recovery functionality, i.e., estimation of the instantaneous optical frequency and phase at the monitor module outputs, usable for providing feedback to the LO laser (assuming a tunable laser is used for the LO) in order to have its instantaneous frequency and phase track that of the incoming optical signal. The opto-electronic layer of the disclosed Joint State-of-Polarization-Locked-Loop (SoPLL) & oPLL, as described in in the Tx and Rx structures in figure 1B, is complemented by suitable signal processing in the electronic-Fabric (eFABRIC) layer, implementing signal processing algorithms collectively referred to as the ‘Algorithmic Intelligence Controller’ (AIC). The AIC top-level block diagram is depicted in figure 8 and the functionality of its blocks is presently described. The relevant top-level structure of the ROSA-FE is also sketched atop the AIC layer in order to facilitate visualizing the mixed opto-electronic-digital feedback loops of the SoPLL and oPLL. The SoPLL and oPLL are mixed analog-digital feedback loops, the digital part of which is implemented in the eFABRIC, the analog part of which is implemented on the Rx ROSA. The D / A and A / D interfaces interconnecting the two layers are part of the eFABRIC but not explicitly depicted. in the AIC block diagram of figure 8, the eFABRIC AIC comprises four relatively slow ADCs fed by the four analog electrical signals ^^^^ from the TIA outputs of the hybrids. An array of DACs is used to electrically actuate the multiple tuning DOFs of the POLtrk AOSP module (the SoPLLact signals) and the LO (the oPLLact signals). The algorithmic operation of the AIC is an inventive element of the disclosure. At the top level, the PILest algo-module processes the IQ-hybrid outputs such that the next two algo-modules in line, namely the Polarization-estimation (POLest) and the Phase&Carrier-Frequency-Offset (^^&CFO) modules be enabled to extract the estimates of the X|Y-POL-cross-talk as well as the estimates of phase-error and frequency-error between the Tx Laser Source, received via the optical channel and LO laser in the Rx. Generally, a linear combination of the two pilots is received in each of the X|Y tributaries, therefore the estimation of the two pilot complex amplitudes amounts to estimating the complex weights of the two pilots in the linear combination received in each POL tributary. From these weights the POLest module works out an estimate of SoP of the signal at the Rx PSR input. The PILest sub-algo extracts the relative amplitudes and phases of the two received pilots with unprecedented precision (relative to the prior art) due to the adoption of vigorous (large OMI) pilot modulation, afforded by utilizing the phase degree of freedom for the insertion of the pilots, without encumbering the dynamic range of the transmitter at all. Moreover, the usage of coherent detection in the slow IQ-hybrids comprised in the MON section of the ROSA provides additional sensitivity, as well as providing the phase information for the X|Y-cross-coupling coefficients (unavailable in the AM-pilots based method). One of our invention contributions is the improved accuracy, wider bandwidth, and improved robustness of the ‘POL-detector’. Taking a bird’s view of the entire SoPLL closed loop operation, the combination of our novel disclosed usage of the auxiliary IQ-hybrids, the PILest sub-algo front-end of the POLest sub-algo and the rest of the POLest algo jointly act as a ‘POL-detector’ aka ‘POL-sensor’ front-end, measuring (estimating) the received SoP with enhanced precision and over wider bandwidth than prior-art. The loop is then closed via the SoPLLact sub-algo and the physical POLtrk 2x2 MIMO module POL-transformer acting as our POL-‘plant’ (‘plant’ in the sense of control theory). Based on the POLest SoP sensing information the POLact sub-module issues in real-time actuation commands to the tunable parameters of the POLtrk that would ideally transform the received SoP into a POL-DEMUXED SoP in which the X”,Y” POL components are respectively proportional (apart from some inevitable impairments) to the X,Y POL components injected in the Tx TOSA, and as variations in the POL-channel occur the POLtrk would be adjusted to track the POL-channel (in effect realizing the inverse matrix of the POL-channel). Note 1: The digitized signals at the ADC output are evidently sequences labelled by the discrete-time integer index, k, however in the sequel we shall use t as either discrete-time index or continuous-time variable, distinguishing between the two cases by context (internally to the AIC, t is evidently discrete-valued). Note 2: the ADC bandwidths sufficiently large to accommodate various intermodulation products of the pilot frequency and prevent aliasing in the A / D process) . A D / A array (DACs) is used to actuate the SoPLL by applying control signals to the tunable electrical parameters of the POLtrk, as well as to actuate the oPLL by applying actuating signal(s) to steer the instantaneous frequency (and phase) of the LO laser. Here again adequate bandwidth must be provided. Another consideration is reducing the latency of the ADC and DAC, as latency is to be generally detrimental to closed- loop performance. The first sub-module in the AIC processing chain, depicted in figure 8 is the Pilots- Estimator’ (PILest). This sub-module forms the pair of digitized complex signals hybrids outputs and acts on these two complex-sequences to extract information on the time-frequency content of these complex waveforms. The PILest sub-module is followed by the Polarization- estimation (POLest) and the Phase-and-CFO (^^&CFO) sub-modules. The PILest sub-module processes its two complex-valued inputs ^̰^HYB^|^^^^^ in order to make them amenable for extracting the POL-estimate and the phase-and-CFO estimate in the two modules following it. The main functionality of the PILest processing is the removal of the POL-induced cross-terms cross-term^^|^^out of the two signals. The spectral structure of the cross-terms will be assessed below, as we are going to account for how the PILest algorithm distinguishes between the cross-terms and the useful direct-terms, singling-out the terms ^^ which carry the sensing information relevant for feeding the feedback loops of the SoPLL and oPLL. The PILest algorithm essentially discards the POL-induced cross-terms, extracting the useful direct-terms ^^ andthese terms on to the POLest and ^^&CFO sub-modules. The POLest module acts like a ‘SoP-detector’ simply extracting from the complex signals^^^^^^^^^^^^ట^௧^, ^^^^^^^^^^^^ట^௧^(as received from the PILest module) their moduli. These moduli are used as input for an actuation algorithm forthe actuation parameters (DOFs) of the POLtrk 2x2 MIMO linear transformation (the POLtrk DOFs) implemented aboard our disclosed ROSA (the exact nature of the POLtrk actuation DOFs is implementation dependent. There are typically more than three tuning DOFs available in the POLtrk PIC module). Note: any unitary 2x2 matrix may be specified - up to a constant common phase - by 3 DOFs. ‘endless’ POL-tracking requires the redundancy of having more tunable stages, hence more than 3 DOFs.The POLact sub-module then maps the moduli of the ^^^ ^^^^ matrix elements into avector of actuation commands of the POLtrk 2x2 MIMO module, required to iteratetowards maximizing the moduli of the direct terms which tends tominimize the moduli of the cross-POL-terms, ^^^^^|^^^^^^. This is the principle of theSoPLL. Concurrently, with the SoPLL operation, the oPLL loop is activated. The complexsignals , passed from the PILest sub-module to the^^&CFOsub-module, are processed by the ^^&CFOmodule, to have their phases (args)evaluated. In principle, a possible algorithm to extract an estimate^^^CFO^^^^ theinstantaneous frequency of the signal-LO beat tones generated in the hybrids is ^^^CFO^^^^ ൌ ^^^^^, though there exists a plethora of alternative algorithms in the literature for estimation of the ‘instant frequency of a relatively-slowly-varying sinusoid’. Note: This is in fact the functionality of an FM receiver does in wireless communication. E.g., an alternative option to estimate the CFO is to chop the digitized ^^^^ signals into blocks of data (possibly with overlaps) and perform moving-window spectral analysis, in particular moving-window Discrete-Fourier-Transforms (DFT) on the discrete time records, determining the peak of the moduli of the DFT output samples within each record. Note that in wireless communication systems, the estimation of Carrier-Frequency- Offset (CFO) is well-established prior art. Any of those CFO estimation algorithms could be adopted. The CFO, ^^CFO^^^^, instantaneous frequency may be estimated by using any of the prior-art multiple CFO estimation algorithm or any of the prior multiple sinusoidal tone frequency estimation algorithm (since over a short time-window ^^^^, ^^^ ^ ^^^ appears as a constant sinusoidal oscillation at frequency The CFO, may be determined by multiple methods e.g. locating the peakmagnitude of the DFT of ^^^ ^^^^^^^ట^௧^^^|^^ over the discrete-time window ^^^^, ^^^ ^ ^^^.Iterating this procedure enables estimating the CFO over a grid of discrete-time values with step T. An alternative method to estimate^^CFO^^^^ extracts the Arg-s (phases) of these complex-signals, and ‘unwraps’ the phase, and takes the time-derivative (denoted ^^௧) of the unwrapped phase, or equivalently fits an affine function (a straight line) to the slope of is an estimate of Other methods are possible as adopted from CFO estimation techniques in wireless or wireline electrical communication. The Four-Wave-Mixing (FWM) advantage of our disclosed PM-pilots-aided POLMUX scheme Another advantage of our pilots-PM modulation, which is applied to the entire transmitted signal is that for DD links operating around the zero-dispersion wavelength of 1.3^^^^, there arises a Four-Wave-Mixing (FWM) penalty (due to the substantial DD-carrier power concentrated in over a tiny spectral support, phase- matched for the non-linear distortion). Fortunately, the PM-pilot effect of multiplying by to multiplying the transmitted optical field by the Fourier Series yielding a beneficial effect upon FWM, by having the spectral power of the optical carrier (which we normalize to unity)distributed into the sidebands, the powers of which satisfy Thus,all terms are smaller than unity; by suitable selection of the OMI, the peakpower may be substantially reduced. E.g., at OMI=0.765, i.e., at ^^ ൌ 2.405, thezeroth harmonic nulls out ^^ ^ ଶ^ 2.405^ ൌ 0 , at which index ^^^^2.405^ ൌ 0.519 ∴^^ଶ i.e., the peak narrowband optical intensity component issubstantially reduced, efficiently mitigating FWM. Pilot Estimation (PILest) algorithm for sorting out the Rx-side PM-pilot interactions The PILest sub-module of the AIC is tasked with extracting the diagonal matrix elements of the 2x2 end-to-end MIMO matrix while blocking the POL-cross- coupling terms, present in the complexified IQ-hybrid outputs. Notably, the off- diagonal matrix elements ^^^^^|^^^^^^ within the cross-terms are subject to phase modulation and instant-frequency modulation by ^^^ట^௧^just as the direct-terms are.This implies, in particular, that spectral shifts of the direct-terms ^^^^^|^^^^^^ due theCFO ^^CFO^^^^ is matched by the same spectral shifts of the cross-terms ^^^^^|^^^^^^,i.e., the direct-terms ^^^^^|^^^^^^ and the cross-terms ^^^^^|^^^^^^ move together, bothare brought to baseband by the oPLL action, which acts to null out the net CFO.Inspecting the POL-cross-coupling terms is apparent that each of ^^^^^|^^^^^^ matrixelements are modulated (multiplied) by the complex-waveform ^^^ఉ ^^^ ଶగఔೊ௧⋅ ^^ି^ఉ ^^^ ଶగఔ^௧representing a ‘PM-cross-term’, namely a product of the X&Y PM-pilot transfer factors ^^^ ଶగఔೊ௧,  ^^ି^ఉ ^^^ ଶగఔ^௧, or its complex-conjugate. In contrast, the PM-pilots modulation is no longer present in desired direct-terms, since the X|Y- pilot-PM inserted at the Tx is cancelled out by the nominally identical X|Y-pilot-PM at the Rx. Note: An IQ-hybrid may be viewed as a ‘phase comparator’ - its output phase is the difference of the phases at the ‘signal’ and ‘reference’ (LO) ports. In our disclosed design, these two pilot-induced-phases are equal (as the pilot phase at the ‘signal’ port is equal to the received pilot phase which in turn is, by design, equal to the transmitted pilot phase). However, when the transmitted PM-Y-pilot mixes with the PM-X-pilot in the Rx (or vice versa), since the two pilot phases now differ, theirdifference ^^ ^^^^^^ 2^^^^^^^ െ ^^ ^^^^^^ 2^^^^^^^ (or its opposite) comes out non-zero. It isinsightful to work the Fourier Transform (FT) (referred to as ‘spectrum’) of the attain a frequency-domain understanding of the identity satisfied by the ‘PM-self-terms’: ^^^ఉ ^^^ ଶగఔೊ௧ ⋅ ^^ି^ఉ ^^^ ଶగఔ^௧ ൌ 1It is shown that the ‘spectrum’ (FT) of the complex PM TF waveform ଶగఔ^௧remarkably features ‘perfect’ delta-function ACOR, displaying nosidelobes, just the autocorrelation peak at ^^ ൌ 0.Note that since ^^^ఉ ^^^ ଶగఔ^௧is periodic it has a Fourier series ^^^ఉ ^^^ ଶగఔ^|ೊ௧ൌ Therefore, the ‘perfect’ ACOR result may be reformulated in terms of the sequence of Fourier series coefficients as a discrete-time ACOR. Inspecting our disclosed ROSA of figure 1B, the PM-pilots (launched at the Tx) are sensed by of IQ-hybrids, modelled as ^̰^HYB^^^^ i.e., the IQ- generate the conjugate product between the input signal ^̰^^|^^^^^ and the LO reference ^̰^^|^^^^^. The FT of a conjugate product is given by an XCOR. In the hybrid I / O model case, this is the XCOR between the FT of the signal ^̰^^|^^^^^ fed into the hybrid and the FT of the signal fed into the reference (LO) port: FT^^̰^HYB^|^ ^^^^^ ൌ FT^^̰^^|^^^^^^ • FT^^̰^^|^^^^^^Thus, the IQ hybrid may be viewed as a frequency-domain XCOR analog evaluation device. It has been shown in US provisional patent 63 / 645,766 that the following situation holds: (i) None of the XCOR sidelobes overlaps in its location with the location of the ACOR mainlobe. (ii) The level of the ACOR mainlobe is much elevated above the level of maximal sidelobe element in the XCOR. The ratio of these two levels is a ‘Signal-to-Interference’ metric – in our exemplary design, the two levels are in the ratio 1:0.27 = 11.37 dB. These features of the signals at the IQ-hybrid enable the PILest algorithm to consistently and accurately discriminate between the desired ACOR terms, which arelinear in ^^^^^|^^ vs. the interference (POL-cross-talk) XCOR terms, linear in ^^^^^|^^.It has been shown, in US provisional patent 63 / 645,766, that one of the key functions of the PILest is to map the complexified outputs of the two hybrids into the frequency domain, by performing Short-Time-DFT as detailed below, and within each DFT output record, identify the spectral line which the strongest modulus (or modulus squared), referred to as the ‘mainlobe’, after which the lower level sidelobes may be ignored. The complex value of this mainlobe spectral line is then passed (in Cartesian form, re-im, or in polar form, magnitude and phase) to the next two estimation sub-modules (the POLest and the CFO&^^est, to estimate the 2x2 MIMO matrix elements (magnitudes and phases), as well to estimate the CFO evolution and the momentary phase. The frequency-domain analysis in this subsection suggests digital signal processing of the two complexified outputs of the two hybrids in the PILest module based on moving-window spectral estimation algorithms. Note: a ‘Moving Window Discrete Fourier Transform’ (MW-DFT) , aka ‘Short-Time DFT’ (ST-DFT), ‘Sliding DFT’, or ‘Windowed DFT’ (W-DFT)), is a technique used in signal processing to analyse the frequency content of a signal over time by applying a Fourier transform within a sliding window that moves across the signal, allowing for the examination of how the frequency components of the signal evolve. The fundamental idea behind the moving window Fourier transform is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each segment. This method involves dividing the signal into several segments or "windows" and performing spectral analysis on each segment individually. The "moving" aspect comes from the fact that these windows are shifted across the signal, usually with some overlap, allowing for a time-resolved analysis of how the spectral content changes. This approach is particularly useful for signals that are non-stationary. This approach provides a time-frequency representation of the signal, offering insights into the frequency content at different time intervals. Variants of this approach differ in whether the records (blocks) of data on which the DFT is evaluated are successive, non-overlapping, or overlapping and the amount of overlap between successive records, and the type of windowing applied (if at all) on the records. This functionality is hosted in the PILest algorithmic module of the AIC. Variable adaptive ST-DFT window length Since our oPLL is tasked not only with analysing stationary random signals (phase noises) but also non-stationary ones (the CFO) both time and frequency resolution are important, thus Short-Time Fourier Transform (STFT) can be used. By segmenting the signal into overlapping windows and applying the DFT to each segment, one can achieve a compromise between time and frequency resolution. The degree of overlap and the window size are parameters that can be adjusted based on the specific requirements of the analysis. Another parameter adjusted adaptively in our disclosed PILest algorithm is the ST- DFT window length (the length of the record on which the DFT is performed). Since the AIC is tasked with both non-stationary CFO estimation and stationary phase- noise and SoP estimation, the non-stationary CFO is the first component to be sensed and closed-loop converged, ideally to null. CFO is decreased in the oPLL feedback loop by actuating the LO towards bringing its instant frequency closer to that of the signals at the hybrid outputs, i.e., reducing the estimated CFO (which equals the difference between the LS and LO instant frequencies). To this end it is useful to perform the CFO convergence (the evolution towards the oPLL locking, wherein the instant frequencies of the LS and LO are equal on a time- average basis) using a sliding window DFT duration that is shorter than the window duration used in the ‘locked-state’ of the oPLL, in order to better approximate the CFO quasi-stationary over the shorter window, i.e., closer to a sinusoid with equally spaced zero-crossings (although the CFO is actually non-stationary over longer time windows). At fixed temporal sampling rate (say 1.024 GHz) the shorter DFT window implies a smaller frequency resolution. Indeed, denoting the number of temporal samples in the sliding window duration (i.e., the DFT size) as M, then an inversemeasure of frequency resolution is given by the frequency step ^^res ൌ ^^samp / ^^, where^^ ି^samp ≡ ^^samp is the sampling frequency and ^^sampis the sampling interval. Then, as Mis initially decreased (to benefit from short-time-quasi-stationarity), ^^resgets larger, indicated operation at coarser, decreased frequency resolution. Thus, the CFO may be advanced in coarser steps towards zero. Once the CFO gets sufficiently small, it is possible to improve the frequency resolution, taking the window duration longer, i.e., increasing the duration of the sliding-DFT-window, as well as increasing the DFT size M, thus reducing ^^res, i.e., using finer frequency steps. Once the oPLL acquires lock, the DFT size may be even further increased, say up to M=1024 points.Assuming the sampling rate is ^^samp ൌ 1.024 GHz such that ^^res ൌ 1.024 GHz / 1024 ൌ 1 MHz ൌ ^^௨, i.e., the frequency resolution now withthe unary-frequency-step, ^^௨ ൌ 1 MHz, consistent with figures 6, 7, 10 and 13.In the locked state, using some exemplary numbers, further to the assumed ^^sampൌ1.024 GHzand ^^ ൌ 1024points, let us assume that the target SoP-trackingBandWidth (BW) is BWSoPLL ൌ 300 KHz, and for the phase-noise tracking (thestationary phase-noise component, excluding the CFO), BWoPPL-థ ൌ 300 KHz. TheCFO bandwidth is actually the Nyquist bandwidth available at the sampling rate i.e., BWoPPL-CFOൌ ^ ଶ ^^sampൌ ^ ⋅ 1.024 GHz=512 MHz; thus, the system is able to‘capture’ (and bring to null) CFO in the range [-512,512] MHz. In case the CFO exceeds the aforementioned range, and assuming that the frequency tuning range of the LO laser is sufficiently wide (exceeding a 1 GHz span) and the LS and LO lasers are reasonably matched in their nominal frequencies, then a relatively straightforward CFO-pre-initialization algorithm would intentionally actuate the laser such as to ramp the CFO up or down (two- sided) until the CFO is captured within the [-512,512] MHz window. The value of M (ST-DFT window size = sliding record length) may be adjusted according to the natural slew-rate of the DFT in order to attain quasi- stationarity, i.e., avoid a ‘blob’ of several adjacent frequency samples turning on to non-negligible values, which amounts to degrading the frequency resolution either due to the non-stationarity (if the window is too long) or due to the inherent reduction in the frequency resolution due to the uncertainty principle (if the window is too short). Once oPLL locking is attained then the SoPLL algorithm (the POL controller) may be converged towards its locked-state. Notice that before the SoPLL converges, i.e.,ahead getting very close to its maximal value of unity (whereat ≅ 0, i.e., we the POL-cross-talk is suppressed), the ‘direct-terms’are not at their peak value of unity (e.g. in figure 13, the ACOR mainlobe falls short of unity, it is rather at ^ଶ ^ଷ (indicative of the cross-term being at ହ ^ଷൌ ^1 െ ^^ଶ ^ଷ ^ଶ). Actually, there is a chancethat the system commence in a state wherein หis quite small relative tosuch that the mainlobe in the XCOR output may be at a lower level than the cross- POL sidelobes (while the sidelobes get elevated). Thus, for the CFO estimation algorithm to function correctly, it is important to get some degree of convergence of the SoPLL algorithm. Thus, a preliminary step ahead of conducting the CFO-convergence stage is to get at least partial convergence of theSoPLL. Due to the CFO, whenever ห^^^^^||^^ห is not too small, then some discerniblemainlobe spectral line rising above the cross-POL-sidelobes, may appear at some arbitrary horizontal shift (which is dependent on the instant CFO). The procedure to perform a discrete scan of the SoP by means of intentional actuation of the POLtrk module, to have the SoP switched between, say, 8 points equi-spread on the Poincare sphere, and determine for each such trial-SoP, whether there is peaking of one of the spectral lines anywhere in the ST-DFT record, which is then identified as the mainlobe instance during the particular ST-DFT window and that for that trial-SoP (this discrete scan is going to occur at the bandwidth available in the POLtrk). From this point on the SoPLL can be actuated to try to vertically maximize the mainlobe that appeared whereas the CFO-loop attempts to reduce the CFO to zero. Synchronization of the Tx and Rx pilots The IQ-hybrids require optical references aka optical Local Oscillators (LO) for their inherent operation. Those are provided from a laser source at the receiver side, which is split to feed the two LO ports of the hybrids. In this respect, another highly beneficial disclosed element of the invention is the incorporation of Phase Modulators (PM) onto the LO paths leading to the hybrid as shown in the figure. These PMs are not to be confused with the Tx-side PMs that generate the X- and Y- pilots. Moreover, the drive signals of these PMs in fact correspond to the pilots at the Tx side, in fact, the PM on the LO branch leading to the X-hybrid should be ideally be driven by a signal as close as possible to the ^^^^^^^ pilot, whereas the Y-hybrid should be ideally driven by a signal as close as possible to the ^^^^^^^ pilot, where ‘close’ having the drive Rx side X|Y- tone frequency deviate as little as possible from the X|Y- tone frequency at pilot tone frequency at the Tx. Thus, ideally the X- and Y- PMs on the LO paths should be driven by identical (corresponding) pilot tones as those of in the Tx.In practice a pair of pilot oscillators of nominal frequencies ^^^ , ^^^are provided in theTx to drive the two PMs there, and a pair of pilot oscillators (in the paths of the twoX- and Y- data tributaries) of identical nominal frequencies ^^^ , ^^^are provided in theRx to drive the two PMs (in the LO paths). In practice the clock frequencies may randomly drift, wander around the nominal frequencies. Therefore, means, such as low-frequency electronic Phase-Locked- Loops may be provided to synchronise the respective (X, Y) pilot clock frequencies at the Tx and Rx sides. In addition, it is necessary to synchronise the phases of the Tx and Rx X|Y pilots, respectively. In fact, while the phase and frequencies synchronisations for the tributary clocks at the Tx and Rx are necessary for the operation of the invention, the means to achieve the requisite synchronization condition are well-known in prior-art, as the need for such synchronization of transmitter and receiver clocks arises in virtually all wireless and wireline electronic links. Phase recovery and carrier frequency offset mitigation are well known prior-art techniques adopted here as well for the respective X|Y pilots' synchronizations between the optical Tx and the optical Rx. In particular if a pair of electronic receivers are adopted for processing in the PILest module then the timing recovery (frame synchronization) techniques between OFDM Tx-s and Rx-s may be applicable here on the Rx side. Note: In fact, similar synchronization requirements arise in the prior-art AM-pilots based scheme, though we have not discussed it in our review. Variants of our PM-pilots-aided POLMUX one-way link. In this subsection we disclose diverse variants of our embodiment of figure 1B, modifying the Tx and / or the Rx in various ways. Digital-domain effective PMs: We first disclose a modification of figure 1B, wherein the PMs on the LO paths in the ROSA are going to be removed. One may wonder why the Rx-side PM-pilots are no longer needed. Actually, the functionality performed by the PM-pilots aboard the ROSA figure 1B is going to be performed digitally in this new variant, depicted in figure 14, based on incorporating ‘virtual pilot-driven-PMs’ in the algorithms of the PILest signal processing sub-module (see figure 8 for the PILest location in the processing chain). In the ROSA block diagram in figure 14, the LO is now split, unmodulated, to the two hybrids. The unmodulated LO is assumed to have constant amplitude ^^^(no Relative Intensity Noise) but be affected by phase noise, ^^LO^^^^. The two hybrid outputs, are now given by Those outputs are passed to the eFabric, fed into an array of ADCs in the AIC interface. The two digitized X|Y-IQ-HYB complex outputs are still denoted but now t denotes discrete-time. The PILest sub-module is now modified to perform the complex multiplications specified in the first equality below: ^^ି^ఉ ^^^ ଶగఔ^|ೊ௧. Thus, the multiplication by the complex transfer factor ^^ି^ఉ ^^^ ଶగఔ^|ೊ௧is now performed in the DSP domain (rather than being realized as originally, by means of physical modulation of the LO by the complex transfer factor ^^^ఉ ^^^ ଶగఔ^|ೊ௧representing propagation via the PM aboard the ROSA, followed by complex conjugation due to the action of the IQ-hybrid onto its reference port input signal). The two approaches generate (in the ideal case) indistinguishable complex signals, notwithstanding that the term^^ି^ఉ ^^^ ଶగఔ^|ೊ௧now virtually originates in the digital domain rather than using physical PMs. We should mention that although the theoretical models for the signals come out identical, ideally, when using this last disclosed embodiment, upon accounting for impairments, there emerge performance trade-offs between the two options: The frequency-domain deterministic ACORs and XCORs pick up more noise when they are executed digitally, as the optical receiver thermal noise at the TIA outputs. as well picking up quantization noise and ADC distortions. Thus, the digital Auto|Cross- Correlations pick up more noise in the PM-in-DSP version. In contrast, in our first proposed embodiment of figure 1, the correlations (ACOR and XCOR) are generated noiselessly in the optical domain, prior to the addition of shot-noise and thermal noise in the PDs+TIAs and prior to the addition of quantization noise and distortion. On the other hand, the physical PMs introduce some optical loss (albeit on the optical LOs, where say 0.5 dB of attenuation would be insignificant if the LOs are sufficiently strong). Another impairment of the ‘PM-in-DSP’ scheme is the following. In the ‘physical’ PMs version the ideally impulsive ACOR effectively occurs ahead of the PD^TIA^ADC chain. The lone frequency-domain impulse that the ACOR features, is effectively generated ahead of the filtering action of the photodetection process. Unfortunately, in the new variant (performing the PM in DSP), the received line spectra of ^̰^^|^^^^^ (see figure 7) are subject to frequency-domain attenuations or ripple in the TIAs and to ADC distortions. This effect is not present in the physical- PMs version of figure 1B. Usage of non-sinusoidal PM-pilots We now disclose a variant replacing the sinusoidal pilots by periodic non-sinusoidal ones. Thus, the sources of the PM-pilot-drive signals, as depicted in figure 1B, are no longer sinusoidal generators but are periodic signal sources (e.g., square waves, triangular waves, or any other periodic waveforms). Note: Such modification of the sinusoidal pilot sources to periodic non-sinusoidal pilots may be applied not only to figure 1B but may be extended to any of the other embodiments depicted in this invention. It turns out that the signal-flow and signal-processing principles do not change when the driving waveform is non-sinusoidal but still periodic. To see this, consider the model derived previously. Now, the PM-transfer factors are now longer ^^^ఉ ^^^ ଶగఔ^|ೊ௧but let us assume that theyhave the generic form with ^^^^^; ^^^|^^ defined as any periodic waveformwith period given by the parameter . It is convenient to constrain ^^^^^; ^^^|^^ tosatisfy ห^^^^^; ^^^|^^ห ^ 1. Since ^^^^^; ^^^|^^ is periodic then so ^^^ఉ⋅^^௧;ఔ^|ೊ^. Thus, the complex waveform ^^^ఉ⋅^^௧;ఔ^|ೊ^may be represented as a Fourier Series where we indicated the dependence of the Fourier coefficients (^^^ ≡ on both the modulation-index ^^, as well on the periodic pulseshape, ^^^⋅^. Moreover, ^^^ఉ⋅^^௧;ఔ^|ೊ^is unimodular: PM-pilot-tones-aided POLMUX COH transmitter – MZMs & oDACs Our PM-pilots-aided IMDD POLMUX inventive concepts disclosed heretofore, pertained to the context of IMDD optical transmission and detection. We now teach how to extend our disclosed schemes from IMDD links to coherent optical links, i.e., links using Coherent Detection (COHD) in their Rx-s. The challenge in the use of pilots in COH Tx-s stems from complex-valued coherent modulation formats having zero-mean. Square QAM modulation formats or AM-PM formats exhibiting rotational symmetries, wherein the center of gravity of the complex constellation is at the origin, and the constellations are symmetric around their centers, hence such COH transmission constellations feature zero-mean. The problem: Starting from the observation that the mean of a transmission constellation is nothing but the level of the transmitted ‘carrier’’ component, it is apparent that conventional QAM links feature zero-carrier (and so do the I and Q BIP-PAM tributaries), since their constellations are symmetric relative to the origin on the IQ plane. Therefore, modulating the transmitted POL signals by either AM or PM pilots would simply not work, since the product of the deterministic sinusoidal PM pilot with the random QAM would also yield random processes of zero mean, i.e., the pilots modulated at the Tx would not be detectible at the Rx, once the pilots get multiplied in the Tx by a bipolar zero-mean ultra-fast random train of data- modulated delayed pulses. We conclude that pilot-based POL-MUX COH transmission techniques are not feasible in their current form used for IMDD. This actually applies to the prior-art AM-pilots based scheme of figure 1A, as well as to our disclosed PM-pilots based scheme figure 1B – neither of the TOSA block diagrams, would be adaptable ‘as is’ to coherent links. The solution, in principle: There is a remedy to the zero-mean impediment: pilot- based schemes may be rendered usable over COH links by providing inventive means at the Tx to enable non-zero optical carriers to be additively superposed atop the transmitted XI,XQ,YI,YQ data-carrying tributaries. To this end, the COH-grade PAM constellations (generated along the IQ-axes of the X,Y-POLs) must be rendered asymmetric (yet generally be of the BIP type, i.e., have at least one positive and one negative level), and means to superpose the X|Y-PM-pilots be concurrently provided, and also provide the means of interferometric phase-balancing of the TOSA PICs. Embodiments of MZMs for pilot-aided POLMUX QAM16 with non-zero carrier We exemplify our disclosures starting with the widespread case of 16QAM transmission, with their IQ tributaries (on each of the X,Y- POLs) conventionally consisting of symmetric Bipolar (BIP) PAM4 constellations of zero-mean, transmitting optical field symbols out of the set {-3A,-A,A, 3A} along the I|Q-axes of the X|Y-POL tributaries. Most generally our disclosures essentially teach how to modify conventional QAM schemes in order to generate multi-level complex constellations of any order that are asymmetric (have non-zero mean, thus have non- zero optical-carrier), and imparting sinusoidal X|Y-PM-pilot modulation onto the optical carrier associated with the ASYM constellation. Moreover, in some of our embodiments, the MZMs are combined in pairs to form the so-called ‘optical-DACs’ (oDAC) driven by simple two-level drivers (rather than 4- level BIP-PAM4 drivers). The oDACs disclosed here differ from prior art oDACs in that the oDACs disclosed here inherently generated ASYM oDAC constellations, i.e., the new oDACs provide for non-zero optical carrier. Moreover, these oDACs are based on optical splitters and combiners of the simplest type, 2x2 symmetric (50:50) MMI or directional coupler devices unlike our previous work in which asymmetric two-by-two split and combine was required. Our embodiments of the said means of asymmetric BIP-PAM4 constellation generation and X|Y-PM-pilot injection, with interferometric phase-balancing of the PICs, are presented in figure 15 (treated here) and in figure 16 (treated in the next subsection). These embodiments enable Dual-Polarization PM-pilot-aided 16QAM POLMUX (Dual-POL) COH links, wherein each quadrature (I|Q) in each POL (X|Y) consists of Bipolar (BIP) PAM4. In this subsection we address Tx-side Building Blocks (BB) for Dual-POL (POLMUX) Coherent 16QAM links, namely MZMs and optical-DAC (oDAC) BBs. The MZMs|oDACs are used in the I|Q-X|Y tributaries of the PM-pilots-aided COH Tx. Note: each oDAC disclosed here itself comprises a pair of MZMs with specific drivers. Commencing with figure 15A, describing an MZM for COH transmission with pilot- injection, in the disclosed block-diagram a pair of slower PMs are placed in the two MZM arms in series with the fast-PMs push-pull-driven by BIP-PAM4-data. This physical layout for the PIC of an MZM is known in prior-art, as a means to apply differential phase offset in order to generate a non-zero carrier. Nevertheless, the novel aspect of our disclosure in figure 15A is the particular driver structure feeding the pair of slower PMs, enabling to concurrently provide three distinct functionalities: (i) to maintain the differential phase-balance between the two arms of the MZM at a desired bias point. (ii) to modify the ‘desired bias point’ at will. (iii) to insert sinusoidal X|Y-PM-pilots. These functionalities are realized in the disclosed electrical driver by generating the sum (common-mode) and difference (delta-mode) of two electrical inputs, whereby the first input being the electrical pilot sinusoidal generator, whereas the second input is the desired bias offset (proportional to an adjustable DC voltage) atop of which a variable zero-mean actuation voltage is added in order to counteract random differential phase drifts between the two arms (assuming zero-mean random environmental differential phase disturbances). Note: An alternative embodiment, not explicitly depicted in a figure, removes the pair of slower PMs in figure 15A, instead adding the two adder outputs to the differential (±) output electrical ports of the BIP-PAM4-eDAC driver (eDAC = electronic DAC). Bias-Tee or diplexer electrical circuitry may be used to affect the said additions. In figure 15B, an MZM is driven by the high-speed BIP-PAM4 symmetric zero-mean signal, such that the mean signal is zero. The carrier is linearly added at the MZM output by means of an interferometric structure with the MZM in its lower arm, whereas the upper arm consists of a reference waveguide, nominally of the same optical length as the lower-arm comprising the MZM. The optical signals splitting and combination are performed by means of variable (or fixed) asymmetric couplers that are ‘matched’ in the sense that their power-split|combine ratios are identical, both given by W1:W0(with W1+W0=1). This ensures maximal combination efficiency. The amplitude of the carrier can be adjusted by adjusting the W1:W0ratio. The X|Y- PM-pilot drives a separate PM preceding the MZM. While the end-to-end transfer factor would not change if the external pilot-driven-PM and the MZM were interchanged in their order (i.e., having the pilot-driven-PM at the MZM output rather than its input), nevertheless the current scheme turns out easier to monitor. At this point let us mention that both MZMs in figure 15A and figure 15B may be monitored (in terms of their optimal interferometric phase-balance bias settings of the two MZM parallel arms) by using for the output combiner in either scheme a 2:2 device – a 2:2 MMI or directional coupler in figure 15A, and a slow-MZM (used as variable 2:2 coupler) in figure 15B. An example of the Control & Calibration (C&C) algorithm for the MZM is illustrated in IS patent 10496069 which is incorporated herein in its entirety, but let us briefly mention that slower frequency pilot tones, referred here as ‘dither tones’ (say in the [1,10] kHz range) which are distinct in frequency from one another are applied to the various PMs and the interferometric impact of those modulations is monitored at the free output port of the combiner. The monitor consists of a slow PD+TIA photodetecting the light at the free port and the AIC (C&C algorithm) performs signal analysis on the monitor signal extracting the amplitudes of the received dither tones and inferring from those amplitudes the bias settings of the device. The reason the low range of [1,10] kHz is selected for the dither tones is that Thermo-Optic (TO)-PMs are available at these low-bandwidths at relatively low power consumption and low-insertion loss. But a disadvantage is that the monitor optical Rx must be ‘DC-coupled’, and it turns out that low-frequency noise affects the PDs and TIAs of DC-coupled optical Rx-s (which perform direct- detection). The inventive C&C element is the following: by having the X|Y-pilot-PM placed ahead of the MZM, since the spectrum of the phase-modulated optical signal comprises Fourier harmonics, then the first few Fourier harmonics at frequencies ^^^^^|^ห^∈ℤof the pilot-PM as optical sub-carriers act as frequency-domain upconverter of the slow dither tones in the [1,10] kHz range up, around the respective harmonic frequencies. We recall our example using X|Y-PM-pilot tones atfrequencies ^^^:ൌ 9 MHz,     ^^^:ൌ 14 MHz.The first harmonic of the X-PM-pilot at 9 MHz is split into two dither tones at 9 േ^^ௗwhere ^^ௗis in the ten kHz range, thus the monitor photo-detection is now at much better SNR than in the case that no PM-pilot traverses the MZM, thus the monitor detects baseband slow spectral tones at േ^^ௗwhereat the photodetection is noisy due to 1 / f-noise and other noise sources. Similar up-conversion effects occur around the higher-order harmonics which are not negligible in amplitude. We should mention that the C&C scheme for the MZM is enabled by having a non- zero optical carrier present in the two MZMs disclosed in figure 15 (and also in the oDACs disclosed in figure 16, described in the next subsection). Efficient generation of uniform Asymmetric Bipolar PAM4 (ASYM-BIP-PAM4) constellations We now disclose the efficient generation of a uniform asym-BIP-PAM-4constellation^^ enabling PM-pilots-aided POL-MUX COH links, based the Multi-Parallel (MP) optical-DACs (oDAC) structures depicted in figure 16. The constellation is normalized relative to the peak optical field level that emerge at the oDAC output(the ‘Most-Significant-Level’ (MSL)). The mean of the constellation is ^^^^ ൌ under the MSO. Structurally figure 16A and figure 16B discloses a pair of two-parallel (2p) ‘optical DAC’ (oDACs) embodiments based on optical splitter and optical combiner devices consisting of 50-50 directional couplers or MMIs. Note: Some prior art Multi-Parallel (MP) oDACs and in particular dual-parallel oDACs were for intended for symmetric (zero-mean) BIP-PAM generation for COHD. Moreover, those prior-art DACs required split and combine ratios that are not 50-50 thus are less convenient than the 50-50 split and combine ratios disclosed in our new embodiments in figure 16. Each of the 2p-oDAC structures in figure 16A and figure 16B comprises a pair of identical parallel MZMs, respectively driven by a Non-Return-to-Zero (NRZ) signal On-Off-Keying signal. A driver comprising two independent NZR and OOK sources, as required here, is typically simpler and more energy-efficient than a driver generating BIP-PAM4 signals, however a disadvantage of a an OOK&NRZ driver over a BIP-PAM4 driver over is that an OOK&NRZ requires twice as many electrical transmission line to the MZM electrodes. The drive voltages for the upper and lower electrodes for the two MZMs are േ ^ ^^ ^^ ^ ଶbkff గfor NRZ-MZM (top one in the figure) and 0| ଶ ^^bkff^^గfor the OOK-MZM(the bottom one), where ^^^^^^is the backoff factor (0 ^ ^^^^^^ ^ 1). Note: Thisassumes that both MZMs are biased such that when the voltage-drops on the two parallel WGs of the two MZMs are zero, then no optical signals are emitted. For the OOK-MZM it may be more convenient to have it biased at the so-called Quadrature point and apply voltages േ ^ ସ ^^గ. The differential phases between the two WGs of the two MZMs are respectively the NRZ and OOK MZM. Using the TF TFMZMൌ ^^^^^^^ ^ ଶ ^^^^^^^ for the MZMs, we have: (i) for the thus േ^^,  where ^^ ≡ ^^^^^^^ ^^గ bkffଶ ^. We shall use the ‘Kronecker Sum’ notation, ⊕, introduced in M. Nazarathy and I. Tomkos, “Energy-Efficient Reconfigurable 4|16|64|256-QAM Transmitter Based on PAM2|4-Driven Optical DACs,” IEEE Photonics Technology Letters, vol.34, no.21, pp.1159–1162, Nov.2022, doi: 10.1109 / LPT.2022.3198369 which is incorporated herein in their entirety (for two RVs A,B then ^^⊕^^, is the RV obtained by adding any of the values of A to any of the values in B (with the results displayed in a particular order). In this notation the end-to-end TF of the oDAC amounts to the following constellation: where the splitter|combiner feature power (intensity) split|combine ratios ^ ^ ଶ or optical field combine ratios ^ √ଶ: ^ √ଶand we multiplied the transfer factors encountered along the top and bottom paths and then summed up the end-to-end TFs of the two paths. Note: The constellation ^^ ^ ଶ ,െ , 1,0^^^ in (10) essentially coincides, with^െ ^ ଶ, 0,^ ଶ, 1^^^ (the order within the set is immaterial). We are going to continue withthe ordered constellation^െ ^ ^ , 0,ଶ, 1^^^.The normalized constellation^െ ^ ^ , 0,ଶ, 1^^^, generated at the output of the oDACs offigure b and figure c has mean ^ ସ^^. In case ^^bkff ൌ 1, i.e., when the MZMs are notbacked off, then ^^ ≡ ^^^^^^^ ^^గ ^ ^ bkffଶ^^bkff:ୀ^ ൌ 1thus the meanସ ^^becomes ସ, which is -12 dB under the peak level (the MSL). This is still a sizable carrier level, which should benefit the performance of the PM-pilots estimation at the Rx side. The trade- off is that now the Full Scale (FS) (defined as difference of the most and least significant levels) of the 1,0^ constellation is (without backoff) given by: The FS may be compared with the FS of a conventional symmetric constellation:FSBIP-PAM4 ൌ 1 െ ^െ1^ ൌ 2 The reduction in FS due to the introduction of the asymmetry (the generation of carrier at the ^ ସ level is then 0.625 ൌ െ4.08 dBNote: It is apparent that the reduction in loss budget is due to the need to generate the -12 dB carrier in the POLMUX COH Tx link is 4 dB. Since COH links are generally known to be ~10 dB more sensitive than their DD counterparts (under ‘equivalent’ conditions, in particular at the same symbol rate for both the COH and DD link), then it follows that our PM-pilots-aided POLMUX COH link still has a net advantage of 6 dB in link budget over the reference DD link. Moreover, the said COH link operates at 4x the spectral efficiency (due to the availability of four I|Q-X|Y ‘lanes’) relative to the reference DD link. The devices labelled TO-PM in figure 15B and in figure 16A are Thermo-Optic Phase Modulators, namely relatively slow PMs with ~10-20KHz bandwidth, negligible insertion loss and relatively low electrical power consumption. The PMs in figure 15A and in figure 16B are driven by pilot tones + possibly slow differential bias voltages, thus these PMs must have bandwidths adequate for the pilot tone frequencies attaining reasonable modulation levels (e.g., use PMs with high-pass- modulation response with low cutoff of a several MHz). The ‘PM (fast)’ devices are driven by high-speed (at baudrate) by waveforms carrying information symbol modulated upon the PAM-pulses. For a complete XY-IQ Tx either of the modulating structures of figure 15 or figure 16 is to be duplicated four times in each of the X|Y-I|Q lanes which are optically multiplexed, just as per prior-art coherent optical transmission, namely first forming IQ-pairs then mapping each IQ-stream onto the X,Y-POL tributaries. A preferred embodiment of the optical Tx of the PM-pilots-aided POLMUX COH 16QAM link is depicted in figure 17. The I|Q-X|Y tributaries in its four lanes are generated by means of our disclosed oDACs of the type of figure 16A. The novelty of the TOSA block diagram in the figure is in the nature of the per-quadrature-per-polarization means (figure 16A) of generating ASYM PAM constellations (having non-zero carrier) which is essential for enabling PM|AM-aided links with COH detection. The four parallel lanes generate the signals XI, XQ, YI, YQ. XI and XQ are 90orelatively phase-shifted, i.e., are in quadrature. They are combined to form the X signal. Similarly for YI and YQ are combined in quadrature to form the Y signal. The X and Y signals are POL-multiplexed by the Polarization Combiner Rotator (PCR) module, the output fiber port of which is the Tx output. The four lanes then comprise optical carriers at -12 dB level. These optical lanes are PM modulated by four orthogonal respective pilots. We aim to have the harmonics of the four pilot tones at mutually non-overlapping frequencies (i.e., form orthogonal sets) in the frequency band of interest. An exemplary ‘frequency-plan’ for the four PM-pilots and their harmonics is the following: ൌ14^^௨ ൌ 14 MHzIt is then apparent that ^^^ூ , ^^^ூare at 9MHz and 14 MHz just equal to the previouslyused ^^^, ^^^. However, we now augment these two frequencies with two newfrequencies ^^^ொ, ^^^ொat 11 MHz and 13 MHz. All four frequencies are co-primemultiples of ^^௨:ൌ 1 MHz. Developing the respective TFs of ^^^ொ^^^^ ≡ similar spectralproperties to those of fact all four TFs satisfy in thefrequency domain the following properties. They all share the same co-domain (set of values), and the spectral locations of these co-domain values are mutually distinct. This indicates that the peak XCOR sidelobeis just as in our prior analysis, e.g., for ^^:ൌ 2.405, we again obtain that the highestsidelobe modulus is 0.27 whereas the mainlobe is at unity. Moreover, as only six harmonics on either side are non-negligible, it is readily verified that there arises no aliasing, provided the sampling rates of the ADCs is 1.024 GHz or higher. It should be appreciated that figure 16A is just one of four possible embodiments of a PM-pilots-aided POLMUX COH Tx enabling COHD over four ‘lanes’ (with four times the spectral efficiency of a baseline DD link and with extra link budget). We disclose that the full PM-pilots-aided POLMUX COH Tx may be alternatively realized in using either our single-lane modulation means of figure 16B, or the modulation means of figure 15A and figure 15B. All we have to do is to replace the four oDACs in figure 17, with either of the three modulation means options. However, the three resulting figures are omitted. Note: The COH Tx system depicted in figure 17 may also comprise optional slow monitor PD+TIAs at the ‘free’ port of the MMI output, as well as at the free ports of the MMIs respectively combining XI, XQ and YI, YQ. However, to keep the figure simple the monitor output waveguides and the slow PD+TIA electronic modules on each of the monitored optical ports, were omitted from the figure. PM-pilot-tones-aided POLMUX COH Receivers (Rx) – for 1-way link Equipped with the Tx treated in 4.4 above, we are ready to disclose the corresponding Rx designs. Disclosing a new type of IQ-hybrid: the PM-Correlated-IQ-Hybrid (PMC-IQ-HYB). The question arises how the reception of the I|Q-X|Y-multiplexed signal generated by means of the PM-pilot-aided Tx of figure 17 (or by means of one of the three additional disclosed Tx-s, the figures of which are omitted) is implemented by processing at the Rx-side the four I|Q-X|Y PM-pilots inserted at Tx. In this subsection we disclose an innovative IQ-hybrid (figure 18B) to be used as Building Block (BB) in order to realize our preferred embodiment of a POLMUX QAM16 COH link exploiting all four PM-pilots injected into the XI|XQ|YI|YQ-POL tributaries (or a subset therefor) for both POL-demux and IQ-demux. The structure of a conventional IQ-hybrid is reviewed in figure 18A. For PM-pilots aided COH detection with all four I|Q-X|Y PM-pilots activated or with just the I and Q PM-pilots of one POL-tributary, be it, X|Y, it turns out that the ROSA-FE structure of figure 1B, comprising PMs and conventional IQ-hybrids, is no longer adequate. In figure 18B we disclose a new kind of IQ-hybrid, referred to as PM-Correlated-IQ-hybrid (PMC-IQ-HYB) to address the new functionality requirement. The disclosed hybrid module may be conceptually put together by starting with the prior-art IQ-HYB of figure 1A and inserting in the split-paths, leading from the LO input to the two 2x250-50 directional couplers or MMIs (which are followed by balanced-Photo-Diode (BPD) pairs), a pair of PMs. Just like in prior-art the LO split- path leading to the BPD pair producing the Imaginary (In-Quadrature) output, features a ±90ophase-shift relative to the LO split-path leading to the Real (in-Phase) output. But now we have pilots-driven-PMs present in the split-LO-paths, just before the inputs into the two 50-50 MMIs, as shown in figure 18B. Note: The new PMC-IQ-HYB is NOT equivalent to placing a single PM externally onto the LO port, using prior-art IQ-hybrid of figure 18A (unlike paradigm disclosed in our ROSA for DD in figure 1A, which is no longer usable to address a pair of I and Q signals on the same POL tributary (be it X|Y). Note: The performance attained performing the phase and POL estimation based on all four quadrature components (XI, XQ, YI, YQ) as enabled PMC-IQ-HYBs, exceeds the performance attained when using just two quadrature components or just one. This is due to the coherent combining (averaging) effect, stemming from having a of pair fully-correlated measurements (I and Q) for each of the X|Y POLs (rather than a single quadrature component in each POL), due to the IQ-vector in each POL having fixed norm at any given moment, and due to the fact that the elements of M- matrix are also correlated (due to unitarity of the M-matrix). The utility of the newly disclosed X|Y-PMC-IQ-HYBs is about to become apparent in the next subsection. PM-pilot-aided COH POLMUX links: COHD Rx with TOSA comprising X|Y-PMC- IQ-HYBs We are now ready to disclose multiple realizations of the TOSA and the corresponding ROSA for operating a PM-pilots-aided COH POLMUX link. The various realizations differ in the number of the PM-pilots in the TOSA at the Rx, in the (sub)set of quadratures components carrying the PM-pilots, as well as in the number and nature of the corresponding IQ-hybrids in the ROSA at the Rx. We teach embodiments inserting 1|2|4 PM-pilot(s) at the Tx, in the TOSA and having it or them detected at the Rx (using the MON module of the ROSA). In principle we could also have three pilots inserted at the Tx but those are less useful. There are eleven useful embodiments overall, four of them using a single pilot, six of them using pilot pairs and one using all four pilots. We shall present figures of and elaborate on just four of the eleven embodiments and justify their principle of operation. The other embodiments may readily be formulated by those trained in the art, by extrapolating our description of the four representative embodiments. Figure 19 depicts the four Tx (TOSA) options, figure 20 depicts the corresponding Rx (ROSA-FE) four options, figure 21 and figure 22 put together all the pieces to form four complete representative PM-pilots-aided COH POLMUX links. The first embodiment inserts, at the Tx in the TOSA (figure 19A), a single PM-pilot into one of the two quadratures of the X-tributary (be it XI|XQ), and a single PM- pilot into the one of the two quadratures of the Y-tributary (be it YI|YQ). The corresponding ROSA-FE is depicted in figure 20A, and the end-to-end link is shown in figure 21A. The second embodiment is most complex yet highest performance one, utilizing all four transmission DOFs by inserting a PM-pilot into each of the XI,XQ,YI,YQ, see the TOSA of figure 19B), the ROSA-FE in figure 20B (resorting to a pair of PMC- IQ-hybrids, the internals of which were seen in figure 18C. The end-to-end link putting the pieces together is depicted in figure 21B. The following two embodiments exploit the redundancy stemming from the correlations (constraints) satisfied by the unitary (or nearly unitary) 2x2 end-to-end MIMO matrix as well as from the fact that phaseshifts amounts to rotations of the vectors in the IQ-plane (the IQ-vector in each POL has fixed norm). The redundancies imply that once one of the four ‘axes’ XI|XQ|YI|YQ is getting “converged” (i.e., the projection of the PM-pilot associated with this axis at the Tx, is maximized or minimized at the Rx), then the remaining axes are “converged” automatically. Note: In fact the first embodiment (figure 19A and figure 20A), figure 21A) also took advantage of the redundancy effect in order to omit inserting the XQ, YQ pilots, just injecting and detecting the XI, YI pilots. In the third embodiment, we take the redundancy to the extreme, operating with a single PM-pilot (we have selected to inject pilot as YQ, but it may be injected into any one of the other three tributaries). See figure 19C, figure 20C, figure 22A. In the fourth embodiment (figure 19C, figure 20C, figure 22B) we again use two pilots, however in this case the two pilots are launched onto the same POL component (on the X-POL in the depicted instance). Here again we must resort to the new PMC-IQ-HYB structure of figure 18C in the ROSA-FE. Evidently, the more pilots we launch, the more complex the Tx and Rx are, but the complexity trades off with performance improvement, as multiple (2,3 or 4) pilots may be ‘coherently combined’ at the Rx, i.e., effectively averaged to improve the SNR. Thus, our second COH embodiment (figure 19B, figure 20B and figure 21B) is the most complex one, albeit the one exhibiting the highest performance. Considering end-to-end link in figure 21B based on our second embodiment, the optical fields at the X’,Y’ outputs of the POLtrk 2x2 MIMO module (and proportionally at the X”,Y” ‘signal’ inputs of the X|Y- IQ-hybrid modules) may be derived similarly, though now there are four alternative paths via the transmitter,modulated by four distinct PM-pilot tones at frequencies ^^^ூ , ^^^ொ for the top IQ-modulator of the X-POL-tributary path and at frequencies ^^^ூ , ^^^ொ for the bottom IQ-modulator of the Y-POL-tributary path. With ^^LS^^^^ the Laser Source phase transfer factor, the optical channel phase transfer factor,^^^ூ^^^^ ^ ^^^^^ொ^^^^ the transfer factor via the X-tributary IQ modulator (the XI,XQpilots contribution ignoring the data-modulations) ,^^^ூ^^^^ ^ ^^^^^ொ^^^^ the transferfactor via the Y-tributary IQ modulator (the imaginary unit factor, j, corresponds to the 90o phaseshifts in the 2ndand 4thmodulation paths in the TOSA). The pilot TFs ^^^|Y,I|ொ^^^^ were defined in (15). Note that each of the four hybrid outputs also comprises a “mainlobe” term, bearing useful information. The interference terms are actually analysed and separated out in the frequency-domain, similarly to the moving-window DFT processing described in the DD case, where it was shown that the maximal interference (the sidelobe with largest modulus) is substantially lower than the ACOR, therefore it is possible to perform short-time sliding-window spectral analysis determine the peak mainlobe value with relatively high accuracy. Note: As stated above sidelobes are actually separated out from the mainlobe, in the frequency-domain (since the processing in this case is just like in the DD case by means of Short-Time-DFT). In the frequency-domain the Re or Im part of the ൈ^ூ|^ொ|^ூ|^ொ^ூ|^ொ|^ூ|^ொ^^^^ sidelobe-terms amounts superposing the spectrum of conjugate reflection of the same spectrum. Themultiplicative factors ^^^ூ|^ொ|^ூ|^ொ, ^^^ூ|^ொ|^ூ|^ொ are less than unity in absolute value,hence only weaken the sidelobes.It is apparent that in order to effectively detect we mustmaximize which occurs at^^^^ ൌ 0|^^ ൌ ^^^^.Practically, let us aim for ^^^^ ൌ 0.However, this tuning control typically directly changes the instant frequency of the LO, and since the phase of the LO is the running integral of its instant frequency, for an instant frequency step a ramp of phase is created. This makes fine control of the phase difficult by means of direct LO actuation. Instead what we disclose is to use the pilot PMs not only for modulation by sinusoidal tones as disclosed heretofore, but additive inject additional control voltages in order to actuate the phases ^^^|^,^|^^^^^, which now need to be redefined asfollows: where ^^^|^,^|^are additive ‘feedback’ phases applied to the pilot-PMs in the ROSA- FE. These ‘feedback’ phases are used in order to close the oPLL loop in terms of reducing the stationary phase component, once the CFO component has converged to sufficiently low values (e.g., representing relatively slow rotation rates of the received constellations). Note: in fact, the process of separating the mainlobe from the sidelobes occurs in the frequency domain, in each of the ST-DFT records – not in the time domain as implied by the somewhat ‘loose’ notation above. Thus, we have sensing means for the magnitudes of the diagonal matrix elements of the end-to-end 2x2 MIMO matrix. It is now apparent that when both the oPLL (CFO&phase) and SoPLL (POL) feedback loops are in-track, |XImon^^^^|, หXQmon^^^^หbring in the same information, namely provide an estimate of Therefore, we may take the arithmetic average of|XImon^^^^|, หXQmon^^^^หin order to improve the accuracy of the ห^^^^^^^^^ห estimate.Similarly, bring in the same information, namely provide anestimate of ห^^^^^^^^^ห. Therefore, we may take the arithmetic average of|YImon^^^^|, หYQmon^^^^หin order to improve the accuracy of theห^^^^^^^^^ห estimate. It is also apparent that we would still be able to operate (and get an estimate of albeit noisier) if one of|XImon^^^^|, หXQmon^^^^หwere not available.Likewise we would still be able to operate (and get an estimate of albeitnoisier) if one of |XImon^^^^|, หXQmon^^^^หwere not available. Now, because of the unitarity of the end-to-end 2x2 MIMO matrix we have ideally,Therefore we could in fact average over as many of the four quantities|XImon^^^^|, หXQmon^^^^ห, as the block diagram enables.PM-pilots-aided Partially Coherent (Φ-diversity) Detection (pCOHD) In this subsection we disclose yet another embodiment of a PM-pilots-aided POLMUX link, representing a trade-off between DD and COHD properties. This embodiment, depicted end-to-end in figure 23, is referred to here as ‘partially- Coherent Detection (pCOHD). The pCOHD Tx is in fact identical to our disclosed POLMUX-IMDD Tx in figure 1B, multiplexing two independent data signals over the X and Y POL tributaries. The new pCOHD Rx still detects the received light coherently, using a pair of IQ-hybrids for the X and Y, but rather than utilizing all four DOFs XI,XQ,YI,YQ (namely the IQ quadrature signals of the X-POL and the IQ quadrature signals of the Y-POL), the two received quadratures in each polarization are combined into a single signal, i.e., XI,XQ are aggregated into a single X’-signal and YI,YQ are aggregated into a single Y’-signal thus we effectively detect just two independent data streams (a pair of DOFs, one DOF for X-POL and one DOF for the Y-POL), corresponding to the two IMDD modulated signals. Compared with the POLMUX DD scheme we disclosed in sec.3, we attain the same Spectral Efficiency (SE) (double the SE of conventional DD links), but the advantage now is in the improved COHD sensitivity stemming from the mixing of the two pairs of quadrature signals (XI,XQ,YI,YQ) with the local oscillators in the X|Y-IQ-hybrids. It remains to specify the method whereby XI,XQ are combined and YI,YQ are combined, to respectively generate two aggregate signals, X’,Y’, and why ideally the received-and-processed X’,Y’ signals would be faithful replicas of the IMDD X-POL and Y-POL tributaries generated at the Tx, carrying two independent data-streams. We disclose processing the I and Q quadratures received in each of the two POL- tributaries (available at the two outputs of the corresponding X|Y-IQ-HYBs) by means of a pair of sum-of-squares circuits. The block diagram of each of the two circuits is depicted in figure 24 (these circuits are also visible aboard the ROSA- Back-End (BE), fed by the output pairs of the two IQ-hybrids, i.e., the two circuits generate the signals RF electronic enabling technology for the sum-of-squares RF module has recently become feasible, as new designs of wideband mixers will be leveraged to analogy generate the squares of IX|Y, QX|Yprior to additive combining. We conclude that the ROSA-FE and ROSA-BE cascaded action amounts to measuring the total intensities of the received X and Y optical POL-tributaries, irrespective of the partitioning of the intensity of each POL-tributary between its IQ quadratures. Thus, the X|Y-IQ-HYBs enable measuring (up to a constant which depends on theLO amplitude) the two quadrature components ^^^ூ , ^^^ொ forming the CE of thereceived X-tributary, ^̰^^^^^^ ൌ ^^^ூ ^ ^^^^^ொ,  ^̰^^^^^^ ൌ ^^^ூ ^ ^^^^^ொThe two sum-of-squares circuits analogly generate the squared moduli (plural ofmodulus) Representing the received X|Y-tributary fields in polar form, it is apparent that the sum-of-squared operation just extract the squares of the moduli , ignoring the phase- arguments ∠^̰^^|^^^^^. We may say that we initially engage in full-COH detection (extracting all four quadrature components of the two complex-fields (which in principle would enable us to reconstitute in the signal processing the complex fields) but we refrain from reconstructing the full complex fields, instead just generating their squared magnitudes, i.e., the optical power. The optical phase information is effectively ‘erased’, discarded. The pCOH scheme operates as a form of ‘synthetic’ direct-detection. The question then arises – why bother? why not just use a pair of photodiodes for the X- and Y- tributaries? The reason is that this scheme affords substantial coherent-detection SNR advantage (only ~2 dB under the level of the coherent sensitivity gain of full COHD, which is typically about 10 dB). The two RFIC sum-of-squares modules, analogly generating the PX|Y(t) RF signals, amount to a pair of ‘virtual PDs’ operating in the nearly-shot-noise-limited regime, at improved Optical SNR (oSNR) relative to conventional DD PDs (which are degraded by thermal noise). This novel pCOHD Rx design renders the LITE-COH detection the COH link more robust, insensitive to rapid variations in the received phase, in particular insensitive to the chirp generated by the MRM MODs (to the extent that that chirp has not been converted into amplitude distortion by the CD in the fiber, prior to our CD EQZs). Thus, the sensitivity and reach (transmission distance) of this Rx are substantially improved relative to (i) by virtue of the disclosed ‘partially-coherent’ detection structure. This stems from the boosting effect of the mixing (multiplication) with theLO that occurs in the IQ-hybrids, wherein typically ห^̰^^|^^^^^ห ≪ |^̰^^^^^^|, but themultiplication by the strong ^̰^^^^^^ boosts the signal level, raising it ahead of adding thermal noise and shot-noise in the PDs+TIAs following the hybrids. In a sense, the disclosed pCOH Rx structure emulates the POL-MUX IMDD Rx of figure 1B synthesizing (by means of a hybrids-based COH-front-end followed by the sum-of-squares circuits) a pair of electrical signals proportional to the X,Y intensities (optical powers) that would be hypothetically generated in a receiver implemented as disclosed in of figure 1B. However, the actual synthesized signals are at higher SNR than attainable in either prior-art POL-DEMUX based AM-pilots-aided links or our own PM-pilots-aided link figure 1B. The pCOHD advantage is attained by virtue of the usage of the COH detection in the IQ-hybrids. The erasure of the optical phases of the X- and Y- tributaries by means of the sum-of-squares is an essential aspect of our disclosure. The disclosed ‘partially-coherent’ link provides a useful trade-off compromise between prior-art coherent receivers, featuring high-spectral-efficiency, high- performance (high-sensitivity and longer-reach) high-complexity and high-power consumption, on-one-hand, vs. the simplicity, energy-efficiency of the POL-DEMUX based prior-art AM-pilots-aided link or our disclosed PM-pilots-aided IMDD link, on the other hand. Compared with prior-art fully-COH links, which attain spectral efficiency 4x that of simple IMDD links, as well attaining high-sensitivity, disclosed pCOHD link attains just half the spectral efficiency of fully-COH detection, yet retains most of the sensitivity advantage of prior-art fully COH links (the penalty due to the ‘partial-coherence’ is estimated to be of the order of 2 dB theoretically). However, in exchange, the disclosed pCOHD link enables eliminating of two of the four ADCs at the Rx-side, eliminating two of the four DACs at the Rx side, replacing the complex power-hungry DSPs by much simpler, more energy-efficient IMDD DSPs and still getting an extended link budget. Viewed in optical engineering terms POLMUX-pCOHD indeed represents a trade-off in between POL-MUX-IMDD and POLMUX-full-COHD. In the pCOHD Rx the quad of ADCs and the DSP module (as used in conventional COH Rx-s) is simplified down to a pair of ADCs followed by a pair of IMDD-DSP modules of lower complexity than the DSP used in conventional COH Rx-s. Yet, we still retain a substantial portion of the sensitivity advantage of a full-COHD link. A variant of the pCOHD scheme (not explicitly depicted in our figures) modifies the analog processing circuit to a square-root-of-the-sum-of-squares circuit extracting the amplitudes (magnitudes) of the two X and Y POL signals by means of RMS combining (as the amplitudes are the square roots of the powers): ^^^ൌ The square-root is an imprecise operation to generate analogly, whereas generating the square root digitally would be quite costly in terms of power dissipation. An alternative disclosed scheme based on the square-root (20) would require that the transmitted constellation as generated in the TOSA be (uniform-in-the-field domain) ASK-m, e.g. ASK4, {0, A, 2A, 3A} for the four optical field levels out of the modulators drive, in case m=4, whereas the sum-of-squares based scheme, would require that the transmitted constellation be UNIP-PAM4, be uniform in the optical intensity or optical power domain, i.e. the optical power levels out of the modulators be {0, P, 2P, 3P} (in this case the optical field levels out of the modulators should be^0,√^^,√2^^,√3^^^,just as if we transmit IMDD over a single lane and use direct-detection at the Rx. To recap, the two pCOH schemes based on the sum-of-squares and root-sum-of- squares, respectively, require different constellation formats to be generated at the Tx. A beneficial feature the sum-of-squares (without the square-root) based pCOHD scheme is that it is compatible with conventional standardized IMDD PAM4 (or more generally PAM-m) modulator and its associated drivers. This bodes well in particular for adopting pCOH based links in Linear Drive Optics (LDO) aka Linear Pluggable Optics (LPO) links wherein the Tx and Rx actually resides in the host ASIC. Moreover, LDO links require extra sensitivity (an extended loss budget) as they use no digital regeneration (no retiming) in the Rx. Thus, sum-of-squares-based pCOHD links reuse standard I / O (Tx and Rx) as conventional IMDD PAM4, while delivering twice the rate (due to POLMUX) and also delivering an extended link budget. Another aspect to consider, in the context of the ROSA-FE block diagram of figure 23, is the signal processing in the AIC. In fact, the DSP functionality may be taken identical to that used in the PM-pilots-aided IMDD scheme of figure 1 The fact that the IQ data paths of the X- and Y- POL tributaries are squared-and-summed bears no impact on the DSP algorithms. Note: Interestingly, the DSP algorithm also implicitly evaluates sum-of-squares (or the root-sum-of-squares) albeit not of the I and Q components of the X|Y-POL- tributary, but rather on the two I and Q monitor outputs of each of the two IQ- hybrids. Indeed, evaluating the magnitude (or equivalently the magnitude squared) of the moving-window DFT samples, entails a (root-)sum-of-squares operation. This sum-of-squares operation on the pilots is analogous to the sum-of-squares operation on the datapath. The least complex disclosed POLMUX links revisited For low-cost solutions in context of mass deployments such as datacenter short-reach interconnects, PON or cellular networks, it may be useful to trade-off performance for complexity, striving for the least complex solutions. Among our embodiments the least complexity amounts to having the least number of PM-pilots, namely a single PM pilot used in the Tx and Rx. Several types single-PM-pilot-aided POLMUX links are then feasible, classified according to their back-end ROSA processing, namely either DD, COHD or pCOHD. In figure 26B we present the single-PM-pilot aided POLMUX IMDD link (part (B) of the figure brings, for comparison, our first disclosed embodiment based on a pair of X and Y PM-pilots). We should also recall figure 22A, which disclosed the single-PM-pilot-aided solution for POLMUX COHD. In another embodiment, not yet presented heretofore (see figure 27) we disclose a phase-diversity partially-coherent (pCOHD) link with a single PM pilot injected in one of the two POLs be it X|Y at the Tx, and using a single monitoring X|Y-IQ- hybrid in the ROSA-FE of the Rx (the ROSA-BE uses a pair of high-speed X|Y- IQ- hybrids with the sum-of-squares RFIC for phase-diversity pCOHD). We should also recall that there are multiple options in the TOSA at the Tx side for modulation means in each of the four parallel XI|XQ|YI|YQ paths. What is needed in each of the four paths is a modulating means capable of generating non- zero-carrier (non-zero mean value of the modulated signal), as well as having the signal PM-modulated by the carrier, albeit in just one of the four parallel XI, XQ, YI, YQ paths. We recall that several embodiments of such means were presented in the four sub- figures of figure 15, figure 16, but we also disclosed other embodiments, in which the PM-pilot is applied not as per the four sub-figures but it is rather added in to the high- speed modulating signal by means of a ‘diplexer’, namely an electronic 3-port that has the MHz-band PM-pilot signal at one input, the high-speed data-modulated signal at a second-input and the sum of these two signals is generated at the output (to be applied to the modulating electrodes), while preserving the signal integrity of the original signal lines. Note: A diplexer consists of two filters (low pass, high pass, or band pass) connected to a single antenna or transmission line which separate signals into lower and higher frequency bands. The primary function of a diplexer is to combine or separate signals based on their frequencies, allowing signals at two distinct frequencies to be sent and received from the same transmission line without interference. But what is needed here is a ‘bias-tee’ type of diplexer, with transition frequency of the order of the injected pilot tone(s) say 10 MHz. This accounting for the fact that high-speed receivers (PDs+TIAs) are AC-coupled with high-pass response having a frequency cutoff of the order of 10 MHz (the baseband [-10 MHz, 10 MHz] around the optical carrier is not accessible). Finally, let us mention an advantage of the single-PM-pilot-aided disclose schemes, namely a simplification of the digital signal processing in the AIC. Now, there are no other interfering pilots therefore the XCOR sidelobes visible in figure 10 and figure 13 are no longer present. The discrimination of the spectral peak due to the PM-pilot then becomes an even more robust task, improving the accuracy, simplicity, and robustness of the DSP in the AIC. In particular, in case two or more PMs are used, during the initial ‘convergence’ stage of the AIC algorithm, when the 2x2 MIMO matrix is still misaligned and the POL-cross-talk (from the X|Y-transmitted POL to the Y’|X’-received POL) then the XCOR sidelobes may come stronger than the ACOR mainlobe, and the convergence algorithm will have to be more-complicated | slower to try several diverse settings until a sizable mainlobe appears. However, when a sole-PM-pilot is used, the convergence issue above is easier to contend with as the interference from XCOR sidelobes among multiple pilots is now not present. On the downside, with a single PM-pilot, we now no longer not have multiple pilots to average over and further improve the detection SNR – thus the benefit of 3 dB or 6 dB SNR improvement is no longer available. Nevertheless, given that strong phase modulation can be, in principle, be tolerated in our invention (as it does not encroach on the data-path, unlike prior-art AM-pilots), then the PM-pilot estimation in the Rx is performed with the benefit of a quite strong PM-pilot. Moreover, the optically coherent monitoring of our lone-PM-pilot in the IQ-hybrid provides improved sensitivity relative to AM-pilots detection, thus in most situations it is most likely that the SNR attainable with the sole-PM-pilot might be sufficient, in which case the preferred embodiments would entail sole-PM-pilot operation. Another advantage of operating with sole-PM-pilot and with a single IQ-hybrid, is that having a single IQ-hybrid rather than a pair of them implies that higher light power may be allocated to the datapath, as the optical power required to be tapped to the sole IQ-hybrid in monitor stage is now half as large, relative to the case of using a pair of IQ-hybrids. It turns out that single PM-pilot operation does not necessarily require imply a single a single IQ-hybrid in the ROSA (on the same POL tributary be it X|Y that the sole pilot has been applied on at the Tx), as we have depicted in our disclosed figures heretofore. In this context we now disclose in figure 28 embodiments injecting a sole- PM-pilot, say, on the X-POL at the Tx, yet using both an X-IQ-HYB and Y-IQ-HYB, although now the LO ports of the two IQ-hybrid monitors should be both PM- modulated in synchronism with the transmitted sole-PM-pilot. The two subfigures disclose the corresponding sole-PM-pilot, dual-X&Y-monitor structures for DD and COHD, respectively. Granted this disclosed scheme does not have the least complexity, but it may still be useful in certain scenarios where somewhat higher ROSA complexity may be traded for extra performance. A case in which usage of a single PM-pilot would not be advisable, but it would be preferred to select, out of our multiple embodiments, one using two or four pilots (and two X|Y-IQ-hybrids) would be when the end-to-end 2x2 matrix of the channel (the concatenation of the PCR in the Tx, the Jones matrix of the (fiber) channel, the PSR and the POLtrk module in the Rx) exhibits substantial deviation from unitarity, e.g., due to POL-dependent-Loss (PDL) in the fiber and / or in the POL components in the Tx and Rx. In this case it is preferrable to have the received X and Y tributaries independently optimized, and this requires the usage of at least two PM-pilots, at least one of them in the X-tributary and one of them in the Y-tributary. Some partial mitigation of PMD may also be attained with the scheme disclosed in figure 28. Even more effective PMD mitigation is attained using at pilot pairs (at least one in each POL). Another advantage of single tone operation is that the ‘frequency-plan’ design is much simplified, as there are no longer multiple constraints re the orthogonality of multiple (2 or 4) pilot tones. This typically allows reducing the sole-PM-pilot frequency (though other factors such as the linewidth of the laser may limit the reduction in PM pilot frequency). Re the digitization of the monitor signals at the two output ports of the sole monitor-IQ-hybrid the sampling rate of the two monitor- ADCs (in the eFabric) is determined by the highest CFO specification, however the DAC in the eFabric, driving the PM-pilot-tone modulating means in the Rx can now be reduced in sampling rate to twice the selected (now reduced) frequency of the sole-PM-pilot. We finally disclose an ultimate reduction in the complexity entailed in using PM- pilot(s): operating without the separate X|Y-IQ-hybrid monitors used throughout our disclosures heretofore – eliminating the MON stage in the ROSA-FE but provisioning means to electronically extract the received PM-pilot tone(s) in the high- speed X|Y-IQ-hybrids used in the datapath. This requires splitting each TIA (+AESP) output onto two output ports, routing the signal low-pass components onto a first output port and the entire wideband data-modulated spectrum onto a second output port. Actually, it would be best not to use a diplexer but rather an ‘RF-tap’. The signals from the TIAs (possibly filtered via the AESP RF module) must be split by the ‘RF-tap’ into two paths – the main full-broadband path which is essentially proportional to the input signal into the ‘RF-tap’, and the ‘tapped’ path, which is a version of the full-broadband pass which has been low-passed with a cutoff approximately equal to the highest-CFO-frequency specification. For example, if the CFO is specified at ±500 MHz, then we need to pass the TIA(+AESP) signals on with their full wideband (say of the order of 100 GHz) on a first port which goes to the ADC, while also downloading on a second port, say, from DC to 1 GHz low-pass carved portion of the full wideband spectrum. This tapped RF signal is terminated in an ADC (one ADC for each port of the high-speed IQ-HYB) in our example having 1 GHz sampling rate (with 500 MHz as its Nyquist frequency to accommodate the CFO). The difficulty with this approach is that for the oPLL operation we actually need access to the ‘DC’ (electrically corresponding to the lightwave carrier). But, as mentioned above, high-speed receivers (PDs+TIAs) are AC-coupled with high-pass response having a frequency cutoff of the order of, say, 10 MHz (the baseband [-10 MHz, 10 MHz] around the optical carrier is not accessible). Therefore, a requisite for this embodiment is having ultra-broadband PDs+TIAs which are nevertheless DC coupled. PM-pilot-tones-aided POLMUX COH Transceiver (TRX) embodiments Heretofore, we have considered POLMUX PM-pilots-aided one-way (aka simplex) transmission embodiments of various kinds, based on IMDD, COHD and pCOHD detection modes. In this section we extend these inventive one-way transmission concepts to the realization of two-way simultaneous transmission (typically on a pair of distinct fibers). The end-terminals are the Transceivers (TRX).. The extension from Tx-Rx pairs to TRXs entails having the TRX host a receiver for the ‘east- bound’ transmission and a Tx for the ‘west-bound’ transmission. For (p)COHD based TRXs, the laser source may be shared between the Tx and Rx, to generate light for both modulation in the Tx part of the TRX and as LO (reference for (p)COHD in the Rx part of the TRX. We shall not show all the possible variants, but those are based on the one-way building blocks as documented in the multiple figures heretofore. Those trained in the art may put together, based on the principles disclosed heretofore, additional variants beyond those comprised in our set of TXR figures to follow. In terms of the building blocks used within the TXR, those have already been largely encountered in our earlier treatment of the one-way POLMUX PM-pilot-aided links. Now the digital interface comprises data conversions both ways, as depicted in the building blocks of figure 29. The next four figures present six TRX configurations differing in the detection mode (DD, pCOHD, COHD) and number of PM-pilots and / or MON-IQ-hybrid used. figure 30 presents two POLMUX DD TRX embodiments, (A): with a pair of PM- pilots and a pair of MON IQ-HYBs. The laser serves as both transmission Light- Source (LS) for the onboard Tx as well as Local Oscillator (LS) light source and is split appropriately to deliver light to all inputs requiring it. This is a motif recurring in all presented TRX embodiments. In the current case after the first stage of splitting the PMs by the two different pilots (to be used in the X- and Y- tributaries) are performed and the output of each PM is again split two-way to supply pilots for both transmission – via the modulators (MOD) as well as for matched correlation – fed into the LO reference port of the corresponding hybrid. Again, this motif recurs in all TRX embodiments. (B): with a single PM-pilot and a single-MON IQ-HYB similar to the embodiment of in figure 26A, as addressed in the one-way context. Figure 31 presents two TRX embodiments (A,B) corresponding to those in figure 30A and figure 30B i.e., differing in having one-PM-pilot and one-IQ-HYB or two of them) albeit now for pCOH phase-diversity detection (rather than for direct-detection in figure 30A and figure 30B. Again, our one-way treatment prepares the reader to follow the capture and comprehend the figure. Figure 32 presents the corresponding two TRX embodiments (A, B) for fully coherent (COH) detection, using one or two PM-pilots and one-or-two IQ-hybrids. These two embodiments may be understood by revisiting the ROSA-FE embodiments of figure 20A and figure 20B which pertained to one-way transmission and its COHD with IQ-HYB0s) Figure 33 presents the corresponding two TRX embodiments (A, B) for fully coherent (COH) detection, using one or two PM-pilots and one-or-two phase- modulated-correlation (PMC)-IQ-hybrids, which building blocks were already introduced in figure 18B. These two embodiments may be understood by revisiting the ROSA-FE embodiments of figure 20B and figure 20D which pertained to one- way transmission and its COHD with PMC-IQ-HYB(s). It is noted that the TRX embodiments figure 30B, figure 31B, figure 32B have the least complexity (at the expense of some reduced performance relative to the other TRX embodiments), as each of these TRXs comprises a single PM-pilot and a single monitor IQ-hybrid: As for figure 33 this TRX also uses a single monitor IQ- hybrid, but it injects a pair of PM-pilot tones in the transmit-section of the TXR (on the two quadratures of the same POL). There is provided a reduction in the complexity entailed in using PM-pilot(s): operating without the separate X|Y-IQ-hybrid monitors used throughout our disclosures heretofore – eliminating the MON stage in the ROSA-FE but provisioning means to electronically extract the received PM-pilot tone(s) in the high-speed X|Y-IQ-hybrids used in the datapath. This requires to split each TIA (+AESP) output onto two output ports, routing the signal low-pass components onto a first output port and the entire wideband data-modulated spectrum onto a second output port. Actually, it would be best not to use a diplexer but rather an ‘RF-tap’. The signals from the TIAs (possibly filtered via the AESP RF module) must be split by the ‘RF-tap’ into two paths – the main full-broadband path which is essentially proportional to the input signal into the ‘RF-tap’, and the ‘tapped’ path, which is a version of the full-broadband pass which has been low-passed with a cutoff approximately equal to the highest-CFO-frequency specification. For example, if the CFO is specified at ±500 MHz, then we need to pass the TIA(+AESP) signals on with their full wideband (say of the order of 100 GHz) on a first port which goes to the ADC, while also downloading on a second port, say, from DC to 1 GHz low-pass carved portion of the full wideband spectrum. This tapped RF signal is terminated in an ADC (one ADC for each port of the high-speed IQ-HYB) in our example having 1 GHz sampling rate (with 500 MHz as its Nyquist frequency to accommodate the CFO). The difficulty with this approach is that for the oPLL operation we actually need access to the ‘DC’ (electrically corresponding to the lightwave carrier). But, as mentioned above, high-speed receivers (PDs+TIAs) are AC-coupled with high-pass response having a frequency cutoff of the order of, say, 10 MHz (the baseband [-10 MHz, 10 MHz] around the optical carrier is not accessible). Therefore, a requisite for this embodiment is having ultra-broadband PDs+TIAs which are nevertheless DC coupled. Figure 36 illustrates a block diagram of POL-MUX coherent transceiver, multiplexing the XI,XQ,YI,YQ data tributaries at the Tx (the TOSA) and demultiplexing the four tributaries at the Rx (the ROSA), implementing the disclosed PM-aided structure according to the teaching of this invention, without separate auxiliary IQ-hybrids, but rather reusing the existing high-speed IQ-hybrids used for detecting the data-streams in the X and Y POL paths. As disclosed, RF- SPLIT means are provisioned following the TIAs of the high-speed IQ-hybrids. Each RF-split provides two copies of the broadband RF signal out of the TIA, both copies carrying the high-speed data-modulation. One copy is routed to its corresponding high-speed data ADC of the ‘Digital section’. The other copy is routed to a slower rate ADC interface of the Algorithmic Intelligence Controller for digitization at reduced bandwidth and for closing the control loop to the POL- Equalizer (EQZ), the Phase-Modulator (PM) means and the laser frequency tuning, in order to effect joint Frequency, Phase and POL control of the end-to-end optical channel. The RF-SPLIT means may or may not comprise low-pass-filtering of the broadband RF signal to the slower bandwidth at which the Frequency, Phase and POL of the end-to-end channel varies. In any case the ADC interface of the AIC is equipped with anti-aliasing filters for each ADC, lowpass filtering down to a bandwidth suitable for tracking the optical channel. In all other respects except for the method of extracting monitor signals by splitting / tapping the high-speed RF signals XI,XQ,YI,YQ (rather than tapping the X and Y optical signals by means of auxiliary IQ-hybrids, as shown in the prior figures, exclusively used for sensing of optical signals carrying the XI,XQ,YI,YQ tributaries). In contrast, in figure 36 the same signals are sensed in the RF domain, reusing the existing high-speed data hybrids rather than provisioning a separate set of hybrids. We note that it is not strictly necessary to RF-split, and digitize in the slower-rate ADCs of the AIC, all four of the XI,XQ,YI,YQ tributaries. In accordance to the teaching of this invention, tapping just three, two or even a single one of the XI,XQ,YI,YQ tributaries may suffice to provide tracking of the slowly varying parameters of the channel, albeit at somewhat reduced SNR performance. Because some aspects of the illustrated embodiments of the present disclosure may, for the most part, be implemented using optical and / or electronic components and circuits known to those skilled in the art, details will not be explained in any greater extent than that considered necessary as illustrated above, for the understanding and appreciation of the underlying concepts of the present invention and in order not to obfuscate or distract from the teachings of the present invention. Any combination of any steps of any method illustrated in the specification and / or drawings may be provided. Any combination of any subject matter of any of claims may be provided. Any combinations of systems, units, components, processors, illustrated in the specification and / or drawings may be provided. Any combination of any module or unit listed in any of the figures, any part of the specification and / or any claims may be provided. Any reference in the specification to a method should be applied mutatis mutandis to a device or system capable of executing the method and / or to a non-transitory computer readable medium that stores instructions for executing the method. Any reference in the specification to a system or device should be applied mutatis mutandis to a method that may be executed by the system, and / or may be applied mutatis mutandis to non-transitory computer readable medium that stores instructions executable by the system. Any reference in the specification to a non-transitory computer readable medium should be applied mutatis mutandis to a device or system capable of executing instructions stored in the non-transitory computer readable medium and / or may be applied mutatis mutandis to a method for executing the instructions. In the foregoing specification, the invention has been described with reference to specific examples of embodiments of the invention. It will, however, be evident that various modifications and changes may be made therein without departing from the broader spirit and scope of the invention as set forth in the appended claims. The specifications and drawings are, accordingly, to be regarded in an illustrative rather than in a restrictive sense. Those skilled in the art will recognize that the boundaries between logic blocks are merely illustrative and that alternative embodiments may merge logic blocks or circuit elements or impose an alternate decomposition of functionality upon various logic blocks or circuit elements. Thus, it is to be understood that the architectures depicted herein are merely exemplary, and that in fact many other architectures may be implemented which achieve the same functionality. Those skilled in the art will recognize that boundaries between the above-described operations merely illustrative. The multiple operations may be combined into a single operation, a single operation may be distributed in additional operations and operations may be executed at least partially overlapping in time. Moreover, alternative embodiments may include multiple instances of a particular operation, and the order of operations may be altered in various other embodiments. Any arrangement of components to achieve the same functionality is effectively "associated" such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality may be seen as "associated with" each other such that the desired functionality is achieved, irrespective of architectures or intermedial components. Likewise, any two components so associated can also be viewed as being "operably connected," or "operably coupled," to each other to achieve the desired functionality. It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity. Further, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word ‘comprising’ does not exclude the presence of other elements or steps then those listed in a claim. Furthermore, the terms “a” or “an,” as used herein, are defined as one or more than one. Also, the use of introductory phrases such as “at least one” and “one or more” in the claims should not be construed to imply that the introduction of another claim element by the indefinite articles "a" or "an" limits any particular claim containing such introduced claim element to inventions containing only one such element, even when the same claim includes the introductory phrases "one or more" or "at least one" and indefinite articles such as "a" or "an." The same holds true for the use of definite articles. Unless stated otherwise, terms such as “first" and “second” are used to arbitrarily distinguish between the elements such terms describe. Thus, these terms are not necessarily intended to indicate temporal or other prioritization of such elements. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to advantage. It is appreciated that various features of the embodiments of the disclosure which are, for clarity, described in the contexts of separate embodiments may also be provided in combination in a single embodiment. Conversely, various features of the embodiments of the disclosure which are, for brevity, described in the context of a single embodiment may also be provided separately or in any suitable sub- combination. It will be appreciated by persons skilled in the art that the embodiments of the disclosure are not limited by what has been particularly shown and described hereinabove. Thus, the scope of the embodiments of the disclosure is defined by the appended claims and equivalents thereof. While certain features of the disclosure have been illustrated and described herein, many modifications, substitutions, changes, and equivalents will now occur to those of ordinary skill in the art. It is therefore to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.

Claims

WE CLAIM 1. A method for reconstructing a first information stream and a second information stream, the method comprising: receiving, by an optical receiver, a received multiplexed optical signal that is a transmitted optical signal that passed through a polarization and phase rotating medium, the transmitted multiplexed optical signal being generated by using at least one transmitter phase-modulated periodical pilot signal, and by allocating a first polarization to the first information stream and a second polarization that differs from the first polarization to the second information stream; and processing the received multiplexed optical signal to provide a first reconstructed information stream and a second reconstructed information stream, wherein the processing comprises using at least one receiver phase-modulated periodical pilot signal that is associated with the at least one transmitter phase- modulated periodical pilot signal.

2. The method according to claim 1, wherein the at least one receiver phase- modulated periodical pilot signal is generated from a non-sinusoidal pilot signal.

3. The method according to claim 1, wherein the at least one receiver phase- modulated periodical pilot signal is generated from a sinusoidal pilot signal.

4. The method according to claim 1, wherein the at least one receiver phase- modulated periodical pilot signal is multiple receiver phase-modulated sinusoidal pilot signals having non-overlapping harmonics.

5. The method according to claim 1, wherein the multiple information streams further comprise a third information stream allocated with the first polarization and a fourth information stream allocated with the second polarization.

6. The method according to claim 5, wherein the processing comprises providing a third reconstructed information stream and a fourth reconstructed information stream.

7. The method according to claim 6, wherein a specified transmitter phase- modulated periodical pilot signal is allocated to the first and third information streams and another specified transmitter phase-modulated periodical pilot signal is allocated to the second and fourth information streams.

8. The method according to claim 1, wherein the at least one receiver phase- modulated periodical pilot signal comprises a first information stream phase- modulated periodical pilot signal and a second information stream phase-modulated periodical pilot signal.

9. The method according to claim 1, wherein the using of the at least one receiver phase-modulated periodical pilot signal is made in an optical domain.

10. The method according to claim 1, wherein the using of the at least one receiver phase-modulated periodical pilot signal is made in an electrical domain.

11. The method according to claim 1, wherein the processing of the received signal comprises at least partially compensating for a polarization and phase rotation introduced by the polarization and phase rotating medium to provide polarization and phase compensated optical signals.

12. The method according to claim 11, wherein the processing further comprises: analyzing the polarization and phase compensated optical signals to determine a state of polarization related to the polarization and phase compensated optical signal; determining, based on the analyzing, whether to further compensate for the polarization and phase rotation; and selectively further compensating for the phase polarization rotation based on the determining.

13. The method according to claim 11, wherein the at least partially compensating comprises reducing a cross-talk between one or more polarization and phase compensated optical signals associated with the first polarization and one or more other polarization and phase compensated optical signals associated with the second polarization.

14. The method according to claim 11, wherein the processing of the received multiplexed optical signal further comprises performing an initial split of polarization components of the received multiplexed optical signal to provide a first intermediate polarization optical signal and a second intermediate polarization optical signal.

15. The method according to claim 11, wherein the processing of the received multiplexed optical signal further comprises analyzing the polarization and phase compensated optical signals by multiple circuits to provide frequency and phase information regarding the received multiplexed optical signal.

16. The method according to claim 11, wherein the processing further comprises analyzing the polarization and phase compensated optical signals by a single analysis unit.

17. The method according to claim 11, wherein the processing further comprises analyzing the polarization and phase compensated optical signals by a first analysis unit and a second analysis unit that operated at a lower operation frequency than the first analysis unit.

18. The method according to claim 17, wherein second analysis unit comprises optical hybrid circuits, and wherein the second analysis unit is a direct detection optical unit.

19. The method according to claim 1, wherein the processing of the received multiplexed optical signal further comprises generating at least one phase modulated local oscillator signal.

20. The method according to claim 19, wherein the processing of the received multiplexed optical signal further comprises estimating at least one phase difference between the at least one phase modulated local oscillator signal and the at least one transmitter phase-modulated periodical pilot signal.

21. An optical receiver, comprising:an input configured to receive a received multiplexed optical signal that is a transmitted optical signal that passed through a polarization and phase rotating medium, the transmitted multiplexed optical signal being generated by using at least one transmitter phase-modulated periodical pilot signal, and by allocating a first polarization to a first information stream and a second polarization that differs from the first polarization to a second information stream; and at least one processing circuit that is configured to process the received multiplexed optical signal to provide a first reconstructed information stream and a second reconstructed information stream, wherein the processing comprises using at least one receiver phase-modulated periodical pilot signal that is associated with the at least one transmitter phase-modulated periodical pilot signal.

22. A method for optically processing a first information stream and a second information stream, the method comprising: receiving, by an optical transmitter, the first information stream and the second information stream; generating at least one transmitter phase-modulated periodical pilot signal; optically processing the first information stream and the second information stream, using the at least one transmitter phase-modulated periodical pilot signal to provide a transmitted multiplexed optical signal; wherein the optically processing comprises allocating a first polarization to the first information stream and a second polarization that differs from the first polarization to the second information stream; and transmitting the transmitted multiplexed optical signal to a polarization and phase rotating medium.

23. The method according to claim 22, wherein the generating of the at least one transmitter phase-modulated periodical pilot signal comprises phase modulating at least one non-sinusoidal pilot signal.

24. The method according to claim 22, wherein the generating of the at least one transmitter phase-modulated periodical pilot signal comprises phase modulating at least one sinusoidal pilot signal.

25. The method according to claim 22, wherein the at least one transmitter phase- modulated periodical pilot signal is multiple transmitter phase-modulated sinusoidal pilot signals having non-overlapping harmonics.

26. The method according to claim 22, further comprising receiving, by an optical transmitter, a third information stream and a fourth information stream; and wherein the processing further comprises optically processing the third information stream and the fourth information stream, using the at least one transmitter phase-modulated periodical pilot signal to provide the transmitted multiplexed optical signal; wherein the optically processing further comprises allocating the first polarization to the third information stream and the second polarization to the fourth information stream.

27. An optical transmitter, comprising: an input configured to receive a first information stream and a second information stream; a pilot circuit that is configured to generate at least one transmitter phase- modulated periodical pilot signal; and at least one processor configured to optically process the first information stream and the second information stream, using the at least one transmitter phase- modulated periodical pilot signal to provide a transmitted multiplexed optical signal; wherein the optically processing comprises allocating a first polarization to the first information stream and a second polarization that differs from the first polarization to the second information stream; and an output that is configured to transmit the transmitted multiplexed optical signal to a polarization and phase rotating medium.

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