Optical multi input multi output (MIMO) demultiplexer

Abstract

To provide a multi-stage optical MIMO demultiplexer.SOLUTION: An optical polarization demultiplexer 200 is formed by: a polarization splitter and rotator (PBSR) 202; two 50 / 50 couplers 204 and 206; and two phase shifters 208 and 210. The two phase shifters 208 and 210 are controlled by another control signals Φ1212 and Φ2214. Each of the two phase shifters 208 and 210 is a differential phase shifter. The phase shifter 208 is mounted as an interferometer having two individual phase shift elements 208a and 208b that adjust an optical phase to one direction with one arm of an interferometer, and adjust an optical phase to an opposite direction with the other arm. The phase shifter 210 also has the same structure.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] This disclosure generally relates to optical demultiplexers. [Background technology]

[0002] In optical communication systems, multiplexing techniques (such as polarization-division multiplexing (PDM)) can improve communication capacity and / or photon efficiency by multiplexing different signals on different channels (e.g., different polarization modes at the same carrier frequency) and transmitting them simultaneously through a single fiber. However, a challenge with PDM is that as polarization modes propagate within the optical communication system, they tend to undergo random and unpredictable rotation and loss due to factors such as stress on the glass fiber (bending and twisting), ambient temperature changes, or other non-ideal properties of the communication system. As a result, signals with different polarization modes become mixed when they are received. In such scenarios, it is necessary to separate the signals at the receiver via multiple-input-multiple-output (MIMO) multiplexing / decoupling. [Overview of the project] [Means for solving the problem]

[0003] The implementation of this disclosure is generally intended for optical demultiplexers, such as optical polarization demultiplexers.

[0004] One common embodiment includes: a pair of MIMO inputs configured to input light into a first pair of optical transmission paths; a first optical phase shifter configured to apply a first relative phase shift between the first pair of optical transmission paths; a first 2x2 optical coupler configured to couple the first pair of optical transmission paths and output a second pair of optical transmission paths; a second optical phase shifter configured to apply a second relative phase shift between the second pair of optical transmission paths; and the second pair of optical transmission paths The system includes a 2x2 optical multi-input multiple-output (MIMO) demultiplexer, which includes a second 2x2 optical coupler configured to couple and output a third pair of optical transmission paths; a third optical phase shifter configured to apply a third relative phase shift between the third pair of optical transmission paths; a third 2x2 optical coupler configured to couple the third pair of optical transmission paths and output a fourth pair of optical transmission paths; and a pair of MIMO outputs configured to output the fourth pair of optical transmission paths. Other embodiments of this aspect include corresponding computer systems, devices, and computer programs recorded in one or more computer storage devices, each configured to perform the operation of the method.

[0005] An implementation may include one or more of the following features: A 2x2 optical MIMO demultiplexer in which the first optical phase shifter is configured to apply a first relative phase shift value, which is a binary number. The first relative phase shift value is a binary number between c+π / 2 and c-π / 2 (where c is a real number). A 2x2 optical MIMO demultiplexer in which the second optical phase shifter is configured to apply a second relative phase shift value within a finite range including -nπ and +nπ (where n is an integer). A 2x2 optical MIMO demultiplexer in which the second optical phase shifter is configured to operate analogously within the range (-nπ, +nπ). A 2x2 optical MIMO demultiplexer in which the third optical phase shifter is configured to apply a third relative phase shift value within a finite range determined by the value of the first relative phase shift. A 2x2 optical MIMO demultiplexer wherein a third optical phase shifter is configured to operate between 0 and +nπ (where n is an integer) based on the value of a first relative phase shift being c-π / 2, and is configured to operate between -nπ and 0 based on the value of a first relative phase shift being c+π / 2. A 2x2 optical MIMO demultiplexer wherein the third optical phase shifter is configured to operate analogously within the range (0, +nπ) or within the range (-nπ, 0). A 2x2 optical MIMO demultiplexer further comprising at least one processor and at least one memory storing instructions that, based on being executed by the at least one processor, perform operations to control the values ​​of a first relative phase shift, a second relative phase shift, and a third relative phase shift. A 2x2 optical MIMO demultiplexer further comprising a first optical attenuator configured to apply a first relative attenuation between a first pair of optical transmission paths. A 2x2 optical MIMO demultiplexer further comprising a second optical attenuator configured to apply a second relative attenuation between a third pair of optical transmission paths. A 2x2 optical MIMO demultiplexer in which each of the first optical phase shifter, the second optical phase shifter, and the third optical phase shifter has a phase shift range of 2π or less. Implementations of the described technology may include hardware, methods or processes, or computer software on a computer-accessible medium.

[0006] Another common embodiment includes an optical multi-input multiple-output (MIMO) receiver comprising: an input port configured to receive input light; means for performing adaptive 2x2 optical MIMO polarization multiplexing and decoupling on the input light using a three-stage optical phase shift to output a first optical signal and a second optical signal; and at least one photodetector configured to detect the first optical signal and the second optical signal. Other embodiments of this embodiment include corresponding computer systems, devices, and computer programs recorded in one or more computer storage devices, each configured to perform the operation of the method.

[0007] An implementation may include one or more of the following features: an optical MIMO receiver in which each of the three stages of optical phase shift has a range of 2π or less. Implementations of the described technology may include hardware, methods or processes, or computer software on a computer-accessible medium.

[0008] Another common embodiment includes a method for performing 2x2 optical multiple-input multiple-output (MIMO) multiplexing, the method comprising: receiving light into a first pair of optical transmission paths via a pair of MIMO inputs; controlling a first optical phase shifter that applies a first relative phase shift between the first pair of optical transmission paths; coupling the first pair of optical transmission paths with a first 2x2 optical coupler to output a second pair of optical transmission paths; and applying a second relative phase shift between the second pair of optical transmission paths. This includes controlling a second optical phase shifter to be applied; coupling the second pair of optical transmission paths with a second 2x2 optical coupler to output a third pair of optical transmission paths; controlling a third optical phase shifter to apply a third relative phase shift between the third pair of optical transmission paths; coupling the third pair of optical transmission paths with a third 2x2 optical coupler to output a fourth pair of optical transmission paths; and outputting the fourth pair of optical transmission paths via a pair of MIMO outputs. Other embodiments of this aspect include corresponding computer systems, devices, and computer programs recorded in one or more computer storage devices, each configured to perform the operation of the method.

[0009] An implementation may include one or more of the following features: A method of controlling a first optical phase shifter, which involves applying a value of a first relative phase shift, which is a binary number. A method in which the value of the first phase shift is a binary number between c+π / 2 and c-π / 2 (where c is a real number). A method of controlling a second optical phase shifter, which involves applying a value of a second relative phase shift within a finite range including -nπ and +nπ (where n is an integer). A method in which the control of the second optical phase shifter is performed by analog operation within the range (-nπ, +nπ). A method of controlling a third optical phase shifter, which involves applying a value of a third relative phase shift within a finite range determined by the value of the first relative phase shift. A method further including controlling the third optical phase shifter so that it operates between 0 and +nπ (where n is an integer) based on the value of the first relative phase shift being c-π / 2, and between -nπ and 0 based on the value of the first relative phase shift being c+π / 2. A method for controlling a third optical phase shifter by analog operation within the range (0, +nπ) or (-nπ, 0) depending on the value of the first relative phase shift. A method further comprising: detecting a first reference signal on a first polarization channel in the first MIMO output of a pair of MIMO outputs; detecting a second reference signal on a second polarization channel in the second MIMO output of a pair of MIMO outputs; determining an error amount measured from the first reference signal and the second reference signal; and controlling at least one of the first optical phase shifter, the second optical phase shifter, or the third optical phase shifter based on the error amount measured from the first reference signal and the second reference signal. A method for 2x2 optical MIMO multiplexing decoupling that is performed endlessly during operation without resetting any of the first optical phase shifter, the second optical phase shifter, or the third optical phase shifter. Implementations of the described technologies may include hardware, methods or processes, or computer software on a computer-accessible medium.

[0010] Another common embodiment includes an optical multi-input multiple-output (MIMO) receiver configured to perform optical MIMO polarization multiplexing and decoupling. The optical MIMO receiver includes an input port configured to receive input light; a polarizing beam splitter rotator (PBSR) configured to split the input light into a pair of optical transmission paths; an optical phase shifter configured to apply a relative phase shift between the pair of optical transmission paths; a 2x2 optical coupler configured to couple the pair of optical transmission paths; and a controller configured to control the optical phase shifter using binary control having two operating states for the relative phase shift applied between the pair of optical transmission paths. Other embodiments of this embodiment include corresponding computer systems, devices, and computer programs recorded in one or more computer storage devices, each configured to perform the operation of the method.

[0011] Another common embodiment includes an optical multi-input multiple-output (MIMO) receiver configured to perform optical MIMO polarization multiplexing and decoupling. The optical MIMO receiver includes an input port configured to receive input light; a polarizing beam splitter rotator (PBSR) configured to split the input light into a pair of optical transmission paths; an optical attenuator configured to apply relative attenuation between the pair of optical transmission paths; a 2x2 optical coupler configured to couple the pair of optical transmission paths; and a controller configured to control the relative attenuation applied by the optical attenuator. Other embodiments of this embodiment include corresponding computer systems, devices, and computer programs, each recorded in one or more computer storage devices, each configured to perform the operation of the method.

[0012] An implementation may include one or more of the following features: an optical MIMO receiver in which the optical attenuator is a differential optical attenuator configured to (i) apply a first attenuation to one of a pair of optical transmission paths and (ii) apply a second attenuation to the other of a pair of optical transmission paths, wherein the first and second attenuations are equal in magnitude and opposite in sign; or an optical MIMO receiver further comprising a second optical attenuator configured to apply a second relative attenuation between a second pair of optical transmission paths, wherein the second pair of optical transmission paths contain light attenuated by the optical attenuator, and a controller further configured to control the second relative attenuation applied by the second optical attenuator. Implementations of the described technology may include hardware, methods or processes, or computer software on a computer-accessible medium.

[0013] In some implementations, the techniques described herein for optical MIMO polarization multiplexing and decoupling can be applied to general 2x2 optical MIMO multiplexing and decoupling. For example, in some implementations, the techniques described herein can be implemented separately from or without PBSR.

[0014] Details of one or more implementations of the subject matter of this disclosure are described in the accompanying drawings and the following description. Other features, embodiments, and advantages of the subject matter will become apparent from the detailed description, drawings, and claims. [Brief explanation of the drawing]

[0015] [Figure 1] Figures 1A and 1B show examples of dual-polarization communication systems using coherent detection and direct detection (IMDD).

[0016] [Figure 2] Figure 2 shows an example of an optical polarization demultiplexer with two control signals.

[0017] [Figure 3] Figure 3 shows an example of an optical polarization demultiplexer according to an embodiment of this disclosure.

[0018] [Figure 4] Figure 4 is a diagram showing another example of an optical polarization demultiplexer according to an embodiment of the present disclosure.

[0019] [Figure 5] Figures 5A and 5B are diagrams showing an example of a transmitter configured to transmit a reference signal (e.g., a pilot tone).

[0020] [Figure 6] Figure 6 is a diagram showing an example of a demultiplexer according to an embodiment of the present disclosure, which is configured to receive a reference signal (e.g., a pilot tone) to generate feedback information.

[0021] [Figure 7] Figures 7A and 7B are diagrams showing an example of a demultiplexer according to an embodiment of the present disclosure, which is configured to receive and process a reference signal (e.g., a pilot tone).

[0022] [Figure 8] Figure 8 is a flowchart showing an example of controlling an optical polarization demultiplexer according to an embodiment of the present disclosure.

[0023] [Figure 9] Figure 9 is a flowchart showing an example of controlling a relative phase shift value in an optical polarization demultiplexer according to an embodiment of the present disclosure.

[0024] [Figure 10] Figure 10 is a flowchart showing an example of controlling a relative attenuation value in an optical polarization demultiplexer according to an embodiment of the present disclosure.

[0025] [[ID=^]] [Figure 11] Figure 11 is a diagram showing an example of a simulation result of an optical polarization demultiplexer according to an embodiment of the present disclosure.

[0026] [Figure 12] Figure 12 shows an example of a computing system that can be used to implement one or more components of a system that performs adaptive control of an optical polarization demultiplexer. [Modes for carrying out the invention]

[0027] (Detailed explanation) This specification discloses systems and techniques that provide novel multi-stage optical MIMO demultiplexers (e.g., optical MIMO polarization demultiplexers) capable of achieving significantly improved efficiency and speed with lower data loss rates. This is achieved by a novel implementation that enables the "endless" characteristic of adaptive multiplexing and demultiplexing without requiring a reset that interrupts data reception. In some embodiments, this is achieved by an adaptive three-stage phase-shift demultiplexer structure, where the first-stage phase shifter is controlled to apply a binary value, and the second and third-stage phase shifts are controlled to operate within a finite range (e.g., a continuous range) of phase shift values. The control of the three-stage phase shifts is tuned to adapt to random and unpredictable rotations and losses of the received polarization without requiring a reset of the phase shift that interrupts signal reception, resulting in a characteristic called the "endless" operation of the demultiplexer.

[0028] Generally, multi-polarization detection is considered difficult because the polarization state tends to drift as the optical waveform passes through the communication system (for example, because the birefringence of fiber transmission lines changes randomly). In long-distance systems, such random polarization drift gradually accumulates indefinitely. In optical communication systems that transmit different signals in two polarization modes using polarization division multiplexing (PDM), random and unknown polarization drift makes it difficult for the receiver to accurately detect the correct orientation of the two polarization modes, resulting in the reception of mixed signals (sometimes called "crosstalk"). Therefore, even if a signal is transmitted in one polarization mode, the signal may actually be received in both polarization modes at the receiver. In addition to polarization drift, other non-idealities in optical communication systems, such as polarization-dependent loss (PDL), which amplifies or attenuates different polarization modes in different ways, can degrade performance.

[0029] To compensate for polarization drift and other non-idealities, multi-polarization receivers need to perform a certain adaptive MIMO multiplexing and demixing to separate and demix signals transmitted in two polarization modes. Such MIMO multiplexing can be performed in the optical domain using optical phase shifters or in the electronic domain using digital signal processing (DSP). Optical MIMO multiplexing and demixing have several advantages compared to DSP-based MIMO multiplexing and demixing. For example, optical multiplexing and demixing can reduce power consumption, complexity, and sensitivity to symbol rate. On the other hand, DSP-based multiplexing and demixing typically require high power consumption and can be very complex in systems with high symbol rates or a large number of modes.

[0030] Furthermore, optical polarization multiplexing can be used in combination with intensity modulation and direct detection (IMDD) transmission methods (which transmit information using only the square of the magnitude of the optical electric field), such as pulse amplitude modulation (PAM). This is because optical multiplexing can be performed before optical detection is performed on the light, using an optical element that separates the two polarization modes of the light. On the other hand, in IMDD, due to the nonlinearity of optical direct detection, information loss occurs that cannot be recovered by DSP technology alone, so IMDD cannot be used in combination with DSP-based polarization multiplexing. Instead, DSP-based multiplexing typically requires coherent reception. In such a system, the two polarization modes of the light are first separated by coherent detection, and then the entire field of each polarization is detected, so that the DSP can perform processing on the signals received in the two polarization modes. An example of this separation will be explained below with reference to Figures 1A and 1B.

[0031] Figures 1A and 1B show examples of dual-polarization communication systems 100 and 150, respectively, utilizing coherent detection and direct detection (IMDD). Transmitters (102 and 152) perform polarization division multiplexing by first splitting the laser input light (104 and 154) into two optical transmission paths leading to two modulators (i.e., a first modulator (106 and 156) and a second modulator (108 and 158)). The first modulators (106 and 156) modulate the light in one optical transmission path with a first data stream x or X (110 and 160), and the second modulators (108 and 128) modulate the light in the other optical transmission path with a second data stream y or Y (112 and 162). In the coherent case, x and y are complex numbers representing the optical field, while in the IMDD case, X and Y are real numbers representing the optical power. In this disclosure, lowercase letters represent complex numbers (fields) and uppercase letters represent real numbers (powers). Two modulated optical waveforms, one modulated by x (X) and the other by y (Y), are combined in a polarizing beam splitter-rotator (PBSR) (114 and 164) to convert one of the optical waveforms into orthogonal polarization. After the PBSR, the two optical waveforms carrying x (X) and y (Y) coexist in the same optical transmission path but have orthogonal polarization.

[0032] This dual-polarized (DP) optical waveform passes through the fiber links (116 and 166). As the DP waveform passes through the fiber, the polarization of the two waveforms may change due to various unknown birefringences and twists within the fiber. If there is no large polarization-dependent loss (PDL) in the fiber links (116 and 166), the two polarizations remain orthogonal. For example, x (X) may change from linear horizontal polarization to clockwise circular polarization, which means that y (Y) will change from linear vertical polarization to counterclockwise circular polarization. However, in the presence of PDL, the orthogonality of the polarizations of the DP optical waveform decreases, and the multiplexing and separation of x (X) and y (Y) becomes more complex.

[0033] At the receivers (118 and 168), the DP waveform enters the PBSR (120 and 162), where it is split into two waveforms, h and v, with orthogonal polarizations. Due to the non-ideal nature of optical communication systems, the outputs h and v of the PBSR are linear orthogonal combinations of x and y, respectively (more precisely, the received signals are noisier versions of x and y due to additive noise in the system, but this explanation assumes a noise-free scenario). In particular, h is a linear combination of x and y, and similarly v is a linear combination of x and y. For example, h = (xy) / sqrt(2) and v = (x+y) / sqrt(2). The purpose of MIMO multiplexing is to extract the original signals x and y from the received h and v. This can be done via DSP-based multiplexing (as shown in Figure 1A for coherent detection) or optical multiplexing (as shown in Figure 1B for direct detection / IMDD).

[0034] In the coherent case shown in Figure 1A, there is a local oscillator (LO) laser (122) in which h and v are interfered with in two optical 90-degree hybrids (124 and 126). The output waveform from hybrid 126 is photodetected by photodetector 128, and the resulting electrical signal is fed to a digital signal processor (DSP) (130) which performs multiplexing and separation using MIMO signal processing to separate signals x' and y'. Thus, in the coherent reception example in Figure 1A, since both the magnitude and phase of the optical wave field are detected by receiver 118, MIMO multiplexing and separation must be performed by DSP 130 after detection by photodetector 128.

[0035] In contrast, in the IMDD reception example in Figure 1B, receiver 168 detects optical power. This nonlinearity results in information loss. In other words, in an IMDD system, MIMO multiplexing and decoupling must be performed optically before optical detection. This is because, in the case of IMDD, optical phase information is lost during optical detection, so no matter how much electrical signal processing is performed, x and y cannot always be reconstructed. In the example in Figure 1B, h and v are linear orthogonal combinations of x and y, respectively. Therefore, if h and v are detected directly using IMDD without first performing multiplexing and decoupling, there is a possibility of losing fundamental information. However, if h and v are optically multiplexed and decoupled into x and y before optical detection, there is no information loss.

[0036] In the case of two orthogonal polarization states, a PDM optical communication system can be represented as a 2x2 optical multiple-input multiple-output (MIMO) channel. Thus, optical transmission can be modeled as a 2x2 matrix F. Matrix F is a transfer function that represents the polarization effects and chromatic dispersion of the communication from transmitter to receiver. For example, matrix F can model the effects of the fiber connecting the transmitter and receiver, and the effects of the optical components of the transmitter and receiver themselves. For the purposes of this disclosure, matrix F is referred to as the "channel matrix F" under the understanding that a "channel" can represent various effects of the optical communication system, such as, for example, the fiber transmission line and the components of the transmitter and / or receiver.

[0037]

number

[0038] To estimate the original signals x and y from the received signals h and v, an optical demultiplexer D is applied to the receiver to generate estimated values ​​x' and y'.

[0039]

number

[0040] Furthermore, if x' = ax and y' = bx (where "a" and "b" are complex constants), the receiver will correctly multiplex and separate the polarizations.

[0041] Let us consider a simple case of a lossless system (where the optical channel matrix F is unitary), which is roughly applicable to most short optical fiber links. In such a scenario, fiber loss, particularly polarization-dependent loss (PDL), can be ignored. The channel matrix F can be characterized by four real numbers. The multiplexing matrix D can be characterized by two real numbers, since the receiver only needs to achieve x'=ax and y'=bx in order to perform multiplexing successfully. Therefore, in the lossless scenario, the four real numbers of the channel matrix F can only be expressed as two independently controlled real parameters that should be compensated for by the multiplexing matrix D.

[0042] Therefore, in the case of a unitary system (lossless scenario), the optical demultiplexer (i.e., matrix D above) requires at least two theoretical minimum values ​​of phase control signals to reverse the effect of the channel matrix F and multiplex demultiplex. An example of a two-stage demultiplexer is described below with reference to Figure 2. However, using only two phase control signals in the demultiplexer presents a problem: achieving "endless" characteristics requires an infinite range of phase shifts in multiplex demultiplexing, which cannot be achieved using a practical phase shifter. Instead, practical phase shifters have a finite limit to the range of phase shifts. Therefore, when multiplex demultiplexing optical signals that have passed through randomly changing phase distortions in the fiber, the phase shifter in the two-stage demultiplexer needs to reach the boundary of its practical range and perform a "reset" which can cause interruption and / or delay in data reception. An example of this problem is described below with reference to Figure 2.

[0043] Figure 2 shows an example of an optical polarization demultiplexer 200 having two control signals. The demultiplexer 200 consists of a polarization splitter-rotator (PBSR) 202, two 50 / 50 couplers 204 and 206, and two phase shifters 208 and 210 (e.g., differential phase shifters). The two phase shifters 208 and 210 are controlled by separate control signals φ1 (212) and φ2 (214). In the example in Figure 2, each of the phase shifters 208 and 210 is a differential phase shifter. For example, the phase shifter 208 is implemented as an interferometer having two separate phase shift elements (208a and 208b) that adjust the optical phase in one direction on one arm of the interferometer and in the opposite direction on the other arm. A similar structure is shown for the phase shifter 210. Alternatively, in some embodiments, each of the phase shifters 208 and 210 can be implemented as a non-differential phase shifter having only one phase shift element on a single arm. The differential implementation shown in Figure 2 has several advantages compared to the non-differential implementation. For example, the differential implementation has the advantage of requiring a smaller range per phase shifter. Furthermore, in the case of thermo-optic phase shifters, differential phase shifters have the advantages of halving the worst-case power consumption, maintaining a constant total power consumption, and mitigating thermal transients compared to single-phase phase shifters. For the purposes of this disclosure, a differential phase shifter (e.g., phase shifter 208) is implemented with two phase shifters (e.g., phase shifter elements 208a and 208b), but is considered as a single phase shifter under the understanding that it has one control signal (e.g., φ1, 212).

[0044] This structure allows the demultiplexer 200 to be represented by matrix D (using Mueller notation for polarization).

[0045]

number

[0046] However, as mentioned above, the configuration of the demultiplexer 200 in Figure 2 has a major problem: in order to achieve "endless" characteristics, multiplexing and demultiplexing require an infinite range of phase shifts relative to φ1(212). In a practical system, this means that when the demultiplexer 200 multiplexes and demultiplexes signals received through a randomly changing fiber, the phase shift control φ1(212) eventually reaches the boundary of its practical range. For example, when the phase shifters 208 and 210 are implemented as thermo-optic phase shifters, there are practical limitations on the amount of input current. If the randomly drifting phase due to channel F requires φ1 to increase continuously, the input limit of φ1 necessitates decreasing the phase shifter 208 by 2π at some point (a so-called "reset"). However, since signal reception must be interrupted during this reset, data loss may occur, potentially leading to significant error bursts in high-speed communication.

[0047] To address this problem, demultiplexers can implement phase shifters with two or more stages. However, as the number of phase shift stages increases (in the case of lossless scenarios using unitary demultiplexers), the algorithms and controls become more complex, and the control speed of the numerous phase shift variables decreases. Furthermore, it can be difficult to guarantee that for any given input, the phase shift control will not be "trapped" into a specific state during operation (and will not escape the trapped state unless the phase shifter exceeds its limits). In addition, more complex control systems may face an increased risk of converging to local states that are not desirable (e.g., suboptimal) multiplexed operation. Due to this complexity and uncertainty, designing dual-polarization IMDD systems can be challenging.

[0048] Furthermore, the presence of polarization-dependent loss (PDL) can complicate the problem. PDL refers to two orthogonal polarizations that are attenuated differently, resulting in the generation of a non-unitary channel matrix F. While PDL may be negligible in fibers, it can be significant in discrete devices such as amplifiers and wavelength-division multiplexers. Designing non-unitary optical demultiplexers is challenging. Generally, a non-unitary demultiplexer can be characterized by four real numbers, and the theoretical minimum control set consists of two optical phase shifters and two optical attenuators.

[0049] This specification discloses an implementation that achieves "endless" characteristics of optical MIMO polarization multiplexing / decoupling using only three stages of finite-range phase shift for lossless scenarios without PDL, an example of which is illustrated with reference to Figure 3 below. In addition, for PDL scenarios, this specification discloses an implementation that achieves "endless" characteristics using only three stages of finite-range phase shift and two stages of optical attenuation, an example of which is illustrated with reference to Figure 4 below.

[0050] Figure 3 shows an example of an optical polarization demultiplexer 300 according to an embodiment of the present disclosure. The demultiplexer 300 can be implemented as part of a direct detection receiver (e.g., receiver 168 in Figure 1). In some embodiments, the demultiplexer 300 is implemented via integrated photonics, which can reduce costs compared to bulk optics.

[0051] The demultiplexer 300 includes three phase shift stages (302, 304, and 306). Each stage is controlled by a phase shift control signal. For example, the first stage 302 is controlled by the first control signal 308, the second stage 304 is controlled by the second control signal 310, and the third stage 306 is controlled by the third control signal 312. Each control signal controls the amount of phase shift performed in its respective phase shift stage.

[0052] In the example shown in Figure 3, each stage has a phase shifter operating on a pair of optical transmission lines and a 2x2 coupler. For example, the first stage 302 has a pair of transmission lines 314 and 316, optical phase shift elements 318 and 320 (together forming a differential phase shifter), and a 2x2 coupler 322. Similarly, the second stage 304 has a pair of transmission lines 324 and 326, optical phase shift elements 328 and 330 (together forming a differential phase shifter), and a 2x2 coupler 332. Finally, the third stage 306 has a pair of transmission lines 334 and 336, optical phase shift elements 338 and 340 (together forming a differential phase shifter), and a 2x2 coupler 342.

[0053] While the example in Figure 3 shows a differential implementation of a phase shifter, some embodiments may use a non-differential implementation having only one optical phase shift element (in one transmission path) within the stage. Throughout this disclosure, whether the phase shift is implemented by a differential phase shifter (i.e., each phase shift element in a differential pair designed to shift by + / -φ / 2, as shown in the example in Figure 3) or by a non-differential phase shifter (shifting the phase of the light in only one transmission path relative to the light in the other by an amount of + / -φ), the phase difference between two optical transmission paths (within the stage) is simply referred to as "φ". Thus, the term "phase shifter" can be applied to either a differential or non-differential phase shifter.

[0054] Phase shifters can be thermo-optic (thermo-optic phase shifters, TOPS), electro-optic (electro-optic phase shifters, EOPS), or other types. TOPS generally have the slowest response speed, but can be made faster by covering them with metal and / or shortening the distance to the heat sink. The power consumption of TOPS can be reduced by having the optical transmission path pass through a heated region multiple times. EOPS can be operated, for example, by current injection, carrier depletion, or the Pockels effect. Each phase shifter can consist of multiple sections, such as a section of a phase shifter with a fast response speed but high power consumption, and a section of a phase shifter with a slow response speed but low power consumption.

[0055] 2x2 couplers can be implemented using, for example, directional couplers, multimode interference couplers, or adiabatic couplers.

[0056] As described above, the three stages (302, 304, and 306) of the demultiplexer 300 are controlled in coordination within a specific range or operating value so that the demultiplexer 300 can achieve "endless" characteristics of multiplexing without requiring any phase shifter resets. In particular, in the example in Figure 3, the first control signal φ1 of the first stage 302 is a digital signal having a value of either -π / 2 or +π / 2. The second control signal φ2 of the second stage 304 is an analog or digital signal operating on a continuous or discrete set of values ​​between -π and +π. The third control signal φ3 of the third stage 306 is an analog or digital signal operating on a continuous or discrete set of values ​​within a range dependent on the first control signal φ1, i.e., operating between 0 and +π when φ1 is -π / 2, and between -π and 0 when φ1 is +π / 2.

[0057] During the operation of the demultiplexer 300, light passing through the fiber first enters a splitter such as a PBSR346, which splits the input light into two optical transmission paths 314 and 316. The PBSR splits the input light into two polarizations and rotates one of the polarizations so that both outputs of the PBSR have the same polarization. Thus, optical transmission path 314 contains light that had one polarization when incident on the PBSR, and optical transmission path 316 contains light that had orthogonal polarization when incident on the PBSR, but once it enters optical transmission paths 314 and 316, the light in both optical transmission paths 314 and 316 has the same polarization. The example in Figure 3 shows a splitter implemented by a PBSR346, but other types of splitters can be used, including passive optical integrated devices such as polarization splitting grating couplers (PSGCs).

[0058] The divided input light enters two optical transmission paths 314 and 316 in the first stage 302, where it undergoes a relative phase shift via phase shift elements 318 and 320, such that the light in one optical transmission path is phase-shifted by an amount φ1 relative to the light in the other optical transmission path. This relative phase shift amount φ1 is controlled by a control signal 308. Next, the phase-shifted light in the two optical transmission paths enters a 2x2 coupler 322 that couples the relatively phase-shifted light. This process is repeated through the second stage 304 and the third stage 306, each undergoing different phase shifts controlled by control signals φ2 (310) and φ3 (312).

[0059] The controller 344 controls the relative phase shift amount of the three stages 302, 304, and 306 via control signals 308, 310, and 312. In a closed-loop feedback scenario, this control can be based on feedback information 348, which is, for example, a measurement of the error in the received signal. Specific algorithms used by the controller 344 to control and adjust the control signals 308, 310, and 312 are described below with reference to Figures 8-10. Figure 3 shows the controller 344 as part of the demultiplexer 300, but in some embodiments, the controller 344 may be implemented separately in the receiver (as another component of the receiver 168 in Figure 1).

[0060] As mentioned above, the Demultiplexer 300 compensates for random birefringence changes that rotate the polarization of light, caused by distortions introduced by optical communication systems. In addition to phase shift compensation, demultiplexers can also be designed to compensate for other non-idealities, such as polarization-dependent loss (PDL). While PDL may be negligible in most short fiber optic links, as the length of the fiber increases, PDL can have a greater impact on the proper reception of the optical signal.

[0061] In polarization-dependent loss (PDL) scenarios, the amount of loss occurring in each of the two polarization modes of the optical fiber may differ; for example, the loss in the transverse magnetic (TM) mode may be greater or less than the loss in the transverse electric (TE) mode. This results in a non-unitary channel matrix F. In this case, multiplexing by phase shift control alone may be insufficient to completely separate signals with two mixed polarization modes. Instead, a combination of optical phase shifters and optical attenuators is implemented in the demultiplexer, as described below with reference to Figure 4. In general, PDL can be caused by the fiber itself or by other elements of the communication system such as fiber connectors, isolators, amplifiers, splitters, fiber couplers, and PBSRs.

[0062] Figure 4 shows an example of an optical polarization demultiplexer 400 according to an embodiment of the present disclosure. The demultiplexer 400 can be implemented as part of a direct detection receiver (e.g., receiver 168 in Figure 1). In some embodiments, the demultiplexer 400 is implemented via integrated photonics, which can reduce costs compared to bulk optics. The demultiplexer 400 provides both relative attenuation control and relative phase shift control between two polarization modes to compensate for PDL of the received optical waveform.

[0063] The demultiplexer 400 includes three stages (402, 404, and 406) for relative phase shift control and / or optical attenuation control. Each stage is controlled by one or more control signals. For example, the first stage 402 is controlled by a first attenuation control signal 408 and a first phase shift control signal 410. The second stage 404 is controlled by a second phase shift control signal 412. The third stage 406 is controlled by a second attenuation control signal 414 and a third phase shift control signal 416. Each control signal controls the amount of phase shift or optical attenuation implemented in its respective stage.

[0064] In the example shown in Figure 4, the first stage 402 includes first and second optical transmission lines 418 and 420, first and second optical attenuators 422 and 424 (together forming a differential attenuator), first and second phase shift elements 426 and 428 (together forming a differential phase shifter), and a 2x2 coupler 430. Similarly, the second stage 404 includes first and second optical transmission lines 432 and 434, first and second phase shift elements 436 and 438 (together forming a differential phase shifter), and a 2x2 coupler 440. Finally, the third stage 406 includes first and second optical transmission lines 442 and 444, first and second optical attenuators 446 and 448 (together forming a differential attenuator), first and second phase shift elements 450 and 452 (together forming a differential phase shifter), and a 2x2 coupler 454.

[0065] The example in Figure 4 shows a differential implementation of an optical attenuator and an optical phase shifter, but in some embodiments, a non-differential implementation may be used, having only one optical attenuator (in one optical transmission path) and one phase shift element (in one optical transmission path) in a single stage. Throughout this disclosure, the relative optical attenuation between two optical transmission paths is simply referred to as "a," regardless of whether the attenuation is implemented by a differential attenuator (i.e., as shown in the example in Figure 4, each attenuator in a differential pair is designed to attenuate light by + / -a / 2) or a single optical attenuator (attenuating light from only one optical transmission path by an amount of + / -a relative to the light in the other optical transmission path). The attenuation amount "a" of the optical attenuator represents any appropriate measure of attenuation, such as exponential loss, where the actual effect on light transmission is exponential at "a" (for example, multiplied by exp{-a / 2} when passing through an optical attenuator labeled a / 2, as is multiplied by exp{-iφ / 2} when passing through a phase shifter labeled φ / 2).

[0066] Similarly, whether the relative phase shift is implemented by a differential phase shifter (i.e., each phase shift element in a differential pair designed to shift by + / -φ / 2, as shown in the example in Figure 3) or by a non-differential phase shifter (which shifts the phase of light in only one optical transmission path relative to the light in the other by an amount of + / -φ), the relative phase difference between two optical transmission paths is simply called "φ".

[0067] As described above, the three stages of the demultiplexer 400 are coordinately controlled within a specific range or operating value so that the demultiplexer 400 can achieve the "endless" characteristic of multiplexing without requiring any phase shifter resets. For phase shift control, in the example in Figure 4, the first phase shift control signal φ1(410) of the first stage 402 is a digital signal having a value of either -π / 2 or +π / 2. The second phase shift control signal φ2(412) of the second stage 404 is an analog or digital signal operating on a continuous or discrete set of values ​​between -π and +π. The third phase shift control signal φ3(416) of the third stage 406 is an analog or digital signal operating on a continuous or discrete set of values ​​within a range dependent on the first control signal φ1(410), i.e., operating between 0 and +π when φ1 is -π / 2, and between -π and 0 when φ1 is +π / 2. For attenuation control, the first attenuation control signal a1(408) and the second attenuation control signal a2(414) each operate within a continuous or discrete set of values ​​within a range. For example, the range may be (-3, +3). For example, the range may be (-1, +1). As yet another example, the range may be (-0.6, +0.6), which corresponds to approximately -5.2 dB to +5.2 dB. Other appropriate ranges may be used.

[0068] During the operation of the demultiplexer 400, the light passing through the fiber first enters a splitter such as a PBSR458, which splits the input light into two optical transmission paths 418 and 420. While the example in Figure 4 shows a splitter implemented by a PBSR458, other types of splitters can be used, including passive optical integrated devices such as a polarization splitting grating coupler (PSGC). The split input light enters the two optical transmission paths 418 and 420 of the first stage 402, where it undergoes relative attenuation via optical attenuators 422 and 424, such that the light in one optical transmission path is attenuated relative to the light in the other. This relative attenuation a1 is controlled by an attenuation control signal 408.

[0069] Then, the relatively attenuated light in the two optical transmission lines undergoes a relative phase shift via phase shift elements 426 and 428 (forming a differential phase shifter) such that the phase of the light in one optical transmission line shifts relative to the phase of the light in the other optical transmission line. This relative phase shift amount φ1 is controlled by a control signal 410. Next, the phase-shifted light in the two optical transmission lines enters a 2x2 coupler 430 that couples the relatively phase-shifted light. This process continues through a second stage 404 and a third stage 406 such that the two polarizations of the light undergo relative phase shifts and / or relative attenuation controlled by phase control signals 412 and 416, as well as an attenuation control signal 414.

[0070] Controller 456 controls the relative attenuation and relative phase shift of different stages 402, 404, and 406 via control signals 408, 410, 412, 414, and 416. By controlling both the relative attenuation and relative phase shift between two polarizations of light, the demultiplexer 400 can compensate for both random phase shift and PDL (non-unitary channel matrix F). In a closed-loop feedback scenario, this control can be based on feedback information 460, which is, for example, a measurement of error in the received signal. Specific algorithms used by controller 456 to control and adjust control signals 408, 410, 412, 414, and 416 are described below with reference to Figures 8-10. Figure 4 shows controller 456 as part of demultiplexer 400, but in some embodiments, controller 456 may be implemented separately in the receiver (as another component of receiver 168 in Figure 1).

[0071] Generally, control (e.g., controller 344 in Figure 3 or 456 in Figure 4) is designed to reduce the amount of crosstalk between signals received in two polarization modes of an optical waveform. In a feedback control scenario, the controller can adjust the control based on feedback information (e.g., feedback 348 in Figure 3 and feedback 460 in Figure 4). Feedback information may include, for example, a measurement of an error in the received waveform. The controller may be designed to adjust the control signal to reduce the measured error. Error measurement can be implemented in various ways. For example, the error measurement may reflect the amount of crosstalk between signals in two polarization modes of light.

[0072] To measure the amount of crosstalk, in some embodiments, the communication system may utilize a reference signal (e.g., a pilot tone or pilot signal) transmitted in addition to the signal carrying the information. The reference signal has waveform characteristics known to both the transmitter and the receiver, and the receiver can estimate and compensate for random influences on the communication channel.

[0073] Figures 5A and 5B show examples of transmitters 500 and 520 according to embodiments of the present disclosure, configured to transmit a reference signal (e.g., a pilot tone). Transmitter 500 in Figure 5A transmits pilot tones 502(A) and 504(B) in the respective optical polarization modes of the laser input. In some embodiments, pilot tones 502 and 504 are low-frequency tones and may have different tone frequencies for the two polarizations. For example, the first pilot tone 502 may be transmitted at a frequency of 1 MHz, and the second pilot tone 504 may be transmitted at a frequency of 2 MHz. The modulation of pilot tones 502 and 504 is a percentage of the signal average power, for example, the modulation of pilot tones 502 and 504 may be 2% of the signal average power.

[0074] In the example in Figure 5A, pilot tones 502(A) and 504(B) are added to electrical signals 506(X) and 508(Y), respectively, before modulating the laser inputs of each waveguide. For example, pilot tones 502(A) and 504(B) can be applied by digitally adding the tones to the digital-to-analog converter (DAC) output. Alternatively, pilot tones 502(A) and 504(B) can be applied analogously by adding them to the inputs of the modulators 510 and 512 drivers, or inside the modulators 510 and 512 drivers, or to the outputs of the modulators 510 and 512 drivers.

[0075] Figure 5B shows an example of transmitter 520, illustrating further details of modulation and pilot tones. In this example, pilot tones 522(A) and 524(B) are applied by adding them to the modulated signals 526(X) and 528(Y) in an analog manner at the outputs of drivers 534 and 536 of modulators 530 and 532, respectively. In the example in Figure 5B, modulators 530 and 532 are shown implemented as Mach-Zehnder interferometer (MZI) modulators, but other suitable optical modulators may be used.

[0076] Therefore, in transmitters 500 and 520 in Figures 5A and 5B, pilot tones A and B are added to input signals X and Y, respectively, and coupled at PBSR 514 and 538 for transmission over fiber. Specifically, pilot tone A and signal X are transmitted in one polarization mode of the light, and pilot tone B and signal Y are transmitted in the other polarization mode of the light. The coupled optical PDM waveform propagates through the communication system toward the receiver, during which time, various non-idealities in the system cause random and unpredictable rotational drift and polarization-dependent loss (PDL) in the two polarization modes. These non-idealities affect both the pilot tone and signal propagating in each polarization mode. Since the pilot tones (A and B) are known, the receiver can measure the deviation (or error) of the received pilot tone compared to the original pilot tones (A and B), thereby allowing the receiver to estimate the error of signals X and Y themselves. Based on the error estimation, the receiver can then compensate for the polarization drift and PDL to more accurately reconstruct signals X and Y.

[0077] Examples of receiver structures for detecting pilot tones and measuring errors in received pilot tones are described below with reference to Figures 6, 7A, and 7B. Examples of using such error measurement in feedback control of relative phase shift and / or relative attenuation are described below with reference to Figures 9 and 10.

[0078] Figure 6 shows an example of a demultiplexer 600 according to an embodiment of the present disclosure, configured to receive pilot tones to generate feedback information. In the receiver 600, the received waveforms 614 and 616 of two polarizations of the received optical light are processed by the pilot tone detector 602 to detect the power of the received pilot tones for each polarization mode 614 and 616. The pilot tone detector 602 then provides one or more pilot tone measurements 604 as feedback information (e.g., as feedback 348 in Figure 3 and feedback 460 in Figure 4) to the controller 606. The controller 606 uses these pilot tone measurements 604 to adapt control signals (608, 610, 612) that apply relative phase shifts and / or relative attenuation to the received optical signal.

[0079] Figure 6 shows the controller 606 and pilot tone detector 602 as part of the demultiplexer 600, but in some embodiments, the controller 606 and / or pilot tone detector 602 may be implemented separately in the receiver (as separate components of receiver 168 in Figure 1). Furthermore, Figure 6 shows the controller 606 and pilot tone detector 602 as separate modules, but in some embodiments, the controller 606 and pilot tone detector 602 may be implemented by an integrated circuit without being separated into separate modules. Furthermore, the example in Figure 6 shows a scenario in which only relative phase shift is adapted via control signals 608, 610, and 612 (e.g., as in demultiplexer 300 in Figure 3), but these techniques can also be applied to adapt both relative phase shift and relative attenuation (e.g., as in demultiplexer 400 in Figure 4).

[0080] In the example in Figure 6, it is assumed that the first pilot tone (A) is transmitted in the first polarization mode (let's call it X), and the second pilot tone (B) is transmitted in the second polarization mode (let's call it Y). At the receiver, it is desirable that the received polarization modes (H, V) satisfy H=X and V=Y. However, as the optical waveform passes through the communication system, polarization drift and PDL can cause the two polarization modes carrying the two pilot tones (A and B) to undergo random and unpredictable rotations. Therefore, when the demultiplexer 600 receives these randomly rotated polarization modes, it can actually detect a mixture of pilot tones A and B in each polarization mode H and V when attempting to detect pilot tones A and B.

[0081] To estimate the effects of this cross-mixing, the receiver can detect the power of each pilot tone (A and B) in each of the two polarization modes (H and V). For example, in Figure 6, the pilot tone detector 602 detects the power of tone A in polarization mode H (P HA (Assuming), the power of tone B in polarization mode H (P HB (Assuming), the power of tone A in polarization mode V (P VA (Assuming), and the power of tone B in polarization mode V (P VB Four different quantities (assuming P) can be detected. Of these four quantities, P HB and P VA This represents the amount of crosstalk between pilot tones A and B in the two polarization modes H and V.

[0082] Next, the controller 610 calculates an error signal based on these received pilot tone components and estimates the amount of crosstalk between the two polarization modes caused by the non-ideal nature of the communication system. For example, in some embodiments, the error can be calculated as follows:

[0083]

number

[0084] However, other measures of error can be used to estimate the amount of crosstalk between pilot tones (A and B) in two polarization modes (H and V). In general, the measure of error is P HB and / or P VA The error should increase as the value of increases. The error measure provides an estimate of how well controller 606 fits the control signals (e.g., 608, 610, and 612) to adjust the relative phase shift and / or relative attenuation between the two polarization modes H and V and compensate for random polarization drift and PDL. Thus, controller 606 can use this error measurement in the feedback control loop to dynamically adjust the control signals (e.g., 608, 610, and 612) to further reduce the error. Details of an exemplary feedback algorithm are described below with reference to Figures 9 and 10.

[0085] Pilot tones A and B can be detected from the waveforms received at various points in the reception process, and examples of this will be explained below with reference to Figures 7A and 7B.

[0086] Figures 7A and 7B illustrate examples of different embodiments of a demultiplexer according to the present disclosure, configured to receive and process pilot tones. Specifically, Figures 7A and 7B show examples of detecting pilot tones (A and B) at different points in the receiving process. As described above, the power of each pilot tone A and B in each of the two polarization modes (H and V) needs to be detected. In the example of demultiplexer 700 in Figure 7A, the pilot tones (A and B) are detected from the received waveform at the outputs of transimpedance amplifiers (TIAs) 704 and TIA 706. Alternatively, as shown in the example of demultiplexer 720 in Figure 7B, the pilot tones (A and B) are detected from the waveform received in the optical domain (specifically, at the outputs of separate photodiodes 724 and 726 coupled to the optical signal received via an optical coupler).

[0087] In both examples in Figures 7A and 7B, the various received powers of the pilot tone component can be detected by using Fourier transform techniques, such as multiplying the received signal by the sine and / or cosine of the pilot tone frequency and summing the results, or filtering the results with a narrowband electrical filter.

[0088] Next, an example of using error measurement in feedback control of relative phase shift and / or relative attenuation will be described below with reference to Figures 8-10. The control system functions to minimize the error measured in the received optical waveform. When the error is minimized, each PDM signal is received in its respective polarization mode with minimal crosstalk (for example, signal X is received in polarization mode H and signal Y is received in polarization mode V).

[0089] Figure 8 is a flowchart illustrating an example of a method 800 for controlling an optical polarization demultiplexer according to an embodiment of the present disclosure. Method 800 can be used to control the relative phase shift in a demultiplexer, such as the demultiplexer 300 shown in Figure 3.

[0090] In step 802, light is received into a first pair of optical transmission lines (314, 316) via a pair of MIMO inputs. In step 804, a first optical phase shifter (e.g., a differential phase shifter formed by 318 and 320) is controlled to apply a first relative phase shift between the first pair of optical transmission lines (314, 316). In some embodiments, the first optical phase shifter can be controlled in a binary manner, for example, of values ​​(c+π / 2) and (c-π / 2), where "c" is a real number reflecting the offset. This control can be based on feedback information (e.g., using a pilot tone).

[0091] In step 806, the first pair of optical transmission lines (314, 316) are coupled with the first 2x2 optical coupler (322) to output the second pair of optical transmission lines (324, 326).

[0092] In step 808, a second optical phase shifter (e.g., a differential phase shifter formed by 328 and 330) is controlled to apply a second relative phase shift between a second pair of optical transmission lines (324, 326). In some embodiments, the second optical phase shifter can be controlled within a finite range of values ​​including -nπ and +nπ, where "n" is an integer. For example, this is possible by analog operation within the range (-nπ, +nπ). This control can be based on feedback information (e.g., using a pilot tone).

[0093] In step 810, the second pair of optical transmission lines (324, 326) are coupled with the second 2x2 optical coupler (332) to output a third pair of optical transmission lines (334, 336).

[0094] In step 812, a third optical phase shifter (e.g., a differential phase shifter formed by 338 and 340) is controlled to apply a third relative phase shift between a third pair of optical transmission lines (334, 336). In some embodiments, the third optical phase shifter can be controlled within a finite range that depends on the value of the first relative phase shift. For example, as described above, the third optical phase shifter can be controlled to operate between 0 and +nπ when the first relative phase shift is equal to (c-π / 2), and between -nπ and 0 when the first relative phase shift is equal to (c+π / 2), where "n" is an integer. This can be done by analog operation within the ranges (0,+nπ) and (-nπ,0). This control can be based on feedback information (e.g., using a pilot tone).

[0095] In step 814, the third pair of optical transmission paths (334, 336) are coupled with the third 2x2 optical coupler (342) to output the fourth pair of optical transmission paths (350, 352). In step 816, the fourth pair of optical transmission paths (350, 352) are output via a pair of MIMO outputs.

[0096] The exemplary method 800 in Figure 8 shows a specific order of steps, but one or more of these steps can be performed in a different order. For example, the control of the first, second, and third optical phase shifters can be performed in a different order. A specific example of controlling and adjusting three phase shifters is described with reference to Figure 9.

[0097] Figure 9 is a flowchart illustrating an example of a method 900 for controlling relative phase shift values ​​in an optical polarization demultiplexer according to an embodiment of the present disclosure. Method 900 demonstrates a specific method for adjusting first, second, and third phase shifters to achieve "endless" characteristics of optical MIMO polarization multiplexing and demultiplexing using only three stages of finite-range phase shifts (in the case of a lossless scenario without PDL). For illustrative purposes, the description of Method 900 is provided with reference to the demultiplexer 300 in Figure 3.

[0098] Method 900 is an iterative process of adapting relative phase shift control signals 308, 310, and 312 to gradually reduce the measured feedback error (e.g., feedback 348 in Figure 3, or feedback 604 in Figure 6).

[0099] In step 902, at the start of the iteration, the demultiplexer initializes the relative phase shift values ​​of three control signals 308, 310, and 312. For example, in some embodiments, the first control signal φ1(308) is a binary (digital) value and is initially set to either -π / 2 or +π / 2. The second control signal φ2(310) is a continuous (analog) or discrete (digital) value and is initially set to a value between -π and +π. The third control signal φ3(312) is also a continuous (analog) or discrete (digital) value and is set to a value between 0 and +π if the first control signal φ1(308) was set to -π / 2; otherwise, the third control signal φ3(312) is set to a value between -π and 0 if the first control signal φ1(308) was set to +π / 2. This relationship between the third control signal φ3(312) and the first control signal φ1(308) is maintained throughout the control process of method 900.

[0100] In step 904, the third control signal φ3(312) is adjusted (within its current range) to reduce the measured error in the feedback (e.g., feedback 348 in Figure 3). The adjustment of the third control signal φ3(312) can be performed by an optimization or pseudo-optimization algorithm (e.g., a gradient descent algorithm) that seeks to minimize or reduce the measured error. For example, the adjustment of the third control signal φ3(312) can be performed by searching within a local neighborhood of the current value of the third control signal φ3(312) to find a new value that reduces the measured error. As a specific example, we will describe the case where the third control signal φ3(312) is adjusted in + / -Δφ3 steps to find a value that reduces the measured error. The step size Δφ3 can be adjusted dynamically in each iteration. If the value of the third control signal φ3(312) is within Δφ3 from the boundary of its range (i.e., within Δφ3 of 0, +π, or -π), the third control signal φ3(312) does not change. Otherwise, the third control signal φ3(312) is first increased by Δφ3, and the error resulting from the feedback 348 is measured. Next, the third control signal f3(312) is decreased by 2Δφ3 (i.e., decreased by Δφ3 from the original value), and the error resulting from the feedback 348 is measured again. The value of the third control signal φ3(312) with the smaller error is assigned as the new adjusted value of the third control signal φ3(312).

[0101] In step 906, the second control signal φ2(310) is adjusted to reduce the measured error. The adjustment of the second control signal φ2(310) can be performed by an optimization or quasi-optimization algorithm (e.g., gradient descent algorithm) that attempts to minimize or reduce the measured error. For example, the adjustment of the second control signal φ2(310) can be performed by searching within the local neighborhood of the current value of the second control signal φ2(310) to find a new value that reduces the measured error. As a specific example, the case of adjusting the second control signal φ2(310) in + / -Δφ2 steps and finding a value that reduces the measured error will be described. The step size Δφ2 can be adjusted dynamically in each iteration. For example, in some embodiments, the step size Δφ2 can be configured to increase as the value sin 2 (φ3) of the (third control signal 312) decreases. In the search process of step 906, the second control signal φ2(310) is first increased by Δφ2, and the error resulting from the feedback 348 is measured. Next, the second control signal φ2(310) is decreased by 2Δφ2 (i.e., decreased by Δφ2 from the original value), and the error resulting from the feedback 348 is measured again. The value of the second control signal φ2(310) for which the error has decreased is denoted as φ2′ for the purposes of this description.

[0102] In step 908, the demultiplexer determines whether the value φ2′ < -π (i.e., outside the lower limit). If so, in step 910, the new adjusted value of the second control signal φ2(310) is set to -2π-φ2′. Furthermore, in step 912, the values ​​of the first control signal φ1(308) and the third control signal φ3(312) are inverted. That is, if the value of the first control signal (308) is φ1 = -π / 2 (meaning the third control signal 312 is within the range of 0 and +π), then the value of π is simultaneously added to the first control signal φ1(308) and subtracted from the third control signal φ3(312). Alternatively, if the value of the first control signal (308) is φ1 = +π / 2 (meaning the third control signal 312 is within the range of -π and 0), then the value of π is simultaneously subtracted from the first control signal φ1(308) and added to the third control signal φ3(312). The control loop needs to pause during this simultaneous addition and subtraction. In some embodiments, the simultaneous addition and subtraction of π may be performed sequentially (for example, adjusting the first control signal φ1(308) and then adjusting the third control signal φ3(312), or vice versa). Nevertheless, the procedure of adjusting the first control signal φ1(308) and the third control signal φ3(312) described above needs to be performed quickly so as not to cause long downtimes and control delays in the control system.

[0103] If, in step 908, it is determined that φ2′ is not outside the lower limit, then in step 914, the demultiplexer checks whether φ2′ > +π (i.e., outside the upper limit). If so, in step 916, the newly adjusted value of the second control signal φ2(310) is set to +2π-φ2′. Furthermore, in step 912 (as described above), the values ​​of the first control signal φ1(308) and the third control signal φ3(312) are inverted.

[0104] If, in step 914, it is determined that φ2′ is not outside the upper limit (meaning φ2′ is within the range of -π to +π), then in step 918, the new adjusted value of the second control signal φ2(310) is set to φ2′. In this case, the first control signal φ1(308) and the third control signal φ3(312) are not inverted. The process then returns to step 904, and the next iteration of adjusting the control signals is performed.

[0105] The control process of method 900 can achieve "endless" operation of multiplexing and decoupling without requiring a reset or interruption of data reception. This characteristic is made possible by the fact that when the second control signal φ2(310) reaches either a boundary point (+π or -π), the phase shift of the second stage (304 in Figure 3) acts as a pass-through. At this time, when the second control signal φ2(310) is at the boundary point of its range, π is simultaneously added to or subtracted from the first control signal φ1(308) and the third control signal φ3(312) (as described above in step 912). In this way, "endless" operation of polarization multiplexing and decoupling is achieved without requiring a reset or interruption of data reception.

[0106] The exemplary method 900 in Figure 9 shows a specific order of steps, but one or more of these steps can be performed in a different order. For example, steps 908 and 914, namely checking whether the second control signal φ2(310) is within the lower and upper limits of the range -π to +π, can be reversed.

[0107] Furthermore, the specific numerical ranges described in step 902 can be changed. For example, the possible values ​​of the first control signal φ1(308) can have a fixed offset so that they are shifted binary values ​​of (-π / 2+c) or (+π / 2+c). The possible values ​​of the second control signal φ2(310) can be shifted by an integer multiple of 2π, as long as the boundary points of its range enable the pass-through characteristics described above. Similarly, the possible values ​​of the third control signal φ3(312) can also be shifted by an integer multiple of 2π.

[0108] Figure 10 is a flowchart illustrating an example of a method 1000 for controlling relative attenuation values ​​in an optical polarization demultiplexer according to an embodiment of the present disclosure. Method 1000 can be used to control relative attenuation signals such as relative attenuation control signals a1(408) and a2(414) in the demultiplexer 400 of Figure 4. For illustrative purposes, a description of method 1000 is provided with reference to the demultiplexer 400 of Figure 4.

[0109] While exemplary method 1000 demonstrates control of both relative attenuation control signals a1(408) and a2(414), in some scenarios only one of the signals is implemented. For example, in some embodiments only the first control signal a1 is implemented. This may be appropriate, for example, in scenarios where the PDL level is moderate (e.g., a scenario where the sole source of PDL is not the fiber transmission line itself, but the receiver). Furthermore, if the PDL value is not expected to change significantly over time, the control value a1 may be set once at the start of operation (e.g., in the factory) and left unchanged.

[0110] Alternatively, as shown in Method 1000, both optical attenuation control signals a1 and a2 can be adjusted (e.g., continuously) using a variable optical attenuator (VOA), for example. This may be appropriate in scenarios where the PDL level is more important (e.g., scenarios where PDL occurs both in the receiver and the fiber transmission line).

[0111] In general, relative attenuation signals a1(408) and a2(414) can be controlled using an optimization or pseudo-optimization process designed to reduce or minimize the measured error of the feedback (e.g., feedback 460 in Figure 4, or feedback 604 in Figure 6). For example, in some embodiments, the relative attenuation control signals a1(408) and a2(414) can be controlled simultaneously by simultaneous optimization. As another example shown in method 1000 in Figure 10, an iterative process can be implemented to adapt the relative attenuation control signals a1(408) and a2(414) to gradually reduce the measured feedback error.

[0112] In step 1002, at the start of the iteration, the demultiplexer initializes two VOA control signals a1(408) and a2(414) to their initial values, for example, zero.

[0113] In step 1004, the first VOA control signal a1(408) is adjusted (within its tolerance range, such as -3 to +3) to reduce the measured error in the feedback. The adjustment of the first VOA control signal a1(408) can be performed by an optimization or pseudo-optimization algorithm (e.g., a gradient descent algorithm) that seeks to minimize or reduce the measured error. For example, the adjustment of the first VOA control signal a1(408) can be performed by searching within a local neighborhood of the current value of the first VOA control signal a1(408) to find a new value that reduces the measured error. As a specific example, we will describe the case where the first VOA control signal a1(408) is adjusted in + / - Δa1 steps to find a value that reduces the measured error. The step size Δa1 can be adjusted dynamically in each iteration. The first VOA control signal a1(408) is first increased by Δa1, and the error resulting from the feedback 460 is measured. Next, the first VOA control signal a1(408) is reduced by 2Δa1 (i.e., reduced by Δa1 from its original value), and the error resulting from the feedback 460 is measured again. The value of the first VOA control signal a1(408) with the reduced error is assigned as the new adjusted value of the first VOA control signal a1(408).

[0114] In step 1006, the second VOA control signal a2(414) is adjusted (within its tolerance range, such as -3 to +3) to reduce the measured error. The adjustment of the second VOA control signal a2(414) can be performed by an optimization or pseudo-optimization algorithm (e.g., a gradient descent algorithm) that seeks to minimize or reduce the measured error. For example, the adjustment of the second VOA control signal a2(414) can be performed by searching within a local neighborhood of the current value of the second VOA control signal a2(414) to find a new value that reduces the measured error. As a specific example, we will describe the case in which the second VOA control signal a2(414) is adjusted in + / - Δa2 steps to find a value that reduces the measured error. The step size Δa2 can be adjusted dynamically in each iteration. For example, in some embodiments, the step size Δa2 is the value sin (of the first VOA control signal 408). 2 It can be configured to increase as (a1) decreases (and vice versa). In the exploration process of step 1006, the second VOA control signal a2(414) is first increased by Δa2 and the resulting error from the feedback 460 is measured. Next, the second VOA control signal a2(414) is decreased by 2Δa2 (i.e., decreased by Δa2 from the original value) and the resulting error from the feedback 460 is measured again. The value of the second VOA control signal a2(414) with the smaller error is assigned as the new adjusted value of the second VOA control signal a2(414). Then, the process returns to step 1004 and the next iteration of adjusting the control signal is performed.

[0115] The exemplary method 1000 in Figure 10 shows a specific order of steps, but one or more of these steps can be performed in a different order. For example, steps 1004 and 1006 can be reversed. Furthermore, the range of specific numerical values ​​can also be changed. For example, the range of values ​​for the first and second VOA control signals from -3 to +3 can be changed to a different range of values.

[0116] In some embodiments, the techniques described herein for optical MIMO polarization multiplexing can be applied to general 2x2 optical MIMO multiplexing. For example, in some embodiments, the techniques described herein can be implemented separately from or without PBSR.

[0117] Figure 11 shows an example of simulation results illustrating the operation of a PDM MIMO demultiplexer according to an embodiment of the present disclosure. In the simulation results of Figure 11, the light input to the demultiplexer (pseudolight received from the fiber optic transmission line) is continuously and randomly polarized and scrambled. The demultiplexer (for example, demultiplexer 300 in Figure 3) is then controlled to continuously multiplex and separate the received signals.

[0118] Graph 1102 shows an example of the time-dependent changes when the three control signals φ1(308), φ2(310), and φ3(312) are adjusted by the control algorithm. Graph 1100 shows an example of the resulting crosstalk amount, i.e., the error "e" mentioned above.

[0119] Figure 12 shows an example of a computing system 1200 that can be used to implement one or more components of a system that performs adaptive control of an optical polarization demultiplexer. The computing system 1200 can be used to implement the techniques described herein. For example, one or more parts of a controller (e.g., controller 344 in Figure 3, controller 456 in Figure 4, controller 606 in Figure 6) and / or a pilot tone detector (e.g., pilot tone detector 602 in Figure 6) can be implemented by components of the computing system 1200 described herein.

[0120] Computing System 1200 is intended to represent a variety of systems, including digital computers such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The components, their connections and relationships, and functions shown herein are merely examples and are not intended to be limiting.

[0121] The computing system 1200 includes a processor 1202, memory 1204, storage device 1206, a high-speed interface 1208 connected to memory 1204 and multiple high-speed expansion ports 1210, and a low-speed interface 1212 connected to a low-speed expansion port 1214 and storage device 1206. Each of the processor 1202, memory 1204, storage device 1206, high-speed interface 1208, high-speed expansion port 1210, and low-speed interface 1212 is interconnected using various buses and may be mounted on a common motherboard or in other configurations as needed. The processor 1202 processes instructions for execution within the computing system 1200, including instructions stored in memory 1204 or storage device 1206, to display graphical information for a GUI on an external input / output device such as a display 1216 coupled to the high-speed interface 1208. In other embodiments, multiple processors and / or multiple buses may be used with multiple memories and various types of memory as needed. Furthermore, multiple computing devices can be connected, with each device contributing to the operation (for example, as a server bank, a cluster of blade servers, or a multiprocessor system). In some embodiments, the processor 1202 is a single-threaded processor. In some embodiments, the processor 1202 is a multi-threaded processor. In some embodiments, the processor 1202 is a quantum computer.

[0122] Memory 1204 stores information within the computing system 1200. In some embodiments, memory 1204 is one or more volatile memory units. In some embodiments, memory 1204 is one or more non-volatile memory units. Alternatively, memory 1204 may be another form of computer-readable medium, such as a magnetic disk or an optical disk.

[0123] The storage device 1206 can provide the computing system 1200 with a large-capacity storage device. In some embodiments, the storage device 1206 may be, or include, computer-readable media such as floppy disk drives, hard disk drives, optical disk drives, or tape drives, flash memory or other similar solid memory devices, or device arrays including devices in a storage area network or other configuration. Instructions may be stored in the information medium. When the instructions are executed by one or more processing units (e.g., processor 1202), they perform one or more of the methods described above. Instructions may be stored in one or more storage devices such as computer-readable media or machine-readable media (e.g., memory 1204, storage device 1206, or memory on processor 1202). The high-speed interface 1208 manages bandwidth-intensive operations of the computing system 1200, and the low-speed interface 1212 manages less bandwidth-intensive operations. Such function assignments are merely examples. In some embodiments, the high-speed interface 1208 is coupled to memory 1204, a display 1216 (e.g., via a graphics processor or accelerator), and a high-speed expansion port 1210 that can accept various expansion cards (not shown). In this embodiment, the low-speed interface 1212 is coupled to a storage device 1206 and a low-speed expansion port 1214. The low-speed expansion port 1214, which may include various communication ports (e.g., USB, Bluetooth, Ethernet, wireless Ethernet), may be coupled to one or more input / output devices such as a keyboard, pointing device, scanner, or networking device such as a switch or router (e.g., via a network adapter).

[0124] The computing system 1200 can be implemented in several different forms, as shown in the figure. For example, it may be implemented as a standard server 1220, or as a group of such servers in multiple configurations. Furthermore, it may be implemented in a personal computer such as a notebook computer 1222. It may also be implemented as part of a rack server system 1224.

[0125] As used in this disclosure, the term “system” may encompass all devices, machines, and equipment for processing data, including, for example, a programmable processor, a computer, or multiple processors or computers. In addition to hardware, a processing system may include code that constitutes the execution environment of the computer program, such as processor firmware, a protocol stack, a database management system, an operating system, or one or more combinations thereof.

[0126] Computer programs (also called programs, software, software applications, scripts, executable logic, or code) can be written in any form of programming language, including compiled or interpreted languages, declarative or procedural languages, and can be deployed in any form, such as standalone programs or as modules, components, subroutines, or other units suitable for use in a computer environment. Computer programs do not necessarily correspond to files in a file system. A program can be part of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), a single file dedicated to the program, or multiple collaborative files (e.g., a file containing one or more modules, subprograms, or parts of code). Computer programs can also be deployed to run on a single computer, or on multiple computers located in one site or distributed across multiple sites and interconnected by a communication network.

[0127] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile or volatile memory, media, and memory devices, including, for example, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks or removable disks or magnetic tapes; magneto-optical disks; and CD-ROM and DVD-ROM disks. Processors and memory may be complemented by or incorporated within application logic circuits. A server may be a general-purpose computer, a custom-made, special-purpose electronic device, or a combination of both.

[0128] An implementation may include a backend component (e.g., a data server), or a middleware component (e.g., an application server), or a frontend component (e.g., a client computer having a graphical user interface or web browser on which a user can interact with the implementation of the subject matter described in this specification), or any combination of one or more such backend, middleware, or frontend components. The components of the system may be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include local area networks (LANs) and wide area networks (WANs) (e.g., the Internet).

[0129] The functions described may be implemented in digital electronic circuits, or in computer hardware, firmware, software, or a combination thereof. The device may be implemented as a computer program product tangibly embodied in an information carrier, such as a machine-readable memory device, for execution by a programmable processor, and the method steps may be executed by a programmable processor that performs the functions of the described implementation by executing a program of instructions, manipulating input data, and generating output. The functions described may be advantageously implemented in one or more computer programs executable on a programmable system including at least one programmable processor coupled to receive and transmit data and instructions from a data storage system, at least one input device, and at least one output device. A computer program is a set of instructions used directly or indirectly within a computer to perform a particular activity or to produce a particular result. A computer program may be written in any form of programming language, including compiled or interpreted languages, and may be deployed in any form, including standalone programs or modules, components, subroutines, or other units suitable for use in a computing environment.

[0130] While this disclosure contains many specific implementation details, these should not be interpreted as limitations on the scope of the invention or the claims, but rather as descriptions of features specific to a particular implementation of a particular invention. Certain features described in this disclosure within the context of individual embodiments may also be implemented in combination within a single embodiment. Conversely, various features described within the context of a single embodiment may also be implemented separately in multiple embodiments or in any suitable subcombination. Furthermore, features are described above as acting in a particular combination, and may even be initially claimed to act in this way, but one or more features from the claimed combination may, in some cases, be removed from the combination, and the claimed combination may cover a subcombination or a variation of a subcombination.

[0131] Similarly, while drawings depict actions in a specific order, this should not be interpreted as requiring that such actions be performed in a specific order or sequentially, or that all illustrated actions be performed, in order to achieve the desired result.

Claims

1. a pair of MIMO inputs configured to input light into the first pair of optical transmission paths; a first optical phase shifter configured to apply a first relative phase shift between the first pair of optical transmission lines; a first 2x2 optical coupler configured to combine the first pair of optical transmission lines to output a second pair of optical transmission lines; a second optical phase shifter configured to apply a second relative phase shift between the second pair of optical transmission lines; a second 2x2 optical coupler configured to combine the second pair of optical transmission lines to output a third pair of optical transmission lines; a third optical phase shifter configured to apply a third relative phase shift between the third pair of optical transmission lines; a third 2x2 optical coupler configured to combine the third pair of optical transmission lines to output a fourth pair of optical transmission lines; a pair of MIMO outputs configured to output the fourth pair of optical transmission paths, the pair of MIMO outputs being outputs from the third 2x2 optical coupler as a pair of demultiplexed output optical signals; and controlling the first optical phase shifter to apply non-continuously varying values ​​of the first relative phase shift; controlling the second optical phase shifter to apply continuously varying values ​​of the second relative phase shift; and a controller configured to control the third optical phase shifter to apply continuously varying values ​​of the third relative phase shift; 1. A 2x2 optical multiple-input multiple-output (MIMO) demultiplexer comprising:

2. The 2x2 optical MIMO demultiplexer of claim 1 , wherein the controller is configured to control the first optical phase shifter to cause a value of the first relative phase shift to change binary.

3. 3. The 2x2 optical MIMO demultiplexer according to claim 2, wherein the value of the first relative phase shift is one of two values ​​between c+π / 2 and c−π / 2 (c is a real number).

4. 2. The 2x2 optical MIMO demultiplexer of claim 1, wherein the controller is configured to control the second optical phase shifter so that the value of the second relative phase shift is continuous within a finite range that includes −nπ and +nπ (n is an integer).

5. 5. The 2x2 optical MIMO demultiplexer of claim 4, wherein the controller is configured to analogically control the second optical phase shifter so that a value of the second relative phase shift varies continuously within a range (-nπ, +nπ).

6. 2. The 2x2 optical MIMO demultiplexer of claim 1, wherein the controller is configured to control the third optical phase shifter so that a value of the third relative phase shift varies within a finite range determined depending on a value of the first relative phase shift.

7. 7. The 2x2 optical MIMO demultiplexer of claim 6, wherein the controller is configured to control the third optical phase shifter so that a value of the third relative phase shift varies between 0 and +nπ (n is an integer) based on the value of the first relative phase shift being c−π / 2, and varies between −nπ and 0 based on the value of the first relative phase shift being c+π / 2 (c is a real number).

8. 7. The 2x2 optical MIMO demultiplexer of claim 6, wherein the controller is configured to analogically control the third optical phase shifter so that a value of the third relative phase shift varies continuously within a range (0, +nπ) or a range (-nπ, 0).

9. The controller at least one processor; and at least one memory storing instructions, when executed by the at least one processor, for the at least one processor to control the first optical phase shifter, the second optical phase shifter, and the third optical phase shifter; 2. The 2x2 optical MIMO demultiplexer of claim 1, comprising:

10. 10. The 2x2 optical MIMO demultiplexer of claim 1, further comprising a first optical attenuator configured to apply a first relative attenuation between the first pair of optical transmission lines.

11. 11. The 2x2 optical MIMO demultiplexer of claim 10, further comprising a second optical attenuator configured to apply a second relative attenuation between the third pair of optical transmission lines.

12. 2. The 2x2 optical MIMO demultiplexer of claim 1, wherein each of the first optical phase shifter, the second optical phase shifter, and the third optical phase shifter has a phase shift range of 2π or less.

13. an input port configured to receive input light; means for performing adaptive 2×2 optical MIMO polarization demultiplexing on the input light by using three-stage optical phase shifting, and outputting a first optical signal and a second optical signal, a first optical phase shifter controlled to apply a discontinuously varying first relative phase shift; a second optical phase shifter controlled to apply a continuously varying second relative phase shift; and a third optical phase shifter controlled to apply a continuously varying third relative phase shift; and at least one optical detector configured to detect the first optical signal and the second optical signal; 1. An optical multiple-input multiple-output (MIMO) receiver comprising:

14. 1. A method for performing 2x2 optical multiple-input multiple-output (MIMO) demultiplexing, the method comprising: receiving light via a pair of MIMO inputs onto a first pair of optical transmission paths; controlling a first optical phase shifter to apply a first relative phase shift between the first pair of optical transmission lines, wherein the first relative phase shift varies non-continuously; coupling the first pair of optical transmission lines with a first 2x2 optical coupler to output a second pair of optical transmission lines; controlling a second optical phase shifter to apply a second relative phase shift between the second pair of optical transmission lines, wherein the second relative phase shift is continuously varied; coupling the second pair of optical transmission lines with a second 2x2 optical coupler to output a third pair of optical transmission lines; controlling a third optical phase shifter to apply a third relative phase shift between the third pair of optical transmission lines, wherein the third relative phase shift is continuously varied; coupling the third pair of optical transmission lines with a third 2x2 optical coupler to output a fourth pair of optical transmission lines; and outputting the fourth pair of optical transmission lines via a pair of MIMO outputs, the pair of MIMO outputs being outputs from the third 2x2 optical coupler as a pair of demultiplexed output optical signals; The method comprising:

15. 15. The method of claim 14, wherein controlling the first optical phase shifter comprises applying a value of the first relative phase shift that varies non-continuously between two values.

16. 16. The method of claim 15, wherein the value of the first relative phase shift is one of two values ​​between c+π / 2 and c−π / 2, where c is a real number.

17. 15. The method of claim 14, wherein controlling the second optical phase shifter comprises applying values ​​of the second relative phase shift that are continuous within a finite range that includes −nπ and +nπ, where n is an integer.

18. 18. The method of claim 17, wherein controlling the second optical phase shifter is performed by analog operation within the range (-nπ, +nπ).

19. 15. The method of claim 14, wherein controlling the third optical phase shifter comprises applying a value of the third relative phase shift that varies within a finite range depending on a value of the first relative phase shift.

20. Controlling the third optical phase shifter controlling the third optical phase shifter to operate between 0 and +nπ (n is an integer and c is a real number) based on the value of the first relative phase shift being c−π / 2, and to operate between −nπ and 0 based on the value of the first relative phase shift being c+π / 2; 20. The method of claim 19, further comprising:

21. 20. The method of claim 19, wherein controlling the third optical phase shifter is performed by analog operation within the range (0, +nπ) or within the range (-nπ, 0) depending on the value of the first relative phase shift.

22. detecting a first reference signal on a first polarization channel at a first MIMO output of the pair of MIMO outputs; detecting a second reference signal on a second polarization channel at a second MIMO output of the pair of MIMO outputs; determining an amount of error in demultiplexing measured from the first reference signal and the second reference signal; and controlling at least one of the first optical phase shifter, the second optical phase shifter, or the third optical phase shifter based on the error amount measured from the first reference signal and the second reference signal; 15. The method of claim 14, further comprising:

23. 15. The method of claim 14, wherein the 2x2 optical MIMO demultiplexing is performed endlessly during operation without resetting any of the first optical phase shifter, the second optical phase shifter, or the third optical phase shifter.

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