Stokes Vector Receiver Research Articles

Research Progress on Carrier-Free Phase-Retrieval Receivers

In order to deal with the chromatic dispersion-induced power fading issue for short-reach direct-detection optical fiber communication applications, such as the ever-increasing data-center interconnections (DCIs), optical filed recovery is intensively being under investigation. To date, various direct detection schemes capable of optical field recovery have been proposed, including the Kramers–Kronig (KK) receiver, asymmetric self-coherence detection (ASCD) receiver, carrier-assisted differential detection receiver (CADD), Stokes vector receiver (SVR), and carrier-free phase-retrieval (CF-PR) receiver. Among those, the CF-PR receiver attracts lots of research attention because it can circumvent the requirement of a strong continuous-wave (CW) optical carrier for the beating with the signal. Generally, the CF-PR receiver consists of only two single-ended photodiodes (PDs) and one dispersive element, for the field recovery of the quadrature amplitude modulation (QAM) signals. Based on the theoretical and experimental studies reported so far, this paper reviews the latest progress of CF-PR receivers designed for high-speed optical short-reach transmission links.

Optimal Shaping for the Stokes Vector Receiver

Optimal Shaping for the Stokes Vector Receiver

Compact and scalable polarimetric self-coherent receiver using a dielectric metasurface

Polarimetric self-coherent systems using direct-detection-based Stokes-vector receivers (SVRs) are a promising technology to meet both the cost and capacity requirements of short-reach optical interconnects. However, conventional SVRs require a number of optical components to detect the state of polarization at high speed, resulting in substantially more complicated receiver configurations compared with the current intensity-modulation–direct-detection counterparts. Here, we demonstrate a simple and compact polarimetric self-coherent receiver based on a thin dielectric metasurface and a photodetector array (PDA). With a single 1.05-µm-thick metasurface device fabricated on a compact silicon-on-quartz chip, we implement functionalities of all the necessary passive components, including a 1×3 splitter, three polarization beam splitters with different polarization bases, and six focusing lenses. Combined with a high-speed PDA, we demonstrate self-coherent transmission of 20-GBd 16-ary quadrature amplitude modulation and 50-GBd quadrature phase-shift keying signals over a 25-km single-mode fiber. Owing to the surface-normal configuration, it can easily be scaled to receive spatially multiplexed channels from a multicore fiber or a fiber bundle, enabling compact and low-cost receiver modules for future highly parallelized self-coherent systems.

High-speed Stokes vector receiver enabled by a spin-dependent optical grating

Stokes vector direct detection is a promising, cost-effective technology for short-distance communication applications. Here, we design and fabricate a spin-dependent liquid crystal grating to detect light polarization states. By separating the circular and linear components of incident light, the polarization states can be resolved with accuracy of up to 0.25°. We achieved Stokes vector direct detection of quadrature phase-shift keying (QPSK), 8PSK, and 16-ary quadrature amplitude modulation signals with 32, 16, and 16 GBd rates, respectively. We integrated the system, including the grating, photodetectors, and optical elements, on a miniaturized printed circuit board and demonstrated high-speed optical communications with 16 GBd rate QPSK signals.

Integrated Components and Solutions for High-Speed Short-Reach Data Transmission

According to different transmission distances, application scenarios of a data center mainly include intra- and inter-data center optical interconnects. The intra-data center optical interconnect is considered as a few kilometers optical interconnect between servers and racks inside a data center, which accounts for nearly 80% of data traffic of a data center. The other one, inter-data center optical interconnect, is mainly applied in tens of kilometers data transmission among different data centers. Since data exchange in data centers generally occurs between many servers and racks, and a lot of transmitter and receiver components are required, optical interconnects become highly sensitive to component costs. In this paper, we firstly review the development and applications of mainstream transmitter components (e.g., VCSEL, DML, EML, MZM, and monolithic integrated transmitter) and receiver components (e.g., single-end photodetector, Kramers-Kronig receiver, Stokes vector receiver, and monolithic integrated receiver), which have been widely applied in short-reach transmission systems. Then, two types of integrated solutions including simplified detection scheme and transceiver integration scheme are presented in detail. Finally, we summarize and discuss the technological and component options for different transmission distances. We believe that monolithic integrated components, especially transceiver integration, will become a powerful solution for next-generation high-speed short-reach transmission systems.

Theoretical and numerical analyses for PDM-IM signals using Stokes vector receivers

Different from current coherent-detection-based long-haul transmission systems, inter- and intradatacenter transmissions require a simpler transmitter and receiver. A promising way to significantly meet the demands of datacenter transmission is polarization division multiplexing intensity modulation with direct detection (PDM-IM-DD) using a Stokes vector receiver (SVR). However, for different SVR architectures, the corresponding demultiplexing matrix is required to recover the Stokes vectors from the detected signals, which are combined with an arbitrary state of polarization (SOP), will change the effect of noise dynamically and significantly influence the system performance. In this study, PDM-IM signals using four SVRs, i.e., a 90° optical hybrid with 2 balanced photodetectors (BPDs) and 2 photodetectors (PDs), a 90° optical hybrid with 4 PDs, a Stokes analyzer and a 3 × 3 coupler with 4 PDs, are studied theoretically and numerically. Theoretical system models using the four SVRs are developed, and the noise power variations are analyzed quantitatively based on these models. Moreover, the performance of the systems is also investigated for 224 Gbit/s polarization division multiplexing pulse amplitude modulation 4 level with direct detection (PDM-PAM4-DD) transmission in a simulation. The simulation results show that the bit error rate (BER) performance of the systems is consistent with the theoretical noise power variation curves. The theoretical analysis scheme is helpful for the practical design of SVR-based systems.

Polarization-diversity receiver using remotely delivered local oscillator without optical polarization control.

Silicon photonics coherent transceivers have integrated all the necessary optics except the lasers. The laser source has become a major obstacle to further reduce the cost, footprint, power consumption of the coherent transceivers for short-reach optical interconnects. One solution is to utilize remotely delivered local oscillator (LO) from the transmitter, which has the benefits of relaxing the requirements of wavelength stability and laser linewidth and simplifying the digital signal processing (DSP) of carrier/phase recovery. However, a sophisticated adaptive polarization controller (APC) driven by a control loop in the electrical domain with a complicated algorithm is required to dynamically track and compensate for the polarization wandering of the received LO. In this paper, we propose a hybrid single-polarization coherent receiver and Stokes vector receiver (SVR) for polarization-diversity coherent detection without a need of optical polarization control for the remotely delivered LO. With such a scheme, we successfully received a 400-Gb/s dual-polarization constellation-shaped 64-QAM signal over 80-km fibers.

Dispersion immune polarization demultiplexing scheme based on extended Kalman filter for Stokes vector Kramers–Kronig receiver

A dispersion immune and dynamic polarization recovery scheme based on extended Kalman filter (EKF) is proposed for Stokes vector Kramers–Kronig (SVKK) receiver. In the transmitter, a carrier is aligned at the edge of the data-carrying signal spectrum in one of the two polarizations. In the receiver, the signal detection is implemented based on Stokes vector receiver (SVR). The proposed dynamic polarization demultiplexing scheme is transparent to modulation formats and can track dynamic polarization rotation up to 30 Mrad/s. Furthermore, the proposed scheme is immune to chromatic dispersion.

Quantum Theory of Noise in Stokes Vector Receivers and Application to Bit Error Rate Analysis

Polarization-modulated optical signals can be demodulated via direct detection of Stokes vectors. In this article, we develop a quantum theory of noise in the Stokes vector receiver. Examining the conditions that enable simultaneous measurement of three elements of the Stokes vector, we demonstrate that an optical pre-amplifier in front of the Stokes vector receiver can reduce the power penalty associated with simultaneous measurements, down to the quantum limit of 3 dB. Then, the 3-D Gaussian noise model for the shot noise and optical pre-amplifier noise is discussed. Subsequently, based on the noise analyses, we derive bit error rate formulae for the cubic-lattice polarization modulation format and evaluate the sensitivity of the Stokes vector receiver.

Complete retrieval of multi-level Stokes vector signal by an InP-based photonic integrated circuit.

An integrated Stokes vector receiver (SVR) that can retrieve state of polarization of light in the three-dimensional (3D) Stokes space has widespread applications, such as short-reach communication links, polarization-sensitive imaging, and sensing. While various approaches have been demonstrated to date, monolithic integration of polarization components on InP has been a challenging issue. In this paper, we develop a novel 4-port SVR circuit integrated on a compact InP chip to retrieve complete Stokes parameters of incoming light with various intensity and degree-of-polarization. By judiciously designing the lengths and positions of asymmetric waveguide sections, we demonstrate that the SV of signal can be projected onto four vertices of a regular tetrahedron inscribed in the Poincaré sphere. Additionally, we employ this device in decoding 10-Gbaud 4-ary and 8-ary Stokes-vector-modulated signals in the 3D Stokes space.

Sensitivity Analysis of Photonic Integrated Direct-Detection Stokes-Vector Receiver

Direct-detection (DD) Stokes vector receiver (SVR) has rapidly gained interest for the high-speed datacenter and short-reach links, owing to its capability of recovering 3D optical signals without using expensive coherent detection. In order to reduce the size and cost of SVR, we have recently proposed and demonstrated a simple and compact device with single-ended photodetectors (S-PDs), which can be monolithically integrated on InP. In this paper, we provide comprehensive analysis on the receiver sensitivity for different SVR configurations. From rigorous theoretical investigations, we derive optimal design of SVR to maximize the sensitivity as well as explicit analytical expression of the bit-error-rate assuming an unamplified thermal-noise-limited case. From the obtained results, we find that the optimized 4-port S-PD-based SVR exhibits a moderate penalty of 2.1 dB with respect to the conventional more complicated SVR configuration based on 3-port balanced PDs. Since the proposed S-PD-based SVR can reduce the number of PDs, and requires neither a polarization-beam splitter nor precisely tuned optical interferometer, it may be an attractive candidate in realizing a low-cost and compact fully integrated DD-based receiver for the future >Tb/s short-reach systems, where the power budget is not the primary concern.

Optimum Three-Dimensional Constellations for Stokes Vector Direct Detect Receivers

We propose optimum 3D signal constellations for short reach intra-datacenter interconnects using stokes vector receivers. These optimum 3D alphabets maximize the so-called constellation figure of merit, which is the ratio between the squared minimum Euclidean distance and the average energy of the constellation points. Compared to dual-polarization 4-ary and 8-ary pulse amplitude modulation formats, the optimized 16-point and 64-point 3D signal constellations theoretically achieve 4 and 6 dB improved receiver sensitivity at low symbol error rates of ~10−5, while delivering similar spectral efficiencies of 4 and 6 bits per 3D symbol, respectively. Next, we experimentally verified the significant improvement in receiver sensitivity at symbol rates of 44 and 64 Gbaud that result from using the proposed optimized 3D signal alphabets.

Optical Field Recovery in Stokes Space

Coherent detection empowers optical receivers the capability of recovering the optical field propagating through the fiber. Field recovery not only increases the degree of freedom for optical modulations, but also enables the digital compensation of fiber dispersion that avoids the sophisticated optical dispersion management. Compared with coherent detection, direct detection (DD) owns a natural advantage—the simplicity, but lacks the capability of field recovery. To increase the modulation dimension for DD, the recent development of Stokes vector receiver takes the advantage of polarization diversity and extends the modulation dimension up to three-dimension with reference to the four-dimensional coherent detection (i.e., dual-polarization intensity and phase). However, a Stokes vector receiver is not inherently capable of field recovery because the second-order signal representation in Stokes space nonlinearizes the first-order linear field information, making it infeasible to digitally compensate the chromatic dispersion. In this paper, we provide a comprehensive review of Stokes-space field recovery (SSFR) that completely or partially recovers the optical field by DD. We analyze the degree of freedom for a variety of Stokes-space modulations compatible with SSFR, and reveal their tradeoff between optical spectral efficiency (that determines fiber capacity) and electrical spectral efficiency (that determines transceiver cost per bit). We review the Stokes-space polarization recovery methods and generalize a novel concept as analog polarization identification to simplify the DSP of SSFR. Furthermore, we compare the OSNR sensitivity among various common direct detection schemes to provide reliable predictions of their transmission performance. With its high spectral efficiency and capability of digital dispersion compensation, SSFR is very promising for future high-capacity short-reach applications over single- or multispan fiber transmission.

.Maximizing the spectral efficiency of Stokes vector receiver with optical field recovery.

Stokes vector receivers (SVR) bridge the 4-D (i.e. dual-polarization complex signals) coherent detection and the conventional intensity-only 1-D direct detection (DD). By multi-dimensional polarization modulation in Stokes space, SVR maximizes the electrical spectral efficiency (ESE) of DD receivers by recovering at most 3-D signals. However, most 3-D schemes lack the capability of optical field recovery, an essential requirement for digital post-compensation of fiber dispersion that elongates the achievable distance. We propose a 3-D Stokes-space field modulation to enable 3-D signal field recovery, verified by a 3-D 32-Gbaud per dimension probabilistic-constellation-shaped 64-QAM transmission over 260-km fiber at C-band. This sets an ESE record of 16.5 (net ESE of 13.9) bit/s/Hz for DD receivers.

Enabling High-Capacity Long-Reach Direct Detection Transmission With QAM-PAM Stokes Vector Modulation

We introduce a three-dimensional modulation format using a Stokes-vector direct-detection system, where a pulse amplitude modulation (PAM) signal is polarization multiplexed with a quadrature amplitude modulation (QAM) signal. The phase reference of the PAM signal enables the retrieval of the phase information of the QAM signal using a Stokes vector receiver (SVR). A dual-polarization in-phase–quadrature modulator is employed to generate QAM-PAM optical signals with chromatic dispersion precompensation. We show direct detection of dual-polarization 16QAM-PAM2 and 16QAM-PAM4 signals delivering 280 and 336 Gb/s (net bit rate 233 and 280 Gb/s) below the soft-decision forward error correction threshold of 2 $\times$ 10 $^{-2}$ at 320 and 80 km, respectively. In addition, we study system performance at different modulation formats and symbol rates. Our findings indicate that increasing the order of modulation formats of the QAM signal is better than increasing that of the PAM signal to achieve the same bit rate. Finally, the performance of a 56 Gbaud 16QAM signal with PAM2 modulation on one polarization and a 56 Gbaud 16QAM signal with a pilot carrier on the orthogonal polarization detected with an SVR is experimentally investigated.

Decoding of Multilevel Stokes-Vector Modulated Signal by Polarization-Analyzing Circuit on InP

Of-late research on Stokes vector receivers for the short-reach optical communications has gained significant attention due to its capability to decode information in multidimension using cost-effective direct-detection technique. Here, we consider the use of InP for potentially low-cost direct-detection-based Stokes vector (SV) receiver. It consists of a 1 × 4 multimode interference power splitter with different combination of polarization converters on output arms, so that input SV is projected onto distinct vectors on the Stokes space. By using the fabricated device, we experimentally demonstrate decoding of two-level and four-level SV-modulated signals at 3 Gbaud. With the potential of monolithically integrating high-speed InP photodetector array on the same chip, it paves the way to realize compact and low-cost SV receivers for multilevel SV modulation formats in future short-reach optical communication links.

Performance comparison among three different Stokes vector direct-detection receivers

Stokes vectors direct detection (SV-DD) is an effective solution for short-reach optical communications. In this Letter, we investigate two-dimensional-modulation direct-detection systems based on three Stokes vector receivers (SVRs). The influences of three key factors including the states-of-polarization (SOP), the splitting ratio of the coupler, and the excess loss (EL) are studied in detail. It is shown that the splitting ratio for achieving optimum performance will be changed with SOP and EL conditions. Among these SVRs, the 3×3 coupler-based receiver with its optimal splitting ratio shows the best bit error rate performance and stability against the change of SOP.

Single wavelength 480 Gb/s direct detection over 80km SSMF enabled by Stokes vector Kramers Kronig transceiver

We propose 4D modulation with directed detection employing a novel Stokes-Vector Kramers-Kronig transceiver. It shows that employing Stokes vector receiver, transmitted digital carrier and Kramers-Kronig detection offers an effective way to de-rotate polarization multiplexed complex double side band signal without using a local oscillator at receiver. The impact of system parameters and configurations including carrier-to-signal-power ratio, guard band of the digital carrier, oversampling ratio and real MIMO is experimentally investigated. Finally, a record 480 Gb/s data rate over 80 km SSMF is achieved in a 60 Gbaud PDM-16QAM single carrier experiment with a BER below the threshold of 2.0x10-2

Data center links beyond 100 Gbit/s per wavelength

Abstract Increased traffic demands within and between data centers now necessitate low-cost and low-power systems with per-wavelength bit rates beyond what can be easily achieved using conventional on/off keying. We review spectrally efficient links based on direct detection, Stokes vector detection, coherent detection and differentially coherent detection for data center applications. We show that limited spectral efficiency and power margin will inhibit scaling of direct detection-compatible formats beyond 100 Gbit/s. Stokes vector receivers can provide higher spectral efficiency without requiring a local oscillator laser, but require power-hungry analog-to-digital converters (ADCs) and digital signal processing (DSP). Similarly, existing DSP-based coherent systems designed for long-haul transmission may be excessively complex and power-hungry for short-reach data center links. We present low-power DSP-free coherent and differentially coherent alternatives that avoid high-speed ADCs and DSP and achieve similar performance to their DSP-based counterparts in intra-data center links and dispersion-compensated inter-data center links.

Monolithic InP Stokes Vector Receiver With Multiple-Quantum-Well Photodetectors

Stokes vector modulation direct-detection (SVM-DD) formats have attained special attention in the short-reach communication links to transmit multilevel signals without using costly coherent receivers. In this paper, we fabricate and experimentally demonstrate a potentially low-cost DD-based SV receiver with on-chip photodetectors (PD) on a compact InP chip. Compressively strained multiple-quantum-well PD array is monolithically integrated with the SV projection circuit, which consists of multimode interference splitter and SV rotators based on self-aligned half-ridge structure. From the photocurrent signals at three on-chip PDs, the SV of input light is retrieved successfully over the entire Poincare sphere. With potentially broad operating bandwidth of InP-based PDs, the demonstrated device may be an attractive candidate to realize low-cost and high-speed receivers for the future short-reach SVM-DD systems.