Sensitivity Analyses of Stokes-Vector Receivers for Cubic-Lattice Polarization Modulation

Data center interconnect has stimulated the research on the short-reach communications with data rate beyond 100G per wavelength and transmission distance of hundreds of kilometers. Aiming at the high-speed short-reach communications, we recently proposed the Stokes vector direct detection (SV-DD) that realizes a linear complex optical channel similar to the coherent detection. In SV-DD, the transmitter places the signal and the carrier onto the orthogonal polarizations, while the receiver achieves the polarization insensitive 3-D detection in the Stokes space with the digital signal processing enabled polarization acquisition. SV-DD achieves 100% spectral efficiency with reference to the single-polarization coherent detection, and simultaneously attains the receiver phase diversity and the cancellation of photo-detection nonlinearity. We experimentally demonstrate the SV-DD signal transmission over 160-km standard single-mode fiber at data rates of both 80 and 160-Gb/s. SV-DD significantly decreases both the system hardware and DSP complexity compared with the polarization multiplexed coherent detection, while increases the system spectrum efficiency compared with the conventional intensity modulation direct detection. Therefore, SV-DD offers a cost-effective solution for the 100G per wavelength and beyond metropolitan area network (MAN). It also owns the potentials to be deployed in the future high-speed passive optical network (PON).

We propose a novel detection scheme called Stokes vector direct detection (SV-DD) to realize high electrical spectral efficiency and cost-effective optical communication for short and medium reach. With SV-DD, the signal is modulated in only one polarization and combined with the carrier in the orthogonal polarization for fiber transmission. At reception, the combined signal is detected in Stokes space by three or four photo-detectors. Compared with conventional DD technique, SV-DD is resilient to both chromatic dispersion and signal-to-signal beat noise. Furthermore, SV-DD does not require polarization tracking or narrow band optical filtering for carrier extraction. In this paper, we present for the first time the numerical analysis and experimental demonstration of single-carrier SV-DD. We report 62.5-Gb/s data rate single-carrier SV-DD transmission over 160-km SSMF using 12.5-Gbaud 32-QAM modulation.

Stokes vectors direct detection (SV-DD) is an effective solution for short-reach optical communications.In this paper, we investigate 2D-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 BER performance and stability against the change of SOP.

We propose the Stokes vector direct detection (SV-DD) algorithm to achieve photo-detection nonlinearity cancellation and phase diversity. A 160-Gb/s single-polarization modulated SV-DD signal is successfully received after 160-km SSMF transmission with 7.76-bit/s/Hz electrical spectrum efficiency.

We review the optical direct detection subsystems based on the Stokes vector receiver (SV-R), which is fit for a variety of modulation formats in Stokes space. SV-R accommodates 2-dimension (2-D) or 3-D detection, greatly increasing the spectrum efficiency.

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.

We propose a hybrid optical Hilbert receiver and Stokes vector receiver (OH-SVR) capable of phase and polarization diversity. We experimentally demonstrate single-wavelength direct detection at 1.6-Tb/s and 1.56-Tb/s line rates at BTB and after 10-km standard single-mode fiber transmission for data-center interconnects.

For the first time, we experimentally demonstrate a 400-Gb/s [4×100-Gb/s wavelength-division multiplexing (WDM)] pulse-amplitude-modulation-4 (PAM-4) transmission based on free space optics (FSO) utilizing the polarization modulation (PolM) and direct detection (DD) scheme. Each WDM channel comprises a polarization modulator, a polarizing beam splitter (PBS), and two photodetectors (PDs). Four wavelengths each carrying a 100-Gb/s PAM-4 signal (aggregate 400 Gb/s) are transmitted over the free space. At the receiver side, the PBS separates the two orthogonal polarizations, and then, the two polarized signals are detected by two PDs. Then, the two detected signals are combined by a subtractor, followed by digital signal processing (DSP). The PolM-DD system can achieve higher data rate while maintaining the required forward-error-correction (FEC) threshold compared with intensity modulation and direct detection (IM-DD) scheme. Moreover, owing to the stable polarization state in the free space and the mitigation of the common mode noise by the subtraction, the PolM-DD system provides enhanced tolerance to the amplitude fluctuations attributable to weather turbulence, which makes it more reliable than the conventional IM-DD FSO system. To the best of our knowledge, this is the first experimental demonstration of a 400-Gb/s FSO system using the PolM-DD scheme with the transmission distance of 1.2 m.

We study and compare two digital signal processing (DSP) approaches to recover the intensity on two orthogonal polarizations and the interpolarization phase modulation using a Stokes-vector direct detection receiver. We focus on higher order modulation of each of the three degrees of freedom allowed in Stokes-vector detection. 2 bits are encoded on each intensity of the two orthogonal polarizations, and 2 bits are encoded in the phase difference between the two polarizations, giving a 6 bits per symbol format. In this study, we propose a novel three-stage DSP algorithm and we compare this new algorithm with our earlier two-stage algorithm using the following metrics: the computational complexity and the bit error rate (BER) performance. Using the three stage approach, waveform filtering and derotation are applied in series rather than in parallel as was done in the two stage algorithm. We show that the three-stage approach exhibits equal BER performance, while significantly reducing the total required number of real additions and real multiplications. Moreover, tracking the state of polarization using the proposed method is m -times more efficient, where m is the number of taps in the first filtering stage.

We review the evolution of modulation formats designed for direct detection, from on-off keying intensity modulation (IM) of a single polarization to three-dimensional formats where the intensity of both polarizations and the interpolarization phase are all independently modulated. We present the transmitter and receiver architectures capable of modulating an increasing number of dimensions, all orthogonal to each other. We detail the digital signal processing for Stokes vector receivers capable of recovering all three dimensions of a lightwave via self-beating direct detection, performing simultaneously polarization derotation and mitigation of intersymbol interference. We also analyze two different transmitter architectures modulating all three dimensions where the interpolarization phase is modulated over two levels using either a direct phase modulator (DPM) or a binary phase modulator, also called a BPSK modulator. We study the impact of increasing the bandwidth efficiency from 4 to 5 b/symbol by adding two level modulation of the interpolarization phase of a dual-polarization 4-level pulse amplitude modulation (PAM4) signal on the signal quality of the PAM4 IM on the polarization bearing the phase modulator by modeling the optical fields generated by both architectures. Assuming equal quality of the driving signals to the PAM4 and phase modulator, we show that a DPM minimizes the impact on PAM4 for short reach direct detect systems operating close to the zero dispersion wavelength where chromatic dispersion is negligible.

We propose a polarization-modulation and direct-detection (PolM-DD) bandwidth-enhanced pulse-amplitude modulation (PAM-4) transmission system with a tunable frequency range and demonstrate, for the first time, its performance after transmissions through a standard single mode fiber (SSMF). By adjusting the polarization angle between one principal axis of the PolM and polarizer, the frequency notch, caused by the spectral dispersion inherent in SSMF, can be shifted to higher frequencies. As a consequence, the available 3-dB bandwidth at the baseband is much more enhanced than it would be in the traditional case of an intensity-modulation and direct-detection (IM-DD) system. Since the output of PolM modulation module are intensity modulated signals with a tunable chirp, the system is free of polarization-mode dispersion. From the analysis in this paper, we conclude that under ideal conditions, the PolM-DD system gains approximately 41.4% in bandwidth over its counterpart IM-DD system. The optimal polarization angle is independent of optical wavelengths and fiber distances, so it can be easily applied in wavelength-division-multiplexing systems. In our experiment, 100-Gbps, 84-Gbps, 68-Gbps, 58-Gbps, and 52-Gbps PAM-4 signals are successfully transmitted by our PolM-DD system over distances of 5-km, 10-km, 15-km, 21-km, and 25-km SSMF, respectively, without dispersion compensation component or single sideband modulation. The experimental results are consistent with our analysis and simulations results, and support more than 41% data rate gain compared to the IM-DD system, given comparable component bandwidths.

Polarization-modulated signals can be demodulated via direct detection of Stokes vectors. We analyze noise characteristics of Stokes vector receivers and derive bit-error-rate formulae for the cubic polarization-modulation format in the circuit-noise-, shot-noise-, and beat-noise-limited states.

Full-duplex hybrid FTTH and RoF transport system based on polarization modulators

The effects of electrode impedance on receiver sensitivity in body channel communication

In optical communication systems, coherent detection permits significant improvements in receiver sensitivity and wavelength selectivity compared with direct detection and allows a variety of modulation/demodulation formats to be used in practical applications. In the 1.3-1.6-µm lightwave band, an ideal coherent receiver requires only 10-20 photons/bit to obtain a bit error rate (BER) of 10−9, while direct detection requires ~1000 photons/bit. Because of its improved wavelength selectivity, the advanced technology of frequency multiplexing with channel spacings of only 100 MHz can be used as in microwave systems instead of the 100 GHz required with conventional optical wavelength-division-multiplexing technology.