Polarization Mode Dispersion Effects Research Articles

Blind Polarization Demultiplexing of Shaped QAM Signals Assisted by Temporal Correlations.

While probabilistic constellation shaping (PCS) enables rate and reach adaption with finer granularity [1], it imposes signal processing challenges at the receiver. Since the distribution of PCS-quadrature amplitude modulation (QAM) signals tends to be Gaussian, conventional blind polarization demultiplexing algorithms are not suitable for them [2]. It is known that independently and identically distributed (iid) Gaussian signals, when mixed, cannot be recovered/separated from their mixture. For PCS-QAM signals, there are algorithms such as [3], [4] which are designed by extending conventional blind algorithms used for uniform QAM signals. In these algorithms, an initialization point is obtained by processing only a part of the mixed signal, which have non-Gaussian statistics. In this paper, we propose an alternative method wherein we add temporal correlations at the transmitter, which are subsequently exploited at the receiver in order to separate the polarizations. We will refer to the proposed method as frequency domain (FD) joint diagonalization (JD) probability aware-multi modulus algorithm (pr-MMA), and it is suited to channels with moderate polarization mode dispersion (PMD) effects. Furthermore, we extend our previously proposed JD-MMA [5] by replacing the standard MMA with a pr-MMA, improving its performance. Both FDJD-pr-MMA and JD-pr-MMA are evaluated for a diverse range of PCS (entropy ) over a first-order PMD channel that is simulated in a proof-of-concept setup. A MMA initialized with a memoryless constant modulus algorithm (CMA) is used as a benchmark. We show that at a differential group delay (DGD) of 10% of symbol period and 18 dB SNR/pol., JD-pr-MMA successfully demultiplexes the PCS signals, while CMA-MMA fails drastically. Furthermore, we demonstrate that the newly proposed FDJD-pr-MMA is robust against moderate PMD effects by evaluating it over a DGD of up to 40% of . Our results show that the proposed FDJD-pr-MMA successfully equalizes PMD channels with a DGD up to 20% of .

PMD tolerant transmission using multiple optical phase conjugators in the discretely amplified systems

Abstract In this paper, the impact of polarization mode dispersion (PMD) on system performance in coherent optical transmission assisted by optical phase conjugation (OPC) technique is numerically investigated for a 9-channel PM-4QAM system at 128Gbit/s. The OPC-aided transmission, amplified with lumped erbium doped fiber amplifier (EDFA), is a variation of the conventional dispersion-managed link, which is also called dispersion-inverted link. We demonstrate that introducing more OPCs along the link can partly suppress the PMD-induced impairments and thus improve the system performance significantly. Results of 960-km dispersion-managed transmission show that PMD effect will cause a performance penalty of 1.8 dB when using mid-link OPC (i.e., only 1-OPC), while this penalty will decrease to about 0.4 dB when employing 6-OPCs along the link. Comparing with conventional digital back-propagation (DBP) technique, a performance improvement of about 3.1 dB is observed with multi-OPCs when fiber PMD is equal to 0.1ps/ k m $\sqrt{km}$ .

Qualitative analysis of PMD-induced long-haul optical fiber link

Abstract This paper studies the detrimental effect of polarization mode dispersion on long-haul optical fiber communication in terms of the quality factor and bit error rate. The dispersion value is varied for different fiber lengths, specifically for long-haul communication, and the results obtained are analyzed in terms of the quality factor. The polarization mode dispersion causes pulse broadening, leading to interchannel interference. There is a need to check the occurrence and the associated effects of this dispersion. The communication range for conducting the analysis varies from 150 km to 350 km. The analysis is first conducted on varied communication fiber link length for different dispersion values, and it is observed that a fiber length of 200 km gives comparatively favorable results, as seen from the BER analysis.

Disentanglement induced by combined effects of polarization mode dispersion and polarization-dependent loss in optical fibers

Disentanglement induced by combined effects of polarization mode dispersion and polarization-dependent loss in optical fibers

CD and PMD Effect on Cyclostationarity-Based Timing Recovery for Optical Coherent Receivers

Timing recovery is critical for synchronizing the clocks at the transmitting and receiving ends of a digital coherent communication system. The core of timing recovery is to determine reliably the current sampling error of the local digitizer so that the timing circuit may lock to a stable operation point. Conventional timing phase detectors need to adapt to the optical fiber channel so that the common effects of this channel, such as chromatic dispersion (CD) and polarization mode dispersion (PMD), on the timing phase extraction must be understood. Here we exploit the cyclostationarity of the optical signal and derive a model for studying the CD and PMD effect. We prove that the CD-adjusted cyclic correlation matrix contains full information about timing and PMD, and the determinant of the matrix is a timing phase detector immune to both CD and PMD. We also obtain other results such as a completely PMD-independent CD estimator, etc. Our analysis is supported by both simulations and experiments over a field implemented optical cable.

Stochastic decoherence induced by polarization mode dispersion

We address the propagation of entanglement in fibers and investigate the decoherence of polarization-entangled photon pairs caused by polarization mode dispersion (PMD). We devise a decoherence model starting from the statistical properties of polarization mode dispersion and obtain the density matrix describing initially maximally entangled states at any time. Using these results, we derive how decoherence depends on the length of the fibers. We calculate the mean concurrence of the entangled states with PMD effects as a function of fiber length, bandwidth, and other parameters in different cases.

Decoherence modeling of polarization mode dispersion for one- and two-photon states in optical fibers

We investigate the effects of polarization mode dispersion (PMD) on the propagation of single- and two-photon states in single-mode fibers. We look at PMD as decoherence due to the system's coupling with the bosonic environment involved in optical birefringence and a thermal bath, respectively. The evolution of the polarization density matrix is described by a master equation, and its solution is used to calculate the differential group delay (DGD) due to the fiber. The PMD effects on the dynamics of EPR states in optical fibers are investigated by using the same method. In both the short-time and long-time regimes, we find that PMD-induced and thermal-induced decoherence behave similarly.

Performance Evaluation of 100 Gb/s WDM DP-QPSK Lightwave System with Reduced PMD Effects

In this paper, a coherent 100 Gb/s Wave Division Multiplexing (WDM)/Dual Polarization-Quadrature Phase Shift Keying (DP-QPSK) transceiver is proposed and optimized. The transmission of 40-channels has been achieved over 25×80 km of Standard Single Mode Fiber (SSMF) at 50-GHz channel spacing. A Digital Signal Processing (DSP) module has been implemented at the receiver for further system performance improvement. Simulation results have showed that the Polarization Mode Dispersion (PMD) effect have been efficiently compensated by 45 ps. The system has obtained a high Quality Factor (Q-Factor) for a wide range of input optical power from -10 dBm to 10 dBm with its maximum of 13.8 dB and has just decreased to 10.4 dB at 2000 km. The system has offered a high Degree of Polarization (DOP) of 0.9, indicating that the PMD compensation has been achieved remarkably. Furthermore, the proposed system has attained a spectral efficiency of 1-bits/s/Hz and the eye opening has improved significantly. It has been found out that the constellation diagrams have been distinguishable with very low data transmission errors and the received Radio Frequency (RF) signal has been strong with a very low level of noise.

Observing the effect of polarization mode dispersion on nonlinear interference generation in wide-band optical links

With the extension of the spectral exploitation of optical fibers beyond the C-band, accurate modeling and simulation of nonlinear interference (NLI) generation is of the utmost performance. Models and numerical simulation tools rely on the widely used Manakov equation (ME): however, this approach when considering also the effect of polarization mode dispersion (PMD) is formally valid only over a narrow optical bandwidth. In order to analyze the range of validity of the ME and its applicability to future wide-band systems, we present numerical simulations, showing the interplay between NLI generation and PMD over long dispersion-uncompensated optical links, using coherent polarization division multiplexing (PDM) quadrature amplitude modulation (QAM) formats. Using a Monte-Carlo analysis of different PMD realizations based on the coupled nonlinear Schr\"{o}dinger equations, we show that PMD has a negligible effect on NLI generation, independently from the total system bandwidth. Based on this, we give strong numerical evidence that the ME can be safely used to estimate NLI generation well beyond its bandwidth of validity that is limited to the PMD coherence bandwidth.

Enhancing capacity of optical links using polarization multiplexing

5G mobile networks targets wireless connection capacity up to 10 Gb/s. For this purpose, we propose a method to considerably increase capacity. In this paper first, we show how to compensate the effects of polarization mode dispersion (PMD) in systems with double polarizations where PMD in such systems could cause fluctuations in optical transmission due to crosstalk and cross phase modulation. Second, we show how to enhance system capacity benefiting from polarization multiplexing (POL-MUX) technique which can provide double bandwidth efficiency. Based on the simulation results, we have achieved optimum system performance and we were able to reduce the PMD effect using pre- and post-compensation. We also have improved the POL-MUX technique using coherent detection in case of 16/64 QAM modulations. The results were achieved by implementing polarization controllers, polarization beam combiners and splitters, as well as polarization phase shifters.

The Impact of PMD on Single-Polarization Nonlinear Frequency Division Multiplexing

The impact of polarization mode dispersion (PMD) is studied on the single-polarization signal transmission over the continuous spectrum (CS) of a long-haul optical fiber link defined by nonlinear Fourier transform (NFT). It is shown that a linear all-order PMD compensation can reverse most of PMD effects in the temporal domain. However, due to the nonlinear interaction of the two polarization modes, the CS is distorted in the nonlinear spectral domain. Simulation results are presented, and a perturbation model is proposed based on the simulation results to describe the impact of PMD for different modulation formats and fiber parameters. It is demonstrated that, after linear PMD compensation, the residual polarization-dependent effects generate a constellation rotation and additional noise in the nonlinear spectral domain. The performance of NFT-based system in the presence of both PMD and amplifier noise is also studied. The results show that the effect of PMD is small provided that an efficient linear PMD compensation is performed in time domain.

Stable radio frequency dissemination via a 1007 km fiber link based on a high-performance phase lock loop.

In this paper, we propose an active-compensation stable radio frequency (RF) transmission scheme based on a high-performance phase lock loop (PLL). In our PLL, a new structure for phase-detection is designed with only one standard RF signal to obtain a simple structure with no interference from other signals. In addition, different optical wavelengths carrying the same RF signal are utilized in the two directions to suppress Rayleigh scattering. The low phase noise homemade bi-directional erbium doped fiber amplifier (EDFA) module is used to reduce signal-to-noise ratio (SNR) deterioration. Hence, the transmission distance is greatly improved. The effects of polarization mode dispersion and phase noise produced by the EDFA on the transmission distance are discussed. Ultimately, a stable RF signal with 2.4 GHz transmitted over a 1007 km fiber link is obtained. The experimental results demonstrate that frequency instabilities of 1.2×10- 13 at 1s and 5.1×10- 16 at 20000s. Therefore, the system can be used for atomic clocks comparisons and provides frequency standard for time transfer systems over a long-haul fiber.

Reduction of four wave mixing efficiency in DWDM systems using optimal PMD

Investigation of polarization mode dispersion (PMD) effect on the performance of nonlinear optical transmission system, in terms of bit error rate and mixing efficiency was conducted. It shows an improvement in the system performance, in the presence of PMD. The effect of PMD was considered for different link lengths and the resulting effects on system performance were studied. It was demonstrated that fiber nonlinearities can be reduced in the presence of optimal amount of PMD, and have achieved average reduction in four wave mixing efficiency of 6.9 dB within the interval of − 18 to 4 dBm launch power, and maximum of 14.5 dB at 2 dBm launch power for an 80 Gbps non-return-to-zero dense wavelength division multiplexing system. OptiSystem software was used for the simulation.

BER Performance of PDM 4-QAM Optical Transmission System Considering the Effects of PMD and GVD Using Exact Probability Density Function

A noble theoretical approach is presented to evaluate the bit error rate (BER) performance of an optical polarization division multiplexed (PDM) 4-multilevel quadrature amplitude modulation (4-QAM) transmission system under the combined influence of polarization mode dispersion (PMD) and group velocity dispersion (GVD) in a single mode fiber (SMF). The analysis is carried out considering a coherent homodyne receiver. The exact probability density function (pdf) fluctuation due to PMD and GVD is evaluated from its moments using a Monte-Carlo simulation technique. Average BER is evaluated by averaging the conditional BER over the pdf of the random phase fluctuation. BER performance results are evaluated for different system parameters. It is found that PDM 4-QAM coherent homodyne system doubles the data rate but suffers more power penalty than the 4-QAM system. Results show that for a BER of 10^-9 at DGD of 0.5T and GVD value of 1700 ps/nm the PDM 4-QAM system needs 2.21 dB more power than 4-QAM systems giving the leverage of doubling the data rate.

Limitations on Hybrid WDM/OTDM Multicast Overlay System Imposed by Nonlinear Polarization Effect and its Mitigation

This paper investigates the nonlinear polarization effect of 120-Gbps polarization and subcarrier multiplexed unicast signal and 40-Gbps multicast signal on transmission performance of hybrid WDM/OTDM multicast overlay system. The interaction between Kerr nonlinearity and polarization mode dispersion (PMD) induced nonlinear cross polarization modulation (XPolM) effect can significant limits the transmission performance of hybrid WDM/OTDM multicast overlay system. The effect of signal input power, extinction ratio, PMD, and differential group delay is studied in multicast enable and disable mode. Also, a mitigation technique of nonlinear polarization effect is introduced by use of group delay compensator, judicious addition of some PMD, and inline pre-DCF in the transmission channel. It is also found that the amplitude to phase interaction between multicast and unicast signal transmission can be suppressed by controlling the loss of orthogonality.

Effects of Polarization-Mode Dispersion on Degenerate Four-Wave Mixing

In this paper, the effects of polarization-mode dispersion (PMD) on degenerate four-wave mixing (FWM) are studied in detail. New solutions of the FWM equations show that PMD can suppress the input-polarization dependence of FWM and reduce the idler growth significantly. The consequences of these results for next-generation passive optical networks are described briefly.

Systematic design of highly birefringent photonic crystal fibers

This article systematically designs and theoretically investigates a highly birefringent photonic crystal fiber (HB-PCF) for reducing the effect of polarization mode dispersion in high-speed optical communication system. To achieve a high modal birefringence in the proposed HB-PCF, four types of HB-PCF were designed by adding some birefringence-enhancing factors step by step in sequence. Ultimately, as per the simulation results, in the condition of single-mode operation, the numeric values of modal birefringence and confinement loss of the proposed HB-PCF is about 21.85 × 10− 3 and 0.47 dB/km at the habitual wavelength λ = 1.55 µm of optical-fiber communications.

Digital backpropagation accounting for polarization-mode dispersion.

Digital backpropagation (DBP) is a promising digital-domain technique to mitigate Kerr-induced nonlinear interference. While it successfully removes deterministic signal-signal interactions, the performance of ideal DBP is limited by stochastic effects, such as polarization-mode dispersion (PMD). In this paper, we consider an ideal full-field DBP implementation and modify it to additionally account for PMD; reversing the PMD effects in the backward propagation by passing the reverse propagated signal also through PMD sections, which concatenated equal the inverse of the PMD in the forward propagation. These PMD sections are calculated analytically at the receiver based on the total accumulated PMD of the link estimated from channel equalizers. Numerical simulations show that, accounting for nonlinear polarization-related interactions in the modified DBP algorithm, additional signal-to-noise ratio gains of 1.1 dB are obtained for transmission over 1000 km.

Effects of polarization mode dispersion on polarization-entangled photons generated via broadband pumped spontaneous parametric down-conversion.

An inexpensive and compact frequency multi-mode diode laser enables a compact two-photon polarization entanglement source via the continuous wave broadband pumped spontaneous parametric down-conversion (SPDC) process. Entanglement degradation caused by polarization mode dispersion (PMD) is one of the critical issues in optical fiber-based polarization entanglement distribution. We theoretically and experimentally investigate how the initial entanglement is degraded when the two-photon polarization entangled state undergoes PMD. We report an effect of PMD unique to broadband pumped SPDC, equally applicable to pulsed pumping as well as cw broadband pumping, which is that the amount of the entanglement degradation is asymmetrical to the PMD introduced to each quantum channel. We believe that our results have important applications in long-distance distribution of polarization entanglement via optical fiber channels.

Applying the data fusion method to evaluation of the performance of two control signals in monitoring polarization mode dispersion effects in fiber optic links

With increasing distance and bit rate in fiber optic links the effects of polarization mode dispersion (PMD) have been highlighted. Since PMD has a statistical nature, using a control signal that can provide accurate information to dynamically tune a PMD compensator is of great importance. In this paper, we apply the data fusion method with the aim of introducing a method that can be used to evaluate more accurately the performance of control signals before applying them in a PMD compensation system. Firstly, the minimum and average degree of polarization (DOPmin and DOPave respectively) as control signals in monitoring differential group delay (DGD) for a system including all-order PMD are calculated. Then, features including the amounts of sensitivity and ambiguity in DGD monitoring are calculated for NRZ data format as DGD to bit time (DGD/T) varies. It is shown that each of the control signals mentioned has both positive and negative features for efficient DGD monitoring. Therefore, in order to evaluate features concurrently and increase reliability, we employ data fusion to fuse features of each control signal, which makes evaluating and predicting the performance of control signals possible, before applying them in a real PMD compensation system. Finally, the reliability of the results obtained from data fusion is tested in a typical PMD compensator.