Second-order Polarization Mode Dispersion Research Articles

Joint Scheme of Dynamic Polarization Demultiplexing and PMD Compensation Up To Second Order for Flexible Receivers

Polarization division multiplexing (PDM) doubles the bitrate of flexible transponders, whereas the joint effects of fast state of polarization (SOP) rotations, first-order polarization mode dispersion (PMD), and second-order PMD (SOPMD) would severely degrade the system performance. In this paper, we propose and experimentally validate a novel dynamic polarization demultiplexing scheme using extended Kalman filter (EKF) in digital signal processing of flexible receivers. The idea comes from two-stage PMD compensator in optical domain to perform SOP tracking and equalization of first-order PMD and SOPMD. After parameters optimization of EKF, the scheme can track up SOP rotations more than 35 times and 50 times faster than that of constant modulus algorithm (CMA) and CMA/multiple modulus algorithm (MMA), respectively. More importantly, when SOP keeps a fast rotation of 1.00, 10.00, or 20.02 Mrad/s, the system tolerances of first-order PMD and SOPMD that the joint scheme achieves are 28.57 ps and 793 ps2 for 28 GBaud PDM-QPSK at optical signal-to-noise rate (OSNR) of 17 dB, and 50 ps and 4836 ps2 for 10 GBaud PDM-16 quadratic-amplitude modulation (QAM) at OSNR of 23 dB, respectively. In addition, the proposed scheme has a fast convergence speed of about 50 symbols (equal to 5 ns). The calculation complexities of each symbol that the proposed scheme consumes are just about 44% of CMA for PDM-QPSK, and 31% of CMA/MMA for PDM-16 QAM.

PMD Emulator based on PZTs attached to pieces of an Hi-Bi fiber

In this paper we demonstrate the development of an adjustable and compact polarization mode dispersion (PMD) emulator device, based on piezoelectric actuators that squeezes a defined pieces of an Hi-Bi fiber. Using this device, the first and second order PMD (SOPMD) can be reproduced in a controlled and compact way, allowing its use as a reliable metrological reference for PMD compensators and for the study of several polarizations phenomena that can represent impairments to the high data transmission networks. This emulator was used to perform an analysis of the correlation between the PMD and SOPMD under different climate chamber temperature.

Controlled and compact first- and second-order polarization mode dispersion emulator

In this article, the development of a controllable and compact polarization mode dispersion (PMD) emulator device, based on piezoelectric actuators, is presented. Using this device, the first- and second-order PMD is reproduced in a controlled and compact way, allowing its use as a reliable metrological reference for PMD compensators. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:765–769, 2015

An Analytic Formulation of PMD-Induced Pulse Distortion

AbstractWe systematically analyze the pulse distortion resulting from polarization mode dispersion (PMD) by deriving an analytic expression for the characteristic function of the system bit error probability (BEP) density in terms of the lowest-order moments of the Fourier transformed input pulse shape. We determine the range of validity of our technique, which implements a second-order expansion of the Jones matrix, by comparing our results for chirped and unchirped input pulses with direct numerical simulations. Our method may be easily applied to analyze the role of the first- and second-order PMD in the interference between adjacent pulses.

A deeper analysis of the second order polarization mode dispersion in optical communications systems

This article presents a new approach to the combined analysis of the first and second-order polarization mode dispersion (SOPMD) and shows their importance in optical communication systems performance. How it affects the relation between second-order polarization mode dispersion (PMD) and the differential group delay (DGD) in a single mode fiber is discussed. The analysis is based on time or wavelength and temperature variations changing/impacting PMD and DGD measured values. We present long term statistical characteristics of second-order PMD over a PMD emulator, and investigate the correlation between SOPMD, depolarization (DEP) and polarization dependent chromatic dispersion (PCD). Some authors calculate these modes from measurements obtained from the first order polarization mode dispersion, assuming a positive correlation between these effects, but this not the real relationship between them. A new interpretation of SOPMD was used to analyze the problem of the spectral stability in terms of the temperature. Actual techniques for determination SOPMD, consequently DEP and PCD, use the variation in time and/or wavelength. In some studies the results obtained for SOPMD are correlated to first-order PMD (FOPMD). This paper shows, based on measurements, that the correlation between first and second order Polarization Mode Dispersion (PMD) in the case where the last one is a function of the temperature can assume positive or negative values.

A new experimental approach to second-order polarization mode dispersion analysis for optical communications systems

This article analyzes the polarization mode dispersion (PMD) in optical fibers and presents a new approach for its measurement. This approach permits the combined analysis of the first-order PMD and the second-order polarization mode dispersion (SOPMD) in optical systems for different values of temperature. The relation between SOPMD and the differential group delay (DGD) in a single-mode fiber is discussed. The analysis is based on time/wavelength and temperature variations changing/impacting PMD and DGD measured values. We present long-term statistical characteristics of SOPMD acquired by a PMD emulator constructed with some pieces of high birefringence fiber, and the correlation between the SOPMD, depolarization (Depol) and polarization-dependent chromatic dispersion (PCD) was investigated. A new interpretation of SOPMD is presented to analyze the problem of the temperature spectral stability. The actual techniques for SOPMD determination, consequently Depol and PCD, use the variation with time and/or wavelength. In some studies, the results obtained for SOPMD are correlated to first-order PMD. We demonstrate experimentally that the temperature is an important factor for the correlation between SOPMD and PMD and cannot be neglected in the optimization of high-speed optical communications links.

Monitoring FO-PMD and SO-PMD over Time with Respect to Environmental Conditions

Environmental conditions affect the birefringence of an optical fibre which in turn leads to fluctuations in its Polarization mode dispersion (PMD). Fluctuations in PMD make compensation for it in optical fibres very complicated. In this paper, fluctuations of first-order polarization mode dispersion (FO-PMD), FO-PMD coefficients and second-order polarization mode dispersion (SO-PMD) are monitored over time and also with respect to the environmental conditions. Long term measurements of FO-PMD have been done before by Mudau (2008) using the Generalized Interferometry Technique (GINTY) only. However, in this current study the FO-PMD coefficients and SO-PMD fluctuations were also monitored in addition to making a comparison between the measurements obtained using the Single-ended Dispersion Analyzer (FTB-5700) and the GINTY. These measurements were made on a 14.8 km long deployed aerial optical fibre that links St. Albans to Rockland transmission stations in Port Elizabeth, South Africa. The weather information was obtained from the Kestrel 4500 pocket weather tracker that was set up at St. Albans transmission station. So, for good PMD compensation, PMD should be monitored for a very long period of time or use an instrument that can accurately measure it even when the optical fibre is exposed to harsh environmental conditions.

Architecture of a Single-Chip 50 Gb/s DP-QPSK/BPSK Transceiver With Electronic Dispersion Compensation for Coherent Optical Channels

The architecture of a single-chip dual-polarization QPSK/BPSK 50 Gigabits per second (Gb/s) DSP-based transceiver for coherent optical communications is presented. The receiver compensates the chromatic dispersion (CD) of more than 3,500 km of standard single-mode fiber using a frequency-domain equalizer. A time-domain four-dimensional MIMO transversal equalizer compensates up to 200 ps of differential group delay (DGD) and 8000 ps <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of second-order polarization-mode dispersion (SOPMD). Other key DSP functions of the receiver include carrier and timing recovery, automatic gain control, channel diagnostics, etc. A novel low-latency parallel-processing carrier recovery implementation which is robust in the presence of laser phase noise and frequency jitter is proposed. The chip integrates the transmitter, receiver, framer and host interface functions and features a 4-channel 25 Gs/s 6-bit ADC with a figure of merit (FOM) of 0.4 pJ/conversion. Each ADC channel is based on an 8-way interleaved flash architecture. The DSP uses a 16-way parallel processing architecture. Extensive measurement results are presented which confirm the design targets. Measured optical signal-to-noise ratio (OSNR) penalty when compensating 200 ps DGD and 8000 ps <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is 0.1 dB, while OSNR penalty when compensating 55 ns/nm CD (corresponding to 3,500 km of standard single-mode fiber) is 0.5 dB.

Impact of second-order PMD in a coherent optical orthogonal frequency division multiplexing system

The second-order, polarization-mode dispersion (PMD) effect for coherent optical orthogonal frequency division multiplexing (CO-OFDM) system in long-haul transmission with single-mode fiber was analyzed in detail. The closed-form expression is presented for the time impulse response of an OFDM signal affected by second-order PMD. Analysis and simulation results show that, compared with polarization-dependent chromatic dispersion (PCD), CO-OFDM system performance is mainly influenced by depolarization rate (DR) which can moderate phase noise induced by chromatic dispersion. For a fiber link of 800 km and DR of 30 ps, the system Q value is improved by about 1.3 dB over the case of no DR.

Second-Order PMD-Induced Crosstalk Between Polarization-Multiplexed Signals and Its Impact on Ultrashort Optical Pulse Transmission

We present an analytical description and experimental demonstration of inter-polarization crosstalk caused by second-order polarization-mode dispersion (PMD). Even if the first-order PMD is completely compensated for, second-order PMD leads to large transmission impairments in ultrashort optical pulse transmissions through signal depolarization, which is caused by the frequency dependence of the principal state of polarization. In particular, depolarization in a polarization-multiplexed transmission inevitably prevents the complete separation of the two channels at the polarization demultiplexing. The analytical results show that the crosstalk increases in proportion to the fourth power of the signal bandwidth and grows by the square of distance as also verified by the experiments.

Polarization dependent loss complications on polarization mode dispersion emulation

Polarization dependent loss (PDL) and polarization mode dispersion (PMD) coexist in an optical network system. So, PMD emulation is normally complicated by PDL. In this paper, an analysis of the implications of PDL on PMD statistics is done using a 35-PMF section emulator. The first order PMD (FO-PMD) and second order PMD (SO-PMD) statistics of the emulator with a PDL value of 0.06dB approached the theoretical Maxwellian and Foschini et al. distributions respectively. On increasing the PDL value to 4.59dB, both FO-PMD and SO-PMD statistics were distorted away from the above theoretical distributions even with presence of high number of random mode coupling sites.

Pulse Propagation in Presence of Polarization Mode Dispersion and Chromatic Dispersion in Single Mode Fibers

The presence of (first and second orders) polarization mode dispersion (PMD), chromatic dispersion, and initial chirp makes effects on the propagated pulses in single mode fiber. Nowadays, there is not an accurate mathematical formula that describes the pulse shape in the presence of these effects. In this work, a theoretical study is introduced to derive a generalized formula. This formula is exactly approached to mathematical relations used in their special cases. The presence of second-order PMD (SOPMD) will not affect the orthogonality property between the principal states of polarization. The simulation results explain that the interaction of the SOPMD components with the conventional effects (chromatic dispersion and chirp) will cause a broadening/narrowing and shape distortion. This changes depend on the specified values of SOPMD components as well as the present conventional parameters.

Insight into PMD Regimes: An Analysis on Buried Optical Fibres

Polarization mode dispersion (PMD) field measurements on deployed buried fibres showed that the PMD variation over the 1520 to 1570 nm wavelength was stochastic. The PMD variation over the 98-hour period for each wavelength was directional and limited; they are due to the presence of random mode coupling along the fibre length and limited influence from extrinsic perturbations over time, respectively. PMD variation in the wavelength domain showed that the mean first-order PMD (FO-PMD) value is independent of whether the FO-PMD statistics of a fibre link approaches the Maxwellian theoretical distribution; the key factor is sufficient random mode coupling. The accompanying second-order PMD (SO-PMD) statistics, with FO-PMD statistics approaching Maxwellian, followed the PDF given by Foschini et al. (1999). The FO- and SO-PMD statistics at a given wavelength gave nonstochastic PMD distributions with time.

Real-Time PMD Tolerance Measurements of a PIC-Based 500 Gb/s Coherent Optical Modem

We present real-time polarization mode dispersion (PMD) tolerance measurement results with a commercially available 500 Gb/s coherent modem. The first- and second-order PMD space is explored, showing that peak values of 500 ps of static, first-order PMD (differential group delay) have small penalties. The system was stressed using fast scrambling, with polarization change of over 10 000 rad/s, along with high mean PMD. Penalties were small with sufficient equalization.

Study on application of local neighborhood artificial fish swarm algorithm for 40 Gb/s adaptive second-order polarization mode dispersion compensation

Based on a newly improved artificial fish swarm algorithm– local neighborhood artificial fish swarm algorithm (LNAFSA), we studied its application for adaptive polarization mode dispersion (PMD) compensation. In the adopted local neighborhood structure, each artificial fish only communicated with other five neighboring artificial fishes. Under a simulated 40 Gb/s adaptive second-order PMD compensation for non-return- to-zero and carrier-suppressed return-to-zero formats, the study demonstrated the effectiveness of LNAFSA. In a defined searching process, the eye diagrams showed that the algorithm resulted in an effective compensation effect and produced the maximum consuming time within 300 ms. Much better performance than simplex algorithm and genetic algorithm was also observed. In tracking process, LNAFSA achieved the goal of compensation in about 14 ms.

Simultaneous optical signal-to-noise ratio and differential group delay monitoring based on degree of polarization measurements in optical communications systems

We present a simultaneous optical signal-to-noise ratio (OSNR) and differential group delay (DGD) monitoring method based on degree of polarization (DOP) measurements in optical communications systems. For the first time in the literature (to our best knowledge), the proposed scheme is demonstrated to be able to independently and simultaneously extract OSNR and DGD values from the DOP measurements. This is possible because the OSNR is related to maximum DOP, while DGD is related to the ratio between the maximum and minimum values of DOP. We experimentally measured OSNR and DGD in the ranges from 10 to 30 dB and 0 to 90 ps for a 10 Gb/s non-return-to-zero signal. A theoretical analysis of DOP accuracy needed to measure low values of DGD and high OSNRs is carried out, showing that current polarimeter technology is capable of yielding an OSNR measurement within 1 dB accuracy, for OSNR values up to 34 dB, while DGD error is limited to 1.5% for DGD values above 10 ps. For the first time to our knowledge, the technique was demonstrated to accurately measure first-order polarization mode dispersion (PMD) in the presence of a high value of second-order PMD (as high as 2071 ps(2)).

256 Tbit/s/ch polarization-multiplexed DQPSK transmission over 300 km using time-domain optical Fourier transformation

We demonstrate a 2.56 Tbit/s/ch polarization-multiplexed single-carrier transmission over 300 km using subpicosecond DQPSK signals. We adopted an ultrafast time-domain optical Fourier transformation technique to reduce waveform distortions. For such an ultrashort optical pulse, depolarization components resulting from second-order polarization-mode dispersion (PMD) become a dominant factor as regards signal distortion because of the broad signal bandwidth. The influence of inter-polarization crosstalk induced by second-order PMD, is presented in detail.

Comparison between polarization-multiplexed DPSK and single-polarization DQPSK in 640 Gbaud, 1.28 Tbit/s–500 km single-channel transmission

We describe two schemes for 1.28 Tbit/s single-channel transmission at 640 Gbaud with polarization-multiplexed DPSK and single-polarization DQPSK, and compare their performance in a 500 km transmission. We found that the polarization multiplexing of ultrahigh-speed DPSK signals, for example at 640 Gbaud, is sensitive to the PMD characteristics of the transmission link. Even when first-order PMD is fully compensated, second-order PMD, which varies over a long period and is difficult to compensate, results in inter-polarization crosstalk induced by depolarization. The single-polarization transmission of a 640 Gbaud DQPSK signal is less vulnerable to PMD and therefore more stable, as the depolarized components induced by second-order PMD can be easily rejected with a polarizer. However, its performance is limited because the OSNR must be higher than for DPSK.

Tuneable polarization mode dispersion emulator: Fixed polarization maintaining fibre sections and rotatable polarization orientations

We design a polarization mode dispersion (PMD) emulator capable of adjusting first-order (FO-) and second-order (SO-) PMD statistics, making it capable to mimick differerent fibre links or fibre plants. The emulator can adjust PMD statistics by controlling mode coupling angles between polarization maintaining fibres (PMFs) of fixed length using its seven rotatable electro-optic polarization rotators which act as half waveplates (HWPs). The stability and repeatability of the emulator under a stable laboratory environment makes PMD statistics reproducible. The control mechanism of the emulator is in real-time.

Automatic PMD Compensation Based on GTPSO Algorithm in Optical Fiber Communication Systems

We demonstrate a universal DSP application for adaptive polarization mode compensation (PMD) compensation utilizing GTPSO algorithm in optical transmission systems. An adaptive PMD compensation experiment is implemented in an 80G/s DQPSK system. We designed a low power-consume DSP-based integrated control system to complete first-order PMD and second-order PMD compensation. The searching process and the tracking process for automatic PMD compensation could be completed in less than 10ms and 1ms.