First-order Polarization Mode Dispersion 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 .

Uniformly high-speed semi-open loop polarization control and PMD suppression

We propose and demonstrate a novel scheme of semi-open-loop polarization control (SOL-PC), which controls the state of polarization (SOP) with high accuracy and uniform high speed. For any desired SOP, we first adjust the initial SOP using open-loop control (OLC) based on the matrix model of a three-unit piezoelectric polarization controller, and quickly move it close to the objective one. Then closed-loop control (CLC) is performed to reduce the error and reach precisely the desired SOP. The response time is three orders faster than that of the present closed-loop polarization control, while the average deviation is on par with it. Finally, the SOL-PC system is successfully applied to realize the suppression of the polarization mode dispersion (PMD) effect and reduce the first-order PMD to near zero. Due to its perfect performance, the SOL-PC energizes the present polarization control to pursue an ideal product that can meet the future requirements in ultrafast optical transmission and quantum communication.

Blind symbol rate estimation using nonlinearity on sample correlation for digital coherent systems

We propose a symbol rate estimation technique by using absolute value of correlation of received signal for single-carrier polarization division multiplexed (PDM) systems in coherent detection system. We analytically show that spectrum of absolute value of correlation contains a peak indicating the symbol rate and has a robust performance which is insensitive to accumulated chromatic dispersion (CD) and first-order polarization-mode dispersion (PMD), amplified spontaneous emission (ASE) noise and laser frequency offset. Simulation result shows that this technique is applicable to long-haul application.

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.

Robust Faster-Than-Nyquist PDM-mQAM Systems With Tomlinson–Harashima Precoding

A training-based channel estimation algorithm is proposed for the faster-than-Nyquist PDM-mQAM (m = 4, 16, 64) systems with Tomlinson-Harashima precoding (THP). This is robust to the convergence failure phenomenon suffered by the existing algorithm, yet remaining format-transparent. Simulation results show that the proposed algorithm requires a reduced optical signal-to-noise ratio (OSNR) to achieve a certain bit error rate (BER) in the presence of first-order polarization mode dispersion and phase noise introduced by the laser linewidth.

Multi-wavelength in-band OSNR monitor based on Lyot-Sagnac interferometer.

A novel in-band OSNR monitor is proposed and experimentally demonstrated for WDM signal. By using a Lyot-Sagnac interferometer, the monitor realized OSNR measurement from 7.5~25 dB (within an accuracy of ± 0.5 dB) for 4-channel 40 Gbaud NRZ-QPSK signals, without requirement for prior knowledge of the noise-free coherence properties of signal. Further investigation proved that this OSNR monitor had high tolerance to chromatic dispersion (0~1152 ps/nm), first-order polarization mode dispersion (0~100 ps), and polarized noise. Moreover, the monitor worked very well even with input optical power as low as -8.24 dBm, and also worked in in C-band. Theoretical analysis and experimental results prove that it is capable of measuring OSNR for polarization-division-multiplexing signals.

On-field distributed first-order PMD measurement based on pOTDR and optical pulse width sweep.

A method for PMD distributed localization and estimation based on polarization optical time domain reflectometer technique, pOTDR and pulse width sweep is used on-field for the first time. The method consists in launching light pulses with variable widths in an optical fiber under test and then analyzes the Rayleigh backscattered signal spatial power distribution after passing through a polarizer. Both localization and PMD magnitude are function of OTDR pulse width and can be obtained from the ripple analysis, enabling the characterization of the fiber links.

Power Penalty Due to First-order PMD in Optical OFDM/QAM and OFDM/OQAM Transmission System

Power Penalty Due to First-order PMD in Optical OFDM/QAM and OFDM/OQAM Transmission System

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.

Periodic Training Sequence Aided In-Band OSNR Monitoring in Digital Coherent Receiver

We propose and demonstrate a new data-aided in-band optical-signal-to-noise ratio (OSNR) monitoring method, which employs the periodic property of a specially de- signed short training sequence to differentiate the signal power from noise and is proved to be insensitive to the first-order polarization mode dispersion (PMD). This method is verified in a typical 112-Gb/s polarization multiplexed-quadrature phase shift keying and a 224-Gb/s polarization multiplexed-16 quadrature amplitude modulation coherent optical transmission system. The results show that the method is highly accurate, with the moni- toring error less than 1 dB in the OSNR range of 7-30 dB under different linewidths and has good robustness to a large amount of residual accumulated CD and first-order PMD.

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.

Simultaneous monitoring of first-order polarization mode dispersion and chromatic dispersion based on RF power detection technique

We propose a novel technique for independent and simultaneous monitoring of first-order polarization mode dispersion (PMD) and chromatic dispersion (CD). For PMD monitoring, radio frequency (RF) power is detected after asymmetric filtering by a band-stop filter (BSF). The RF tone power ratio (PR) of the double sideband (DSB) to the single sideband (SSB) signal components is utilized for CD monitoring. We discuss the performance for 80Gb/s NRZ-DQPSK signal by simulation. Simultaneous monitoring of 246.7ps/nm CD with a 22.3dB dynamic range (DR) and 50ps differential group delay (DGD) with a 42.7dB DR can be realized at 10GHz detection band. When only CD is monitored, the detection frequency can be further decreased to 5GHz, where the monitoring range (MR) is 356ps/nm and DR is 30.5dB. The influences of other parameters, such as the BSF offset, the bandwidths of BSF and electrical-band-pass-filter (EBPF), the filter shape, and the modulation rate and format, are investigated in the paper.

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.

Focus on photonics and biomedical optics

Focus on photonics and biomedical optics

Essence of re-calibrating optical instruments: analysis of the digital delay line

In this work a digital delay line (DDL) from Oz Optics was used. The DDL introduces a delay in optical paths between the fast and slow orthogonal polarizations by adjusting the relative travel distance of the two orthogonal modes. The insertion loss of the DDL is 1.5 dB. A Labview programme was used to write and read from the DDL. The DDL was adjusted from 0 to 60 ps and the observed first order polarization mode dispersion (FO-PMD) was measured. With 1018 random values between 0 and 60 ps, written to the DDL to adjust it, the resulting FO-PMD values give a histogram approaching the Maxwellian distribution, although not well populated on the tail. This therefore means the DDL alone can be controlled to generate a distribution approximating the Maxwellian distribution over a large sample size as would be expected theoretically.

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.

Fast and Robust Blind Chromatic Dispersion Estimation Using Auto-Correlation of Signal Power Waveform for Digital Coherent Systems

We propose a chromatic dispersion (CD) estimation technique by using the auto-correlation of signal power waveform for DSP based coherent systems. For single-carrier polarization-division-multiplexed (PDM) systems assuming Gaussian pulse shapes, we analytically show that the auto-correlation of signal power waveform contains a peak whose location is indicative of the accumulated CD and is insensitive to amplified spontaneous emission (ASE) noise, laser frequency offset, laser phase noise and first-order polarization-mode dispersion (PMD) and applicable to single-carrier phase-shift keyed (PSK) and quadrature-amplitude modulation (QAM) systems. As a linear scan of a preset range of CD is not needed, the number of symbols of the proposed technique is dramatically reduced. Simulation results show that to estimate the link CD for 112 Gb/s PDM-QPSK and 224 Gb/s PDM-16-QAM systems, 8192 symbols are sufficient for NRZ/RZ pulse shapes and 32768 symbols are sufficient for root-raised-cosine pulse shapes with the roll-off factor as low as 0.1 with estimation error below 175 ps/nm and 400 ps/nm, respectively.

Simultaneous and Independent OSNR and Chromatic Dispersion Monitoring Using Empirical Moments of Asynchronously Sampled Signal Amplitudes

We analytically investigate and derive equations for the empirical moments of asynchronously sampled signal amplitudes as functions of signal power, noise power, and accumulated chromatic dispersion (CD) of a transmission link. The solutions of these equations enable low-cost, simultaneous and independent monitoring of in-band optical signal-to-noise ratio (OSNR) and CD of the fiber link for various modulation formats and data rates. Numerical simulations are performed to validate the proposed technique and the results demonstrate independent OSNR and CD monitoring with good accuracy and large monitoring ranges. The influence of first-order polarization-mode dispersion (PMD) on the accuracy of the proposed monitoring technique is also investigated.