Polarization Mode Dispersion Compensation Research Articles

Emulation and Inversion of Polarization Mode Dispersion: A Lumped System and Pade Approximation Perspective

Polarization mode dispersion (PMD) has been a major impediment in achieving higher speeds in optical fiber communication systems. Various approaches and techniques for the basic theoretical analysis, modeling, simulation, and compensation of PMD have been proposed in the literature. In this paper, we present a novel and fresh approach to the modeling, emulation and inversion of PMD in optical fibers. In our approach, we first build a full PMD model based on coupled mode theory as a continuous-time, lumped and lossless system. We then develop systematic model dimension reduction techniques, adapted from Krylov-subspace based methods for large electronic systems, in order to obtain compact and low complexity PMD models. The reduced complexity models produced by our technique match the full PMD model over a specifiable frequency range of interest, have the same structure as the full model, and are amenable to efficient software and low complexity hardware implementations for emulation and inversion. Furthermore, the reduced compexity PMD modeling framework we develop in this paper can serve as a general formalism for studying the compressibility of PMD models and emulators.

Evaluation of large girth LDPC codes for PMD compensation by turbo equalization

Large-girth quasi-cyclic LDPC codes have been experimentally evaluated for use in PMD compensation by turbo equalization for a 10 Gb/s NRZ optical transmission system, and observing one sample per bit. Net effective coding gain improvement for girth-10, rate 0.906 code of length 11936 over maximum a posteriori probability (MAP) detector for differential group delay of 125 ps is 6.25 dB at BER of 10(-6). Girth-10 LDPC code of rate 0.8 outperforms the girth-10 code of rate 0.906 by 2.75 dB, and provides the net effective coding gain improvement of 9 dB at the same BER. It is experimentally determined that girth-10 LDPC codes of length around 15000 approach channel capacity limit within 1.25 dB.

Analytical performance evaluation of an adjustable PMD compensator using high-birefringence linearly chirped FBG

System performance of a high-speed WDM transmission system in the presence of PMD can be improved significantly by using an adjustable PMD compensator. We have analytically evaluated the performance of a tunable PMD compensator based on high-birefringence linearly chirped fiber Bragg grating. The device can adjust differential group delay in a linearly continuous way without affecting the wavelength outside the bandwidth. Various properties of the device such as relative group delay, differential group delay, reflectivity, etc. are investigated in terms of wavelength and grating length. Results show that under stretched condition the device generates a time delay between fast and slow polarization axes, which is adjustable from 0 to 55 ps and is tunable within 2.4 nm wavelength range.

Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization

We study a turbo equalization scheme based on low-density parity-check (LDPC) coded turbo equalization (TE). This scheme is suitable for simultaneous: (i) suppression of intra-channel nonlinearities, (ii) chromatic dispersion compensation, and (iii) polarization-mode dispersion (PMD) compensation. LDPC coding is based on large girth (g ges 8) block-circulant codes, and maximum a posteriori probability (MAP) equalizer is based on Bahl-Cocke-Jelinek-Raviv (BJCR) algorithm. The ultimate channel capacity limits, assuming an independent identically distributed (i.i.d.) source are reported as well. In the presence of intrachannel nonlinearities the LDPC-coded TE provides almost 12 dB improvement over BCJR equalizer at BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> . For an NRZ system operating at 10 Gb/s with residual dispersion of 11200 ps/nm and for differential group delay of 50 ps, the LDPC-coded TE is only 1 dB away from the i.i.d channel capacity. The efficiency of LDPC-coded TE in PMD compensation is demonstrated experimentally, with decoding performed off line.

Analysis of Degree of Polarization as a Control Signal in PMD Compensation Systems Aided by Polarization Scrambling

The performance of degree of polarization (DOP) is investigated as a control signal in polarization-mode dispersion (PMD) compensation systems aided by polarization scrambling. The relation between the input and output polarization states of a signal propagating through a polarization scrambler and a PMD-induced optical fiber is described by a 3 times 3 Stokes transfer matrix. The average DOP of the output signal over a period of polarization scrambling is derived as an alternative to the conventional DOP-based control signal, i.e., minimum DOP. In the presence of first- and all-order PMDs, the performance of the average and minimum DOPs in monitoring of differential group delay (DGD) for different data formats (i.e., RZ and NRZ) is evaluated. The performance of the two control signals are further investigated by calculating the outage probability of a feedforward first-order PMD compensation system. The results show that the average DOP outperforms the minimum DOP and also gives a wider DGD monitoring range.

Electrical Joint Equalization for PMD-Induced Performance Degradation in Direct-Detection Polarization-Multiplexed Transmission Systems

Polarization-division-multiplexed (PDM) systems are sensitive to polarization-mode dispersion (PMD), since PMD induces not only intersymbol distortion but also interchannel crosstalk. Electrical equalization for individual channels is not sufficient for the lack of information from another channel. In this letter, electrical joint equalization including both the decision-feedback equalizer and Viterbi equalizer for PMD compensation in direct-detection PDM systems is investigated. Simulation shows that joint equalizers can effectively combat PMD-induced performance degradation and lower the requirement for dynamic polarization control.

A Change of Perspective on Single- and Double-Stage Optical PMD Compensation

We present a rigorous investigation on how to optimize the degrees of freedom of optical polarization mode dispersion (PMD) compensators composed of differential group delay sections and polarization controllers, up to two stages. The analytical treatment relies on the extracted Jones matrices of the transmission and compensation fibers. The analysis of a single-stage compensator with two degrees of freedom (fixed DGD) is based on the maximization of the eye opening, as provided by the generalized Chen formula. The outage probability is quantified through a fast semi-analytical technique. It is shown how the benefits of single-stage compensation are strongly reduced and can lead to outage events, when certain critical input states of polarization are launched into transmission fibers with strong eigenmodes depolarization (i.e., strong higher order PMD). Focusing on such transmission fibers and input configurations, a novel algorithm is introduced for controlling a double-stage compensator with five degrees of freedom. The algorithm is based on an ideal equalization of the transmission fiber at half the bit-rate, realized resorting to spherical geometry. To this aim, we show that the first compensator stage must be a PMF fiber with very large DGD, equal to the bit period, in order to compensate the most critical configurations associated with outage events.

Automatic PMD Compensation by Unsupervised Polarization Diversity Combining Coherent Receivers

A new automatic scheme to compensate the intersymbol interference caused by fiber polarization mode dispersion (PMD) is introduced. The proposed method makes use of the orthogonal polarization components by combining them through adaptive electronic filters, which are adjusted through a low-complexity unsupervised updating method. The simplicity of the proposed unsupervised method is its most critical feature in terms of enabling real-time and all-hardware implementation. Simulation results are provided for a fiber channel with 40 Gsymbols/s signalling rate and a mean DGD level greater than the symbol period, where it is demonstrated that the PMD can be effectively compensated with a 2 dB signal-to-noise ratio penalty relative to PMD-free channel.

Simultaneous chromatic dispersion and PMD compensation by using coded-OFDM and girth-10 LDPC codes

Low-density parity-check (LDPC)-coded orthogonal frequency division multiplexing (OFDM) is studied as an efficient coded modulation scheme suitable for simultaneous chromatic dispersion and polarization mode dispersion (PMD) compensation. We show that, for aggregate rate of 10 Gb/s, accumulated dispersion over 6500 km of SMF and differential group delay of 100 ps can be simultaneously compensated with penalty within 1.5 dB (with respect to the back-to-back configuration) when training sequence based channel estimation and girth-10 LDPC codes of rate 0.8 are employed.

Simple adaptive first‐order PMD compensator using a Faraday rotator and a variable DGD element

AbstractA two‐degree‐of‐freedom (DOF) polarization mode dispersion (PMD) compensator has been developed to cancel the effects of first‐order PMD. The compensator comprises of a Faraday rotator (FR) and a dynamically varying crystal differential‐group‐delay (DGD) element. Because of the reduced number of control parameters, the compensator potentially possesses the desirable features of simple control, fast response, and cost saving. Principle of operation is validated by theoretical analysis and successful automatic PMD compensation is achieved in a 40 Gbit/s nonreturn‐to‐zero (NRZ) system. The compensator increased the average DGD allowed from less than 23% per bit‐slot for the uncompensated case to 42% at an outage probability of 10−4. Fast response of the compensator is also observed. The optimum setting of the compensator can be found in about 10 nregulating steps for all PMD emulator (PMDE) setting. These features allow the effective mitigation of the first‐order PMD effects within an optical fiber channel. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 2417–2420, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23669

First-order PMD compensation using optical FIR filter

We present a synthesis algorithm to design an optical finite impulse response (FIR) filter for compensating a first-order polarization mode dispersion (PMD) by minimizing the differential group delay (DGD). The desired frequency response was approximated using two widely used methods in designing digital FIR filters: the Fourier series expansion method and the frequency sampling method. A numerical simulation was performed for an eighth-order filter to demonstrate the difference between the two methods. The simulation results produced a sharper cutoff for the Fourier series expansion and higher stopband attenuation for the frequency sampling method. The Fourier series method produced better results in reducing the DGD.

Ultralow-power second-harmonic generation frequency-resolved optical gating using aperiodically poled lithium niobate waveguides [Invited

We discuss ultralow-power second-harmonic generation (SHG) frequency-resolved optical gating (FROG) in the telecommunication C-band using aperiodically poled lithium niobate (A-PPLN) waveguides as the nonlinear medium. A key theme of this work is that the phase-matching curve of the nonlinear medium is engineered to obtain an optical bandwidth adequate for measurement of subpicosecond pulses while retaining the optimum nonlinear efficiency consistent with this constraint. Our experiments demonstrate measurement sensitivity (defined as the minimum product of the peak and average pulse powers at which a reliable nonlinear signal can be detected) of 2.0×10−6 mW2 in a collinear SHG FROG geometry, approximately 5 orders of magnitude better than previously reported for any FROG measurement modality. We also discuss asymmetric Y-junction A-PPLN waveguides that permit background-free SHG FROG and a polarization-insensitive SHG FROG technique that eliminates the impairment that frequency-independent random polarization fluctuations induce in the FROG measurement. Finally, we applied these SHG FROG techniques in chromatic dispersion and polarization mode dispersion compensation experiments. In these experiments the FROG data enabled complete correction of distortions incurred by subpicosecond pulses passing through optical fibers; these results also demonstrate the ability to retrieve extremely complex pulses with high accuracy.

Tracking and separation of time-varying principal states of polarization in optical fiber link for first-order PMD compensation and its filter-dependent performance

We propose a simple method for tracking and separating time-varying principal states of polarization (PSP) occurring in a fiber-optic transmission link with polarization mode dispersion (PMD) for use in PMD compensation. The proposed method uses as a feedback monitoring signal the bandpass-filtered RF power at bit-rate frequency for NRZ signal format. We demonstrated the operating principle of the method through theoretical simulation and experiment using an automatically adaptive PMD compensator employing a single polarization beam splitter (PBS). The effects of electrical filtering on the PSP tracking performance were also investigated by using three types of filters, i.e., a low-pass filter (LPF), a band-pass filter (BPF), and a high-pass filter (HPF). The simulation results showed that only a BPF centered at bit-rate frequency was found to allow for tracing and separation of two PSPs via PBS. The proposed method, when applied to a conventional PMD compensator that alternately controls a polarization controller and a delay line, enables separation of PSP control from differential-group-delay (DGD) control, thus allowing fast tracking of rapidly changing PSP in a PMD-impaired optical fiber link and reducing compensation time.

All-Order Polarization-Mode Dispersion (PMD) Compensation via Virtually Imaged Phased Array (VIPA)-Based Pulse Shaper

We demonstrated all-order polarization-mode dispersion compensation using a virtually imaged phased-array-based transmission pulse shaper. We reduced the pulsewidth of polarization-mode dispersed pulses from more than 100 ps to their original 15 ps.

Digital filters for coherent optical receivers

Digital filters underpin the performance of coherent optical receivers which exploit digital signal processing (DSP) to mitigate transmission impairments. We outline the principles of such receivers and review our experimental investigations into compensation of polarization mode dispersion. We then consider the details of the digital filtering employed and present an analytical solution to the design of a chromatic dispersion compensating filter. Using the analytical solution an upper bound on the number of taps required to compensate chromatic dispersion is obtained, with simulation revealing an improved bound of 2.2 taps per 1000ps/nm for 10.7GBaud data. Finally the principles of digital polarization tracking are outlined and through simulation, it is demonstrated that 100krad/s polarization rotations could be tracked using DSP with a clock frequency of less than 500MHz.

PMD compensation using birefringence photonic crystal fiber in 40Gbit/s optical communication system

A birefringence photonic crystal fiber is used for PMD compensation in a single-channel 40Gbit/s-speed optical communication system with CSRZ format. The experimental results of transmission show that the PMD compensation system works effectively.

Digital self-coherent detection

We review recent progresses on digital self-coherent detection of differential phase-shift keyed (DPSK) signal using orthogonal differential direct detection followed by high-speed analog-to-digital conversion and digital signal processing (DSP). Techniques such as data-aided multisymbol phase estimation for receiver sensitivity enhancement, unified detection scheme for multi-level DPSK signals, and optical field reconstruction are described. The availability of signal field information brings the possibility to compensate for some linear and nonlinear transmission impairments through further DSP. An adaptive DSP algorithm for simultaneous electronic polarization de-multiplexing and polarization-mode dispersion compensation is also presented.

不同调制格式的偏振模色散补偿性能分析

不同调制格式的偏振模色散补偿性能分析

The effects of PMD and PDL on the performance of OOK and DPSK systems

Using multiple importance sampling (MIS) technique, the optical communication system performance affected by polarization-mode dispersion (PMD) and polarization-dependent loss (PDL) is simulated numerically. The power penalties and system outage probabilities are obtained for optical communication systems with on-off keying (OOK) or differential phase shift keying (DPSK) modulation. The simulation results show that DPSK always performs better than OOK. When the system has moderate PDL (about 1.5 dB), it is necessary to compensate effectively the fiber PMD in order to enhance the system tolerance to the PMD and PDL. However, the efficiency of PMD compensation will degrade rapidly when the PMD of the whole optical link drops into the low value.

LDPC-coded OFDM in fiber-optics communication systems [Invited

Low-density parity-check (LDPC) coded orthogonal-frequency-division multiplexing (OFDM) is studied as an efficient coded modulation technique suitable for fiber-optics communication systems. We show that in long-haul fiber optics communications LDPC-coded OFDM increases spectral efficiency and requires simple equalization to deal with chromatic dispersion. LDPC-coded OFDM is also a promising polarization-mode dispersion compensation technique. Several power efficient OFDM schemes and LDPC codes suitable for use in LDPC-coded OFDM optical communication systems are discussed.