Impact Of Polarization Mode Dispersion Research Articles

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 $\sqrt{km}$ .

Solitons in birefringent optical fibers and polarization mode dispersion

The early work on solitons in optical fibers was all done using single-mode fibers, and these fibers remain important for many applications. The modes in single-mode fibers are for all practical purposes weakly confined plane waves and have two polarizations. The basic equation that describes light evolution in these fibers is the coupled nonlinear Schrödinger equation. The soliton robustness hypothesis and its origins, which were the original motivation for studying these equations, is first described. Limits on robustness due to birefringent walkoff and the impact of random birefringence variations in stabilizing solitons is then described. Questions and controversies that arose shortly after the publication of these equations are addressed. These include their relationship to the Maker and Terhune coefficients, the requirements for the validity of the nonlinear Schrödinger equation and the impact of polarization mode dispersion, and the conditions under which the birefringence can be considered linear. It is a consequence of the fluctuation-dissipation theorem that the birefringence must be linear in any homogeneous, low-loss optical medium with a local dielectric response. Any ellipticity is associated with non-locality, as would occur for example in a twisted optical fiber. This important result, which is not well-known in the optics community, is reviewed.

Nonlinear frequency domain PMD modeling and equalization for nonlinear frequency division multiplexing transmission.

Polarization mode dispersion (PMD) is one of the fundamental properties of a standard single-mode fiber. It affects the propagating signals and degrades the performance of high-speed optical fiber communication systems. PMD also gives an effect on the nonlinear spectra or scattering data in nonlinear frequency division multiplexing (NFDM) systems. However, PMD is usually described in the linear frequency domain, and there are few investigations about the influence of PMD in the nonlinear frequency domain (NFD). An NFD-PMD model is needed to understand the impact of PMD in the NFD. In this work, using a linear approximation method, we first propose an NFD-PMD model and verify its effectiveness. With the guide of the NFD-PMD model, a blind NFD-PMD equalization scheme is designed. The simulation results indicate that the proposed NFD-PMD equalization scheme has better performance than the training sequence method based on linear frequency domain equalization.

Digital nonlinearity compensation in the presence of polarization mode dispersion

The impact of polarization mode dispersion (PMD) on the performance of coherent transmission systems employing different digital nonlinearity compensation (NLC) schemes is numerically investigated for a seven-channel PM-16QAM Nyquist-wavelength division multiplexing system at 256 Gbit / s. In these nonlinearity compensation schemes, the digital signal processing is divided between the transmitter (Tx) and receiver (Rx) with different splitting ratios. We demonstrate that by splitting the NLC equally between the Tx and Rx, one can always obtain the best performance improvement regardless of whether PMD is present or not. Results of 1000-km dispersion-unmanaged transmission show that when fiber PMD is equal to 0.05 ps / km, splitting the NLC can give a signal-to-noise ratio improvement of 1.1-dB over receiver-side NLC, while it is 0.9 dB for 0.1 ps / km of the fiber PMD coefficient.

Inter-modal Raman amplification of OAM fiber modes

Raman scattering among conventional linearly polarized (LP) modes in single mode optical fibers is generally accepted as a promising way to achieve distributed amplification due to the fact that Raman amplification may provide gain at any wavelength, determined by the used pump wavelength, and excellent noise performance. Here, we show that Raman scattering among orbital angular momentum (OAM) modes in optical fibers have similar properties. We show theoretically that the Raman gain among OAM modes is independent on the topological charge of the OAM modes and that the gain efficiency when the pump and signal are parallel (orthogonally) polarized is similar to the Raman scattering among LP modes in parallel (orthogonal) states of polarization. In addition, we experimentally characterize Raman gain among OAM modes in a fiber supporting multiple OAM modes for both the pump and signal. Finally, we discuss the impact of polarization mode dispersion.

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.

Impact of GVD on Polarization-Insensitive Self-Homodyne Detection Receiver

We investigate the transmission performance of a polarization-insensitive self-homodyne detection receiver. The receiver uses a hybrid coherent and direct detection scheme, followed by digital signal processing (DSP) to rebuild the information signal and provide dispersion compensation. Performance is evaluated using quadrature phase-shift-keyed signals at 12.5-Gbaud produced with 500-kHz and 30-MHz linewidth lasers. Transmission distances up to 120 km are achieved with less than 1 dB penalty. We address the impact of polarization mode dispersion showing that the proposed DSP requires average differential group delay below 10% of the symbol period for less than 1 dB of $Q$ -factor penalty.

PMD tolerant nonlinear compensation using in-line phase conjugation.

In this paper, we numerically investigate the impact of polarisation mode dispersion on the efficiency of compensation of nonlinear transmission penalties for systems employing one of more inline phase conjugation devices. We will show that reducing the spacing between phase conjugations allows for significantly improved performance in the presence polarisation mode dispersion or a significant relaxation in the acceptable level of polarization mode dispersion. We show that these results are consistent with previously presented full statistical analysis of nonlinear transmission appropriately adjusted for the reduced section length undergoing compensation.

Simple and robust symbol rate estimation method for digital coherent optical receivers

A novel symbol rate estimation (SRE) technique utilizing the clock tone (CT) obtained by Godard timing recovery algorithm is proposed. By this technique, the known sampling rate of the analog-to-digital converter (ADC) in digital coherent optical receivers can used as a reference to directly determine the unknown signal symbol rate. The impact of polarization mode dispersion (PMD) on the CT magnitude can be mitigated by using the hybrid correlation function (HCF) consisting of both auto-correlation function (ACF) and cross-correlation function (XCF) of the received signal spectrum, while the chromatic dispersion (CD) impact can be mitigated by adaptive CD compensation techniques. This technique is simple, accurate, applicable to advanced modulation formats commonly used, and robust to various link impairments. Numerical simulations and experimental results are presented to validate this technique.

Impact of polarization mode dispersion and nonlinearities on 2-channel DWDM chaotic communication systems

This paper has designed 2-channel dense wavelength division multiplexing (DWDM) chaotic system at the frequencies of 193.1 and 193.2 THz, respectively. The optical chaotic signals were produced by using the semiconductor laser that is numerically modeled by employing laser rate equations. These two channels were multiplexed and then propagated through single mode optical fiber (SMF) of 80 km length with dispersion compensating fiber of 16 km length. Erbium doped fiber amplifier (EDFA) was used to compensate the power losses in the SMF. In this paper, we investigated the effects of polarization mode dispersion (PMD) and nonlinearities especially stimulated Raman scattering (SRS) on 2 channel DWDM chaotic communication system by varying the length of the SMF and value of differential group delay (DGD).

Degree of polarization detection: a dual‐polarized antenna based spectrum sensing algorithm for cognitive radio

SUMMARYA new spectrum sensing algorithm‐degree of polarization (DoP) sensing algorithm is proposed in this paper. By exploiting a pair of dual‐polarized antenna at the receiver, DoP of the received vector signal is estimated and utilized to detect the presence of primary users based on the polarization characteristics of electromagnetic waves. The dual‐polarized narrowband and broadband systems are both considered for DoP detection. In theoretical analysis, we derive the probability of detection, the probability of false and detection threshold of the proposed algorithm. It is shown that our algorithm overcomes the noise uncertainty problem. Considering the polarization‐sensitive channel impairments, the impact of polarization mode dispersion on DoP detector is discussed. This method can be utilized for various signal detection applications without requiring the knowledge of signal, transmission channel, and noise power. In simulations based on wireless microphone signals, by applying polarization information signal carries, DoP achieves a better detection performance than arithmetic‐to‐geometric mean detector, the maximum‐to‐minimum ratio eigenvalue detector, and energy detector with noise uncertainty. The simulations based on digital video broadcasting‐terrestrial signals are also presented, which may show the detection performance of the proposed method may be affected by polarization mode dispersion. Copyright © 2013 John Wiley & Sons, Ltd.

Impact of polarization mode dispersion on the performance of optical CDMA transmission system

The impact of fiber polarization mode dispersion (PMD) on the bit error rate (BER) performance of a direct sequence optical code-division multiple-access system is analyzed by the split-step Fourier method based on the coupled nonlinear Schrödinger equation, the three-dimensional Poincare sphere theory and the Jones matrix method. When the incident pulse's width is bigness than the chip duration, which causes spreading and overlapping of chips and degrades system performance due to increased interchip interference and reduced received optical power conduce cannot decoding or error decoding. When the incident pulse's width is less than the chip duration, good encoding/decoding performance can be achieved.

Effect of Polarization Mode Dispersion on the BER Performance of Optical CDMA

In this paper, impact of polarization mode dispersion (PMD) on the bit error rate (BER) performance of direct sequence optical code division multiple access with in-line optical amplifiers is analytically investigated. Intensity modulation direct detection technique is employed in optical correlator receiver. Optical orthogonal codes are used as address sequence. The system BER performance is determined in presence of PMD and different noises induced from receiver, optical amplifiers, and multiple access interference. The power penalty suffered by the system is evaluated at BER of 10 -9 . It is found that the BER performance of the proposed system degraded more at high chip rate, chirp parameter and long fiber length due to the effect of PMD. Further, the BER performance of the proposed system is studied in presence of PMD compensation with frequency advanced higher order PMD vectors. The results demonstrate that the system BER performance is improved significantly for a particular fiber length and third-order PMD compensation technique shows better performance compared to first-, and second-order compensations.

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INFLUENCE OF POLARIZATION MODE DISPERSION ON THE EFFECT OF CROSS-PHASE MODULATION IN INTENSITY MODULATION-DIRECT DETECTION WDM TRANSMISSION SYSTEM

Cross-phase modulation (XPM) changes the state-of-polarization (SOP) of the channels through nonlinear polarization rotation and induces nonlinear time dependent phase shift for polarization components that leads to amplitude modulation of the propagating waves in a wavelength division multiplexing (WDM) system. Due to the presence of birefringence, the angle between the SOP changes randomly and as a result polarization mode dispersion (PMD) causes XPM modulation amplitude fluctuation random in the perturbed channel. In this paper we analytically determine the probability density function of the random angle between the SOP of pump and probe, and evaluate the impact of polarization mode dispersion on XPM in terms of bit error rate, channel spacing etc for a two channel intensity modulation-direct detection WDM system at 10 Gb/s. It is found that the XPM induced crosstalk is polarization independent for channel spacing greater than 3 nm or PMD coefficient larger than 2 ps/√km. We also investigate the dependence of SOP variance on PMD coefficient and channel spacing.

Mitigating PMD in Fiber Optical Parametric Amplifiers With Alternating Fiber Twists

We show by means of analytical calculations and numerical simulations that the impact of polarization-mode dispersion (PMD) on the gain spectrum of fiber optical parametric amplifiers (OPAs) can be reduced by imposing twists along the fiber axis. Alternating twists are used in order to cancel the induced circular birefringence.

High-speed transmission limitations due to Polarization Mode Dispersion

In this paper, the impacts of Polarization Mode Dispersion (PMD) on the performance of high-speed optical communication system have been reported at different bit rates. The two systems are modeled using older fibers with same PMD coefficient at different bit rates and third is with the new fiber with less PMD coefficient than that of the previous two. The attenuation, chromatic dispersion and non-linear effects have been disabled, so that all the variation of the results is due to PMD. The bit rate is varied from 2.5 to 40 Gbps and the length is varied from 1000 to 20,000 km. It is shown that the impact of PMD increases with the bit rate of system. It is also reported that the impact of PMD becomes intolerable at the bit rates of more than 40 Gbps. And also the PMD produces very minute impact on the system performance for same bit rate with the variation in the fiber length.

Impact of PMD in Single-Receiver and Polarization-Diverse Direct-Detection Optical OFDM

Polarization-mode dispersion (PMD) can cause frequency-selective fading in direct-detection optical orthogonal frequency division multiplexing (DDO-OFDM) systems. In this paper, we examine the effects of this fading. We begin with an analysis of the frequency-selective fading caused by first-order PMD. We then estimate the impact of PMD in single-receiver DDO-OFDM using all-order simulations to generate outage probabilities as a function of signal-to-noise ratio (SNR) penalty. The performances of three single-receiver DDO-OFDM formats are compared and a new format that minimizes the frequency difference between the carrier and sideband is found to be more tolerant to PMD. We then introduce a DDO-OFM system that includes polarization diversity and carrier boost in the receiver. The effects of various configurations are simulated and the results suggest that a data rate of 42.7 Gb/s can be achieved within an optical bandwidth of 40 GHz, and with negligible PMD penalties.

Impact of PMD induced Timing Misalignment Jitter in a Dispersion Managed IM-DD Optical Transmission Link

The Bit Error Rate (BER) performance of a dispersion managed optical transmission link in the presence of timing misalignment jitter induced by Polarization Mode Dispersion (PMD) has been investigated. The present work focuses on analytical evaluation of the timing jitter variance of the recovered signal, which is impaired by the pulse distortion induced by PMD. The system penalty is obtained as a function of system parameters and the signal jitter characteristics. Our investigation shows that the random signal perturbations can seriously degrade clock recovery performance and have a considerable degradation in the optical receiver performance. The robustness of different modulation format against the PMD induced random perturbation has also been studied.

Impact of Polarization Mode Dispersion on CPFSK Transmission Systems using MZI Based Direct Detection Receiver

Impact of Polarization Mode Dispersion on CPFSK Transmission Systems using MZI Based Direct Detection Receiver