Publisher Summary Polarization mode dispersion (PMD) is a linear effect that can be compensated in principle. In an ideal circularly symmetric fiber, the two orthogonally polarized modes have the same group delay. However, in reality, fibers exhibit a certain amount of birefringence because of imperfections in the manufacturing process or mechanical stress on the fiber after manufacture. It is noted that fluctuations in the polarization mode and fiber birefringence produced by the environment lead to dispersion that varies statistically with time and frequency. PMD causes different delays for different polarizations and when the difference in the delays approaches a significant fraction of the bit period, it leads to pulse distortion and system penalties. Environmental changes— including temperature and stress—cause the fiber PMD to vary stochastically in time. PMD, illustrating the basic concepts, the measurement techniques, the PMD measurement, the PMD statistics for first- and higher orders, the PMD simulation and emulation, the system impairments, and the mitigation methods has been summarized in the chapter. Both the optical and the electrical PMD compensations are considered.

Polarization-Mode Dispersion

Polarization mode dispersion in an optical signal transmitted through a waveguide of a communications system is compensated by separating the dispersed signal into components corresponding to principal polarization states. The components are delayed by respective delays differing by a delay increment which is controlled to correspond to the dispersion delay and the delayed components are recombined to provide a dispersion compensated optical output signal. Each of the delays is provided by an chirped Bragg reflector forming part of a delay line, the Bragg reflectors comprising optical fibres with chirped intracore index gratings. Transducers or temperature controllers acting on one of the fibres allows dimensional control of the grating periodicity such that the position of Bragg reflection is variable. Wavelength division multiplexed optical signals are compensated using sampled gratings which allow a common Bragg reflection position for each wavelength.

Polarization mode dispersion compensation

An imaging guidewire can include one or more optical fibers communicating light along the guidewire. At or near its distal end, one or more blazed or other fiber Bragg gratings (FBGs) directs light to a photoacoustic transducer material that provides ultrasonic imaging energy. Returned ultrasound is sensed by an FBG sensor. A responsive signal is optically communicated to the proximal end of the guidewire, and processed to develop a 2D or 3D image. In one example, the guidewire outer diameter is small enough such that an intravascular catheter can be passed over the guidewire. Techniques for improving ultrasound reception include using a high compliance material, resonating the ultrasound sensing transducer, using an attenuation-reducing coating and/or thickness, and/or using optical wavelength discrimination. Techniques for improving the ultrasound generating transducer include using a blazed FBG, designing the photoacoustic material thickness to enhance optical absorption. Techniques for distinguishing plaque or vulnerable plaque may be used to enhance the displayed image.

Systems and methods for minimally-invasive optical-acoustic imaging

Power-coupling models are inherently unable to describe certain mode coupling effects in multimode fiber (MMF) when using coherent sources at high bit rates, such as polarization dependence of the impulse response. We develop a field-coupling model for propagation in graded-index MMF, analogous to the principal-states model for polarization-mode dispersion in single-mode fiber. Our model allows computation of the fiber impulse response, given a launched electric-field profile and polarization. In order to model both spatial- and polarization-mode coupling, we divide a MMF into numerous short sections, each having random curvature and random angular orientation. The model can be described using only a few parameters, including fiber length, number of sections, and curvature variance. For each random realization of a MMF, we compute a propagation matrix, the principal modes (PMs), and corresponding group delays (GDs). When the curvature variance and fiber length are small (low-coupling regime), the GDs are close to their uncoupled values, and scale linearly with fiber length, while the PMs remain highly polarized. In this regime, our model reproduces the polarization dependence of the impulse response that is observed in silica MMF. When the curvature variance and fiber length are sufficiently large (high-coupling regime), the GD spread is reduced, and the GDs scale with the square root of the fiber length, while the PMs become depolarized. In this regime, our model is consistent with the reduced GD spread observed in plastic MMF.

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Principal Modes in Graded-Index Multimode Fiber in Presence of Spatial- and Polarization-Mode Coupling

Aspects of the interaction of the Kerr nonlinearity and polarization mode dispersion (PMD) are reviewed. The basic equation that governs this interaction on the length scale of interest in optical fiber communications systems is the Manakov-PMD equation. This equation is derived using multiple-length-scale techniques. The focus of the derivation is the elucidation of common misunderstandings and pitfalls rather than mathematical rigor. It is shown that the scalar nonlinear Schro/spl uml/dinger equation is valid when PMD is absent and the signal is initially in a single polarization state. Two examples are then presented that illustrate the complexity of the interaction between nonlinearity and PMD. The first example considers the interaction of a nonlinearly induced chirp with PMD. As the power increases, one can obtain an improved eye opening relative to the case when PMD is absent. The second example considers the effect of nonlinear polarization rotation in a wavelength-division-multiplexed system. When nonlinear polarization rotation is important, the principal states of polarization become time dependent and PMD compensation becomes ineffective. This problem can be mitigated through the use of line codes.

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Interaction of polarization mode dispersion and nonlinearity in optical fiber transmission systems

We investigate both experimentally and theoretically a new technique to realistically emulate polarization-mode dispersion (PMD). We propose and demonstrate a PMD emulator using rotatable connectors between sections of polarization-maintaining fibers that generates an ensemble of high PMD fiber realizations by randomly rotating the connectors. It is shown that: (1) the DGD of this emulator is Maxwellian-distributed over an ensemble of fiber realizations at any fixed optical frequency; and (2) the frequency autocorrelation function of the PMD emulator resembles that in a real fiber when averaged over an ensemble of fiber realizations. A realistic autocorrelation function is required for proper emulation of higher order PMD and indicates the feasibility of using this emulator for wavelength-division-multiplexing (WDM) systems.

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Time and frequency domain characteristics of polarization-mode dispersion emulators

We analyze polarization mode dispersion (PMD) emulators comprised of a small number of sections of polarization-maintaining fibers with polarization scattering at the beginning of each section. Unlike previously studied devices, these emulators allow the emulation of a whole ensemble of fibers. We derive an analytical expressions and determine two main criteria that characterize the quality of PMD emulation. The experimental results are in good agreement with the theoretical predictions.

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Comparison of polarization mode dispersion emulators

We demonstrate, both experimentally and numerically, polarization-mode dispersion (PMD) compensation in wavelength-division-multiplexing (WDM) systems without wavelength demultiplexing. Our technique improves the overall system performance by reducing the fading probability for the worst-performing channel at any given time. The effectiveness of our approach is based on the fact that, for moderate PMD, the probability that all channels are severely degraded at the same time is extremely small. A single-section PMD compensator reduces the 2% worst-case power penalty for a four-channel 10-Gb/s WDM system with /spl sim/42 ps average differential group delay from 9.6 to 5.3 dB.

Polarization-mode dispersion compensation in WDM systems

A nonlinearly chirped fiber grating (1020a) for achieving tunable dispersion compensation, dispersion slope compensation, polarization mode dispersion, chirp reduction in directly modulated diode lasers, and optical pulse manipulation. A dynamical dispersion compensation mechanism can be implemented in a fiber communication system (1001) based on a such a nonlinearly chirped fiber grating (1020a).

Dispersion compensation by using tunable nonlinearly-chirped gratings

We show both numerically and experimentally that the nonlinear phase change due to cross-phase modulation (XPM) induces a bit-pattern-dependent change in the state-of-polarization that translates to uncertainty in the principal states of polarization (PSP). This effect severely limits the effectiveness of first-order polarization mode dispersion (PMD) post-compensation and suggests the use of in-line compensation.

R. Khosravani

Papers

Time and frequency domain characteristics of polarization-mode dispersion emulators

Comparison of polarization mode dispersion emulators

Polarization-mode dispersion compensation in WDM systems

Dispersion compensation by using tunable nonlinearly-chirped gratings

Limitations to first-order PMD compensation in WDM systems due to XPM-induced PSP changes