We report here on our investigations of the Manakov-polarization mode dispersion (PMD) equation which can be used to model both nonreturn-to-zero (NRZ) and soliton signal propagation in optical fibers with randomly varying birefringence. We review the derivation of the Manakov-PMD equation from the coupled nonlinear Schrödinger equation, and we discuss the physical meaning of its terms. We discuss our numerical approach for solving this equation, and we apply this approach to both NRZ and soliton propagation. We show by comparison with the coupled nonlinear Schrödinger equation, integrated with steps that are short enough to follow the detailed polarization evolution, that our approach is orders of magnitude faster with no loss of accuracy. Finally, we compare our approach to the widely used coarse-step method and demonstrate that the coarse-step method is both efficient and valid.
We describe a relatively simple derivation of the bit-error probability for a lightwave communications system using an amplitude-shift-keying (ASK) pulse modulation format and employing optical amplifiers such that amplified spontaneous emission noise dominates all other noise sources. This noise may be either polarized in the same direction as the signal or it may be unpolarized. Mathematically, it is represented as a Fourier series expansion with Fourier coefficients that are assumed to be independent Gaussian random variables. Prior to square-law detection, signal and noise passed through an optical bandpass filter. The detected current is finally filtered by temporal integration over the time slot occupied by one bit (integrate-and-dump receiver). The bit-error probability is given in a closed analytical form that is derived by the approximate evaluation of several integrals appearing in the analysis. Finally, we use our theory to derive the wellknown Gaussian approximation and find that it overestimates the biterror rate by one to two orders of magnitude. Derivations of the biterror probability of binary ASK signals are not new, the contribution of this paper consists in its simplified approach (Fourier series expansion of the noise) and in the closed analytical form in which the final result is presented in terms of elementary functions.
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