Wavelet based spectral analysis of optical solitons

Abstract

The propagation of solitons or a pulse or a signal through optical fibers has been a major area of research given its potential applicability in all optical communication systems. In a modern optical communication system, the transmission link is composed of optical fibers and amplifiers. This manifests in noise, clutters and distortion when the signal propagates through optical fibers, consequently affecting the capacity and performance of the optical system. The dynamics of solitons has therefore become an active field of research in nonlinear optics for couple of decades. The nonlinear Schrodinger's equation (NLSE) with log law nonlinearity governs the propagation of optical solitons through optical fibers and its dynamics. Most of the studies reveal that the optical solitons have Gaussian wave profile called Gaussons. This entails the use of wavelet techniques for the processing of optical solitons.Signal processing in optical fiber has two distinct areas of investigations; one, the pulse propagation and the other, signal analysis and synthesis. We, in this work, focus on the later, the signal analysis and synthesis in wavelet spectral framework. For this, new wavelet formalism is proposed for analyzing the Gausson signals transmitted through optical fiber by introducing a nonlinear wavelet-like basis of scaling functions leading to wavelet spectra. The proposed method provides computational algorithm to obtain the Gausson parameters – amplitude and the dispersion, the width and velocity of the traveling soliton, which completely characterize the Gaussian signal. In the end, some of the spectral measures useful for further synthesis of the signal are discussed.