Generalized Hermite?Gaussian functions and pulse propagation in optical fiber systems

Abstract

Chirped Hermite–Gaussian functions shows outstanding potentialities in mathematical models for linear and non linear pulse propagation in optical fibers. We propose three generalized subclasses of Hermite–Gaussian functions as natural extension to the complex domain. We exemplify the properties of these subclasses by analyzing some relevant cases of pulse oscillatory dynamics governed by nonlinear Schrodinger equation with constant or periodic coefficfients.