Discrete orthogonal Gauss–Hermite transform for optical pulse propagation analysis

Abstract

A discrete orthogonal Gauss–Hermite transform (DOGHT) is introduced for the analysis of optical pulse properties in the time and frequency domains. Gaussian quadrature nodes and weights are used to calculate the expansion coefficients. The discrete orthogonal properties of the DOGHT are similar to the ones satisfied by the discrete Fourier transform so the two transforms have many common characteristics. However, it is demonstrated that the DOGHT produces a more compact representation of pulses in the time and frequency domains and needs less expansion coefficients for a given accuracy. It is shown that it can be used advantageously for propagation analysis of optical signals in the linear and nonlinear regimes.