Time-frequency Approach to Gaussian and Sinh-Gaussian Pulse Profiles Propagating in a Dispersive Medium

Abstract

In this paper, we use time-frequency analysis for pulse propagation in a linear dispersive medium. The Gaussian and sinh-Gaussian profiles are used as input ultra-short pulses
(0, ) in the time domain. E(0, ω) is the corresponding spectral profile. This spectral profile is decomposed into several wavelets centered at frequency Ω and the propagation constant (ω) is expanded to the third order in Taylor series. Using inverse Fourier transform, we obtain numerically the profile of the pulse simultaneously both in time and frequency by means of Matlab software. We investigate the influence of the third order dispersion coefficient. Khelladi et al. previously used a Gaussian input pulse to derive time-frequency profile of a pulse up to second order. Our work is an extension up to third order by using Gaussian input pulse and sinh-Gaussian input pulse. The result showed that the presence of the third order dispersion term exhibits broadening of the pulse, and the sinh- Gaussian pulse undergoes broadening at much slower rate in comparison to Gaussian pulse.