Nonlinear pulse propagation using an advanced wavelet transform

Abstract

Problems associated with nonlinear pulse and beam propagation, especially those involving higher-order terms in the nonlinear Schroedinger equation, usually require robust numerical techniques for their solution. In this paper we utilize an adaptive wavelet transform in order to investigate optical pulse self-steepening and optical beam self-focusing, as well as higher-order nonlinear terms which cannot be approximated by higher-order derivatives. Additionally, we show that the numerical method developed herein can be used to approximate any order of nonlinearity in the self-phase modulation term. The adaptive capability of the discrete wavelet transform developed herein allows this technique to accurately track the steep pulse gradients associated with higher-order terms by adaptively switching to higher, more accurate wavelet levels. By utilizing this adaptive wavelet transform technique, one can perform analysis of any terms in the NLS equation entirely in the wavelet domain without the need for resorting to a split-step method, as is often the case.