A split-step finite difference method for nonparaxial nonlinear Schrödinger equation at critical dimension

Autores: Kamyar Malakuti, Evgueni Parilov
Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 61, Nº. 7, 2011, págs. 891-899
Idioma: inglés
DOI: 10.1016/j.apnum.2011.02.006
Texto completo no disponible (Saber más ...)
Resumen
- The critical nonlinear Schrödinger equation (NLS) is the model equation for propagation of laser beam in bulk Kerr medium. One of the final stages in the derivation of NLS from the nonlinear Helmholtz equation (NLH) is to apply paraxial approximation. However, there is numerical evidence suggesting nonparaxiality prevents singularity formation in the solutions of NLS. Therefore, it is important to develop numerical methods for solving nonparaxial NLS. Split-step methods are widely used for finding numerical solutions of NLS equation. Nevertheless, these methods cannot be applied to nonparaxial NLS directly. In this study, we extend the applicability of split-step methods to nonparaxial NLS by using Padé approximant operators. In particular, split-step Crank�Nicolson (SSCN) method is used in conjunction with Padé approximants to provide examples of numerical solutions of nonparaxial NLS.