Non-paraxial beam propagation methods

Chamorro-Posada, P; Mcdonald, GS; New, GHC

Abstract

Exact analytical results are employed in the testing of split-step and finite difference approaches to the numerical solution of the non-paraxial non-linear Schrodinger equation. It is shown that conventional split-step schemes can lead to spurious oscillations in the solution and that fully finite difference descriptions may require prohibitive discretisation densities. Two new non-paraxial beam propagation methods, that overcome these difficulties, are reported. A modified split-step method and a difference-differential equation method are described and their predictions are validated using dispersion relations, an energy flow conservation relation and exact solutions. To conclude, results concerning 2D (transverse) beam self-focusing, for which no tract analytical solutions exist, are presented.

Citation

Chamorro-Posada, P., Mcdonald, G., & New, G. (2001). Non-paraxial beam propagation methods. Optics Communications, 192(1-2), 1-12. https://doi.org/10.1016/S0030-4018%2801%2901171-3

• Journal Article Type: Article
• Publication Date: May 16, 2001
• Deposit Date: Oct 14, 2011
• Journal: Optics Communications
• Print ISSN: 0030-4018
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 192
• Issue: 1-2
• Pages: 1-12
• DOI: https://doi.org/10.1016/S0030-4018%2801%2901171-3
• Keywords: Non-linear optics, self-focusing, optical solitons, computational techniques
• Publisher URL: http://dx.doi.org/ 10.1016/S0030-4018(01)01171-3