Volume 116, Number 2, October 2016
|Number of page(s)||5|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||30 November 2016|
Wide-angle parabolic approximations for the nonlinear Helmholtz equation in the Kerr media
1 Il'ichev Pacific Oceanological Institute - 43 Baltiyskaya str., 690041, Vladivostok, Russia
2 Far Eastern Federal University - 8 Sukhanova str., 690950, Vladivostok, Russia
3 Bergische Universität Wuppertal - Gaußstrasse 20, D-42119 Wuppertal, Germany
Received: 15 September 2016
Accepted: 15 November 2016
A multiscale approach is used to derive parabolic approximations for the nonlinear Helmholtz equation in a Kerr medium. The resulting approximation has the form of a system of iterative parabolic equations. The zeroth-order approximation coincides with the solution of the standard nonlinear Schrödinger equation. High-order corrections are obtained by solving certain linear parabolic equations with input terms computed from the solutions of the previous equations of the iterative system. The developed approach is applied to the modeling of a nonparaxial optical soliton propagation. We show that our novel wide-angle parabolic approximations allow to take nonparaxiality effects into account and eliminate significant phase error produced by the nonlinear Schrödinger equation.
PACS: 42.25.Bs – Wave propagation, transmission and absorption / 42.65.Tg – Optical solitons; nonlinear guided waves / 02.30.Mv – Approximations and expansions
© EPLA, 2016
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