Robust iterative method for nonlinear Helmholtz equation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1-9
Journal / PublicationJournal of Computational Physics
Online published24 Apr 2017
Publication statusPublished - 15 Aug 2017


A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

Research Area(s)

  • Helmholtz equation, Iterative method, Kerr nonlinearity, Optical bistability, Wave propagation