Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 343, Issue -, Pages 1-9Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2017.04.046
Keywords
Helmholtz equation; Wave propagation; Kerr nonlinearity; Iterative method; Optical bistability
Funding
- National Natural Science Foundation of China [11201508]
- Natural Science Foundation of Chongqing [cstc2016jcyjA0491]
- Research Grants Council of Hong Kong [CityU 11301914]
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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. (C) 2017 Elsevier Inc. All rights reserved.
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