2DNLH

Code for solution of the scalar Nonlinear Helmholtz equation for modeling collapsing optical beams.

These files contain Matlab code for solving the Nonlinear Helmholtz equation for collapsing optical beams, as published in: G. Baruch, G. Fibich, S.V. Tsynkov: High-Order Numerical Solution of the Nonlinear Helmholtz Equation in Multidimensional Layered Media'', J. of Comp. Physics, 228 (10), 2009 pp. 3789-3815. G. Baruch, G. Fibich, S.V. Tsynkov: Simulations of the Nonlinear Helmholtz Equation: Arrest of Beam Collapse, Nonparaxial Solitons, and Counter-Propagating Beams'', Optics Express, 16 (17), pp.13323-13329 (2008).

Permission is granted to use or modify the code freely, but without any warranty. If this code was used to aid a scientific publication, please cite our JCP and Optics Express papers above.

The repository contains four directories: ./run An empty directory holding the results of a run. ./freezing_nlh Holding a reference implementation of the freezing-iteration schemes. The reader may benefit from understanding this simpler code before the more involved Newton code. ./newton Holding the Newton solver, including the Jacobian and iteration code. ./shared Holding shared code between the fixed-point freezing method and the Newton solver. Mostly definitions of the linear operator, and some utils. ./shared/longitudinal Holding definition of the longitudinal Laplacian ./shared/transverse Holding definition of the transverse Laplacian

The code stores all parameters, variables and operators in the global structure T. To run the freezing code: cd to the freezing_nlh subdir and run the matlab routine freezing_NLH. To run the Newton code: cd to the newton subdirectory, optionally modify run parameters at the file newton_params.m, and run the matlab routine newton_NLH. See the code for explanation of the different parameters.

Author: Guy Baruch mailto:guy.baruch@gmail.com