Spatial Grid Symmetries and Reduced Models in the Simulation of Beam Counterpropagation in a Nonlinear Medium

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Abstract
In the context of the nonlinear interaction of counterpropagating light beams, we demonstrate the unrealistic symmetries that arise in the simulation of spontaneous pattern formation when using square computational grids. We have formulated a generalization of the split-step Fourier method which allows for non-orthogonal spatial grids. Implementation is shown to be simple and to entail negligible computational overheads. Results for two-dimensional Gaussian and extended cosine-bell input beam profiles are presented.