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An efficient parallel implementation of a nonparaxial beam propagation method for the numerical study of the nonlinear Helmholtz equation is presented. Our solution focuses on minimizing communication and computational demands of the method which are dependent on a nonparaxiality parameter. Performance tests carried out on different types of parallel systems behave according theoretical predictions...
In their most general form, wave-interface problems are inherently angular in nature. For instance, the interaction between light waves and material boundaries essentially defines the entire field of optics. The seminal works of Aceves et al. [1,2] considered scalar bright spatial solitons impinging on the planar interface between two Kerr-type media with different χ(3) susceptibilities. While these...
We present a generalized Snell's law that governs grey soliton refraction at the interface separating two defocusing Kerr media. The analysis, based on the Helmholtz theory, is valid for arbitrary angles of incidence and reveals that grey solitons undergo either external or internal refraction depending on the soliton contrast parameter.
A new parallel implementation of the split-step Fourier method is presented. The computational core of our scheme focuses on the parallelization of the whole linear step using a combination of fast cyclic convolutions and fast Fourier transforms. For all problems and cluster sizes tested, our method exhibits better performance than conventional parallel implementations of the split-step Fourier method...
We give a brief overview of some new results in Helmholtz soliton theory. Firstly, fundamental considerations are made in terms of new contexts for Helmholtz solitons that arise directly from Maxwells equations. We then detail applications of Helmholtz solitons in material interface geometries: generalising Snells law to nonlinear beams and reporting new qualitative phenomena. Novel families of bistable...
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