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Finite element method resolution of non-linear Helmholtz equation

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Abstract

A non-paraxial beam propagation method for non-linear media is presented. It directly implements the non-linear Helmholtz equation without introducing the slowing varying envelope approximation. The finite element method has been used to describe the field and the medium characteristics on the transverse cross-section as well as along the longitudinal direction. The finite element capabilities as, for example, the non-uniform mesh distribution, the use of adaptive mesh techniques and the high sparsity of the system matrices, allow one to obtain a fast, versatile and accurate tool for beam propagation analysis. Examples of spatial soliton evolution describe phenomena not predicted in the frame of the slowing varying envelope approximation.

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Selleri, S., Vincetti, L. & Cucinotta, A. Finite element method resolution of non-linear Helmholtz equation. Optical and Quantum Electronics 30, 457–465 (1998). https://doi.org/10.1023/A:1006953912607

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