Finite element method resolution of non-linear Helmholtz equation

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.