Finite Element Method Resolution of Non-Linear Helmholtz equation

A non-paraxial beam propagation method for non-linear media is presented. It directlyimplements the non-linear Helmholtz equation without introducing the slowing varyingenvelope approximation. The finite element method has been used to describe the fieldand the medium characteristics on the transverse cross-section as well as along thelongitudinal direction. The finite element capabilities as, for example, the non-uniformmesh distribution, the use of adaptive mesh techniques and the high sparsity of thesystem matrices, allow one to obtain a fast, versatile and accurate tool for beampropagation analysis. Examples of spatial soliton evolution describe phenomena notpredicted in the frame of the slowing varying envelope approximation.