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.
Finite Element Method Resolution of Non-Linear Helmholtz equation / S., Selleri; Vincetti, Luca; A., Cucinotta. - In: OPTICAL AND QUANTUM ELECTRONICS. - ISSN 0306-8919. - STAMPA. - 30:(1998), pp. 557-565. [10.1023/A:1006953912607]