A finite element analysis of spatial solitons in optical fibres
Résumé
Purpose – This paper concerns the study of non-linear effects in optical fibres with a core made of a Kerr type medium. The aim is to propose an algorithm to find spatial solitons, i.e. solutions with an harmonic behaviour in time and along the fibre but with a field distribution in the cross section corresponding to a self-trapped propagation of the electromagnetic field. Design/methodology/approach – The field is supposed to be harmonic in time and along the direction of invariance of the fibre but inhomogeneous in the cross section. This modifies the refractive index profile of the fibre (a step-index one in this study). A scalar model of the fibre together with the finite element method (that is well suited to deal with inhomogeneous media) are used and a new iterative algorithm is proposed to obtain the non-linear solutions. An adaptive meshing is necessary to guarantee the accuracy of the model. Findings – The new algorithm converges to self-coherent solutions that are different from the ones obtained via a fixed power algorithm. Both the equivalent of a fundamental mode and of a second order mode are studied. Originality/value – The approach allows the findings of the previously known spatial solitons (with a slight modification of our algorithm) together with a new family of solutions. It opens a new field of investigation to understand this whole family of non-linear solutions as it shows that only a small part of them where known up to now.