Models for few-cycle optical solitons
Résumé
The propagation of few-cycle optical pulses (FCPs) in nonlinear media can be described by means of a model of modified Korteweg-de Vries-sine Gordon (mKdV-sG) type. This model has in some special situations the advantage of being 'integrable', which allows us to study the interactions between FCPs. In addition, it is very general: we show that all other non-slowly varying envelope approximation models of FCP propagation which can be found in the literature, especially the so-called 'short pulse equation', are in fact approximations or special cases of the mKdV-sG model. Finally, an analogous model valid in the case of a quadratic nonlinearity will be discussed.