Weakly nonparaxial eects on the propagation of (1+1)D spatial solitons in inhomogeneous Kerr media

The widely used approach to study the beam propagation in Kerr media is based on the slowly varying envelope approximation (SVEA) which is also known as the paraxial approximation. Within this approximation, the beam evolution is described by the nonlinear Schrodinger (NLS) equation. In this paper, we extend the NLS equation by including higher order terms to study the eects of nonparaxiality on the soliton propagation in inhomogeneous Kerr media. The result is still a one-way wave equation which means that all back-re ections are neglected. The accuracy of this approximation exceeds the stan-dard SVEA. By performing several numerical simulations, we show that the NLS equation produces reasonably good predictions for relatively small degrees of nonparaxiality, as expected. However, in the regions where the envelope beam is changing rapidly as in the break up of a multisoliton bound state, the nonparaxiality plays an important role