Nonparaxial Propagation of Parametric Spatial Solitons

Abstract

All-optical devices based on cascading effects in second order nonlinear materials seem to be very promising for the next generation of optical telecommunication systems [1]. A beam propagation method (BPM) based on paraxial approach [2] is a most popular technique employed to investigate light propagation in such devices. The drawback of this technique is necessity to accurately guess reference indices to satisfy slowly varying envelope approximation. This limitation of the conventional BPM is removed by using nonparaxial, wide-angle formulation of BPM [3, 4]. The nonparaxial BPM can simulate fields with rapidly changing envelopes and there is no need to accurately guess reference indices. In implementation of nonparaxial BPM for simulation of boundless space propagation boundary conditions play a very important role, because popular technique, transparent boundary conditions (TBC) [5], have very limited effectiveness [4]. Recently, novel boundary conditions, perfectly matched layer (PML) boundary conditions, were proposed by Bérenger [6]. In this paper, an investigation of effectiveness of nonlinear PML (NL-PML) boundary conditions terminated by different realisations of TBC (adaptive, controlled and uniform TBC) is reported. NL-PML boundary conditions terminated by controlled TBC were proposed that extremely improve out-going wave absorbing for small tilted propagation angles of narrow parametric spatial solitons and are most suitable for nonparaxial simulations.