Mathematical modeling of beam reflection, transmission and trapping at nonlinear optical interfaces

The propagation of laser beams as self-focussed channels in nonlinear dielectric media, their mutual interaction and interaction with one or more dielectric interfaces can be described in a unified manner in terms of the dynamics of one or more equivalent particles in equivalent potentials. Beam reflection, transmission and trapping as nonlinear surface waves is described by the phase space trajectories of the appropriate equivalent particle. The equivalent particle theory can, with minor extensions, provide quantitative estimates on beam break-up at the interface into multiple self-focussed channels and accurately estimate the amount of incident beam power converted into scattered radiation. The theoretical predictions are supported by full scale numerical simulations.