Abstract

We will present an equivalent particle theory which reduces the problem of interaction of an incident self-focussed channel with an interface separating two nonlinear dielectric media, to a much simpler Newtonian dynamical problem of an equivalent particle moving in an equivalent potential (Figure 1a). The theory provides the first analytic instability prediction for earlier known nonlinear surface waves. Phase portraits of the equivalent particle’s trajectories (Figure 1b) correspond directly to angles of reflection and transmission of the propagating self-focussed channel. The modular structure of the theory makes it straightforward to extend it to multiple-particle interactions and multiple interface problems. All of the theoretical predictions are confirmed numerically by solving the original modified Nonlinear Schrödinger equation describing the full problem. The theory provides quantitative estimates of radiation generated due to interaction with the interface and explains how an incident self-focussed channel can break up into multiple (reflected or transmitted) channels. Contact will be made with the familiar Snell’s law linear limit and we will demonstrate the existence, in the nonlinear case, of a sharp phase transition from total internal reflection to total transmission as a function of varying incidence angle as the scaled self-focussed channel width is decreased.

© 1988 Optical Society of America