Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface

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Abstract
A theory is presented that describes the global reflection and transmission characteristics of a self-focused channel propagating at an oblique angle of incidence to an interface separating two or more self-focusing nonlinear dielectric media. The nonlinear wave packet representing the self-focused channel is represented as an equivalent particle moving in an equivalent potential. The dynamics of the particle is described by Newton’s equations of motion, with the asymptotic propagation paths of the channel being read off from the associated phase portraits of the equivalent potential. Equilibria of the potential, or equivalently, critical points in the phase plane, represent stationary (stable or unstable) nonlinear surface waves. Stability of the latter follows immediately from a simple inspection of the potential. The shape of the equivalent potential changes with the power in the incident beam. Our theory provides the nonlinear analog of the well-known linear Snell’s laws of reflection and transmission. Conditions on the validity of the theory are established in parameter space by extensive numerical solution of the nonlinear partial differential equation describing beam propagation. One important conclusion of the paper is that the predictions of the equivalent-particle theory encompass a wide physical parameter space. As an illustration of an application of the theory, we show how to design an all-optical angle or power adjustable spatial scanning element. Contact is made with earlier numerical studies of beam propagation and nonlinear surface-wave stability at a linear-nonlinear interface.

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