Abstract

We consider a plane wave of arbitrary angle of incidence and polarization impinging on a slab of nonlinear material bounded by two linear regions. The stability of the usual 1-D solution can be investigated by introducing fluctuations in ϵ₃(r) about a uniform value ϵ₃, $\tilde{\epsilon }\left(r\right)\equiv {\epsilon }_3\left(r\right)-{\epsilon }_3$. This leads by scattering to an inhomogeneity in the intensity and energy deposited in the slab. We complete a feedback loop by adopting various models for the response of the slab in which the dielectric function is assumed to depend on intensity, temperature, or electron density. Coupling between different heights z is eliminated in the thin-film limit, and the Fourier components of $\tilde{\epsilon }$ are shown to obey a time-dependent differential equation that predicts the growth or decay of an initial inhomogeneity. We note that the feedback is much enhanced around a specific wave vector q, and thus, when the nonlinearity strength (slope of the dielectric function multiplied by the incident intensity) is large enough (in practice ≳ 1), we can expect the 1-D solution to be unstable to the growth of a fringe pattern with spacing (2π/|q|. We emphasize that the unstable modes of the system can arise from surface excitations, in the case of a surface–polariton active substrate, or from nonpropagating field structure radiation remnants. Furthermore, for non-normal incidence and $\widehat{p}$ polarization we show that the pattern produced by the instability should move across the film.

© 1987 Optical Society of America