Exact analytical results for the scattering of a plane transverse-electric electromagnetic wave with a nonlinear thin film is derived. Optical bistable and multistable behaviors in the reflectivity as a function of the input intensity are found.
We show that the optical response of a nonlinear dielectric film may exhibit optical bistability even in the thin-film limit. Using a rigorous numerical treatment, we also show that the resonant excitation of nonlinear guided modes propagating along the film leads to switching intensities 104 times lower than those obtained with use of the resonances associated with the Airy function.
The optical transmissivity of a mirrorless, nonlinear, absorbing dielectric thin film is investigated numerically. The dielectric function in the film region is dependent on the intensity of the electromagnetic field. Multivalued solutions of transmissivity as a function of incident power are calculated for the steady-state wave equation. The numerical solution is applied to two different model dielectric functions. As the absorption parameter is increased, larger values of incident intensity are required to switch the systems between stable output states. Also, the peak values of transmissivity are reduced as the absorption is increased.
In a recent paper1 I formulated a method for calculating propagation through nonlinear media for a number of nonlinear optical phenomena. This method does not use the SVEA and can therefore solve nonlinear propagation problems when refraction and reflection at the boundary interfaces are important. Here, I report the first calculation using this exact (albeit numerical) method. For this first test of the utility of the method, I have chosen to study optical bistability in a thin film whose index of refraction is intensity dependent.
We develop an approximate analytical theory for the reflection of a finite-width square-wave light beam at a nonlinear interface and make use of the results to assess the effect of the finiteness of the incident beam on the bistability of the signal reflected from a triple boundary interface under conditions for excitation of a waveguide mode. The nonlinearity of the interface is assumed to result from a substrate medium that has a Kerr-type quadratic dependence on the local electric-field amplitude. Our results indicate that the finiteness of the width of the incident beam substantially reduces the magnitude of the reflectance jump at the bistable switching point in comparison with that predicted by an exact plane-wave theory. Nevertheless, we conclude that a bistable reflectivity should still exist for the geometry that we consider at the switching intensity predicted by the plane-wave theory.
We present a theoretical study, with reference to experimental results, of transverse self-phase modulation effects in the transmission of a laser beam through a nonlinear thin film. The occurrence of interference rings, intensification or dimming of the on-axis beam intensity, and transverse optical bistability in the presence of a feedback can all be systematically documented in terms of geometrical/optical parameter classifications. These studies provide further insights and useful guides for experimental studies.