The method of invariant imbedding is used to obtain exact equations for reflection and transmission coefficients for a plane wave incident on a slab of nonlinear material. These equations are solved for thin slabs of InSb and clear bistability is obtained.
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.
Recently1, an exact theory of the irradiated nonlinear Fabry-Perot cavity and the ensuing multistability has been published. In this paper this approach is developed further and an exact treatment for the reflectivity and transmissivity of an optically isotropic structure of dielectric layers characterised by a third-order polarisation tensor at arbitrary angles of incidence is presented. The calculations use exact2 solutions of the nonlinear wave equation, rather than the commonly used ray treatment. This takes into account fully the standing wave effect and permits a precise examination of the interaction between the forward and backward travelling waves and the relationship between the transmissivity resonance condition and changes in the field profile. For an s-polarised incident wave an analytical solution is found for arbitrary angles of incidence and layer thicknesses. It is discovered that for certain ranges of layer thickness the system displays a multivalued response only above a critical angle. This bistability is achieved for irradiances much lower than those reported previously1 for normal incidence and indicates possible applications for optical processing. This plane wave treatment is supplemented by a numerical beam simulation which goes beyond the usual Fresnel approximation by utilising novel boundary conditions which permit the demostration of bistability.
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.