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Physical review. B, Condensed matter

Optical response of a nonlinear dielectric film

Wei Chen, D. L. Mills

Published Jan 15, 1987• 148 citations
Publisher

Abstract

We present a theoretical discussion of the optical reflectivity and transmissivity of a dielectric slab of arbitrary thickness, with index of refraction that contains a term proportional to the intensity of the optical wave in the slab. An exact solution is found for the problem, in terms of a single parameter whose value is determined through a straightforward numerical search procedure. We present numerical studies of the power dependence of the transmissivity, with emphasis on bistability, and the multivalued behavior of the transmissivity considered as a function of incident power.

DOI
10.1103/physrevb.35.524

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We present a theoretical discussion of the optical reflectivity and transmissivity of a dielectric slab of arbitrary thickness, with index of refraction that contains a term proportional to the intensity of the optical wave in the slab. An exact solution is found for the problem, in terms of a single parameter whose value is determined through a straightforward numerical search procedure. We present numerical studies of the power dependence of the transmissivity, with emphasis on bistability, and the multivalued behavior of the transmissivity considered as a function of incident power.
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.
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.
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 study the nonlinear optical bistability and multistability of a nonlinear ferroelectric (FE) Fabry-Perot (FP) interferometer assumed coated with partial dielectric mirrors on its interfaces. The FE material is considered to have an intensity-dependent refractive index where the third order nonlinear susceptibility χ ilmn (3) acts like Kerr coefficient. The nonlinear response of the FE medium is modeled by the Landau-Khalatnikov (LK) dynamical equation. Within a single frequency approximation, the nonlinear wave equation is written in terms of polarization P rather than the electric field E as the dependent variable. The resulting nonlinear polarization equation is numerically integrated across the FP film using the fourth order Runge-Kutta method. The behavior of the resulting polarization and transmission as a function of the field input intensity is investigated.
An investigation is made of the reflection of light from a nonlinear pile of thick plates. Assuming a small difference between the refractive indices of neighboring plates Δn/n<1, an analytic solution is found in the approximation of a continuous number of plates. It is shown that beginning with a certain intensity, the transmission regime becomes multivalued. At a moderate intensity, high reflection changes to transmission. Numerical calculations are made for the case Δn/n~1. It is found that the qualitative behavior of the transmission coefficient as a function of the incident radiation intensity is similar in both cases.