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Soviet Journal of Quantum Electronics

Reflection of light from a nonlinear interference mirror

Leonid A Bol'shov, V. P. Reshetin

Published Mar 31, 1980• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe1980v010n03abeh009977

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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.
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.
A study is made of the problem of transmission of light pulses by a boundary of a nonlinear medium under conditions of coherent interaction with matter. It is shown that in the case of a semiinfinite nonlinear medium the reflection coefficient is governed by the linear characteristics of the media in contact so that the boundary-value problem reduces to the Cauchy problem. In another case, when a nonlinear medium is a thin film at the interface between two linear media, it is found that such a film is an almost perfect mirror reflecting weak pulses but it becomes transparent to pulses of sufficiently high intensity and the mirror then modulates the amplitude of such pulses.
The interference of two opposing coherent waves in a thin layer was studied. Expressions for energy fluxes outside and inside the layer are obtained for normal incidence. It is shown that the interference flux, whose magnitude and direction vary markedly with layer parameters, amplitude and phase of incident waves may be derived together with incident, transmitted and reflected wave fluxes. The distribution of the total energy flux by thickness inside absorbing and amplifying layers was examined for single incident wave. The dependence of transmission and reflection energy coefficients, T and R, on the thickness of a layer with negative absorption has been studied numerically in detail for the case of normal incidence.
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.
We develop an analytic approach for reflection of light at a temporal boundary inside a dispersive medium and derive frequency-dependent expressions for the reflection and transmission coefficients. Using the analytic results, we study the temporal reflection of an optical pulse and show that our results agree fully with a numerical approach used earlier. Our approach provides approximate analytic expressions for the electric fields of the reflected and transmitted pulses. Whereas the width of the transmitted pulse is modified, the reflected pulse is a mirrored version of the incident pulse. When a part of the incident spectrum lies in the region of total internal reflection, both the reflected and transmitted pulses are distorted considerably.