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Physical Review A

Effective-medium theory of a nonlinear composite medium using theT-matrix approach: Exact results for spherical grains

Nitin C. Kothari

Published Apr 1, 1990• 31 citations
Publisher

Abstract

An effective-medium theory for nonlinear spherical particles embedded in a linear host medium is developed. The formulation is based on a T-matrix approach. Introduction of a field-dependent T matrix enables one to obtain an exact expression for effective dielectric constant of a medium with spherical grains. In the special cases of low-field values, the results obtained previously for the third- and fifth-order nonlinear susceptibilities of the medium are recovered. The resonance behavior of the effective dielectric constant and intrinsic optical bistability are also discussed.

DOI
10.1103/physreva.41.4486

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An effective-medium theory for nonlinear spherical particles embedded in a linear host medium is developed. The formulation is based on a T-matrix approach. Introduction of a field-dependent T matrix enables one to obtain an exact expression for effective dielectric constant of a medium with spherical grains. In the special cases of low-field values, the results obtained previously for the third- and fifth-order nonlinear susceptibilities of the medium are recovered. The resonance behavior of the effective dielectric constant and intrinsic optical bistability are also discussed.
We examine the nonlinear dielectric response of small spherical grains ϵ m embedded in a linear dielectric ϵ d . The models for the spherical grains are a Kerr medium1,2 and a two-level system.3 The expression for the dielectric function ϵ m is dependent of the grain size; in addition it also depends on the local electric field E L . This field is related to the external applied field E0 by the equation E L = (3ϵ d /ϵ m + 2ϵ d )E0. The steady-state equation for the averaged external field is ∇2E0 + (ω2/c2)ϵ*E0 = 0, where ω is the frequency of the field, ϵ* is the dielectric function from the effective medium approximation, and it is obtained from the self-consistency relation4 〈ϵ(r) − ϵ*/ϵ(r) + 2ϵ*〉 = 0; the angular brackets denote an average taken over the ensemble of dielectric spheres distributed in a small volume. Using the slowly varying-envelope approximation we solve these equations for a distribution of grain radii and the affect this has on the effective optical nonlinearities. In particular, we show its effect on the optical bistability for these composite systems.
The mean-field approximation method is proposed to investigate the intrinsic optical bistability in nonlinear composite media, which consists of nonlinear metallic granules embedded in nonlinear dielectric host. The effect of nonlinear susceptibility on the bistable behavior is analyzed. It is found that nonlinear metallic granules and nonlinear host medium have different effects and the nonlinearity of metallic granules is more effective in minimizing the threshould value of the bistable behavior. We also investigate the effect of the shape factor of metallic granules on the threshold value.
Nonlinear optical properties of microstructures immersed in a linear dielectric are investigated. The microstructures are assumed to be composed of simple saturable two-level atoms. The local field corrections are included in a self-consistent manner leading to multiple solutions for the absorptive part of the dielectric constant of the microstructure as noted earlier by Chemla and Miller.1 For a given structure we use the effective medium theory and average over the random positions of the grains to obtain the effective medium dielectric constant in the quasistatic limit (λ ≪ grain size) as a function of the volume fraction of the grains. The results exhibit sharp hysteresis effects. However, in the study of the propagation in the medium these effects are modified considerably. While defined switches are observed in the mean field at certain points in the medium where the absorption jumps from the upper to lower branch, the optical intensity undergoes only a change of slope.
The propagation of electromagnetic waves in a nonlinear medium composed of semiconductor microcrystallites embedded in a host medium has been investigated. Explicit results are given for the case of cadmium sulfide grains in glass when a saturable two-level approximation is used for the nonlinear dielectric function. The bistable behavior, noticed earlier by Chemla and Miller [ Opt. Lett.11, 522 ( 1986)], for single grains is manifested in the propagation studies conducted here by the occurrence of a discontinuity in the index of refraction in the medium. Various approximations are used to obtain the optical bistability properties. Possible applications of this feature are pointed out.
Abstract Optically bistable behaviour is demonstrated for systems consisting of optically nonlinear microcrystallites embedded in an optically linear metal or dielectric. The most simple version of the local‐field correction serves as feedback mechanism thus avoiding external mirrors. The dielectric function for macroscopic samples is calculated with Garnett's effective medium theory. Numerical examples for the reflectivity and the transmissivity are given for an embedded dielectric with exciton‐like nonlinearity.