Abstract

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 medium^1,2 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.

© 1987 Optical Society of America