Theory of third harmonic generation in random composites of nonlinear dielectrics

We consider the effective nonlinear susceptibility tensor χ for third harmonic generation (THG) in a nonlinear composite medium in which the components may have nonvanishing second- and third-order nonlinear susceptibilities. We derive an expression for this susceptibility in terms of the positional-dependent second- and third-order susceptibilities within the composite, as well as several factors which describe the local field effect in a corresponding linear medium. We consider both the THG due to the presence of THG susceptibility in the components, and the induced THG due to the presence of second-order nonlinear susceptibilities in the components. The resulting expression can be used to calculate both local field and percolation effects on χ in a wide range of geometries. The general expression reduces to a simple result in the dilute limit, which is similar to that previously derived. An effective medium approximation, which is applicable to the whole range of concentration, is proposed for both the effective second and third harmonic susceptibilities. Results obtained from the general expression and the effective medium approximation are found to be in good agreement with those obtained by numerical simulations for a model system of nonlinear composites consisting of a nonlinear metallic component and a linear insulating component.