THEORY OF 3RD-HARMONIC GENERATION IN RANDOM COMPOSITES OF NONLINEAR DIELECTRICS

We consider the effective nonlinear susceptibility tensor chi for thir d harmonic generation (THG) in a nonlinear composite medium in which t he components may have nonvanishing second- and third-order nonlinear susceptibilities. We derive an expression for this susceptibility in t erms of the positional-dependent second- and third-order susceptibilit ies within the composite, as well as several factors which describe th e local field effect in a corresponding linear medium. We consider bot h the THG due to the presence of THG susceptibility in the components, and the induced THG due to the presence of second- order nonlinear su sceptibilities in the components. The resulting expression can be used to calculate both local field and percolation effects on chi in a wid e range of geometries. The general expression reduces to a simple resu lt in the dilute limit, which is similar to that previously derived. A n effective medium approximation, which is applicable to the whole ran ge of concentration, is proposed for both the effective second and thi rd harmonic susceptibilities. Results obtained from the general expres sion and the effective medium approximation are found to be in good ag reement with those obtained by numerical simulations for a model syste m of nonlinear composites consisting of a nonlinear metallic component and a linear insulating component. (C) 1998 American Institute of Phy sics. [S0021-8979(98)06319-1].