Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L-x, L-y) is assumed to be 2Delta(-2)theta(L-x-1/3+Delta/3)theta(L-y-1/3+Delta/3)theta(2/3+Delta/3-L-x-L-y), where theta(...) is the Heaviside function, Delta is the shape variance and L-i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Delta on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption alpha similar to omegaIm(rootepsilon(e)((0))) and the modulus of the effective third-order optical nonlinearity enhancement \chi(e)((3))\/chi(1)((3)) exhibit the nonmonotonic behavior with Delta. Moreover, with increasing Delta, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Delta from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Delta --> 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of \chi(e)((3))\/chi(1)((3)) on Delta becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does.