Higher-order nonlinear responses in weakly nonlinear composite materials within the effective medium approximation

Abstract

Based on the spectral representation theory and the perturbative expansion metho d, the general expressions for effective nonlinear responses (χe a nd ηe) are derived for any complicated micro structures. The higher_orde r nonlinear response of two_component composite is studied by using the effectiv e medium approximation. The effective dielectric constant of the composite is gi ven by ε～e=εe+χe|E0|2+ηe|E0|4. The effe ctive cubic order nonlinear response χe and the higher_order response ηe for the whole volume fraction p of the nonlinear component ar e investigated and the general expressions of χeand ηeare g iven in this paper. We also perform numerical simulations for χe and ηe in the case of complex dielectric constant of the nonlinear co mponent. The effect of the higher order nonlinear responses on the effective di electric constant of the composite is theoretically studied.