Effect of weak nonsphericity on linear and nonlinear optical properties of small particle composites

A small particle composite in which the inclusions are slightly nonspherical and distributed in shape is considered. Within the framework of the mean-field approximation, the functions of linear and nonlinear optical responses are calculated in terms of a nonsphericity parameter specifying the width of the distribution function in shape. To estimate the effect of weak nonsphericity on the functions, their second derivatives with respect to the nonsphericity parameter are computed. The derivatives are shown to be complexly structured surfaces in the coordinates (Re(epsilon(i)/epsilon(m),), Im(epsilon(i)/epsilon(m))) where epsilon(i) and epsilon(m), are the inclusion and matrix permittivity, respectively. Based on the results obtained, applicability area of the classical Maxwell Garnett theory is discussed. The main conclusion is that weak nonsphericity is significant only in the close vicinity of a dipole resonance of a single ball made of inclusion material. At the same time, the role of nonsphericity increases with decreasing the imaginary part of inclusion permittivity.