Nonlinear effective behavior of a dispersion of randomly oriented coated ellipsoids with arbitrary temporal dispersion

This work deals with the determination of the linear and nonlinear effective properties of an heterogeneous material composed of a dispersion of coated ellipsoidal particles (core-shell structure). The particles are considered randomly oriented and positioned within the matrix. Moreover, all constitutive equations (matrix, cores, shells) exhibit an hereditary behavior, leading to an arbitrary temporal dispersion. While matrix and shell are considered linear, the particles core shows an additional third-order nonlinearity. We develop an effective medium theory, which allows us to calculate the linear and nonlinear response in terms of the microstructure features. In particular, we can investigate the effects of the inter-phase on the overall behavior, in combination with the randomness of the orientations and with the linear and nonlinear hereditary phenomena. The results may find relevant applications in material science and, more specifically, in nonlinear optics, bulk plasmonics and metamaterials.