Effective dielectric response of nonlinear composites

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Abstract
A perturbative approach is developed to compute the local field for the case of a nonlinear inclusion embedded in a nonlinear host. The result is applied to nonlinear composites. General formulas for calculating the effective nonlinear susceptibility up to the case of fifth-order nonlinearity are given. The formulation is applied to problems in two dimensions (2D) and in three dimensions (3D). For 2D problems, the cases of cylindrical inclusions and concentric cylindrical inclusions are studied. By invoking an exact mapping, the problem of the concentric cylinder can be mapped onto the problem of an elliptic cylinder. A general expression of the effective nonlinear susceptibility for a dilute composite of randomly oriented elliptic cylinders embedded in a linear host is derived. For 3D problems, the cases of spherical inclusions and coated spherical inclusion are studied. General expressions for the effective nonlinear susceptibility are given in the dilute limit up to the case of fifth-order nonlinearity. For composites consisting of spherical inclusions coated by a nonlinear material and embedded in linear host, it is possible to enhance the nonlinear response of the composite by tuning material parameters such as the linear dielectric constants of the host, coating and core materials, and by adjusting the thickness of the coating.