Effective linear and nonlinear response of fractal clusters

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Abstract
We generalize a differential effective-medium approximation previously developed for the effective linear response of a fractal cluster, to treat the effective nonlinear response. We consider a material having a nonlinear J-E characteristic which forms a cluster in another, possibly nonlinear material. A differential equation for the cluster-size-dependent nonlinear susceptibility is derived and a general solution is obtained. Numerical examples are given for two special cases: a cluster of a nonlinear material in a linear host, and a cluster of a linear material in a nonlinear host. An enhancement in the nonlinear response due to clustering is found for the case of clustering of a nonlinear material in a linear host.

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