NUMERICAL-STUDIES OF THE NONLINEAR PROPERTIES OF COMPOSITES

Using both numerical and analytical techniques, we investigate various ways to enhance the cubic nonlinear susceptibility chi(e) of a compos ite material. We start from the exact relation chi(e) = Sigma(i)P(i) c hi(i)[(E.E)(2)](i,lin)/E(o)(4), where chi i and pi are the cubic nonli near susceptibility and volume fraction of the ith component, E(o) is the applied electric field, and [E(4)](i,lin) is the expectation value of the electric field in the ith component, calculated in the linear limit where chi(i)=0. In our numerical work, we represent the composit e by a random resistor or impedance network, calculating the electric- field distributions by a generalized transfer-matrix algorithm. Under certain conditions, we find that chi(e) is greatly enhanced near the p ercolation threshold. We also find a large enhancement for a linear fr actal in a nonlinear host. In a random Drude metal-insulator composite chi(e) is hugely enhanced especially near frequencies which correspon d to the surface-plasmon resonance spectrum of the composite. At zero frequency, the random composite results are reasonably well described by a nonlinear effective-medium approximation. The finite-frequency en hancement shows very strong reproducible structure which is nearly und etectable in the linear response of the composite, and which may possi bly be described by a generalized nonlinear effective-medium approxima tion. The fractal results agree qualitatively with a nonlinear differe ntial effective-medium approximation. Finally, we consider a suspensio n of coated spheres embedded in a host. If the coating is nonlinear, w e show that chi(e)/chi(coat) >> 1 near the surface-plasmon resonance f requency of the core particle.