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 composite material. We start from the exact relation chi(e) = Sigma(i)P(i) chi(i)[(E.E)(2)](i,lin)/E(o)(4), where chi i and pi are the cubic nonlinear 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 composite 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 percolation threshold. We also find a large enhancement for a linear fractal in a nonlinear host. In a random Drude metal-insulator composite chi(e) is hugely enhanced especially near frequencies which correspond 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 enhancement shows very strong reproducible structure which is nearly undetectable in the linear response of the composite, and which may possibly be described by a generalized nonlinear effective-medium approximation. The fractal results agree qualitatively with a nonlinear differential effective-medium approximation. Finally, we consider a suspension of coated spheres embedded in a host. If the coating is nonlinear, we show that chi(e)/chi(coat) >> 1 near the surface-plasmon resonance frequency of the core particle.