Fourier approach to the electric field and the nonlinear susceptibility for a periodic composite

By using series expressions of space-dependent electrical field in a periodic composite, which are obtained by a simple Fourier; approach, the frequency dependence of the effective third-order nonlinear susceptibility chi(e) of the metal-insulator composites with simple cubic arrays of coated spheres has been exactly calculated. The results show that the frequency-dependent nonlinear response of the composites has two sharp peaks when the metal phase forms a shell structure. The strengths of the peaks are very sensitive to the relaxation time of the metal. The dependences of both the shapes and strengths of the peaks on the radii of the cores of the coated spheres are also studied. [S0163-1829(98)01642-7].