Enhancement of optical nonlinearity through shape distribution

The effect of the shape distribution of granular inclusions on the effective nonlinear optical properties of granular metal/dielectric composites is considered. The study is based on a generalized Maxwell-Garnett type approximation for the spectral density function of two-component composites in which the metallic inclusions possess a 'beta function' distribution of geometric shapes. Numerical results show that the spectral density function is increased (decreased) in the range 0.35 less than or equal to s' less than or equal to 0.5 (0.8 less than or equal to s' less than or equal to 1.0) with increasing shape distribution parameter alpha. By invoking the mean-field approximation, we calculate the optical nonlinearity and find the nonlinearity enhancement peak is separated from the absorption peak in the range 0.45 less than or equal to omega/omega (p) less than or equal to 0.6, while a large enhancement of the optical nonlinearity is found in the range 0.8 less than or equal to omega/omega (p) less than or equal to 1.0. Thus by introducing a shape distribution of metallic particles, we are able to make the figure of merit attractive in this frequency range. In the dilute limit, the shape distribution leads to an anomalous farinfrared optical absorption. Moreover, an exact formula for the effective optical nonlinearity is derived and a sharp nonlinearity enhancement peak is observed near the resonant frequency omega/omega (p) approximate to 0.47.