Abstract
The effect of the shape distribution of granular inclusions on the effective non-linear 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 ≤ s′ ≤ 0.5 (0.8 ≤ s′ ≤ 1.0) with increasing shape distribution parameter α. 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 ≤ ω/ωp ≤ 0.6, while a large enhancement of the optical nonlinearity is found in the range 0.8 ≤ ω/ωp ≤ 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 far-infrared 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 ω/ωp ≈ 0.47.
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