Effective Propagation Constants and Attenuation Rates in Media of Densely Distributed Coated Dielectric Particles with Size Distributions

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Abstract
The effective propagation constants and attenuation rates in dense nontenuous media with coated dielectric particles governed by size distributions are studied. A coated particle consists of two layers with different materials. In a dense medium, particles do not scatter independently and the effects of correlated scattering have to be included. The correlated scattering can be taken into account by using the quasicrystalline approximation (QCA) or the quasicrystalline approximation with coherent potential (QCA-CP). The Lippmann-Schwinger equation for coated particles is solved analytically to calculate the T-matrix for both QCA and QCA-CP. We also consider the dense medium with particle sizes governed by size distribution. The pair distribution functions for particles of different sizes are computed by using the Percus-Yevick approximation. For small particles, closed form analytic expressions are obtained for the complex effective propagation constants. For moderate size particles, the complex effective propagation constants are calculated numerically by searching for complex roots of a determinantal equation. We illustrate the numerical results of the complex effective propagation constants using the modified gamma size distribution. The case of ice particles coated with a thin water layer studied shows a strong attenuation due to absorption. We also show that a medium consisting of a broad size distribution of particles tends to follow independent scattering more than a medium with a narrow size distribution.