Scattering of electromagnetic waves by composite spherical particles: experiment and effective medium approximations

We have measured the differential scattering cross sections (phase functions I22) and the normalized extinction and scattering cross sections (efficiences) of composite spherical particles. The size parameter x = 2πr/λ was around 2π. Composite spheres consisted of nonabsorbing matrix containing a small amount (1.6 and 2.7% by volume) of highly absorbing inclusions. Such composite particles may represent a realistic model of fog or cloud droplets containing small amounts of carbon or a composite atmospheric aerosol particle. We have compared measured data with those calculated using seven different effective medium approximations. We have found that the approximations of Bruggeman and Maxwell Garnett, the generalization of dynamic effective medium approximation derived by Chylek and Srivastava, and the experimental waveguide method of determination of the effective refractive index lead to an acceptable agreement between calculated and measured values. The reduced χ2 values for these approximations ranged between 0.6 and 2.0. The remaining three approximations (volume averages of refractive indices or dielectric constants and the Maxwell Garnett relation with matrix and inclusion materials interchanged) lead to reduced χ2 values between 4.0 and 12.0 demonstrating a large disagreement between calculated and measured scattering characteristics.