Employing self-consistency, the multiple-scattering problem is formulated for periodic arrays of particles having constitutive parameters distinct from those of the embedding material. A T-matrix description of individual particle scattering is employed, so that particles need not be spherical. Explicit analytical and numerical results are obtained for the effective complex dielectric constant ε̄ and permeability μ̄ in the quasistatic and infinitesimal lattice limits for several lattice geometries, and shown to agree with existing static computations under appropriate conditions. Random arrays are also considered briefly, and the role of single-particle resonance effects is examined. Finally, longitudinal electric and magnetic waves are predicted to exist at certain discrete frequencies where ε̄ or μ̄ vanish.

A microwave technique has been developed for obtaining total cross sections and angular distributions for the scattering of electromagnetic radiation by nonspherical particles whose size is of the order of the wavelength. The scattering by spheroidal and cylindrical refracting particles has been measured for three orthogonal orientations of the symmetry axis. Comparison of the results with exact and approximate theoretical calculations for spheres, spheroids, and finite and infinite cylinders indicates the possibility of developing useful approximation methods. Some interesting effects have been noted, particularly a very large resonance in the scattering by finite cylinders. The results have been given preliminary application to the problem of the nature of the interstellar material which absorbs and polarizes starlight.

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