The problem of the scattering and absorption of a plane electromagnetic wave by a gyrotropic sphere is solved in this paper. This is a generalization of the classic Mie scattering problem to the case where the dielectric constant is a tensor having axial symmetry. For this problem, Maxwell's equations are not separable in spherical coordinates. The method of solution involves the expansion of the electromagnetic field. inside the sphere in a complete set of vector spherical waves, which are solutions of the ordinary vector wave equation. The amplitudes of the scattered spherical waves are found to be expressible in the form of a series of ratios of determinants dependent upon the components of the dielectric tensor, the wavelength of the incident plane wave, and the sphere radius. These scattering amplitudes are examined in various limits. In the limit when the dielectric tensor is a scalar, the Mie results are recovered. When the wavelength of the incident plane wave is large in comparison to the sphere radius, our previous results for helicon oscillations are obtained in addition to new resonant structure induced by the incident electric field. Under conditions when the wavelength inside the sphere is also large compared to the sphere radius (but large compared to the incident wavelength), previous results in the Rayleigh limit are obtained. Selected applications of the results of this paper have been made by Dixon and Furdyna (helicon oscillations, electric dimensional resonances and cyclotron resonance in metals and semiconductors, Alfvén resonances in semimetals), and by Markiewicz (Alfvén oscillations in electron-hole droplets).

• Received 7 August 1978

DOI:https://doi.org/10.1103/PhysRevB.18.6752