Plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material with arbitrarily oriented constitutive principal axes

The extended boundary condition method can be formulated to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability dyadic when the constitutive principal axes are arbitrarily oriented with respect to the shape principal axes. Known vector spherical wave functions are used to represent the fields in the surrounding matter-free space. After deriving closed-form expressions for the vector spherical wave functions for the scattering material, the internal fields are represented as superpositions of those vector spherical wave functions. The unknown scattered-field coefficients are related to the known incident-field coefficients by a transition matrix. The total scattering and absorption efficiencies are highly affected by the orientation of the constitutive principal axes relative to the shape principal axes, and the effect of the orientational mismatch between the two sets of principal axes is more pronounced as the electrical size increases. The dependence of the total scattering efficiency, but not of the absorption efficiency, on the angle of rotation about a shape principal axis can be predicted qualitatively from the variation of a scalar function with respect to the angle of rotation. The total scattering and absorption efficiencies do not depend on the polarization state of incident plane wave when the scattering material is impedance-matched to free space. The polarization state of the incident plane wave has a more discernible effect on the total scattering and absorption efficiencies for ellipsoids compared to spheres.