A Fourier Space Approach to the Pointwise Singularity of An Anisotropic Dielectric Medium

We present a new method to calculate the depolarization dyadic of the dyadic Green function of an anisotropic dielectric medium. An infinitesimally small exclusion region of spherical shape is chosen. Our method is based on an analysis of the representation of the dyadic Green function in Fourier space, which is calculated explicitly. We derive a relation between the asymptotic behavior of the dyadic Green function for high spatial frequencies and the depolarization dyadic. The practical calculation of the depolarization dyadic amounts in performing a two-dimensional angular integration. For a uniaxial medium, symmetry leads to a reduction of the integral to a one-dimensional one, which is evaluated analytically. We find an expression for the depolarization dyadic which is identical to that recently made available by Lakhtakia and Weiglhofer (1997, this journal).