A method is given for investigating the behaviour of electromagnetic fields in a homogeneous, anisotropic medium characterized by a dielectric tensor which is diagonal, with two of the three diagonal elements equal. It is shown that each such field is related by a simple scaling procedure to a corresponding vacuum field. The vacuum field is expressed as the superposition of a transverse magnetic field, in which the magnetic vector is everywhere perpendicular to the axis of symmetry of the anisotropic medium, and a coplanar transverse electric field; and different scaling is applied separately to each partial field. The method is illustrated by application to plane-wave and dipole fields. In particular, the field is obtained of a time-harmonic electric dipole of arbitrary orientation situated in the anisotropic medium.
List of symbolsE, H,J -Electric, magnetic and current density vectors E { , Hy, J v = Electric, magnetic and current density vectors for a TM-field E 2 , H 2 , J 2 = Electric, magnetic and current density vectors for a TE-field E°, H°, J° = Electric, magnetic and current density vectors for a vacuum field x, y, z = Rectangular Cartesian co-ordinates £, 7], £ = Rectangular Cartesian co-ordinates for a vacuum field r, 6, -Spherical polar co-ordinates co = Angular frequency e 0 , (JL 0 = Vacuum permittivity and permeability Z = VOo/ € o) k = ajy(c o /x o ) K, K$ = Diagonal elements of the dielectric tensor X = Square of ratio of plasma to wave frequency [j, = Refractive index «i, -n 2 ,n 3 = Direction cosines of plane wave P = Dipole strength, A-m + y 2 ) + Kz 2 ]