Theory of Gyrotropic Birefringence
Abstract
A theoretical treatment of the optical effect known as gyrotropic or nonreciprocal birefringence is presented. By suitably renormalizing the electric dipole moment tensor, it is shown, for the case of lossless media, that 10 of the 18 independent quantities in the gyrotropicbirefringence tensor have their origin in electric quadrupole effects. The other eight are shown to be related to the magnetoelectric effect. The general results are applied to the materials Cr_{2}O_{3} and MnTiO_{3}. The propagation of a plane wave along one of the crystalline axes of Cr_{2}O_{3} is then considered. It is shown that the gyrotropic birefringence exhibits itself as a rotation of the principal optic axes, together with a change in the velocity of propagation of the wave in the medium. Next, the modified boundary conditions corresponding to the renormalized field vectors are given, and the case of a plane wave normally incident on a gyrotropically birefringent medium is discussed. It is noted that the field relations at a boundary will be modified even when the quadrupole contribution vanishes and the magnetoelectric tensor is isotropic, a case in which there is no gyrotropic birefringence in the medium itself. Foinally, a quantummechanical calculation of the gyrotropicbirefringence tensor at 0°K is given. The expression obtained is applied to the case of Cr_{2}O_{3}, and the electric quadrupole and magnetoelectric contributions are separated. It is roughly estimated that, at optical frequencies, the electricquadrupoleinduced rotation of the principal optic axes of Cr_{2}O_{3} is of the order of 10^{6} rad, and the magnetoelectricinduced shift is two orders of magnitude less.
 Publication:

Physical Review
 Pub Date:
 July 1968
 DOI:
 10.1103/PhysRev.171.1065
 Bibcode:
 1968PhRv..171.1065H