Accurate method to determine the eigenstates of polarization in gyrotropic media

Many practical modulator materials include combinations of electrooptically induced birefringence, optical activity, and/or Faraday rotation. Thus, there is a need for a procedure to design and analyze devices fabricated with materials exhibiting any or all of these effects. In this paper a simple procedure employing an extension of the general Jacobi method is introduced for determining the properties of the two allowed elliptical eigenpolarizations for an arbitrary direction of propagation and for the principal indices and axes of a general lossless, electrooptic, and gyrotropic medium. The procedure uses an iterative application of unitary transformations to diagonalize the Hermitian impermeability tensor. A complex polarization variable is defined from elements of the unitary transformation matrix to determine the ellipticity, azimuth angle, relative amplitude and phase, and handedness of the two orthogonal elliptical polarizations. The phase velocity indices of refraction are readily calculated with simple derived expressions. The procedure is numerically stable and accurate for any crystal class, external field direction, and direction of propagation.