Kiehn, R. M., Kiehn, G. P., and Roberds, R. B., Phys Rev A, 43 , (1991) p. 5665 Also see: Schultz, A., Kiehn, R. M., Post, E. J., and Roberds, R. B., 1979, "Lifting of the four fold EM degeneracy and PT asymmetry", Phys Lett 74A, p.384.
Abstract: The method of exterior differential systems is applied to the
problem of finding propagating singular solutions to Maxwell's equations.
Fresnel ray and wave surfaces are computed for systems that are not restricted
to the topology imposed by the symmetries of the Lorentz transformations. The
methods distinguish the measurable polarization phase differences between global
behavior in optically active and Faraday media. In addition, an example is
presented for which time-reversal and parity symmetries are broken: the inbound
polarization states propagate with speeds different from the outbound
A Maple program fresnel.mws is available to
compute the Fresnel wave surfaces.