PARITY AND TIME-REVERSAL SYMMETRY-BREAKING, SINGULAR SOLUTIONS, AND FRESNEL SURFACES

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 polarization states.