Parity and time-reversal symmetry breaking, singular solutions, and Fresnel surfaces.

The method of exterior di®erential systems is applied to the problem of ̄nding 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 di®erences 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 di®erent from the outbound polarization states.