Cavity tests of parity-odd Lorentz violations in electrodynamics

Electromagnetic resonant cavities form the basis for a number modern tests of Lorentz invariance. The geometry of most of these experiments implies unsuppressed sensitivities to parity-even Lorentz violations only. Parity-odd violations typically enter through suppressed boost effects, causing a reduction in sensitivity by roughly four orders of magnitude. Here we discuss possible techniques for achieving unsuppressed sensitivities to parity-odd violations by using asymmetric resonators.