Mirror Birefringence in a Fabry-Perot Cavity and the Detection of Vacuum Birefringence in a Magnetic Field

We discuss the effect of mirror birefringence in two optical schemes designed to detect the quantum-electrodynamics (QED) predictions of vacuum birefringence under the influence of a strong magnetic field, B. Both schemes make use of a high finesse Fabry-Perot cavity (F-P) to increase the average path length of the light in the magnetic field. The first scheme, which we called the frequency scheme, is based on measurement of the beat frequency of two orthogonal polarized laser beams in the cavity. We show that mirror birefringence contributes to the detection uncertainties in first order, resulting in a high susceptibility to small thermal disturbances. We estimate that an unreasonably high thermal stability of ~10-9 K is required to resolve the effect to 0.1%. In the second scheme, which we called the polarization rotation scheme, laser polarized at 45 relative to the B field is injected into the cavity.