  Interference of orthogonal modes in a birefringent crystal is known to lead
to interesting physical effects (Solli et al., Phys. Rev. Lett. 91, 143906
(2003)). In this paper we show that the cavity with an intra-cavity rotator can
enhance the mixing to the extent of normal mode splitting and avoided crossing
depending on the orientation of the rotator with respect to the optic axis of
the crystal. A high finesse cavity is shown to be capable of resolving small
angles. The results are based on direct calculations of the cavity
transmissions along with an analysis of its dispersion relation.
