  Numerical calculation of vector electromagnetic modes of plano-concave
microcavities reveals that the polarization-dependent reflectivity of a flat
Bragg mirror can lead to unexpected cavity field distributions for nominally
paraxial modes. Even in a rotationally symmetric resonator, certain pairs of
orbital angular momenta are necessarily mixed in an excitation-independent way
to form doublets. A characteristic mixing angle is identified, which even in
the paraxial limit can be designed to have large values. This correction to
Gaussian theory is zeroth-order in deviations from paraxiality. We discuss the
resulting nonuniform polarization fields. Observation will require small
cavities with sufficiently high Q. Possible applications are proposed.
