  We present a passive, resonant, single-frequency gyroscope design that
utilises polarisation modes of an optical cavity to readout rotation and
generate a laser frequency discriminant. This design is notable for its
simplicity, requiring no modulation electronics or frequency counters. We
extract both the cavity length signal and rotation signal from two
co-propagating beams with orthogonal polarisations. This readout scheme can be
applied to an optical cavity whose polarisation eigen-modes experience
different phase shifts such as fibre rings; whispering gallery mode resonators;
and folded free-space cavities. We apply this technique to the passive
free-space gyroscope and achieve a bias stability of 0.03 degree/h and a
sensitivity of $5 \times 10^{-8}$ rad/sqHz above 1 Hz, with a cavity of area
400 cm^2 and finesse of 10^4. Below 1 Hz the sensitivity of the gyroscope is
limited by the backscattering in the optical cavity and beam jitter of the
laser beam.

Optics;Applied Physics