Passive optical gyroscope with double homodyne readout

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.