Resonator optical gyroscope having input beam modulation optimized for high sensitivity and low bias

Systems and methods for optimizing input beam modulation for high gyro sensitivity and low bias errors. The present invention is a resonator optical gyroscope having an optimized phase-modulation amplitude (frequency) for a selected modulation frequency (amplitude) that maximizes the gyro signal-to-noise (S/N) sensitivity. For selected values of the phase modulation amplitude, the polarization cross-coupling induced intensity modulation can be nulled. By setting the phase modulation amplitudes substantially close to these nulling points (e.g. M= 3.832 or 7.016 radians, which causes the first order Bessel function to be zero J 1 ( M ) = 0) and then optimizing the modulation frequency, the intensity modulation induced bias is reduced to zero and gyro S/N sensitivity is maximized.