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 J1(M)=0) and then optimizing the modulation frequency, the intensity modulation induced bias is reduced to zero and gyro S/N sensitivity is maximized.