Theoretical Analysis of a New Technique for Inertial Rotation Sensing Using a Semiconductor Ring Laser

We introduce a new technique for the measurement of inertial rotations using a semiconductor ring laser. Inertial rotation introduces a frequency deviation of the optical frequency of the two counterpropagating waves in the laser cavity, whereas mode coupling causes frequency attraction (frequency pushing) and finally locking at low rotation rates, washing out the small Sagnac frequency difference to be measured. Here we propose to measure inertial rotation whitin the so-called locking band using the phase/amplitude dependence on detuning found for the oscillating modes under the gain line. The dephasing accumulated by the two counterpropagating waves unbalances the fields´ amplitudes within the locking region. We analytically derive the responsivity function quantifying the two-mode power unbalance versus rotation rate, by means of a two-mode rate equations model. Noise performance of a possible rotations sensor are also discussed by calculating the noise equivalent rotation rate.