Phase modulation of a ring-laser gyro - Part I: Theory

The theory of a multimode ring-laser gyro with intracavity phase modulation is developed, starting from the wave equation for a rotating reference frame. The approach is to extract physical information without actually solving the equations. Considering each of the oppositely directed traveling waves (ODTW) separately, the behavior is similar to that of an ordinary two-mirror phase-modulated laser. However, when the waves are heterodyned to measure a beat frequency, small mode-pulling effects become important, and, if the ODTW are treated unequally by the system, a frequency error or offset results. Sources of offset include time variation of the modulator length, reactance of the gain medium, and detuning of the modulator frequency from axial mode spacing. When back reflections are included in the theory, the results reduce to the single-mode ring-laser case, with the coupling coefficient dependent upon overlap between the ODTW at the reflector. It is predicted that at low rotation rates the ODTW frequencies will still become locked together, except in a very special case where the lock-in threshold vanishes. Significance of the nature of the reflecting elements is discussed. Comments are made on the predicted merits of phase modulation as an improvement in the low-rotation-rate measuring capabilities of the device.