Theory of a Ring Laser

A systematic formulation of the theory of a ring laser is given, based on first principles and using a well-known model for laser operation. The discussion begins with a simple physical derivation of the electromagnetic field equations to first order in $\Omega$ for a noninertial reference frame in uniform rotation, and a qualitative analysis of the traveling-wave Fox-Li modes for a polygonal cavity. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory. The formalism can also be applied to another problem of current interest: the absorption line shape for a weak wave in the presence of a strong one traveling in the opposite direction. In the last few sections, the small-signal ring-laser theory is recovered as a special case, and a systematic calculation of the various equations of this theory is included. The limitations of laser gyroscopes arise mainly because of effects of backscattering of radiation and nonreciprocities of the optical path, leading, for example, to frequency-locking phenomena. Non-reciprocal losses have been used to shift the locking threshold, but for rotation rates above this threshold the observed beat note departs from the desired rotation rate in a typical manner shown in previous articles. However, the theory indicates that if more-detailed measurements are made, they should provide sufficient information for determining the rotation rate (apart from noise fluctuations).