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The semiclassical theory of a ring laser gyro is reviewed including discussion of the Sagnac effect, mode coupling, mode locking, dither, bias techniques, role of isotopes, and gaseous laser media. In addition a fully quantized theory for media with nonmoving atoms is used to examine the stability of unidirectional operation.
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Murray Sargent III, "Basic Ring Laser Gyro Theory," Proc. SPIE 0487, Physics of Optical Ring Gyros, (4 October 1984); https://doi.org/10.1117/12.943244