Spatially resolved eigenstates for traveling and standing waves in ring lasers

The spatially generalized Jones matrix formalism is applied to ring lasers with several propagation axes. Local spatial separation is theoretically and experimentally shown to be a convenient means for controlling the coupling, frequencies, and oscillation regime of the eigenstates of a ring laser. It is applied successively to four locally circularly polarized eigenstates, four linearly polarized eigenstates, and a combination of two traveling-wave and one standing-wave linearly polarized eigenstates. In all cases, novel types of optical diodes based on either the Zeeman or the Faraday effect permit the selection of the desired eigenstates. In particular, three kinds of ring laser gyroscope designs that incorporate these optical diodes are shown to circumvent the problem of frequency locking. The first two sustain two counterpropagating frequency-biased traveling waves with orthogonal polarizations. The third one exhibits the Sagnac effect on a single traveling wave, the standing-wave eigenstate being used as a local oscillator. In all cases, fluctuations in the bias can be eliminated, and good agreement is observed between experiments and the predictions obtained from a spatially generalized Jones matrix formalism.