Theoretical and experimental study of eigenmodes and eigenstates in ring lasers. Applications to gyrometry and to the detection of small effects

A spatial and vectorial description of the eigenmodes and eigenstates of ring lasers is provided. After having studied the tangential and sagittal mode size dynamics due to resonant lenslike effects in one- and two isotope- ring lasers, the non-reciprocity of these mechanisms is shown to explain the biases observed in ring laser gyroscopes. The role of diffraction in the lock-in region is also isolated, allowing us to observe the so-called reverse Sagnac effect. The spatial separation of laser eigenstates is investigated and permits then to build cavities with several propagation axes whose eigenstates must be calculated in the framework of a spatially generalized Jones matrix formalism. This allows, in the case of Fabry-Perot cavity lasers, to control the coupling between eigenstates, to create forked eigenstates, and to build a two-tunable-frequency laser, and, in the case of ring lasers, to cancel the coupling between two counterpropagating eigenstates. The study of the stability and dynamics of eigenstates allows, first, to control the stability of the two eigenstates of various lasers, second, to measure small effects like the Goos-Hänchen shift or to build a mean-field magnetometer in the case where no eigenstate exists, and, third, to investigate the behavior of the four circularly polarized eigenstates of a ring laser in order to create an oscillation regime with two biased counterpropagating eigenstates, whose application as a ring laser gyroscope is discussed