Laser eigenstates in the framework of a spatially generalized Jones matrix formalism

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Abstract
A theoretical model is developed to predict the longitudinal and transversal distributions of polarization and intensity and the eigenfrequencies of the laser eigenstates in the case where the transversal degeneracy of the eigenstates is broken up by a birefringent element inducing a polarization walk-off. This formalism, which generalizes the Jones matrix formalism, is necessary for interpreting the existence of ordinary and extraordinary eigenstates that have different paths in the cavity. Moreover, it leads to the prediction of so-called forked eigenstates, in which a single laser eigenstate itself is split into two spatially separated orthogonally polarized branches in one part of the cavity containing an extra normal birefringent plate. This formalism also allowed us to design and realize a two-frequency laser in which two eigenstates can oscillate simultaneously at easily adjustable frequencies. Experimental evidence of these phenomena was gathered and showed excellent agreement with the theoretical predictions.