Vectorial nonlinear dynamics in lasers with one or two stable eigenstates

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Abstract
The dynamical behavior of the polarization of a laser with one or two stable eigenstates subjected to the action of an ac longitudinal magnetic field with or without a dc longitudinal magnetic field is investigatged both theoretically and experimentally. In the case of an ac magnetic field only, the low-field linear and high-field nonlinear behaviors of the laser are isolated. For the low-field case, a typical cutoff frequency due to pure cavity effects is introduced. For the high-field case, two locations of the motion are isolated, depending on the amplitude and frequency of the ac magnetic field. This provides the tools used to understand the locking between the rotation of the polarization induced by the dc magnetic field and the vibration of the polarization induced by the ac magnetic field. In particular, thanks to the two dimensions of the polarization vector, it is shown that the ratio of locked frequencies depends on the number of stable polarization eigenstates. Unlike mechanical systems where coalescence of Arnold tongues is possible, our system, without any inertia, exhibits typical twisted Arnold tongues, for which a theoretical model provides a great precision and a good agreement between theory and experiment.