We have theoretically explored the behavior of a coherently pumped ${J}^{\ensuremath{''}}=\stackrel{\ensuremath{\rightarrow}}{1}J=\stackrel{\ensuremath{\rightarrow}}{0}{J}^{\ensuremath{'}}=1$ isotropic cavity laser and compared it with the behavior of other related laser systems involving atomic or molecular levels with angular quantum numbers
0 and
1. It is shown that at low and moderate pumping strengths it behaves very differently from the ${J}^{\ensuremath{''}}=\stackrel{\ensuremath{\rightarrow}}{0}J=\stackrel{\ensuremath{\rightarrow}}{1}{J}^{\ensuremath{'}}=0$ laser exhibiting no pump-induced gain anisotropy and allowing for linearly polarized (LP) solutions with arbitrary azimuth and circularly polarized (CP) solutions, depending on the values of the molecular relaxation rates. Above the instability threshold, a variety of dynamic regimes involving the polarization degree of freedom can be found, including LP states with rotating azimuth (as in incoherently pumped $J=\stackrel{\ensuremath{\rightarrow}}{0}{J}^{\ensuremath{'}}=1$ or $J=\stackrel{\ensuremath{\rightarrow}}{1}{J}^{\ensuremath{'}}=0$ lasers), antiphase dynamics, and full polarization chaos.
The interplay between the polarization state of light and transverse effects in lasers is analyzed through an amplitude equation description of an atomic transition between spin sublevels. Linearly polarized traveling waves are found, whose stability is restricted by a phase instability associated with the direction of polarization. The instability persists for polarization stabilized lasers. Novel states of laser light such as standing waves with a spatially periodic linear polarization or coexisting traveling waves with different wave numbers and circular polarizations are also found.
We address polarization instability in a freely decaying polariton condensate created by 2-ps-long linearly polarized laser pulses in the upper sublevel of the lower-polariton (LP) branch in a GaAs-based microcavity with reduced symmetry. The generated linearly polarized condensate is found to lose its stability at excitation densities above the threshold value: it passes into the regime of inner Josephson oscillations with strongly oscillating circular and diagonal linear polarization degrees, as well as monotonically decreased oscillations in linear polarization accompanied by a gradual increase in the condensate of the low-sublevel component. These phenomena occur with a relatively small decrease in the total polarization and spatial coherence of the spinor condensate. At high LP densities, the LP-LP interaction leads to the nonlinear Josephson effect. All effects are found to be well reproduced by the model based on spinor Gross-Pitaevskii equations. The cause of the instability was clarified by considering a simplified model of the spinor 0D oscillator: it is spin anisotropy of the LP-LP interaction. The threshold density was shown to increase with decreasing difference $\mathrm{\ensuremath{\Delta}}\ensuremath{\alpha}$ of the constants of the interparticle interaction of LPs with identical and opposite spins as ${\ensuremath{\delta}}_{l}/\mathrm{\ensuremath{\Delta}}\ensuremath{\alpha}$, where ${\ensuremath{\delta}}_{l}$ is the LP level splitting. The reduction in the linear polarization is connected with the fact that the LPs escaping from the condensate with oscillating circular polarization carry off more energy than from the linearly polarized one.