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Physical Review A

Polarization states and coherent effects in a coherently pumped J″=1→J=0→J′=1 isotropic-cavity laser

Alexander M. Kul'minskii, Ramon A. Vilaseca, R. Corbalán, N. B. Abraham

Published Aug 17, 2000• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.62.033818

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We have theoretically explored the behavior of a coherently pumped J\ensuremath′′=1\ensuremath→J=0\ensuremath→J\ensuremath′=1{J}^{\ensuremath{''}}=\stackrel{\ensuremath{\rightarrow}}{1}J=\stackrel{\ensuremath{\rightarrow}}{0}{J}^{\ensuremath{'}}=1J\ensuremath′′=1\ensuremath→​J=0\ensuremath→​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 000 and 1.1.1. It is shown that at low and moderate pumping strengths it behaves very differently from the J\ensuremath′′=0\ensuremath→J=1\ensuremath→J\ensuremath′=0{J}^{\ensuremath{''}}=\stackrel{\ensuremath{\rightarrow}}{0}J=\stackrel{\ensuremath{\rightarrow}}{1}{J}^{\ensuremath{'}}=0J\ensuremath′′=0\ensuremath→​J=1\ensuremath→​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=0\ensuremath→J\ensuremath′=1J=\stackrel{\ensuremath{\rightarrow}}{0}{J}^{\ensuremath{'}}=1J=0\ensuremath→​J\ensuremath′=1 or J=1\ensuremath→J\ensuremath′=0J=\stackrel{\ensuremath{\rightarrow}}{1}{J}^{\ensuremath{'}}=0J=1\ensuremath→​J\ensuremath′=0 lasers), antiphase dynamics, and full polarization chaos.
We study theoretically the dynamic behavior of a J′=1→J″=0 laser (J is the angular momentum quantum number) optically pumped by means of a linearly polarized coherent field (coupled to an adjacent transition J=0→J′=1) when the pump field polarization is rotated at a constant angular velocity Ω and the laser field polarization either is fixed by the cavity or is free (isotropic cavity). Because of a strong pump-induced gain anisotropy, the dynamic behavior is completely different in each case. In the case of fixed laser field polarization, rich amplitude dynamics, which depend on the pump field strength, are found. At slow modulation frequencies (with respect to the molecular and the cavity relaxation rates), the system does not always follow the sequence of stationary and dynamic solutions that correspond to the autonomous laser as a function of the relative orientation angle between the polarizations of the pump and the laser fields. Phenomena such as delayed switching and suppression of chaos and stabilization of unstable steady states are found. In the case of an isotropic cavity, the pump field vector rotation is transferred to the laser field vector and amplitude unstable regimes are also strongly inhibited.
The field intensity and polarization behaviour of an optically pumped laser is investigated in different operating conditions. For a linearly polarized pump field, a strong gain anisotropy is induced which favours generation of light with a polarization parallel to that of the pump field. Thus gain anisotropy can be counterbalanced by cavity-loss anisotropy only at low pumping field intensities, and the interplay between both types of anisotropy leads to polarization switching phenomena. In contrast to the case of the incoherently pumped laser, the decay rate for the magnetic dipole induced on the J = 1 level plays a minor role in determining the polarization dynamics. The influence of a longitudinal magnetic field or of modulation of the pump-field polarization orientation leads to new features and complex dynamic behaviour which includes full polarization (or vector ) chaos.
We show that, in an optically pumped resonant $J=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0$ laser, a gain anisotropy is induced by a linearly polarized coherent pump beam that can be balanced or countered by xxx-yyy cavity-loss anisotropies, leading to switching between the xxx and yyy linearly polarized states of the generated laser field as the laser intensity is increased. This switching is not brought about by selection of the mode with the maximum emission intensity. A domain of bistability between the two linearly polarized states is found, whose width depends on the value of the decay rate of the two photon coherence induced among the sublevels of the J=1J=1J=1 level manifold. Differently from the incoherently pumped $J=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0$ laser, the decay rate for the magnetic dipole in that manifold has no influence on the polarization of the emission.
We study the dynamic behavior of an optically pumped J = 0 → J = 1 → J = 0 laser operating with an isotropic ring cavity and a linearly polarized pump field whose direction of polarization is modulated by the sinusoidal law θ(t) = m sin Ωt. Modulation frequencies Ω of the same order of magnitude as the transverse relaxation rate of the laser transition are considered here. At large enough modulation amplitudes, and for a detuned cavity, we obtain fully developed polarization chaos, which affects both the ellipticity and the orientation of the polarization ellipse as well as the laser intensity.
A model for a nondegenerate cascade J '' = 0→ J = 1→ J ' = 0 vector laser is presented. It takes into account the two polarization degrees of freedom associated with each of the two laser fields as well as possible constraints in the polarization states imposed by the cavity anisotropies. The cases of cavities with strong and weak anisotropy and perfect isotropy are studied. It is shown that in all cases bimode instabilities can occur independently of the `bad cavity' limit and for small pumping. Stability of the bimode solution is very sensitive to misalignment of the linear cavity anisotropies, to differences in the cavity isotropic losses, and to phase anisotropy. The time-dependent dynamics has been analysed.