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Journal of Optics B Quantum and Semiclassical Optics

Nonlinear behaviour of a cascadeJ''= 0→J= 1→J' = 0 vector laser

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

Published Apr 1, 2001• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1464-4266/3/2/374

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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.
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 000 and 1.1.1. 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 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 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 emission of a resonant nondegenerate cascade laser in which up to two fields can be simultaneously amplified inside a cavity is theoretically investigated. Each field is resonantly coupled with one of the transitions of a ladder three-level atomic system, in conditions of homogeneous broadening. General analytical expressions for zero-, one-, and two-field solutions are given. Cooperative emission between both fields is found. Through the linear stability analysis of these solutions we obtain phase diagrams showing their respective domains of stability. Together with the existence of Hopf bifurcations associated with one-photon processes, which coincide with those of a Lorenz-Haken laser, a genuine Hopf bifurcation due to two-photon processes has been found. This last bifurcation does not require the ``bad cavity'' nor the ``Lorenz threshold'' conditions. The stability of the orbits that bifurcate from these critical points is analytically investigated. For this we have rewritten one of the standard criteria in a useful and straightforward way. Finally, the dynamic regimes exhibited by the system well above the instability thresholds is numerically investigated revealing transitions to chaos via quasiperiodicity.
A cascade laser model based on a J = 0 M J = 1 M J = 0 ladder atomic-level scheme is proposed. The cases of relative parallel and orthogonal linear field polarizations are studied. The parallel configuration reduces to a three-level cascade laser model in the limit of minimal Zeeman-coherence relaxation rate. Contrarily, the absence of two-photon processes in the orthogonal configuration makes this case equivalent to a pair of incoherently coupled two-level laser models. The stability properties and dynamic behaviour of the orthogonal configuration are analysed.
A theoretical treatment is given of the dynamical and steady-state behavior of an anisotropic laser. The model is based on a homogeneously broadened, pumped J=1/2\ensuremath{\leftrightarrows}J=1/2 atomic transition, and is solved to all orders of the electric field, in contrast to previous studies of anisotropic lasers. A survey of the system behavior is presented, and complementary analytic descriptions developed to describe the small- and large-field evolutions are given. The small-field polarization behavior is shown to be oscillatory in general, and dominated by the properties of the cavity. The large-field description allows the polarization stability of the final output states to be analyzed, and shows that stable steady states in this regime must be linearly polarized along either one or the other of the two anisotropy axes. The possible range of cavity lengths which allows bistable output between these two polarizations is characterized analytically, and a regime identified where the polarization undergoes sustained oscillation.