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Journal of Modern Optics

Dynamics of a Gain Anisotropic Optically Pumped Laser with Arbitrary Angle Between Linear Polarizations of Pump and Laser Fields

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

Published Nov 1, 1995• 10 citations
Publisher

Abstract

The dynamic behaviour of an optically pumped J = 0 ↔ J = 1 ↔ J = 0 laser for any arbitrary value of the relative orientation angle between the linear polarizations of the pump and laser fields is analysed. By changing this angle, the steady states show a smooth monotonic variation, but the dynamic states undergo a complex sequence of bifurcations, including a generalized class of type-I intermittency that leads to the glueing of attractors. Small variations in the polarization angle bring about structural attractor modifications as large as those produced by large variations in the pump intensity.

DOI
10.1080/09500349514551991

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The dynamic behaviour of an optically pumped J = 0 ↔ J = 1 ↔ J = 0 laser for any arbitrary value of the relative orientation angle between the linear polarizations of the pump and laser fields is analysed. By changing this angle, the steady states show a smooth monotonic variation, but the dynamic states undergo a complex sequence of bifurcations, including a generalized class of type-I intermittency that leads to the glueing of attractors. Small variations in the polarization angle bring about structural attractor modifications as large as those produced by large variations in the pump intensity.
We have carried out a series of numerical experiments on the dynamic behavior of J=0 yields J=1 yields J=0 lasers optically pumped by a linearly polarized laser field and operating either: (1) with a strongly anisotropic cavity yielding fixed linear laser field polarization at any angle (theta) with that of the pump beam, or (2) with an isotropic cavity and an axial magnetic field. In the first case (1) we show that by changing (theta) the steady-states experience a smooth monotonic variation, but the dynamic states undergo a complex sequence of bifurcations. In case (2) we find that the laser field is always linearly polarized, but for some parameter settings we report the first observation that the plane of polarization together with the laser intensity change chaotically.
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.
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.
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.