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Optics Letters

Full polarization chaos in a pump-polarization modulated isotropic cavity laser

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

Published Dec 1, 1995• 18 citations
Publisher

Abstract

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.

DOI
10.1364/ol.20.002390

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Multistability, self-Oscillation and Chaos in Nonlinear Optics

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We describe a system comprising two circularly polarized ring-cavity modes coupled via a J=½ to J=½ transition. Both modes are equally excited by a linearly polarized incident laser. The steady-state transmission of the cavity shows optical tristability and polarization switching as predicted by Kitano et al.(1) and recently observed.(2) We generalise the model of Kitano et al. with the inclusion of saturation and absorption. In addition to optical tristability we find quadrastability (four stable output configurations for the same input intensity), self-oscillation, and chaos.(3) We have studied the chaotic region numerically as the incident laser intensity and the detuning of the cavity modes is varied. The routes to chaos appear to be analogous to those in the Lorenz equations. For a decreasing incident intensity the passage to chaos involves a new period doubling sequence of periodic windows embedded in chaos, where in each periodic window conventional period-doubling of the Feigenbaum type is observed. We have estimated the experimental parameters required to observe chaos in this system and find that power requirements are modest, although the limitations imposed by the adiabatic elimination and single-mode assumptions used in our theory cause some difficulties -- chaos may well remain, however, when these theoretical restrictions are relaxed.

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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.
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.
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.
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 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.
We consider the statistical properties of the fluctuations in the orientation of the vector laser field for a nearly isotropic laser, addressing the competition between the randomizing influence of noise and the preference for linearly or circularly polarized emission induced by saturation in the laser medium and/or cavity anisotropies. We describe, through a nonperturbative analysis, a crossover regime from diffusion-induced polarization-isotropic emission to emission of nearly fixed polarization characteristics. In this crossover the linewidth of intensity fluctuations associated with one of the circularly polarized components of the vector field amplitude changes from decreasing to increasing with output power. This behavior can be expressed in terms of a single parameter that measures the pump or the total output intensity in terms of the ratio of the noise amplitude to the degree of cross saturation of the amplitudes of the circularly polarized components of the vector field amplitude. Analytical results are given for the linewidth of the intensity fluctuations. When the laser has a preference for linearly polarized emission, there is a weakly non-Lorentzian spectrum in the crossover region. When the laser has a ``preference'' for circularly polarized emission the crossover regime is characterized by a non-Lorentzian spectrum due to fast hopping between two circularly polarized eigenstates. We also describe ellipticity fluctuations induced by the diffusion of the direction of the main axis of the polarization ellipse in the presence of cavity birefringence.
We describe a system comprising two circularly polarized ring-cavity modes coupled via a J=½ to J=½ transition. Both modes are equally excited by a linearly polarized incident laser. The steady-state transmission of the cavity shows optical tristability and polarization switching as predicted by Kitano et al.(1) and recently observed.(2) We generalise the model of Kitano et al. with the inclusion of saturation and absorption. In addition to optical tristability we find quadrastability (four stable output configurations for the same input intensity), self-oscillation, and chaos.(3) We have studied the chaotic region numerically as the incident laser intensity and the detuning of the cavity modes is varied. The routes to chaos appear to be analogous to those in the Lorenz equations. For a decreasing incident intensity the passage to chaos involves a new period doubling sequence of periodic windows embedded in chaos, where in each periodic window conventional period-doubling of the Feigenbaum type is observed. We have estimated the experimental parameters required to observe chaos in this system and find that power requirements are modest, although the limitations imposed by the adiabatic elimination and single-mode assumptions used in our theory cause some difficulties -- chaos may well remain, however, when these theoretical restrictions are relaxed.