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Topical Meeting on Optical Bistability (OB)

Polarization Switching with J = 1 2 to J = 1 2 Atoms in a Ring Cavity

Weston J. Sandle, M. W. Hamilton, R. J. Ballagh

Published Jan 1, 1983• 1 citation
Publisher

Abstract

This paper reports a steady-state theory for the polarization behaviour1 of the output of a ring optical cavity that contains a vapour of atoms with a driven J = 1 2 to J = 1 2 transition. The input laser radiation may have arbitrary polarization and detuning. We have extended a previously reported theory2 (which includes analytic results for zero detuning of the incident laser and zero magnetic field) to include detunings and magnetic fields.

DOI
10.1364/obi.1983.thb24

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This paper reports a steady-state theory for the polarization behaviour1 of the output of a ring optical cavity that contains a vapour of atoms with a driven J = 1 2 to J = 1 2 transition. The input laser radiation may have arbitrary polarization and detuning. We have extended a previously reported theory2 (which includes analytic results for zero detuning of the incident laser and zero magnetic field) to include detunings and magnetic fields.
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.
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.
Results are given of an experiment which demonstrates switching of the polarization state of the output of a near-concentric Fabry-Perot containing sodium vapour, excited via the homogeneously broadened Dl transition. An example of the output, for linearly polarized laser input, at 1.5 GHz below line center shows switching with hysteresis at high input power (approximately 400 mW) due to saturation, as well as the switching at lower power (approximately mW) due to optical pumping effects. Purely absorptive polarization switching at approximately 50 mW input power was observed. Polarization switching has been predicted in the context of three state atoms in an optical cavity, and the lower power switchin has been previously observed using the inhomogeneously broadened Dl transition of sodium in a Fabry-Perot with the laser detuned above line center. By using argon buffer gas at up to 100 torr, importance of hyperfine structure and inhomogeneous broadening was reduced so as to make the transition approximate a J + 1/2 to J - 1/2 transition.
Experiments on the steady-state, nonlinear behavior of the 7F1^{7}\mathrm{F}_{1}7F1​${\mathrm{\ensuremath{-}}}^{7}$F0o{\mathrm{F}}_{0}^{\mathrm{o}}F0o​ 570.68-nm transition of atomic samarium in a laser-driven, near-concentric Fabry-Perot cavity are reported. For zero applied magnetic field, only simple optical bistability, symmetric in both ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\mathrm{\ensuremath{-}}}$ transmitted polarizations, is observed for a linearly polarized excitation beam. However, for a magnetic field applied parallel to the propagation direction, polarization-sensitive switching appears, with lowest power threshold near the edge of the Doppler-broadened region. Subsidiary measurements of atomic parameters are also given to enable the transition to be experimentally well characterized.