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Physical Review A

Quasipatterns in a polarization instability

Dominique Leduc, Martine Le Berre, Elisabeth Ressayre, Andree A. Tallet

Published Feb 1, 1996• 26 citations
Publisher

Abstract

The nonlinear analysis of the model equation for the single-feedback-mirror device with rubidium atoms predicts that a stable quasipattern of eightfold orientational order occurs in the profile of the output light beam. This pattern is numerically reproduced for different transverse shapes, either rhombohedric or circular, of the input beam. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.1072

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The nonlinear analysis of the model equation for the single-feedback-mirror device with rubidium atoms predicts that a stable quasipattern of eightfold orientational order occurs in the profile of the output light beam. This pattern is numerically reproduced for different transverse shapes, either rhombohedric or circular, of the input beam. \textcopyright{} 1996 The American Physical Society.
The occurrence of polarization instabilities in alkaline vapours and their coupling with spatial degrees of freedom are considered. We discuss experiments in which a laser beam is transmitted through a vapour cell without external feedback or with feedback by a single mirror. In both cases a lateral separation of the light field into domains of orthogonal circular polarization is found. Without feedback, relatively simple structures like rings or two spots are obtained. With feedback, more complicated polarization patterns result from spontaneous symmetry breaking. We emphasize the crucial role of the polarization ellipticity of the input beam. Changing this control parameter we observe a transition from positive to negative hexagons in one of the circular polarization components, while simultaneously the opposite transition occurs in the other one. The transition is mediated by square patterns occurring for linear input polarization. This metamorphosis is governed by symmetry principles and therefore provides an example of the ease of influencing the symmetry properties of systems consisting of multilevel atoms interacting with a vector light field.
The use of polarization degrees of freedom in optimizing the conditions for optical pattern formation is investigated by discussing the particular example of single-mirror feedback systems. It is demonstrated that in a quasi-scalar saturable medium pattern formation may be completely suppressed by the interplay of saturation and diffusion. This effect takes place for the optical pumping nonlinearity between Zeeman ground states in alkaline vapour cells. It is shown that these limitations can be circumvented by introducing additional polarization components either in the input beam or in the feedback beam. The latter is achieved by introducing polarization-changing elements such as a quarter-wave plate in the feedback loop. In the optimized scheme, pattern formation is obtained with rather low thresholds. Thus, investigations with a rather high aspect ratio and far beyond threshold become feasible.
Spatiotemporal instabilities of a single-feedback-mirror device are investigated with the help of the linear stability analysis of the stationary regime for a saturable medium that has a complex nonlinear susceptibility; the outcome is compared with experimental results. The first striking result of the analysis is the occurrence of an oscillation with a period nearly twice the round-trip time, regardless of its value with respect to the atomic linewidth for given physical situations, when only longitudinal grating effects are considered. This result cannot be interpreted as a pure phase-conjugate resonator operation, which is expected to occur only when transverse grating effects are included. When such effects are included, the second striking feature is the prediction of the spontaneous breaking of the revolution symmetry; symmetry is broken by rotating light spots, with an instability threshold that depends on the number of spots; this prediction agrees with experiment.
A transverse optical bistability would not occur with a plane-wave input; it is characterized by pronounced changes in transverse profiles, but not in total transmission.1 The systems studied here consist of a single feedback mirror and a nonlinear medium (Na vapor) sufficiently thin that diffraction is negligible during the nonlinear radially dependent phase encoding. With the input focused beyond (before) the Na and the mirror center of curvature on the input (output) side of the Na, self-defocusing (self-focusing) optical bistability is seen--but only when the feedback is nonconcentric, i.e., the feedback beam is displaced off-axis relative to the input beam. If cylindrical lenses are used to form an elongated focus in the Na, bistability is still seen. This suggests that one-transverse-dimension (ID) theories may be adequate to describe the system's steady-state and transient behavior. ID numerical simulations with nonconcentric feedback are under way.