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Physical Review A

Pattern formation in an alkali-metal vapor with a feedback mirror

Andrew J. Scroggie, W. J. Firth

Published Apr 1, 1996• 38 citations
Publisher

Abstract

We study spontaneous pattern formation in a system consisting of an alkali-metal vapor cell placed in front of a feedback mirror and driven by a vector optical field. Through a combination of linear and nonlinear analysis we are able to predict the formation of squares, rolls, rhomboids, hexagons or ``honeycombs'' for appropriate parameter values. Our predictions are confirmed by numerical integration of the model equations. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.2752

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We study spontaneous pattern formation in a system consisting of an alkali-metal vapor cell placed in front of a feedback mirror and driven by a vector optical field. Through a combination of linear and nonlinear analysis we are able to predict the formation of squares, rolls, rhomboids, hexagons or ``honeycombs'' for appropriate parameter values. Our predictions are confirmed by numerical integration of the model equations. \textcopyright{} 1996 The American Physical Society.
The development of spontaneous stationary equilibrium patterns induced by the injection of a laser pump field into a purely absorptive two-level atomic sodium vapour ring cavity is investigated by means of various weakly non-linear stability analyses applied to the appropriate governing evolution equation for this optical phenomenon. In the quasi-equilibrium limit for its atomic variables, the mathematical system modelling that phenomenon can be reduced to a single modified Swift–Hohenberg non-linear partial differential time-evolution equation describing the intracavity field on an unbounded 2D spatial domain. Diffraction of radiation can induce transverse patterns consisting of stripes, squares and hexagonal arrays of bright spots or honeycombs in an initially uniform plane-wave configuration. Then, these theoretical predictions are compared with both relevant experimental evidence and existing numerical simulations from some recent non-linear optical pattern formation studies.
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.
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.
We study the selection between hexagonal and square polarization patterns in a sodium vapour cell with optical feedback provided by a single mirror. Scanning an external magnetic field, a transition sequence from squares via negative hexagons, squares, and positive hexagons again to squares is observed close to the instability onset. Well above threshold the hexagons give way to squares in a secondary bifurcation. These observations demonstrate how the macroscopic symmetries of optical patterns can be controlled by manipulating the microscopic symmetries of the light-matter interaction. The key to this control is the vectorial degrees of freedom of the optical pattern-forming system.