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Nonlinear optics and quantum optics
Institute of Applied Physics
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Intrinsic dynamics: spirals and target patterns


In the field of pattern formation wide spread structures are spirals and target patterns. They can be found in aggregation clusters of the slime mold Dictyostelium discoideum, in waves of electric activity of myocardic tissue, in an experiment considering Rayleigh-Bénard-convection and last but not least in the concentration of chemical species in chemical reactions, e.g. the Belousov-Zhabotinsky-reaction.

In our group an experiment concerning pattern formation in nonlinear transverse optics is investigated which uses a so-called single mirror feedback scheme with sodium vapor in a buffer gas atmosphere as nonlinear medium. At appropriate experimental parameters this system shows  rotating spirals and drifting target patterns in the transverse intensity profile of the laser beam.

    

The spirals can have a varying number of arms each in form of an archimedian spiral. Surprisingly these structures are observed rotating in both directions, clockwise and anticlockwise.

        

        

A mutual feature of these dynamic patterns, the various spirals as well as the target patterns, is the intensity of a point in the transverse plane showing an oscillating behavior in time.  Frequency of oscillation can be varied according to experimental parameters in a wide range (from tens of kHz up to hundreds of kHz). The intensity oszillation is due to a hopf bifurcation existing in the system. this originates from the interaction of the magnetic moment of the sodium atoms with an external oblique magnetic field.

Furthermore, spirals and target patterns possess -as indicated by the animated GIFs above- a radial motion of maxima and minima of intensity, which direction points towards the center of the structure. This motion is in contrast to nearly every other known pattern forming system in which motion of spirals and target patterns is directed from center towards the edge. According to first investigations radial inhomogenities evoked by the gaussian profile of the pump beam lead to a directed radial motion in the structures.  In a plane wave the Hopf bifurcation would give rise to "winking hexagons" (AVI movie).

Some of the presently investigated aspects are:
a more quantitativ description,
the mechanisms of selection between spirals and target patterns, the directions of rotation, the numbers of spiral arms and
the interaction between spirals and target patterns and other structures, e.g. localized structures.

The theoretical description of the interaction between light and sodium atoms is based on an established semi-classical, microscopic model. Both analytic as well as numeric calculations are employed in the interpretation of the experimental observations. Results of the preliminary theoretic investigation are in good agreement with the observed properties of spirals and target patterns.


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AG Lange & Ackemann
Institut für Angewandte Physik · Universität Münster Corrensstr. 2/4 · 48149 Münster