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.
 List of publications
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