Optical Pattern Formation

Introduction

Nonlinear effects occur in many media and in many different configurations. Concerning the medium, we focus on experiments using sodium vapour. The nonlinearity is due to optical pumping. Beside technical advantages (high optical quality, easy variation of parameters over a broad range, high resonant nonlinearity) the benefit of using an atomic vapour is that the equations governing the light-matter interaction can be derived directly from quantum mechanics via the density matrix approach. Regarding the investigated configurations, investigations have been done in most of the situations in which spatial optical structures are known to occur. Since we are interested in the fundamentals, we work in a so-called single-mirror feedback system because of its conceptual simplicity.

Main results

Our experiments yielded:

  1. The first demonstration of a secondary instability of a hexagonal pattern due to a two-dimensional wavevector resonance at sqrt(3) of the original wavenumber.
  2. The first detailed investigation and interpretation of polarization patterns.
  3. The demonstration of intensity spiral and target patterns in a rotationally symmetric system but with a radially varying control parameters.
    (examples on upper row on right; slow motion picture obtained by sampling method)
  4. The demonstration that there is a finite locking range if drifting patterns are to be induced by a tilt of the feedback mirror and its interpretation.
  5. The demonstration of spontaneous quasiperiodic patterns with a twelve and an eight-fold rotational symmetry by a spontaneous breaking of the rotational symmetry.
  6. The demonstration of a new type of a self-organized superlattice.
    (example on lower row on the right; left: real space; right: Fourier space)
  7. A careful analysis of the properties of dissipative solitons, i.e. self-localized structures. In particular, we provided first experimental evidence for the existence of multiple, discrete distances in clusters of dissipative solitons due to interactions via oscillating tails.
  8. The first experimental demonstration of a discrete family of high order dissipative solitons.
  9. The first experimental demonstration of a t^0.5 growth law for the coarsening of domains of equivalent states nested in each other and how these lock to form localized structures.

The experiment is discontinued but some data analysis is ongoing.

People involved with Optical pattern formation

Over the years (1994-2007), many people contributed to the success of these investigations at the University of Muenster (Germany):

  • PI: Thorsten Ackemann, Wulfhard Lange
  • Postdocs: Ramon Herrero, Yuri A. Logvin
  • Postgraduate students: Andreas Aumann, Florian Huneus, Edgar Grosse Westhoff, Matthias Pesch, Burkhard Schaepers, Jens Seipenbusch, Jens Schuettler
  • Undergraduate students: Burghard Berge, Monika Boelscher, Marc Feldmann, Benedikt Giese, Andreas Heuer, Volker Kneise, Daniel Rudolph, Jens-Uwe Schurek, Michael Tegeler

  • Collaborators
    • IMEDEA (Palma de Mallorca): Damia Gomila, Pere Colet
    • University of Strathclyde: Thorsten Ackemann, Willie J. Firth, Gian-Luca Oppo

Funding

We are grateful for funding by the Deutsche Forschungsgemeinschaft and the Deutsche Akademische Austauschdienst.