W. Lange

Phase singularities via nonlinear beam propagation in sodium vapor

Abstract The creation of phase singularities in a nonlinear optical system without feedback is observed experimentally after a singlepass of a focused laser beam through a high-density sodium vapor. Their appearance is reproduced in a numerical model which allows for a slight astigmatism of the incoming beam and can be qualitatively understood by the astigmatic deformation of the phase fronts, to first order by means of self-induced astigmatic lensing. Alternatively, the phase singularities can be interpreted to result from the interference of symmetry broken modes whose mutual phases are determined by the astigmatic lens.

Investigations of pattern forming mechanisms by Fourier filtering: properties of hexagons and the transition to stripes in an anisotropic system

The properties of patterns in an anisotropic system are studied experimentally and numerically in an optical pattern forming system with single-mirror feedback. A controlled anisotropy is introduced by a slit filter in Fourier space. If the slit width is reduced, a transition between hexagons and stripes via nonequilateral hexagons and rhomboids is observed. The scenario is reproduced in numerical simulations. The bifurcation to stripes is found to be supercritical whereas the one to hexagons is subcritical in accordance with expectation. The results illustrate the potential of Fourier filtering as a tool for investigating mechanisms of pattern formation.

Robust control of switching of localized structures and its dynamics in a single-mirror feedback scheme

Experimental results of a study of the switching dynamics of bistable localized states in a single-mirror feedback system with sodium vapor as the nonlinear medium are presented. The type of switching (on or off) is determined by the polarization state of the addressing beam, which gives a robust—because it is phase insensitive—way of controlling the direction of switching. Critical and noncritical slowing down are demonstrated.

Spontaneous optical patterns in an atomic vapor: observation and simulation

Abstract Optical pattern formation in an experiment with single mirror feedback is described. The nonlinear medium is sodium vapor in a buffer gas atmosphere. A microscopic model is given and a stability analysis and numerical simulations are performed. Good agreement between the results of the experiment and the simulation is obtained. By numerical treatment of the model for the case of a plane incident wave (large aspect ratio), the results obtained with a narrow Gaussian beam (small aspect ratio) are traced back to the transition from hexagon to roll formation via ‘mixed’ states.

Polarization degrees of freedom in optical pattern forming systems : alkali metal vapour in a single-mirror arrangement

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.

Characteristics and possible applications of localized structures in an optical pattern forming system

We report on the observation of dissipative localized structures in an optical pattern-forming system. After an experimental and theoretical analysis of the mechanism which stabilizes these structures we focus on the demonstration of possible applications of localized structures for information processing.

TRANSITION TO SPATIOTEMPORALLY IRREGULAR STATES IN A SINGLE-MIRROR FEEDBACK SYSTEM

In an optical pattern forming system (sodium vapor with feedback from a single plane mirror) different scenarios for the destabilization of stationary patterns in favor of states that are irregular in space and in time are studied experimentally and numerically. Secondary bifurcations from hexagons to squares occur via a time dependent state whose origin is traced back to noise-driven hexagon–square competition in a region of bistability between the two states. Squares can display a transition to another state with irregular — probably intrinsic — time dependence in which a whole band of wave vectors is excited. In real space pentagons are a prominent feature.

Pattern formation in the presence of an intrinsic polarization instability

The interaction of pattern formation with an intrinsic polarization instability is studied in a modified single feedback mirror experiment. We report on hexagonal patterns in an inversion symmetric system which occur due to a symmetry-breaking polarization instability and on domain patterns which are stabilized by the modulational instability. For parameter values for which no symmetry breaking bifurcation occurs, we observe rhombic and triangular patterns.

Fabry-Pérot and ring cavity configurations and transverse optical patterns

Abstract The properties of travelling- and standing-wave resonators and their influence on the modal composition and propagation of transverse patterns are analysed and a prescription for constructing a travelling-wave resonator ‘equivalent’ to a standing-wave resonator is given. It is shown that the presence of an intracavity nonlinear medium invalidates the equivalence between the two kinds of cavity, even when the interference between the counterpropagating waves can be neglected. Therefore great care has to be taken when comparing experimental and theoretical results obtained in different types of cavity, since in general their properties differ. Some implications concerning the appearance of phase singularities in the two kinds of resonator are discussed.

INTERPLAY OF DISPERSION AND ABSORPTION IN A NEW OPTICAL PATTERN-FORMING SYSTEM

We present a new experimental optical pattern-forming system that allows a continuous transition from the purely dispersive to the purely absorptive limiting case. This system is based on a single feedback mirror arrangement with an alkaline vapour and a polarization changing element inside the feedback loop. We present a microscopic model for this system that accounts for both absorption and dispersion and successfully describes the observed phenomena by means of a linear stability analysis.