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T Ackemann

Publications and source records attributed to T Ackemann.

11 recordsLinked to original sources
PubMed2006

Competition of pattern forming instabilities due to phase front curvature in an optical system.

In this paper we analyze experimentally and theoretically the competition between two pattern forming instabilities in a single mirror feedback scheme with sodium vapor as the nonlinear medium. Two types of structures with different transverse wave numbers are observed experimentally, if the spatial phase modulation of the light field is varied. This phenomenon results from the combination of a nonlinear self-lensing effect on the one hand and of the externally controlled phase front curvature of the light field on the other. A linear stability analysis yields two instabilities whose length scales match quite well the experimental findings. Further analysis reveals the mechanism of length-scale selection in this system and demonstrates the possibly crucial role of phase front curvature in optical pattern formation.

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PubMed2005

Observation of a discrete family of dissipative solitons in a nonlinear optical system.

We report on the observation of a discrete family of spatial dissipative solitons in a simple optical pattern forming system, which is based on a modified single-mirror feedback arrangement. After a pitchfork bifurcation the system possesses two (nearly) equivalent coexisting states of different polarizations. The spatial solitons correspond to excursions from one of the two states serving as a background state towards the other one. The members of the soliton family differ in the number of high-amplitude radial oscillations. The observations are in good agreement with numerical simulations and general expectations for dissipative solitons.

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PubMed2004

Eigenmodes and symmetry selection mechanisms in circular large-aperture vertical-cavity surface-emitting lasers.

The characteristics of the spatial eigenmodes of vertical-cavity surface-emitting lasers with a large circular aperture are considered close to the lasing threshold. Experiments yield patterns based on rotational symmetry ("flowerlike" patterns) or on Cartesian symmetry (stripelike patterns) for very close operating conditions. The former are compatible with the boundary conditions whereas the latter are expected in infinite devices. Theoretically, the problem is considered in the framework of an eigenmode analysis of a linear partial differential equation for the optical field valid at threshold. This formulation allows for a simple implementation of asymmetries due to the reflection properties of Bragg mirrors as well as of transverse variations of gain and refractive index due to the device structure or due to imperfections in the growth process. A sharp transition between flowerlike modes and stripelike modes is shown to occur, if the device aperture is increased.

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PubMed2003

Direct measurement of multiple instability regions via a Fourier filtering method in an optical pattern forming system.

We determine the limits of stability of the homogeneous state of a pattern forming optical system in dependency on the wave number by experimental means. The measurement becomes feasible by adopting a scheme based on a Fourier filtering technique. The system under study is a single-mirror feedback arrangement using sodium vapor as the nonlinear medium. The experiment confirms the existence of multiple instability regions of the homogeneous state expected by theory. The measurements do not agree quantitatively with the marginal stability curve determined by a linear stability analysis of an infinitely extended homogeneous system. We study the system numerically and demonstrate that the results of the simulations for the case of a Gaussian beam can be reproduced by a simple modification of the linear stability analysis which accounts for the finite diameter of the input beam. This explains the wave number dependent systematic deviations between the experiment and the linear stability analysis of the infinitely extended system.

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PubMed2003

Self-organized superlattice patterns with two slightly differing wave numbers.

We report on the observation of superlattices that occur spontaneously in a nonlinear optical system with O(2) symmetry. A secondary bifurcation from hexagons yields patterns formed by twelve wave vectors. Besides irregular patterns these may either be quasiperiodic patterns or superlattices built from two classes of wave vectors differing slightly in their length. Both classes of wave vectors stem from only one pattern-forming instability. The wave vectors fit on a hexagonal or a square grid. In the former case the set of wave vectors can be decomposed into two hexagonal triads, whereas in the case of the square grid squeezed triads occur.

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PubMed2002

Eightfold quasipatterns in an optical pattern-forming system.

Quasipatterns with an eightfold rotational symmetry and irregular two- and three-mode patterns are found in an experiment on optical pattern formation. The patterns exist in the transverse cross section of a laser beam that traverses a system built from a sodium vapor cell and a plane feedback mirror with a quarter-wave plate placed into the feedback loop. The occurrence of the quasipatterns is reproduced by numerical simulations and explained by amplitude equations that contain only odd-order terms and are derived from the microscopic model. The selection process is governed by the angle dependence of the cubic cross coupling coefficients in the amplitude equations. Up to our knowledge it provides the first experimental example for a stabilization mechanism proposed earlier that is based on an oscillatory dependence of the cubic cross coupling coefficient on the angle between the interacting wave vectors. The relationship to the prediction of quasipatterns in a similar setup without additional wave plate [Phys. Rev. A 53, 1072 (1996)] is discussed.

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PubMed2000

Interaction of localized structures in an optical pattern-forming system

We report on the observation and interaction of dissipative localized structures in an optical pattern-forming system. Single localized structures are found to have oscillatory decaying tails originating from diffraction. We observe bound states of two or more constituents. These clusters contain several preferred mutual distances. Numerical simulations show that the corresponding interactions are mediated by the oscillatory tails.

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PubMed2000

Stationary and drifting localized structures near a multiple bifurcation point

Localized states embedded in a patterned background are found in numerical simulations of spontaneous pattern formation in a spin-1/2 atomic system with optical feedback. In the vicinity of a parameter region with bistability between two homogeneous states large amplitude peaks as well as dark holes exist as stable localized states on a hexagonal background. Moreover, resonant interaction between oscillatory and stationary inhomogeneous modes produces a nonstationary background which may force the localized states to drift.

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