2005 European Quantum Electronics Conference

Intensity spiral patterns in a semiconductor microresonatorYe. Larionova', 0. Egorov2, E. Cabrera-Granado3, A. Esteban-Martin4, C.O. Weiss'

'Physikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germanyyevgeniya.Iarionova@ptb.de

2 Institutffir Festkorpertheorie und Theoretische Optik Friedrich-Schiller Universitat, Jena, D-07743, Germany3Dpto. Optica, Facultad de C. C. Fisicas, Universidad Complutense, 28040 Madrid, Spain

JDepartament D'Optica, Universitat de Valencia, Vakncia, Spain

Spiral waves appear frequently in nature. In contrast to chemical and hydrodynamic processes where the field amplitudeexhibits the spiral patterns (intensity spirals), in optics the spiral structures relate generally to the phase structure of theoptical field (so called "optical vortices"). Thus the question arises whether amplitude spiral patterns can exist also inoptics.

In [1] it was theoretically predicted that at least in one optical system (using a homogeneous field with planewave fronts), the internally pumped optical parametric oscillator, intensity spiral patterns could exist. The prediction [6]has not yet been demonstrated in an optical experiment. However, the existence of spiral patterns was shown for a caseof relaxed requirements [2]. Spiral pattems are supported there by the intensity distribution of the excitation.

We show here another case of spiral pattern existence with relaxed requirements, namely, both the intensity- andthe phase structure of the exciting light field imposed externally, support stable amplitude spiral patterns.

The semiconductor resonator used for the experiments consists of flat Bragg mirrors of about 99.8% reflectivity,with 18 GaAs/GaosAlosAs quantum wells between them. The optical resonator length is about 3 pm so that a Fresnelnumber of several 100 is excited, sufficient for complex structure to form. A phase gradient of the incident Gaussianbeam was imposed by shifting the resonator sample by several 100 pm beyond the beam waist after the focusing lens. Inthis case the beam waist is between the lens and the sample, and the Gaussian beam on the sample surface has a wavefront curvature (which we define as positive). Fig. la shows typical snapshot of intensity spiral patterns observed in thetransverse intensity profile of the reflected light beam. The spirals have one arm and occur left- and right- handed. Thespiral patterns form spontaneously from spot-stripe structures in the switched area during the illumination. During theillumination time the spirals are formed, changed and destroyed influenced by heating of the semiconductor materialleading to the change in the semiconductor cavity detuning.

. || t 50_- _~~~~~~~5

xa b

Fig.l. The spiral patterns a) observed experimentally (Beam FWHM is 60 gm, X =878 nm, 1=18 kW/cm2, 600pm beyond the beam waist), b) calculated theoretically (Beam FWHM is 400 pm, radius of phase front Rph=100 pm).

In simulations a phenomenological semiconductor resonator model with spiral initial conditions and a wideGaussian-shaped input beam was used. In a wide range of wavelengths corresponding to dispersive and absorptivenonlinearities, intensity spirals are found stable, qualitatively similar to the experimental structures (Fig.1b). Thesimulations show a rotation of the spiral patterns. The rotation period is of the order of microseconds and the speed ofrotation, among other parameter dependences, is found to be inversely proportional to the radius of wave frontcurvature. The reason why in the experiment we could not see a clear rotation of spirals is discussed. The spirals arefound, experimentally and theoretically, to exist only for a certain range of wave front curvature. Influence of bothamplitude and phase gradient distributions on the existence range of spiral patterns are investigated in details.Experimental search for free (soliton-like) spirals as predicted in [I] is foreseen.

References:1. P. Lodahl, M. Bache, M. Saffman: Phys. Rev. Lett. 85,4506 (2000)2. F. Huneus, B. Schiipers, T. Ackemann, and W. Lange, AppI. Phys. B 76, 191-197 (2003)

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