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The rapidly developing field of optomechanics aims at the combined control of optical and mechanical modes. In cold atoms, the spontaneous emergence of spatial structures due to optomechanical back-action has been observed in one dimension in optical cavities or highly anisotropic samples. Extensions to higher dimensions that aim to exploit multimode configurations have been suggested theoretically. Here, we describe a simple experiment with many spatial degrees of freedom, in which two continuous symmetries-rotation and translation in the plane orthogonal to a pump beam axis-are spontaneously broken. We observe the simultaneous long-range spatial structuring (with hexagonal symmetry) of the density of a cold atomic cloud and of the pump optical field, with adjustable length scale. Being based on coherent phenomena (diffraction and the dipole force), this scheme can potentially be extended to quantum degenerate gases. [ABSTRACT FROM AUTHOR]

The process of switching on bistable spatial dissipative solitons in a VCSEL with frequency selective feedback is analyzed experimentally and theoretically. Two regimes of successful writing of spatial solitons with an external pulse are identified: for short durations of the writing beam pulse, the input amplitude has to increase, while for longer durations, the input amplitude can remain constant. Switch on spectrograms of the frequency spectrum show a transient dynamics over many modes of the external cavity with a drift of the central frequency from higher to lower frequency. Such a multi-mode regime is almost independent of the frequency of the writing beam. It is interpreted to be due to the existence of multiple unstable solitons with different frequencies which channel the transient dynamics. Good agreement between experimental results and numerical simulations in both the time and frequency domains is found. [ABSTRACT FROM AUTHOR]

It is shown that the ‘flower-like’ emission patterns along the perimeter of broad-area circular vertical-cavity surface-emitting lasers can be interpreted in a first approximation as annular standing waves. Their modulation period follows the dispersion relation of tilted plane waves for a plano-planar cavity. For high enough divergence angle, they show a very peculiar polarization behavior of radial polarization in near field and azimuthal polarization in far field. The polarization selection is qualitatively explained by the breaking of the isotropy between s- and p-components for waves propagating off axis in the Bragg reflectors. [ABSTRACT FROM AUTHOR]

The coherence of broad-area laser diodes with quantum dot gain medium is improved by frequency-selective feedback. A linewidth of 5–10 GHz at power levels of 10–140 mW is achieved in the wavelength region around 1240 nm, where no other good semiconductor lasers are available. The tuning range is at least 20 nm. [ABSTRACT FROM AUTHOR]

We present an experimental study of nonlinear lensing of near-resonant light by a cloud of laser-cooled rubidium atoms, specifically aimed at understanding the role of the interaction time between the light and the atomic vapor. We identify four different nonlinear mechanisms, each associated with a different time constant: electronic nonlinearity, Zeeman optical pumping, hyperfine optical pumping and radiation pressure. Our observations can be quite accurately reproduced using a simple rate equation model which allows for a straightforward discussion of the various effects. The results are important for planning more refined experiments on transverse nonlinear optics and self-organization in samples of cold atoms. [ABSTRACT FROM AUTHOR]

The length-scale selection in complex emission patterns spontaneously arising in broad-area vertical-cavity surface-emitting lasers is studied experimentally. The wavenumbers of individual tilted wave modes show a square-root-like dependence on the detuning between emission frequency and longitudinal cavity resonance, in accordance with theoretical expectations. The absolute values of the wavenumbers are in good qualitative agreement with calculations taking into account the reflection properties of the Bragg reflectors and dispersion. [ABSTRACT FROM AUTHOR]

We investigate the response of a system far from equilibrium close to an oscillatory instability to the induction of phase singularities. We base our investigation on a numerical treatment of the complex Ginzburg–Landau equation (CGLE) in two spatial dimensions, which is considered as an order-parameter equation for lasers and other nonlinear optical systems. Defects are randomly generated by a spatially modulated linear growth rate. In the amplitude-turbulent regime, no qualitative change of behaviour can be detected. Phase-turbulent patterns emerging due to the Benjamin–Feir instability are destroyed by the externally injected defects. One observes either states consisting of spiral structures of various sizes which resemble the vortex glass states of the unperturbed system or a travelling wave pattern containing moving topological defects. In parameter space, both states are separated by a well-defined phase boundary which is close to the line separating convectively from absolutely stable travelling waves. [ABSTRACT FROM AUTHOR]

The dynamics of vertical-cavity surface-emitting lasers with isotropic optical feedback from a distant reflector is studied experimentally and numerically. Low-frequency fluctuations with sudden drop-outs of power are found to be qualitatively independent of the amount of excitation of the second polarization component. The latter is shown to be controlled to a great extent by the intrinsic dichroism of the solitary laser. The experimental findings are in very good qualitative agreement with simulations. The characteristic features of a doublet in the radio-frequency spectra around the external-cavity round-trip frequency are discussed. [ABSTRACT FROM AUTHOR]

First experimental investigations are reported on nonlinear beam shaping due to the interaction between an intense laser beam and a cloud of laser cooled rubidium atoms. Resonant excitation of the F = 3 ↔ F' = 4 hyperfine transition is considered. The single-pass interaction through the cold vapor causes an increase in the laser beam intensity in the forward direction (zero transverse wavevector component) when observed in Fourier space, for sufficiently high values of saturation. A qualitative explanation of the observations based on a two-level model for a resonantly excited transition proves acceptable. The observations are compatible with an interpretation based on nonlinear index-induced focusing of an incident beam with curved wavefront, as is used in z-sean measurements. Simple physical considerations allow us to deduce the conditions for the observability of optical patterns in the beam transmitted by a cold atomic cloud. [ABSTRACT FROM AUTHOR]

Spatio-temporal structures with a regular time dependence are observed in a nonlinear optical system consisting of a sodium-vapour cell and a single feedback mirror. Target and spiral patterns appear spontaneously in the intensity of the transmitted light field as a result of a self-organisation process. In contrast to the results obtained in most other pattern-forming systems, the radial motion of the waves is directed towards the centre. The emergence of oscillatory structures is traced back to a Hopf bifurcation at a finite wave number. The preference for a radial drift motion is due to a nonlinear guiding effect which results from phase gradients created by the inhomogeneous pump profile. The direction of the drift can be reversed by externally applied phase gradients. The system is a striking example of a case in which the radial variation of the pump profile has a decisive influence on pattern formation. [ABSTRACT FROM AUTHOR]

Abstract. The phenomena in optical pattern formation am reviewed using a single mirror feedback experiment as an example. The nonlinear medium is sodium metal vapor. We discuss the mechanism responsible for the spontaneous formation of spatial structures and the selection between simple periodic patterns as hexagons and squares. Introducing a polarization changing element in the feedback loop, quasiperiodic patterns with a twelve-fold rotational symmetry are obtained and their properties are studied by filtering methods in Fourier space. Finally, we discuss the formation of localized states as spatial solitons due to a self-induced lensing effect. Their interaction is studied and the formation of clusters provides a link between localized states and extended patterns. Genuine optical features, such as the polarization degrees of freedom, the experimental accessibility of the Fourier space, and the possibility to control the optical susceptibility of atomic vapors by means of an external magnetic field, provide very powerful tools for investigating the principles of pattern formation. [ABSTRACT FROM AUTHOR]

Cold atom setups are now commonly employed in simulations of condensed matter phenomena. We present an approach to induce strong magnetic interactions between atoms on a self-organized lattice using diffraction of light. Diffractive propagation of structured light fields leads to an exchange between phase and amplitude modulated planes which can be used to couple atomic degrees of freedom via optical pumping nonlinearities. In the experiment a cold cloud of Rb atoms placed near a retro-reflecting mirror is driven by a detuned pump laser. We demonstrate spontaneous magnetic ordering in the Zeeman sublevels of the atomic ground state: anti-ferromagnetic structures on a square lattice and ferrimagnetic structures on a hexagonal lattice in zero and a weak longitudinal magnetic field, respectively. The ordered state is destroyed by a transverse magnetic field via coherent dynamics. A connection to the transverse (quantum) Ising model is drawn. Cold and ultracold atomic gases can be used as simulators in order to analyse classical and quantum features of exotic magnetic phenomena. By applying an external magnetic field to a cold atomic gas in a self-organised optical lattice the authors demonstrate transitions between different magnetic phases via optically mediated spin-spin interactions. [ABSTRACT FROM AUTHOR]

A letter to the editor is presented which discusses a study by researcher M. Sich and colleagues of the presence of bright polariton solitons in semiconductor microcavities.

A correction to the article "Switching spatial dissipative solitons in a VCSEL with frequency selective feedback," is presented.