Eur. Phys. J. D 59, 133–137 (2010) DOI: 10.1140/epjd/e2010-00091-x Regular Article T HE EUROPEAN P HYSICAL JOURNAL D Boundary-induced localized structures in a nonlinear optical feedback experiment M. Ayoub 1, a , F. Papoff 2 , G.L. Oppo 2 , and C. Denz 1 1 Institute of Applied Physics and Center for Nonlinear Science, Westf¨alische Wilhelms-Universit¨at M¨ unster, Corrensstr. 2/4, 48149 M¨ unster, Germany 2 Institute of Complex Systems, SUPA and Department of Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, Scotland, UK Received 6 January 2010 Published online 6 April 2010 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2010 Abstract. Experimental and numerical evidence of symmetry-breaking bifurcations of a circular dissipative soliton with additional boundary conditions in the feedback of a liquid crystal light valve are reported. By tuning the strength of the nonlinearity or the size of the additional boundaries, the circular structure breaks up into polygonal symmetries and the system exhibits multistability. The experimental results are confirmed by numerical simulations with different configurations of the polarizers thus demonstrating the universality of the phenomenon. 1 Introduction The existence of dissipative localized structures in opti- cal cavities, also known as cavity solitons, is well-known for many nonlinear photonic devices driven far from an equilibrium state [1]. Dissipative solitons are static or dy- namical localized objects that experience gain and loss of their energy during the propagation. They can form where the overall gain, loss and diffraction are balanced [1,2]. In optical systems they have been observed in active and passive optical cavities, but also in single mirror feedback experiments with different optical nonlinearities [1,3–6]. Formation of dissipative localized structures is combined, in general, with an organized nonlinear behavior such as optical bistability. Due to bistability, dissipative solitons have binary features and a robust spatial shape based on the balance of diffraction and nonlinearity, allowing one to control and guide them easily in intensity and phase gra- dients [7–10]. This latter fact can be attractive for applica- tions in the context of all optical information processing where solitary structures are used as ‘optical bits’ [3,7]. Systems based on liquid crystal light valves (LCLV) dis- play a rich set of different spatial structures such as regu- lar patterns (hexagons, negative hexagons, rolls), spatio- temporal chaos, and localized structures [11,12]. Spatially localized structures in LCLV mainly exist in the range of optical bistability [11] and can have circular or other reduced symmetries. Different symmetries may coexist in the same system, due to the breaking of the rotational symmetry for certain ranges of control parameters. In these cases, triangular symmetry of localized states has a e-mail: ayoubm@uni-muenster.de been observed [13] and accompanied by the appearance of phase singularities [14]. Here we investigate, both ex- perimentally and numerically, the breaking of the circular symmetry of localized states with the aim of explaining bi- furcations to symmetries that are more complex than the triangular one when imposing boundary limitations and choosing a suitable control parameter range. These novel localized states with peculiar symmetries may be used as multi-state pixels in nonlinear optical information process- ing and allow a considerable increase in storage capacity of ‘optical bits’ with respect to the standard localized state of circular symmetry. 2 Experimental set-up and theoretical model Experimentally, the Kerr medium used is a reflective LCLV used as a hybrid nonlinear element placed in a feed- back loop. LCLV, in spite of the relatively slow response time estimated in the range of 50 ms, are attractive as nonlinear elements in this type of experiments due to the high nonlinear sensitivity and the large aspect ratio. This enables the observation of patterns of broad area and the choice of one of several spatially periodic structures when using Fourier filtering [15]. The LCLV device works as an optically addressable spatial light modulator as a function of the writing inten- sity and the external applied voltage. The LCLV is con- structed of a set of thin layers, which are two transparent indium tin dioxide-coated glass electrodes, a liquid crystal layer (LC), a dielectric mirror, a sensitive absorber, and a photoconducting layer. The LCLV can be divided into