Cavity solitons in broad-area vertical-cavity surface-emitting lasers below threshold Xavier Hachair, Stéphane Barland, Luca Furfaro, Massimo Giudici, Salvador Balle, * and Jorge R. Tredicce Institut Non-linéare de Nice, UMR 6618 Center National de la Recherche Scientifique-Université de Nice Sophia-Antipolis, 06560 Valbonne, France Massimo Brambilla, Tommaso Maggipinto, and Ida M. Perrini INFM, Dipartimento di Fisica Interateneo, Università e Politecnico di Bari,Via Orabona 4, 70126 Bari, Italy Giovanna Tissoni and Luigi Lugiato INFM, Dipartimento di Scienze, Universitá dell’Insubria, Via Valleggio 11, 22100 Como, Italy (Received 7 November 2003; published 21 April 2004) Cavity solitons are stationary self-organized bright intensity peaks which form over a homogeneous back- ground in the section of broad area radiation beams. They are generated by shining a writing/erasing laser pulse into a nonlinear optical cavity, driven by a holding beam. The ability to control their location and their motion by introducing phase or amplitude gradients in the holding beam makes them interesting as mobile pixels for all-optical processing units. We show the generation of a number of cavity solitons in broad-area vertical cavity semiconductor microresonators electrically pumped above transparency but slightly below threshold. We ana- lyze the switching process in details. The observed spots can be written, erased, and manipulated as indepen- dent objects, as predicted by the theoretical model. An especially tailored one is used to simulate the studied phenomena and to compare our simulations to the experimental findings with good agreement. DOI: 10.1103/PhysRevA.69.043817 PACS number(s): 42.65.Sf, 42.70.Nq, 42.65.Tg I. INTRODUCTION The analysis of unstable and chaotic phenomena [1,2] found a fertile ground in the field of nonlinear optics. In the late eighties, the main focus shifted from temporal effects to spatial pattern formation in the structure of the electromag- netic (e.m.) field in the transverse sections of broad-area ra- diation beams, when they interact with nonlinear media (see Refs. [3–5] and references quoted therein). The investiga- tions in this domain offer an approach to parallel optical information processing, by encoding information in the transverse structure of the field. The idea is of considering the transverse planes as a blackboard on which light spots can be written and erased in any desired location and in a controlled way. Optical patterns may display an array of light spots, but are unsuitable for this task becausethe intensity peaks are strongly correlated with one another, so that they cannot be manipulated as independent objects. This task be- comes possible, instead, using cavity solitons (CSs), a pecu- liar type of spatial solitons [6] which arise in a dissipative environment. They belong to the class of localized structures, which were discovered in other fields (see, e.g., Refs. [7,8] and for a general theory [9]) and arise under conditions of coexistence, in a nonlinear dynamical system, of a homoge- neous stationary state and a patterned stationary state: for the same values of the parameters, according to the initial con- dition, the system may approach the homogeneous or the pattern state. Localized structures are intermediate between the two, in the sense that they coincide with the pattern state in a certain restricted region of the plane, and with the ho- mogeneous state outside. By definition, localized structures must be independent of the boundary. A cavity soliton corre- sponds to a localized structure with a single peak. After pio- neering works in the eighties [10–12], noteworthy attention was focussed on CSs since the midnineties [5,13–17]. They are generated in optical resonators containing nonlinear ma- terials and driven by a broad area, coherent, and stationary holding beam (Fig. 1). The device is operated under paramet- ric conditions such that the output is basically uniform over an extended region. However, by injecting a localized laser pulse one can write a CS where the pulse passes (at the location in the device cross section where the pulse im- pinges) and the CS persists after the pulse. The CSs written in this way can be erased by injecting again pulses in the locations where they lie; these pulses must be coherent and out of phase with respect to the holding beam [15]. Cavity solitons are not standard optical spatial solitons which arise from the balance of nonlinear self-focusing and diffraction or from nonlinear phase modulation, such as those considered in Ref. [6]. As a matter of fact, CSs may emerge even in *Also at Institut Mediterrani d’Estudis Avançats, IMEDEA (CSIC–Universitat de les Illes Balears), C/Miquel Marquès 21, E-07190 Esporles, Spain. FIG. 1. A coherent, stationary, quasi-plane-wave holding field drives an optical cavity containing a nonlinear medium. The injec- tion of narrow laser pulses creates persistent localized intensity peaks in the output (cavity solitons). PHYSICAL REVIEW A 69, 043817 (2004) 1050-2947/2004/69(4)/043817(13)/$22.50 ©2004 The American Physical Society 69 043817-1