Escaping Solitons from a Trapping Potential Marco Peccianti, 1,2 Andriy Dyadyusha, 3 Malgosia Kaczmarek, 3 and Gaetano Assanto 1, * 1 NooEL - Nonlinear Optics and OptoElectronics Lab, Department of Electronic Engineering, INFN and CNISM, University ‘‘Roma Tre’’, Via della Vasca Navale 84, 00146, Rome - Italy 2 Res. Center SMC INFM-CNR, ‘‘Sapienza’’ University, P. A. Moro 2, 00185, Rome - Italy 3 School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom (Received 13 March 2008; published 7 October 2008) Solitons propagating within a confining potential undergo momentum-dependent scattering and eventually escape for large excitations. We experimentally highlight this phenomenon in the presence of a nonperturbative nonlinear response using self-confined light beams in a reorientational medium. DOI: 10.1103/PhysRevLett.101.153902 PACS numbers: 42.65.Tg, 42.25.Gy, 42.70.Df Spatial solitary waves or solitons are known to occur in several areas of physics including fluids, plasmas, biology, matter waves, and optics [1,2]. They are often considered ubiquitous and share a number of fundamental properties relying on the combination of a nonlinear response and the natural tendency of a wave packet to spread as it propa- gates. Spatial solitons in optics (bright transversely self- localized light beams) are recognized as fundamental non- linear electromagnetic wave objects with potential appli- cations to all-optical signal processing [3,4] and have been explored in several materials and configurations for signal readdressing [5–11]. Owing to their self-guided nature and robust particlelike behavior, in the presence of dielectric inhomogeneities, soliton dynamics embraces various phe- nomena, from oscillations and breathing [12–14] to refrac- tion and reflection, [5,15,16], steering [17,18], as well as confinement near a surface [19,20]. As predicted in the early days of soliton optics [21–23], they undergo scatter- ing at interfaces and are known to oscillate within a wide (preestablished) waveguide, with a period depending on launch conditions, [13,14,16,18,24]. Solitons are also ex- pected to escape a trapping potential when their effective kinetic energy becomes comparable with the barrier depth [23,25], i.e., when the nonlinear disturbance induces a transverse acceleration large enough to overcome linear confinement. Such wealth of effects extends beyond optics [25–28] including, among others, Bose Einstein conden- sates [29]. In spite of the predictions and interest in nonlinear scat- tering and trapping [30,31], soliton escape from a potential well was not reported to date mainly because of limitations in propagation length and nonlinearity. Soliton tunneling phenomena were recently reported in Ref. [32]. In this Letter, we investigate the interaction of spatial solitons with an externally defined potential and demonstrate for the first time soliton escape above a certain level of exci- tation. To this aim, we exploit the giant nonlinear optical response of nematic liquid crystals (NLC). Nematic liquid crystals are molecular dielectrics with properties intermediate between solids and liquids, with a high degree of orientational order resulting in large optical birefringence [33]. Electric fields at optical frequencies can reorient the optic axis (‘‘director’’) towards the polariza- tion direction, inducing a Coulombian torque counteracted by intermolecular (elastic) forces. As a result, their non- linear response is highly nonlocal, i.e., the index perturba- tion extends well beyond the excitation region and supports stable and robust (2D þ 1) spatial solitons [34]. Moreover, NLC can undergo all-optical index changes which, at milli- watt power levels, are comparable to the size of their birefringence. We consider a cell layout as in Fig. 1: two parallel glass slides confine a layer of nematic liquid crystals and provide anchoring for molecular alignment in the plane ^ t ^ p , being ^ p normal to the input facet. The optic axis (molecular di- rector) ^ n forms an angle  with the plane ^ t ^ p and  with the planar interface parallel to ^ x ^ t and sealing the sample at the entrance [see Figs. 1(a) and 1(b)]. Voltages can be applied via thin film electrodes and alter the molecular alignment (and optical properties) in the bulk NLC. The front elec- trode is split into two by an L-wide gap along ^ p; hence, distinct potentials can be applied to each of them with re- spect to the ground plane at the bottom [see Fig. 1(a)]. The two corresponding NLC regions, labeled 1 and 2, are ideally separated by the plane ^ x ^ p . The director distribu- tion is described by ^ nðx;t;pÞ¼ ^ nðsin; cos cos; cos sinÞ and, for a constant director alignment along FIG. 1 (color online). (a) Sketch of the cell. (b) Molecular director (optic axis) and coordinate system. PRL 101, 153902 (2008) PHYSICAL REVIEW LETTERS week ending 10 OCTOBER 2008 0031-9007= 08=101(15)=153902(4) 153902-1 Ó 2008 The American Physical Society