We reveal a generic connection between the effect of time-reversals and nonlinear wave dynamics in systems with parity-time (PT ) symmetry, considering a symmetric optical coupler with balanced gain and loss where these effects can be readily observed experimentally. We show that for intensities below a threshold level, the amplitudes oscillate between the waveguides, and the effects of gain and loss are exactly compensated after each period due to periodic time-reversals. For intensities above a threshold level, nonlinearity suppresses periodic time-reversals leading to the symmetry breaking and a sharp beam switching to the waveguide with gain. Another nontrivial consequence of linear PTsymmetry is that the threshold intensity remains the same when the input intensities at waveguides with loss and gain are exchanged.

We present the experimental observation of scalar multi-pole solitons in highly nonlocal nonlinear media, including dipole-, tri-pole, quadru-pole, and necklace-type solitons, organized as arrays of out-of-phase bright spots. These complex solitons are meta-stable, but with a large parameters range where the instability is weak, enabling their experimental observation.

We address the stability of multipole-mode solitons in nonlocal Kerr-type nonlinear media. Such solitons comprise several out-of-phase peaks packed together by the forces acting between them.We discover that dipole-, triple-, and quadrupole-mode solitons can be made stable, whereas all higher-order soliton bound states are unstable.OCIS codes: 190.5530, 190.4360, 060.1810 The interactions arising between optical solitons generate a variety of phenomena. Unlike interactions of scalar solitons that tend to repel or attract each other depending on their relative phase difference only [1], the interaction between solitons incorporating several field components may be more complex. Thus, the formation of vector multipole-mode solitons is possible in local saturable [2,3] and in quadratic [4-6] media. The properties and interactions of solitons are also strongly affected by a nonlocality in the nonlinear response. Nonlocality is typical for photorefractive [1,2,7] and liquid [8,9] crystals; it is characteristic for thermal self-actions [10] and can be met in plasmas [11]. Nonlocality suppresses modulational instability of plane waves [12,13], and it can arrest collapse and instabilities of two-dimensional and vortex solitons (for a

We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discover that the nonlocality of the nonlinear response can profoundly affect the soliton mobility, hence all the related phenomena. Such behavior manifests itself in significant reductions of the Peierls-Nabarro potential with an increase in the degree of nonlocality, a result that opens the rare possibility in nature of almost radiationless propagation of highly localized solitons across the lattice.

We study the interaction of two optical beams of different wavelengths ͑colors͒ in a nematic liquid crystal. We consider the case for which one component carries an optical vortex and the other component describes a localized beam. It is shown that a beam in one color can stabilize a vortex in the other color, the vortex being unstable in the absence of the second beam. We also show that the bright vortex can guide the beam in a stable manner, provided that the nonlocality is large enough. In this context we find that a different type of solitary wave ͑nematicon͒ instability can arise, one for which a ring structure develops at its peak. The results of approximate modulation solutions for the interaction between the vortex and the beam are found to be in good quantitative agreement with direct numerical simulations.

We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response can dramatically enhance the field coupling leading to the stabilization of the vortex beam when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically. c 2013 Optical Society of America OCIS codes: 190.4420; 190.5530; 190.5940 Optical vortices are usually introduced as phase singularities in diffracting optical beams [1] and can be generated in both linear and nonlinear media. The well known effect accompanying the propagation of such singular beams and vortex solitons in self-focusing, nonlinear media is vortex breakup into several fundamental solitons via a symmetry-breaking azimuthal instability [2]. However, recent numerical studies have revealed that spatially localized vortex solitons can be stabilized in highly nonlocal self-focusing nonlinear media [3][4][5]. This stabilization effect was later explained analytically [6] by employing a modulation theory for the vortex parameters based on an averaged Lagrangian.Spatial optical vector solitons can form when several beams propagate together, interacting parametrically or via the effect of cross-phase modulation [7]. The simplest vector solitons are known as shape-preserving, selflocalized solutions of coupled nonlinear evolution equations [7]. A novel class of vector solitons in the form of two color spatial solitons in a highly nonlocal and anisotropic Kerr-like medium were predicted to exist in nematic liquid crystals [8][9][10]. The first experimental observations of anisotropic, nonlocal vector solitons in unbiased nematic liquid crystals were reported by Alberucci et al. [10], who investigated the interaction between two beams of different wavelengths and observed that two extraordinarily polarized beams of different wavelengths can nonlinearly couple, compensating for the beam walk-off, so creating a vector soliton.The main purpose of this Letter is twofold. Firstly, we introduce a novel class of vector solitons in nonlocal, nonlinear media, such as nematic liquid crystals and study their properties. These vector solitons appear as two color, self-trapped beams for which one of the components carries angular momentum and describes a vortex beam. Secondly, we demonstrate that the nonlocal, nonlinear response may dramatically enhance the field coupling, leading to the stabilization of the vortex for much weaker nonlocality when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically.We consider the propagation of two light beams of different wavelengths in a cell filled with a nematic liquid crystal. The light propagates in the z direction, with the (x, y) plane orthogonal to this. The electric fields of the light beams are assumed to be polarized in the x dire...

We uncover a strong coupling between nonlinearity and diffraction in a photonic crystal at the supercollimation point. We show that this is modeled by a nonlinear diffraction term in a nonlinear-Schrödinger-type equation in which the properties of solitons are investigated. Linear stability analysis shows solitons are stable in an existence domain that obeys the Vakhitov-Kolokolov criterium. In addition, we investigate the influence of the nonlinear diffraction on soliton collision scenarios.

We introduce vector soliton complexes in nonlocal Kerr-type nonlinear media. We discover that under proper conditions the combination of nonlocality and vectorial coupling has a remarkable stabilizing action on multihumped solitons. In particular, we find that stable bound states featuring several field oscillations in each soliton component do exist. This affords stabilization of vector soliton trains incorporating a large number of humps, a class of structures known to self-destroy via strong instabilities in scalar settings.