arXiv subjects
Publications and source records attributed to Wieslaw Krolikowski.
We reveal that nonlocality can provide a simple physical mechanism for stabilization of multi-hump optical solitons, and present the first example of stable rotating dipole solitons and soliton spiraling, known to be unstable in all types of realistic nonlinear media with local response.
We demonstrate experimentally all-optical beam steering in modulated photonic lattices induced optically by three beam interference in a biased photorefractive crystal. We identify and characterize the key physical parameters governing the beam steering, and show that the spatial resolution can be enhanced by the additional effect of nonlinear beam self-localization.
We predict a sharp crossover from nonlinear self-defocusing to discrete self-trapping of a narrow Gaussian beam with the increase of the refractive index contrast in a periodic photonic lattice. We demonstrate experimentally nonlinear discrete localization of light with defocusing nonlinearity by single site excitation in LiNbO$_3$ waveguide arrays.
We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square photonic lattice superimposed on a refractive index ramp, and demonstrate the tunneling of light from the first to the higher-order transmission bands of the lattice bandgap spectrum, associated with the spectral dynamics inside the first Brillouin zone and corresponding oscillations of the primary beam.
We demonstrate theoretically and experimentally a novel type of localized beams supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making them promising candidates for optical routing in nonlinear lattices.
We generate double-charge white-light optical vortices by sending a circularly polarized partially incoherent light through an uniaxial crystal. We show that the generated polichromatic vortices are structurally stable, and their correlation properties can be altered by the beam focusing, resulting in changes of the vortex core visibility.
We study nonlinear coupling of mutually incoherent beams associated with different Floquet-Bloch waves in a one-dimensional optically-induced photonic lattice. We demonstrate experimentally how such interactions lead to asymmetric mutual focusing and, for waves with opposite diffraction properties, to simultaneous focusing and defocusing as well as discreteness-induced beam localization and reshaping effects.
We study tunable refraction of light in one-dimensional periodic lattices induced optically in a photorefractive crystal. We observe experimentally both positive and negative refraction of beams which selectively excite the first or second spectral bands of the periodic lattice, and demonstrate tunability of the output beam position by dynamically adjusting the lattice depth. At higher laser intensities, the beam broadening due to diffraction can be suppressed through nonlinear self-focusing while preserving the general steering properties.
We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons.
We demonstrate the first fully controlled generation of immobile and slow spatial gap solitons in nonlinear periodic systems with band-gap spectra, and reveal the key features of gap solitons which distinguish them from conventional counterparts, including a dynamical transformation of gap solitons due to nonlinear inter-band coupling. We also predict theoretically and confirm experimentally the effect of anomalous steering of gap solitons in optically-induced photonic lattices.
We study, both theoretically and experimentally, the Bragg scattering of light in optically-induced photonic lattices and reveal the key physical mechanisms which govern nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.
We study experimentally the Bloch-wave instabilities in optically-induced lattices. We reveal two different instability scenarios associated with either the transverse modulational instability of a single Bloch wave, or the nonlinear inter-band coupling between different Bloch waves. These effects are compared with the transverse instability in homogeneous media, and it is shown that the periodic modulation of the refractive index greatly enhances the transverse instability.
We study, both theoretically and experimentally, the scattering properties of optical dipole-mode vector solitons - radially asymmetric composite self-trapped optical beams. First, we analyze the soliton collisions in an isotropic two-component model with a saturable nonlinearity and demonstrate that in many cases the scattering dynamics of the dipole-mode solitons allows us to classify them as ``molecules of light'' - extremely robust spatially localized objects which survive a wide range of interactions and display many properties of composite states with a rotational degree of freedom. Next, we study the composite solitons in an anisotropic nonlinear model that describes photorefractive nonlinearities, and also present a number of experimental verifications of our analysis.
We study experimentally nonlinear localization effects in optically-induced gratings created by interfering plane waves in a photorefractive crystal. We demonstrate the generation of spatial bright solitons similar to those observed in arrays of coupled optical waveguides. We also create pairs of out-of-phase solitons which resemble ``twisted'' localized states in nonlinear lattices.
We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric, but can be of completely arbitrary shape. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.
The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general, localized, response function. It is shown that there always exists a finite number of well-separated MI gain bands, with each of them characterised by a unique maximal growth rate. This is a general property and is demonstrated here for the Gaussian, exponential, and rectangular response functions. In case of a focusing nonlinearity it is shown that although the nonlocality tends to suppress MI, it can never remove it completely, irrespectively of the particular shape of the response function. For a defocusing nonlinearity the stability properties depend sensitively on the profile of the response function. It is shown that plane waves are always stable for response functions with a positive-definite spectrum, such as Gaussians and exponentials. On the other hand, response functions whose spectra change sign (e.g., rectangular) will lead to MI in the high wavenumber regime, provided the typical length scale of the response function exceeds a certain threshold. Finally, we address the case of generalized multi-component response functions consisting of a weighted sum of N response functions with known properties.
We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespectively of the particular profile of the nonlocal response function. For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose-Einstein condensates.
We report on the first experimental observation of a novel type of optical vector soliton, a {\em dipole-mode soliton}, recently predicted theoretically. We show that these vector solitons can be generated in a photorefractive medium employing two different processes: a phase imprinting, and a symmetry-breaking instability of a vortex-mode vector soliton. The experimental results display remarkable agreement with the theory, and confirm the robust nature of these radially asymmetric two-component solitary waves.