Polariton surface solitons under a resonant pump.

We address the formation of stable dissipative surface solitons in the exciton-polariton condensate in a one-dimensional array of microcavity pillars under the action of a localized resonant pump acting in the edge resonator. We show that the localization degree and peak amplitudes of surface solitons can be effectively controlled by the pump frequency and that the allowed energy gap of the periodic structure determines the energy range, where surface solitons can form. One observes bistability at sufficiently large pump amplitudes and a nonlinearity-induced shift of the position of the resonance peak from the allowed energy band of the periodic array into its forbidden energy gap. The growth of the spatial period of the array reduces coupling between pillars and currents from a surface pillar into bulk pillars which leads to the increase of the surface soliton amplitude. Strong expansion into the depth of the array occurs for pump frequencies corresponding to the middle of the allowed energy band. Surface solitons can be excited from the broadband Gaussian noise. Above certain threshold noise levels, solitons from a stable upper branch of the bistability curve are excited while, below threshold, solitons from the lower branch form.

Edge and bulk dissipative solitons in modulated PT-symmetric waveguide arrays.

We address dissipative soliton formation in modulated parity-time (PT)-symmetric continuous waveguide arrays composed from waveguides with amplifying and absorbing sections, whose density gradually increases (due to decreasing waveguide separation) either towards the center of the array or towards its edges. In such a structure, the level of gain/loss at which PT-symmetry gets broken depends on the direction of increase of waveguide density. Breakup of PT-symmetry occurs when eigenvalues of modes localized in the region where waveguide density is largest collide and move into a complex plane. In this regime of broken symmetry, the inclusion of focusing Kerr-type nonlinearity of the material and weak two-photon absorption allows to arrest the growth of amplitude of amplified modes and may lead to the appearance of stable attractors either in the center or at the edge of the waveguide array, depending on the type of array modulation. Such solitons can be stable; they acquire specific triangular shapes and notably broaden with increase of gain/loss level. Our results illustrate how spatial array modulation that breaks PT-symmetry "locally" can be used to control the specific location of dissipative solitons forming in the array.

Rotating vortex clusters in media with inhomogeneous defocusing nonlinearity.

We show that media with inhomogeneous defocusing cubic nonlinearity growing toward the periphery can support a variety of stable vortex clusters nested in a common localized envelope. Nonrotating symmetric clusters are built from an even number of vortices with opposite topological charges, located at equal distances from the origin. Rotation makes the clusters strongly asymmetric, as the centrifugal force shifts some vortices to the periphery, while others approach the origin, depending on the topological charge. We obtain such asymmetric clusters as stationary states in the rotating coordinate frame, identify their existence domains, and show that the rotation may stabilize some of them.

Localized waves supported by the rotating waveguide array.

We show that truncated rotating square waveguide arrays support new types of localized modes that exist even in the linear case, in complete contrast to localized excitations in nonrotating arrays requiring nonlinearity for their existence and forming above the energy flow threshold. These new modes appear either around an array center, since the rotation leads to the emergence of the effective attractive potential with a minimum at the rotation axis, or in the array corners, in which case localization occurs due to competition between the centrifugal force and total internal reflection at the interface of the truncated array. The degree of localization of the central and corner modes mediated by the rotation increases with the rotation frequency. The stable rotating soliton families bifurcating from linear modes are analyzed in both focusing and defocusing media.

Asymmetric soliton mobility in competing linear-nonlinear parity-time-symmetric lattices.

We address the transverse mobility of spatial solitons in competing parity-time-symmetric linear and nonlinear lattices. The competition between out-of-phase linear and nonlinear lattices results in a drastic mobility enhancement within a range of soliton energies. We show that within such a range, the addition of even a small imaginary part in the linear potential makes soliton mobility strongly asymmetric. For a given initial phase tilt, the velocity of soliton motion grows with an increase of the balanced gain/losses. In this regime of enhanced mobility, tilted solitons can efficiently drag other solitons that were initially at rest to form moving soliton pairs.

Efficient mode conversion in guiding structures with longitudinal modulation of nonlinearity.

We describe power-dependent dynamics of conversion of the guided modes of various guiding structures due to nearly resonant longitudinal modulation of the nonlinear coefficient of the medium. It is shown that the control of the energy exchange integrals, as well as of the input weights of the interacting modes, is especially crucial for efficient mode conversion in the setting considered here. Complex dynamics of conversion incorporates various scenarios, including nonharmonic oscillations of the energy weights, which mimics Jacoby elliptical functions.

Resonant mode conversion in the waveguides with unbroken and broken PT symmetry.

We study resonant mode conversion in parity time (PT)-symmetric multimode waveguides, where symmetry breaking manifests itself in the sequential destabilization (i.e., the appearance of complex eigenvalues) of the pairs of adjacent guided modes. We show that efficient mode conversion is possible even in the presence of the resonant longitudinal modulation of the complex refractive index. The distinguishing feature of the resonant mode conversion in the PT-symmetric structure is a drastic growth of the width of the resonance curve when the gain/losses coefficient approaches a critical value, at which symmetry breaking occurs. We found that in the system with broken symmetry, the resonant coupling between the exponentially growing mode and the stable higher-order one effectively stabilizes dynamically coupled pairs of modes and remarkably diminishes the average rate of the total power growth.

Observation of asymmetric solitons in waveguide arrays with refractive index gradient.

We study light propagation in waveguide arrays made in Kerr nonlinear media with a transverse refractive index gradient, and we find that the presence of the refractive index gradient leads to the appearance of a number of new soliton families. The effective coupling between the solitons and the localized linear eigenmodes of the lattice induces a drastic asymmetry in the soliton shapes and the appearance of long tails at the soliton wings. Such unusual solitons are found to be completely stable under propagation, and we report their experimental observation in fs-laser written waveguide arrays with focusing Kerr nonlinearity.

Resonant Bloch-wave beatings.

We introduce Bloch-wave beatings in arrays of multimode periodically bent waveguides with a transverse refractive index gradient. The new phenomenon manifests itself in the periodic drastic increase of the amplitude of the Bloch oscillations that accompanies resonant conversion of modes guided by the individual waveguides. The Bloch-wave beatings are found to be most pronounced when the length of the resonant mode conversion substantially exceeds the longitudinal period of the Bloch oscillations. The beating frequency decreases when the amplitude of waveguide bending decreases, while the beating amplitude is restricted by the amplitude of the Bloch oscillations that emerge from the second allowed band of the Floquet-Bloch lattice spectrum.

Enhancement and inhibition of light tunneling mediated by resonant mode conversion.

We show that the rate at which light tunnels between neighboring multimode waveguides can be drastically increased or reduced by the presence of small longitudinal periodic modulations of the waveguide properties that stimulate resonant conversion between the eigenmodes of each waveguide. Such a conversion, available only in multimode guiding structures, leads to periodic power transfer into higher-order modes, whose tails may considerably overlap with neighboring waveguides. As a result, the effective coupling constant for neighboring waveguides may change by several orders of magnitude upon small variations in the longitudinal modulation parameters.

Light dynamics in materials with radially inhomogeneous thermal conductivity.

We study the properties of bright and vortex solitons in thermal media with nonuniform thermal conductivity and homogeneous refractive index, whereby the local modulation of the thermal conductivity strongly affects the entire refractive index distribution. While regions where the thermal conductivity is increased effectively expel light, self-trapping may occur in the regions with reduced thermal conductivity, even if such regions are located close to the material boundary. As a result, strongly asymmetric self-trapped beams may form inside a ring with reduced thermal conductivity and perform persistent rotary motion. Also, such rings are shown to support stable vortex solitons, which may feature strongly noncanonical shapes.

Generation of arbitrary complex quasi-non-diffracting optical patterns.

Due to their unique ability to maintain an intensity distribution upon propagation, non-diffracting light fields are used extensively in various areas of science, including optical tweezers, nonlinear optics and quantum optics, in applications where complex transverse field distributions are required. However, the number and type of rigorously non-diffracting beams is severely limited because their symmetry is dictated by one of the coordinate system where the Helmholtz equation governing beam propagation is separable. Here, we demonstrate a powerful technique that allows the generation of a rich variety of quasi-non-diffracting optical beams featuring nearly arbitrary intensity distributions in the transverse plane. These can be readily engineered via modifications of the angular spectrum of the beam in order to meet the requirements of particular applications. Such beams are not rigorously non-diffracting but they maintain their shape over large distances, which may be tuned by varying the width of the angular spectrum. We report the generation of unique spiral patterns and patterns involving arbitrary combinations of truncated harmonic, Bessel, Mathieu, or parabolic beams occupying different spatial domains. Optical trapping experiments illustrate the opto-mechanical properties of such beams.

Light scattering in disordered honeycomb photonic lattices near the Dirac points.

We address Anderson localization in disordered honeycomb photonic lattices and show that the localization process is strongly affected by the spectral position of the input wavepacket within the first Brillouin zone of the lattice. In spite of the fact that in regular lattices expansion of the beam is much stronger for excitation near the Dirac points-where light exhibits conical diffraction-than for excitation at the center of the Brillouin zone-where light exhibits normal diffraction-we found that disorder leads to pronounced Anderson localization even around the Dirac points. We found that for the same disorder level the width of the averaged output intensity distribution for excitations around the Dirac points may be substantially larger than that for excitations at the center of the Brillouin zone.

Dynamics of topological light states in spiraling structures.

We expose a mechanism for the dynamical generation and control of light states with diverse topologies in spiraling guiding structures. Specifically, we show that spiraling shallow refractive index landscapes induce coupling and periodic energy exchange between states with different topological charges. Such a resonant effect enables excitation of optical vortices by vortex-free inputs and allows the output topological charge of the beam to be controlled. The presence of nonlinearity results in a strong asymmetrization of the resonant curves and a shift of the resonant frequencies. Resonant vortex dynamic generation, including revivals, is shown to be possible not only in waveguides mediated by total internal reflection but also in Bragg-guiding hollow-core geometries.

Hybrid Bloch-Anderson localization of light.

We investigate the interplay of Bloch oscillations and Anderson localization in optics. Gradual washing out of Bloch oscillations and the formation of nearly stationary averaged intensity distributions, which are symmetric for narrow and strongly asymmetric for broad input excitations, are observed experimentally in laser-written waveguide arrays. At large disorder levels Bloch oscillations are completely destroyed and both narrow and wide excitations lead to symmetric stationary averaged intensity distributions with exponentially decaying tails.

Solitons in spiraling Vogel lattices.

We address light propagation in Vogel optical lattices and show that such lattices support a variety of stable soliton solutions in both self-focusing and self-defocusing media, whose propagation constants belong to domains resembling gaps in the spectrum of a truly periodic lattice. The azimuthally rich structure of Vogel lattices allows generation of spiraling soliton motion.

Soliton generation by counteracting gain-guiding and self-bending.

We introduce a concept for stable spatial soliton formation, mediated by the competition between self-bending induced by a strongly asymmetric nonlocal nonlinearity and spatially localized gain superimposed on a wide pedestal with linear losses. When acting separately both effects seriously prevent stable localization of light, but under suitable conditions they counteract each other, forming robust soliton states that are attractors for a wide range of material and input light conditions.

Anderson localization in Bragg-guiding arrays with negative defects.

We show that Anderson localization is possible in waveguide arrays with periodically spaced defect waveguides having a lower refractive index. Such localization is mediated by Bragg reflection, and it takes place even if diagonal or off-diagonal disorder affects only defect waveguides. For off-diagonal disorder the localization degree of the intensity distributions monotonically grows with increasing disorder. In contrast, under appropriate conditions, increasing diagonal disorder may result in weaker localization.

Light localization in nonuniformly randomized lattices.

We address Anderson localization of light in disordered optical lattices where the disorder strength varies across the transverse direction. Such variation changes the preferred domains where formation of localized eigenmodes is most probable, hence drastically impacting light localization properties. Thus, step-like disorder results in formation of modes with different decay rates at both sides of the interface, while a smoothly varying disorder yields appearance of modes that are extended within weakly disordered domains and rapidly fade away in strongly disordered domains.

Solitons supported by spatially inhomogeneous nonlinear losses.

We uncover that, in contrast to the common belief, stable dissipative solitons exist in media with uniform gain in the presence of nonuniform cubic losses, whose local strength grows with coordinate η (in one dimension) faster than |η|. The spatially-inhomogeneous absorption also supports new types of solitons, that do not exist in uniform dissipative media. In particular, single-well absorption profiles give rise to spontaneous symmetry breaking of fundamental solitons in the presence of uniform focusing nonlinearity, while stable dipoles are supported by double-well absorption landscapes. Dipole solitons also feature symmetry breaking, but under defocusing nonlinearity.