Optical beaming of electrical discharges.

Igniting and guiding electrical discharges to desired targets in the ambient atmosphere have been a subject of intense research efforts for decades. Ability to control discharge and its propagation can pave the way to a broad range of applications from nanofabrication and plasma medicine to monitoring of atmospheric pollution and, ultimately, taming lightning strikes. Numerous experiments utilizing powerful pulsed lasers with peak-intensity above air photoionization and photo-dissociation have demonstrated excitation and confinement of plasma tracks in the wakes of laser field. Here, we propose and demonstrate an efficient approach for triggering, trapping and guiding electrical discharges in air. It is based on the use of a low-power continuous-wave vortex beam that traps and transports light-absorbing particles in mid-air. We demonstrate a 30% decrease in discharge threshold mediated by optically trapped graphene microparticles with the use of a laser beam of a few hundred milliwatts of power. Our demonstration may pave the way to guiding electrical discharges along arbitrary paths.

Comparative analysis of ferroelectric domain statistics via nonlinear diffraction in random nonlinear materials.

We present an indirect, non-destructive optical method for domain statistic characterization in disordered nonlinear crystals having homogeneous refractive index and spatially random distribution of ferroelectric domains. This method relies on the analysis of the wave-dependent spatial distribution of the second harmonic, in the plane perpendicular to the optical axis in combination with numerical simulations. We apply this technique to the characterization of two different media, Calcium Barium Niobate and Strontium Barium Niobate, with drastically different statistical distributions of ferroelectric domains.

Self-structuring of stable dissipative breathing vortex solitons in a colloidal nanosuspension.

The self-structuring of laser light in an artificial optical medium composed of a colloidal suspension of nanoparticles is demonstrated using variational and numerical methods extended to dissipative systems. In such engineered materials, competing nonlinear susceptibilities are enhanced by the light induced migration of nanoparticles. The compensation of diffraction by competing focusing and defocusing nonlinearities, together with a balance between loss and gain, allow for self-organization of light and the formation of stable dissipative breathing vortex solitons. Due to their robustness, the breathers may be used for selective dynamic photonic tweezing of nanoparticles in colloidal nanosuspensions.

Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation.

We present a novel single-shot cross-correlation technique based on the analysis of the transversally emitted second harmonic generation in crystals with random distribution and size of anti-parallel nonlinear domains. We implement it to the measurement of ultrashort laser pulses with unknown temporal duration and shape. We optimize the error of the pulse measurement by controlling the incident angle and beam width. As novelty and unlike the other well-known cross correlation schemes, this technique can be implemented for the temporal characterization of pulses over a very wide dynamic range (30 fs-1ps) and wavelengths (800-2200 nm), using the same crystal and without critical angular or temperature alignment.

Laser-writing inside uniaxially birefringent crystals: fine morphology of ultrashort pulse-induced changes in lithium niobate.

This work presents a detailed analysis of the morphology of femtosecond laser-induced changes in bulk lithium niobate (LiNbO3) - one of the most common host materials in photonics - using second-harmonic generation microscopy and scanning electron microscopy. It is shown that focused linearly polarized near-infrared pulses can produce two or three distinct axially separated regions of modified material, depending on whether the pulse propagation is along or perpendicular to the optical axis. When laser writing in LiNbO3 is conducted in multi-shot irradiation mode and the focused light intensity is kept near the bulk damage threshold, periodic planar nanostructures aligned perpendicular to the laser polarization are produced inside the focal volume. These results provide a new perspective to laser writing in crystalline materials, including the fabrication of passive and active waveguides, photonic crystals, and optical data storage devices.

Self-Organization of Light in Optical Media with Competing Nonlinearities.

We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.

Visualizing polarization singularities in Bessel-Poincaré beams.

We demonstrate that an annulus of light whose polarization is linear at each point, but the plane of polarization gradually rotates by π radians can be used to generate Bessel-Poincaré beams. In any transverse plane this beam exhibits concentric rings of polarization singularities in the form of L-lines, where the polarization is purely linear. Although the L-lines are invisible in terms of light intensity variations, we present a simple way to visualize them as dark rings around a sharp peak of intensity in the beam center. To do this we use a segmented polarizer whose transmission axes are oriented differently in each segment. The radius of the first L-line is always smaller than the radius of the central disk of the zero-order Bessel beam that would be produced if the annulus were homogeneously polarized and had no phase circulation along it.

Transverse spin angular momentum of tightly focused full Poincaré beams.

We show theoretically that by tightly focusing a full Poincaré beam one can create states of light whose average spin angular momentum (SAM) is purely transverse. Moreover, the transverse SAM is significantly increased if a narrow annular aperture is inserted into the Poincaré beam. In this case the state with transverse SAM can exist over an extremely long distance along the optical axis. To avoid diffraction on the aperture and increase the light conversion efficiency we employ the phenomenon of conical diffraction in biaxial crystals to convert a Gaussian beam into a ring-shaped beam, with a high ratio of the ring radius to its width.

Optical vault: a reconfigurable bottle beam based on conical refraction of light.

We employ conical refraction of light in a biaxial crystal to create an optical bottle for photophoretic trapping and manipulation of particles in gaseous media. We show that by only varying the polarization state of the input light beam the optical bottle can be opened and closed in order to load and unload particles in a highly controllable manner.

Nonlocal dark solitons under competing cubic-quintic nonlinearities.

We investigate properties of dark solitons under competing nonlocal cubic-local quintic nonlinearities. Analytical results, based on a variational approach and confirmed by direct numerical simulations, reveal the existence of a unique dark soliton solutions with their width being independent of the degree of nonlocality, due to the competing cubic-quintic nonlinearities.

Enhanced Cerenkov second-harmonic emission in nonlinear photonic structures.

We study experimentally and theoretically the Cerenkov-type second-harmonic generation in a one-dimensional nonlinear photonic crystal. We demonstrate that the power of emitted second-harmonic can be enhanced 270 times by varying the angle of incidence of the fundamental beam such that the reciprocal lattice vector of the crystal can be used to compensate for the phase mismatch in the transverse direction enabling interaction in the nonlinear Bragg diffraction regime.

Rydberg-induced solitons: three-dimensional self-trapping of matter waves.

We propose a scheme for the creation of stable three-dimensional bright solitons in Bose-Einstein condensates, i.e., the matter-wave analog of so-called spatiotemporal "light bullets." Off-resonant dressing to Rydberg nD states is shown to provide nonlocal attractive interactions, leading to self-trapping of mesoscopic atomic clouds by a collective excitation of a Rydberg atom pair. We present detailed potential calculations and demonstrate the existence of stable solitons under realistic experimental conditions by means of numerical simulations.

The role of ferroelectric domain structure in second harmonic generation in random quadratic media.

We study theoretically and numerically the second harmonic generation in a nonlinear crystal with random distribution of ferroelectric domains. We show that the specific features of disordered domain structure greatly affect the emission pattern of the generated harmonics. This phenomena can be used to characterize the degree of disorder in nonlinear photonic structures.

Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media.

We study parametric frequency conversion in quadratic nonlinear media with disordered ferroelectric domains. We demonstrate that disorder allows realizing broadband third-harmonic generation via cascading of two second-order quasi-phase matched nonlinear processes. We analyze both spatial and polarization properties of the emitted radiation and find the results in agreement with our theoretical predictions.

Rotating soliton solutions in nonlocal nonlinear media.

We discuss generic properties of rotating nonlinear wave solutions, the so called azimuthons, in nonlocal media. Variational methods allow us to derive approximative values for the rotating frequency, which is shown to depend crucially on the nonlocal response function. Further on, we link families of azimuthons to internal modes of classical non-rotating stationary solutions, namely vortex and multipole solitons. This offers an exhaustive method to identify azimuthons in a given nonlocal medium.

Limits to compression with cascaded quadratic soliton compressors.

We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong. This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find that it is theoretically possible to reach the single-cycle regime by compressing high-energy fs pulses for wavelengths lambda = 1.0-1.3 microm in a beta -barium-borate crystal, and it requires that the system is in the stationary regime, where the phase mismatch is large enough to overcome the detrimental GVM effects. however, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account.

Solitons in one-dimensional nonlinear Schrödinger lattices with a local inhomogeneity.

In this paper we analyze the existence, stability, dynamical formation, and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schrödinger equation with a linear point defect. We consider both attractive and repulsive defects in a focusing lattice. Among our main findings are (a) the destabilization of the on-site mode centered at the defect in the repulsive case, (b) the disappearance of localized modes in the vicinity of the defect due to saddle-node bifurcations for sufficiently strong defects of either type, (c) the decrease of the amplitude formation threshold for attractive and its increase for repulsive defects, and (d) the detailed elucidation as a function of initial speed and defect strength of the different regimes (trapping, trapping and reflection, pure reflection, and pure transmission) of interaction of a moving localized mode with the defect.

Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor.

We show that ballistic transport of optically excited atoms in an atomic vapor provides a nonlocal nonlinearity which stabilizes the propagation of vortex beams and higher order modes in the presence of a self-focusing nonlinearity. Numerical experiments demonstrate stable propagation of higher order nonlinear states (dipole, vortices, and rotating azimuthons) over a hundred diffraction lengths, before dissipation leads to decay of these structures.

Stability of two-dimensional spatial solitons in nonlocal nonlinear media.

We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating dipole solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function.

Nonlocal description of X waves in quadratic nonlinear materials.

We study localized light bullets and X waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multidimensional nonlinear waves. For X waves we show that a local cascading limit in terms of a nonlinear Schrödinger equation does not exist-one needs to use the nonlocal description, because the nonlocal response function does not converge toward a function. Also, we use the nonlocal theory to show that the coupling to the second harmonic is able to generate an X shape in the fundamental field despite having anomalous dispersion, in contrast to the predictions of the cascading limit.