Gouy phase of Bessel-Gaussian beams: theory vs. experiment.

It is well-known that the wave of a freely propagating Gaussian beam experiences an additional π phase shift compared to a plane wave. This phase shift, known as the Gouy phase, has significant consequences in, e.g., nonlinear optics, since the nonlinear processes require high peak intensity and phase matching of the focused beams. Hence, determining and controlling the Gouy phase is crucial in many fields of modern optics and photonics. Here, we develop an analytical model for the Gouy phase of long-range Bessel-Gaussian beams obtained by annihilating highly charged optical vortices. The model accounts for the influence of the relevant experimental parameters (topological charge, radius-to-width ratio of the initial ring-shaped beam, and focal length of the Fourier-transforming lens). We find an evolution of the Gouy phase varying nearly linearly with propagation distance and confirm this result experimentally.

Long-range quasi-non-diffracting Gauss-Bessel beams in a few-cycle laser field.

Many applications ranging from nonlinear optics to material processing would benefit from pulsed ultrashort (quasi-)non-diffracting Gauss-Bessel beams (GBBs). Here we demonstrate a straightforward yet efficient method for generating such zeroth- and first-order GBBs using a single reflective spatial light modulator. Even in the sub-8-fs range there are no noticeable consequences for the measured pulse duration. The only effect is a weak "coloring" of the outer-lying satellite rings of the beams due to the spectrum spanning over more than 300 nm. The obtained beams have diffraction half-angles below 40 µrad and reach propagation distances in excess of 1.5 m.

Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams.

Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.

Supercontinuum generation with optical vortices.

We employ an optical vortex beam for the generation of femtosecond supercontinuum in a solid state medium. We demonstrate that the continuum generation process is initiated by the filamentation of the vortex, resulting in a spatially divergent continuum. Despite the strong self-focusing and the formation of multiple hot-spots along the vortex ring, the singularity is preserved in both the near- and far-fields.

Zeroth- and first-order long range non-diffracting Gauss-Bessel beams generated by annihilating multiple-charged optical vortices.

We demonstrate an alternative approach for generating zeroth- and first-order long range non-diffracting Gauss-Bessel beams (GBBs). Starting from a Gaussian beam, the key point is the creation of a bright ring-shaped beam with a large radius-to-width ratio, which is subsequently Fourier-transformed by a thin lens. The phase profile required for creating zeroth-order GBBs is flat and helical for first-order GBBs with unit topological charge (TC). Both the ring-shaped beam and the required phase profile can be realized by creating highly charged optical vortices by a spatial light modulator and annihilating them by using a second modulator of the same type. The generated long-range GBBs are proven to have negligible transverse evolution up to 2 m and can be regarded as non-diffracting. The influences of the charge state of the TCs, the propagation distance behind the focusing lens, and the GBB profiles on the relative intensities of the peak/rings are discussed. The method is much more efficient as compared to this using annular slits in the back focal plane of lenses. Moreover, at large propagation distances the quality of the generated GBBs significantly surpasses this of GBBs created by low angle axicons. The developed analytical model reproduces the experimental data. The presented method is flexible, easily realizable by using a spatial light modulator, does not require any special optical elements and, thus, is accessible in many laboratories.

Nonlinear dynamics of two-color optical vortices in lithium niobate crystals.

We study experimentally the nonlinear dynamics of two-color optical vortex beams in the presence of second-harmonic generation combined with the effects of photo- and thermal refraction, as well as self- and induced-phase modulation. We use an iron-doped lithium niobate crystal as a nonlinear medium for the vortex propagation and observe experimentally, depending on the laser wavelength, a decay of a double-charge vortex, splitting and reshaping of background beam, pattern formation, and controllable nonlinear rotation of a vortex pair.

Observation of polychromatic gap solitons.

We study theoretically and observe experimentally polychromatic gap solitons generated by supercontinuum light in an array of optical waveguides. The solitons are formed through a sharp transition from diffraction-induced broadening and color separation to the simultaneous spatio-spectral localization of supercontinuum light inside the photonic bandgap with the formation of the characteristic staggered phase structure for all colors.

Two-dimensional self-trapped nonlinear photonic lattices.

We predict theoretically and generate in a photorefractive crystal two-dimensional self-trapped periodic waves of different symmetries, including vortex lattices-patterns of phase dislocations with internal energy flows. We demonstrate that these nonlinear waves exist even with anisotropic nonlocal nonlinearity when the optically-induced periodic refractive index becomes highly anisotropic, and it depends on the orientation of the two-dimensional lattice relative to the crystallographic c-axis.

Polychromatic nonlinear surface modes generated by supercontinuum light.

We study propagation of polychromatic light near the edge of a nonlinear waveguide array. We describe simultaneous spatial and spectral beam reshaping associated with power and wavelength-dependent tunneling between the waveguides. We present experimental verifications of the effects predicted theoretically including the first observation of supercontinuum nonlinear surface modes.

Observation of polychromatic vortex solitons.

We demonstrate experimentally the formation of polychromatic single- and double-charge optical vortex solitons by employing a lithium niobate crystal as a nonlinear medium with defocusing nonlinearity. We study the wavelength dependence of the vortex core localization and observe self-trapping of polychromatic vortices with a bandwidth spanning over more than 70 nm for single-charge and 180 nm for double-charge vortex solitons.

Experimental reconstruction of nonlocal response of thermal nonlinear optical media.

We study experimentally and theoretically the nonlocal response of a medium with thermal nonlinearity and show that despite its inherently infinite range it can be accurately characterized by a well-defined nonlocal response function. We retrieve the shape of this function and analyze its transformation with the change of boundaries.

Nonlinear spectral-spatial control and localization of supercontinuum radiation.

We present the first observation of spatiospectral control and localization of supercontinuum light through the nonlinear interaction of spectral components in extended periodic structures. We use an array of optical waveguides in a LiNbO3 crystal and employ the interplay between diffraction and nonlinearity to dynamically control the output spectrum of the supercontinuum radiation. This effect presents an efficient scheme for optically tunable spectral filtering of supercontinua.

Observation of attraction between dark solitons.

We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems, such as Bose-Einstein condensates with repulsive long-range interparticle interaction.