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Singularities, i.e. places of discontinuities of parameters are extremely general objects appearing in electromagnetic waves and thus are the key to understanding fundamental wave processes. These structures commonly occur in purely coherent, highly directional waves, such as laser beams, determining additional spatial or "`topological"' properties of the wave fields independently of their propagational dynamics. For instance, topologies of wave fronts, called phase singularities, add orbital degrees of freedom to electromagnetic waves. These singularities are common to all types of scalar waves described only by their intensity and phase distributions. As the electromagnetic wave is a vector wave, its topological properties generally depend on all field components leading to complex field patterns in space and time. These patterns may contain singular points of undefined instantaneous orientation of the vector field, i.e. the instantaneous field (IF) singularities. In zero-order paraxial approximation of purely transverse electromagnetic waves, some instantaneous field distributions may carry apparent topological monopoles, when the originally source-free wave exhibits spatial structure associated with the 2D "virtual" sources of electromagnetic fields. Here we present systematic description of topological singularities in both electric and magnetic field of the electromagnetic waves in a paraxial approximation. We also consider the important types of paraxial electromagnetic waves with complex transverse field structures containing instantaneous field singularities., Comment: 13 pages, 6 figures (revised)

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., Comment: 4 pages, 4 figures

We employ conical refraction of light in a biaxial crystal to create an optical bottle for trapping and manipulation of particles. We show that by just varying the polarization of the input light the bottle can be opened and closed at will. We experimentally demonstrate stable photophoretic trapping and controllable loading and unloading of light absorbing particles in the trap., Comment: 4 pages, 5 figures

We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the nonlocality-induced finite correlation length of the noise in the transverse plane, by means of both numerical simulations and analytical estimates. In fact, solitons are practically insensitive to noise when the correlation length of the noise becomes comparable to the extent of the wave packet. We characterize soliton stability using two different criteria based on the evolution of the Hamiltonian of the soliton and its power. The first criterion allows us to estimate a time (or distance) over which the soliton preserves its form. The second criterion gives the life-time of the solitary wave packet in terms of its radiative power losses. We derive a simplified mean field approach which allows us to calculate the power loss analytically in the physically relevant case of weakly correlated noise, which in turn serves as a lower estimate of the life-time for correlated noise in general case.

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 $\lambda=1.0-1.3 \mu{\rm m}$ 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., Comment: 16 pages, 5 figures, submitted to Optics Express

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 lowest and higher order vortices over a hundred diffraction lengths, before dissipation leads to decay of these structures., Comment: 3 figures

We demonstrate generation and frequency doubling of unit charge vortices in a linear astigmatic resonator. Topological instability of the double charge harmonic vortices leads to well separated vortex cores that are shown to rotate, and become anisotropic, as the resonator is tuned across resonance.