We theoretically and experimentally investigate the self-focusing of optical vortices in Kerr media. We observe collapse to a distinct self-similar profile, which becomes unstable to azimuthal perturbations. We analyze the azimuthal modulational instability for ring-shaped vortices and predict the number of azimuthal maxima solely as a function of power and topological charge. In our experiments, the observed multiple-filamentation patterns are in excellent agreement with our theoretical analysis.

Circularly polarized electric fields incident on subwavelength apertures produce near-field phase singularities with phase vorticity AE1 depending on the polarization handedness. These near-field phase singularities combine with those associated with orbital angular momentum and result in polarizationdependent transmission. We produce arbitrary phase vorticity in the longitudinal component of scattered electric fields by varying the incident beam and aperture configuration. DOI: 10.1103/PhysRevLett.104.083903 PACS numbers: 42.25.Fx, 42.25.Gy, 42.25.Ja, 42.50.Tx Phase singularities in the electric field are locations at which the field amplitude is strictly zero. Given a fixed polarization or ''spin'', the phase integral over the transverse field components enclosing a phase singularity provides a measure of the phase vorticity or orbital angular momentum (OAM) topological charge [1,2]. The threedimensional electric field of an inhomogeneously polarized propagating electromagnetic wave produces three different types of polarization phase singularities [3], the evolution of which is studied in a rich array of literature [4]. Our understanding of phase singularities allows us to probe materials, characterize surfaces, study light propagation dynamics, and manipulate microparticles [5].Within the last decade, there have been observations of near-field phase singularities (NFPS) in the evanescent waves produced by propagating [6] and scattered [7] light. The locations of NFPS produced by chiral ''gammadion' ' [8] and spiral grating structures [9] depend on incident polarization handedness. These NFPS are connected to the extraordinary transmission of light through subwavelength slits [10], where whirlpool-like power flows and singularities in the Poynting vector are shown to exist [11,12]. Azimuthally and radially polarized vortices, beams with different polarization singularities, are transmitted through apertures with different efficiencies [13] but in spite of numerous measurements and observations of NFPS, the polarization-dependent transmission that occurs at subwavelength structures is not fully understood and light-metal interactions are neither fully optimized nor controlled.Here, we show that the polarization-dependent transmission at sub-wavelength-structured materials are concisely explained by a coupling between electromagnetic spin and OAM. ''Spin-orbit interactions'' describe the modified light propagation due to their coupling where the longitudinal component of an electric field generally plays a crucial role. It has been shown that spin-orbit interactions occur via oblique reflections and refraction [14], in wave guiding structures [15], and in the focal plane of highly focused beams [16]. In these situations, a change in either the direction of the phase vorticity or the polarization handedness results in a shift of the observed light intensity patterns.Our work explains, for the first time, that polarizationdependent NFPS describe which modes and to what extent light is transmitted through th...

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We investigate the self-focusing dynamics of super-Gaussian optical beams in a Kerr medium. We find that up to several times the critical power for self-focusing, super-Gaussian beams evolve towards a Townes profile. At higher powers the super-Gaussian beams form rings which break into filaments as a result of noise. Our results are consistent with the observed self-focusing dynamics of femtosecond laser pulses in air [1] in which filaments are formed along a ring about the axis of the initial beam where the initial beam did not form a ring.

We investigate numerically and experimentally the spatial collapse dynamics and polarization stability of radially and azimuthally polarized vortex beams in pure Kerr medium. These beams are unstable to azimuthal modulation instabilities and break up into distinct collapsing filaments. The polarization of the filaments is primarily linear with weak circular components at the filaments' boundaries. This unique hybrid linear-circular polarization collapse pattern persists to advanced stages of collapse and appears to be a general feature of beams with spatially variant linear polarization.