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.

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.

The performance of long distance imaging systems is typically degraded by phase errors imparted by atmospheric turbulence. In this paper we apply coherent imaging methods to determine, and remove, these phase errors by digitally processing coherent recordings of the image data. In this manner we are able to remove the effects of atmospheric turbulence without needing a conventional adaptive optical system. Digital holographic detection is used to record the coherent, complex-valued, optical field for a series of atmospheric and object realizations. Correction of atmospheric phase errors is then based on maximizing an image sharpness metric to determine the aberrations present and correct the underlying image. Experimental results that demonstrate image recovery in the presence of turbulence are presented. Results obtained with severe turbulence that gives rise to anisoplanatism are also presented.

We investigate the effects of beam ellipticity on the dynamics of multiple filamentation. We find that increasing the ellipticity of the initial beam decreases the power required for multiple filamentation. At lower input ellipticities, the beam breaks into filaments along its widest dimension, whereas for higher ellipticities the pulse breaks into bands and then into filaments as the power is increased. The breakup patterns of the beam along the wider dimension are consistent with the modulational instability, and these patterns are independent of polarization and noise. Numerical simulations are in qualitative agreement with these features of multiple filamentation breakup.

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.

We investigate the spatial dynamics of optical necklace beams in Kerr media. For powers corresponding to less than the critical power for self-focusing per bead, we experimentally confirm the confinement of these necklace beams as proposed in [Phys. Rev. Lett. 81, 4851 (1998)10.1103/PhysRevLett.81.4851]. At higher powers, we observe a transition from collective necklace behavior to one in which the beads of the necklace collapse independently. We observe that, below the transition power, the perturbed necklace still behaves in a collective manner with coupling between individual beads but that, at higher powers, it undergoes a similar transition to a decoupled state of the necklace.

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We theoretically and experimentally investigate the mutual collapse dynamics of two spatially separated optical beams in a Kerr medium. Depending on the initial power, beam separation, and the relative phase, we observe repulsion or attraction, which in the latter case reveals a sharp transition to a single collapsing beam. This transition to fusion of the beams is accompanied by an increase in the collapse distance, indicating the effect of the nonlinear coupling on the individual collapse dynamics. Our results shed light on the basic nonlinear interaction between self-focused beams and provide a mechanism to control the collapse dynamics of such beams. [5]. Over the past decade, with the advent of high peak power ultra-short pulsed lasers, self-focusing dynamics of optical beams have revealed a remarkable richness of spatial and temporal nonlinear phenomena. These include observation of the universal self-similar spatial collapse profile known as the Townes profile [6], multiple filamentation [7], self steepening and pulse splitting [8,9], multiphoton ionization, and supercontinuum generation [9,10], along with saturation and plasma generation that typically arrest the collapse [11].Related optical beam interactions within the context of spatial solitons [12,13] have drawn considerable interest in recent years. Spatial solitons in 1D Kerr media are shown to interact in a particle-like elastic manner, where the number of solitons and the corresponding directions and propagation velocities are conserved [12,14]. Depending on the relative phase, attractive and repulsive forces and power transfer are observed between interacting solitons [15]. In saturable nonlinear media, which can support (2+1)D solitons, phenomena such as soliton fusion, fission, annihilation, and spiraling occur [16,17,18,19]. The interaction between incoherent solitons, where the medium responds non-instantaneously, exhibits similar effects as those observed with coherent solitons in nonlinear saturable media [20].In the regime of optical beam collapse in a Kerr medium, where self focusing is dominant and beams do not maintain their spatial distribution, only a few theoretical studies of beam interactions have been reported [21,22,23,24], and to the best of our knowledge no experiments have been performed. While in these initial theoretical studies several qualitative trends, such as repulsion, attraction, and fusion of two beams, were identified, the detailed dynamics and the transition to fusion of two beams, especially when each beam has a power near P cr , has not been explored.In this Letter, we investigate both theoretically and experimentally the spatial collapse dynamics of two coherently coupled beams in Kerr media. We observe repulsion and attraction between the collapsing beams, and a sharp transition to fusion of the beams, which is dependent on their initial power, spatial separation and relative phase. We further show that this transition, accompanied by a peak in the collapse distance, can be exploited to control and manipulat...