Square vortex solitons with a large angular momentum

Abstract

We show the existence of square shaped optical vortices with a large value of the angular momentum hosted in finite size laser beams which propagate in nonlinear media with a cubic-quintic nonlinearity. The light profiles take the form of rings with sharp boundaries and variable sizes depending on the power carried. Our stability analysis shows that these light distributions remain stable when propagate, probably for unlimited values of the angular momentum, provided the hosting beam is wide enough. This happens if the peak amplitude approaches a critical value which only depends on the nonlinear refractive index of the material. A variational approach allows us to calculate the main parameters involved. Our results add extra support to the concept of surface tension of light beams that can be considered as a trace of the existence of a liquid of light.

Atmospheric propagation of gradient-shaped and spinning femtosecond light pulses

“…When repeating this analysis for the academic cubic-quintic problem α = = 1 (λ ≤ 0.16), AMI takes place with maximal azimuthal index M max 2|m| and ceases when λ > λ cr ∼ 0.147 for m = 1. These results recover those deduced from numerical shooting techniques [19][20][21][22][23][24][25].…”

“…These will apply to vortex states subject to AMI and will later be extended to arbitrary waveforms. Because optical vortices are strong attractors towards which experimental pulses are expected to converge rapidly, we shall not target them by means of numerical relaxation methods, which have often been exploited in the past [18][19][20][21][22][23][24][25]. Instead, a variational method will approach spinning beams, whose azimuthal stability will be studied in the framework of spatially uniform, ring-shaped structures with constant intensity.…”

“…The existence and stability of these peculiar states have been studied for several years. First, considering 2D media with self-focusing (cubic) and defocusing (quintic) nonlinearity, Quiroga-Teixeiro and Michinel [18] showed the possibility for spinning beams having high enough power to preserve their radial shape when |m| = 1 (see also [19][20][21][22][23][24][25][26][27]). For larger values of m, vortices cover long distances before breaking up into small-scale cells.…”

Interactions of three-dimensional solitons in the cubic-quintic model

“…[29] and [30], respectively (stability regions for S > 3 exist too, but they are extremely narrow); see also Refs. [31] and [32]. In 3D, stability regions for toroidal solitons with S = 1 in single-and twocomponent NLSE systems with the CQ nonlinearity were found, respectively, in Refs.…”

Filamentation and coalescence of singular optical pulses in narrow-gap semiconductors and modeling of self-organization of vortex solitons using two-photon absorption

“…This topological charge is proportional to the angular momentum that can be large. 5 In self-defocusing Kerr media the OVS with m = 1 is stable for small perturbation. 6 In self-focusing media, ordinary saturating nonlinearities make the LOVS stable against radial perturbation, but do not prevent azimuthal instabilities.…”