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

Short intense laser pulses with phase singularity propagating in narrow-gap semiconductors are modeled. The saturating nonlinearity is a prerequisite for self-organization of pulses into solitons. The cubic-quintic saturation appears due to the conduction-band nonparabolicity in synergy with the free carriers excitation through two-photon absorption. The pulse stability analyzed using Lyapunov’s method is confirmed by numerical simulations. Depending of its power, a singular Gaussian pulse far from equilibrium either filaments or subsequently coalesces evolving toward vortex soliton. Above breaking power, such a vortex soliton resists to azimuthal symmetry-breaking perturbations

Three-dimensional spatial solitons in CS2

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Extension of the stability criterion for dissipative optical soliton solutions of a two-dimensional Ginzburg–Landau system generated from asymmetric inputs

The evolution and stability of dissipative optical spatial solitons generated from an input asymmetric with respect to two transverse coordinates x and y are studied. The variational approach used to investigate steady state solutions of a cubic–quintic Ginzburg–Landau equation is extended in order to consider initial conditions without radial symmetry. The stability criterion is generalized to the asymmetric case. A domain of dissipative parameters for stable solitonic solutions is determined. Following numerical simulations, an asymmetric input laser beam with dissipative parameters from this domain will always give a stable dissipative spatial soliton

Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials

Complex Ginzburg-Landau (CGL) models of laser media (with the cubic-quintic nonlinearity) do not contain an effective diffusion term, which makes all vortex solitons unstable in these models. Recently, it has been demonstrated that the addition of a two-dimensional periodic potential, which may be induced by a transverse grating in the laser cavity, to the CGL equation stabilizes compound (four-peak) vortices, but the most fundamental "crater-shaped" vortices (CSVs), alias vortex rings, which are, essentially, squeezed into a single cell of the potential, have not been found before in a stable form. In this work we report families of stable compact CSVs with vorticity S=1 in the CGL model with the external potential of two different types: an axisymmetric parabolic trap, and the periodic potential. In both cases, we identify stability region for the CSVs and for the fundamental solitons (S=0). Those CSVs which are unstable in the axisymmetric potential break up into robust dipoles. All the vortices with S=2 are unstable, splitting into tripoles. Stability regions for the dipoles and tripoles are identified too. The periodic potential cannot stabilize CSVs with S>=2 either; instead, families of stable compact square-shaped quadrupoles are found

Stability and nesting of dissipative vortex solitons with high vorticity

Using the variational method extended to dissipative systems and numerical simulations, an analytical stability criterion is established allowing the determination of stability domains of parameters for vortices with high topological charge S. Parameters from these domains are used as inputs for numerical self-generation of previously unexplored coexisting stable vortex solitons with topological charge ranging from S=3 to S=20. The nesting of low-vorticity solitons within those of higher vorticity is discovered. Such a self-organized structuring of light allows for selective dynamic nanophotonic tweezing

Stable One-Dimensional Dissipative Solitons in Complex Cubic-Quintic Ginzburg-Landau Equation

The generation and nonlinear dynamics of one-dimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the (1 + 1)-dimensional complex cubic-quintic Ginzburg-Landau equation. A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of any input pulse from this domain leads to stable dissipative temporal solitons. Analytical predictions are confirmed by numerical evolution of input temporal pulses towards stable dissipative solitons

Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses

Using a combination of the variation approximation and direct simulations, we consider the model of the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provides for the hitherto elusive stabilization of vortex solitons, in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, including spinning elliptically shaped ones, eccentric elliptic vortices which feature double rotation, spinning crescents, and breathing vortices