Najdan B. Aleksić

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.

Dynamics of electromagnetic beam with phase dislocation in saturable nonlinear media

Abstract The nonlinear dynamics of laser beams carrying phase singularity in media with cubic–quintic nonlinearity is studied. In such media can be generated not only localized vortex solitons but also a novel kind of stable nonlocalized optical vortices. Stability in the defocusing regime is confirmed numerically. In the focusing regime such a vortex breaks into filaments. Dynamics of a singular Gaussian beam is investigated. Numerical simulations show a new behavior of the supercritical Gaussian beam which first breaks into filaments coalescing after.

Breathing solitons in nematic liquid crystals

Dynamical and steady-state behavior of beams propagating in nematic liquid crystals (NLCs) is analyzed. A well-known model for the beam propagation and the director reorientation angle in a NLC cell is treated numerically in space and time. The formation of steady-state soliton breathers in a threshold region of beam intensities is displayed. Below the region the beams diffract, above the region spatiotemporal instabilities develop, as the input intensity and the material parameters are varied. Curiously, the only kind of solitons we could demonstrate in our numerical studies was the breathers. Despite repeated efforts, we could not find the solitons with a steady profile propagating in the NLC model at hand.

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.

Counterpropagating beams in nematic liquid crystals.

The behavior of counterpropagating self-trapped optical beam structures in nematic liquid crystals is investigated. A time-dependent model for the beam propagation and the director reorientation in a nematic liquid crystal is numerically treated in three spatial dimensions and time. We find that the stable vector solitons can only exist in a narrow threshold region of control parameters. Below this region the beams diffract, above they self-focus into a series of focal spots. Spatiotemporal instabilities are observed as the input intensity, the propagation distance, and the birefringence are increased. We demonstrate undulation, filamentation, and convective dynamical instabilities of counterpropagating beams. Qualitatively similar behavior as of the copropagating beams is observed, except that it happens at lower values of control parameters.

Self-stabilized spatiotemporal dynamics of dissipative light bullets generated from inputs without spherical symmetry in three-dimensional Ginzburg-Landau systems

In order to meet experimental conditions, the generation, evolution, and self-stabilization of optical dissipative light bullets from non-spherically-symmetric input pulses is studied. Steady-state solutions of the (3+1)-dimensional complex cubic-quintic Ginzburg-Landau equation are computed using the variational approach with a trial function asymmetric with respect to three transverse coordinates. The analytical stability criterion is extended to systems without spherical symmetry, allowing determination of the domain of dissipative parameters for stable solitonic solutions. The analytical predictions are confirmed by numerical evolution of the asymmetric input pulses toward stable dissipative light bullets. Once established, the dissipative light bullet remains surprisingly robust.

Self-structuring of stable dissipative breathing vortex solitons in a colloidal nanosuspension

The self-structuring of laser light in an artificial optical medium composed of a colloidal suspension of nanoparticles is demonstrated using variational and numerical methods extended to dissipative systems. In such engineered materials, competing nonlinear susceptibilities are enhanced by the light induced migration of nanoparticles. The compensation of diffraction by competing focusing and defocusing nonlinearities, together with a balance between loss and gain, allow for self-organization of light and the formation of stable dissipative breathing vortex solitons. Due to their robustness, the breathers may be used for selective dynamic photonic tweezing of nanoparticles in colloidal nanosuspensions.

Ground-state counterpropagating solitons in photorefractive media with saturable nonlinearity

We investigate the existence and form of (2+1)-dimensional ground-state counterpropagating solitons in photorefractive media with saturable nonlinearity. General conditions for the existence of fundamental solitons in a local isotropic model that includes an intensity-dependent saturable nonlinearity are identified. We confirm our theoretical findings numerically and determine the ground-state profiles. We check their stability in propagation and identify the coupling constant threshold for their existence. Critical exponents of the power and beam width are determined as functions of the propagation constant at the threshold. We finally formulate a variational approach to the same problem, introduce an approximate fundamental Gaussian solution, and verify that this method leads to the same threshold and similar critical exponents as the theoretical and numerical methods.

Using graphical processing units to solve the multidimensional Ginzburg-Landau equation

We demonstrate the use of ultrafast hardware, based on a graphical processing unit (GPU), to solve the complex Ginzburg–Landau equation. We implement an improved finite-difference time-domain method. We utilize parallel processing of our numerical procedure, resulting in tremendous acceleration in the execution of routines and substantial reduction of cost. Simulations are performed in two and three spatial dimensions with time as the marching variable. The numerical algorithm is also implemented on a CPU to make a comparison with the GPU. An acceleration of about 95 times is achieved. The benefits are discussed in detail and the results are presented visually to achieve the best solution strategy for the given problem.

Modulation stability analysis of exact multidimensional solutions to the generalized nonlinear Schrödinger equation and the Gross-Pitaevskii equation using a variational approach

We analyze the modulation stability of spatiotemporal solitary and traveling wave solutions to the multidimensional nonlinear Schrödinger equation and the Gross-Pitaevskii equation with variable coefficients that were obtained using Jacobi elliptic functions. For all the solutions we obtain either unconditional stability, or a conditional stability that can be furnished through the use of dispersion management.