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Dissipative Optical Solitons

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The generation and nonlinear dynamics of multi-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 one-, two-, and three-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 even asymmetric input pulse from this domain leads to stable dissipative solitons and light bullets.
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Time-dependent rotation of counterpropagating mutually incoherent self-trapped Gaussian beams in periodic optically induced fixed photonic lattices is numerically investigated. Rotation occurs for some values of control parameters. For parameters of such rotation, the solitonic solutions are found using modified Petviashvili's method. It is shown that they correspond to the lowest values of propagation constant in the power diagrams and relation between observed rotation and less confined discrete solitonic solutions are demonstrated.
EN
A review of work on the dynamical behavior of counterpropagating incoherent laser beams in photorefractive crystals is presented. Numerical study of counterpropagating beams of different type is carried out, in both space and time, using an appropriate theoretical model. The development of patterns in broad hyper-Gaussian counterpropagating beams in saturable Kerr-like media is investigated, by varying the width of beams. Rotational properties of counterpropagating mutually incoherent self-trapped vortex beams in optically induced fixed photonic lattices are also investigated numerically. One of the fundamental quantum mechanical phenomena is observed for the counterpropagating beams in photonic lattices, the tunneling of light from the first to the higher-order bands of the lattice band gap spectrum. The transfer of angular momentum from vortex beams to optically induced photonic lattices is also demonstrated. For the interacting beams it is found that the sum of angular momenta of counterpropagating components is not a conserved quantity, but the difference is. In the fixed lattices there is always a considerable loss of angular momentum.
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Propagation Effects in Superfluorescence

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The evolution of a superfluorescent pulse is studied in the region of large sample lengths. A solution to the Maxwell-Bloch semiclassical equations is found by using the inverse scattering method. It has the form of a one-soliton solution with varying parameters. Dependence on the pulse width and the retarded time is found without further approximations. These parameters are shown to be independent of the inhomogeneous broadening time. Their values are in good agreement with experiment. Asymmetry of the pulse is also investigated.
EN
Nonlinear dissipative systems, particularly optical dissipative solitons are well described by complex Ginzburg-Landau equation. Solutions of two- and three-dimensional complex cubic-quintic Ginzburg-Landau equation assuming exponential dependence on propagation parameter are studied. Approximate analytical stationary solutions of cubic-quintic Ginzburg-Landau equation are found by solving systems of ordinary differential equations. We are solving two-point boundary problems using adapted shooting method. Stable and unstable branches of the bifurcation diagram are identified using linear stability analysis. In this way we established conditions for generation and propagation of stable dissipative solitons in two and three dimensions. These results are in agreement with numerical simulation of cubic-quintic Ginzburg-Landau equation and the recently established approach based on variational method generalized to dissipative systems and therein established stability criterion.
EN
The unique features of the families of bright spinning spatiotemporal solitons (doughnuts or vortex light bullets) in dispersive quadratic media, including their stability, are presented. Both analytical results, obtained by means of a simple variational approximation, and numerical simulations are presented and compared. It was found that though the variational approximation is not very accurate, it correctly describes the qualitative features of the spinning spatiotemporal solitons. The spinning light bullets are subject to a strong azimuthal instability, which leads to the break-up of the spinning soliton into a set of fragments, each being a stable nonspinning spatiotemporal soliton.
EN
Propagation of an intense femtosecond laser pulse through a transparent nonlinear medium such as dielectric leads to a number of phenomena. In our experiment we observed complex spatial, spectral, and temporal structures appearing in the initially smooth femtosecond laser pulse when the pulse power is comparable to or higher than the critical power for self-focusing. We have also developed a complete, 3-dimensional theoretical model to describe the observed phenomena.
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Analytical and numerical investigation of the propagation of "necklace-ring" optical beams in Kerr-like saturable photorefractive media with square-root nonlinearity is carried out. Analytic expression for the propagation dynamics of the necklace beams is in good agreement with numerical findings.
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Beam Propagation in Nematic Liquid Crystals

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EN
We investigate the behavior of beams propagating in nematic liquid crystals. A spatiotemporal model for the beam propagation and the director reorientation in a nematic liquid crystal is treated numerically in three spatial dimensions and time. We demonstrate the formation of stable solitons in a narrow threshold region of beam intensities for a set of fixed parameters and display soliton breathing. Below the threshold region the beams diffract, above the region spatiotemporal instabilities are observed, as the input intensity and the optical and static permittivity anisotropies of the liquid crystal molecules are increased. We demonstrate the filamentation of solitons above the threshold with increasing input intensity.
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EN
We investigate the behavior of counterpropagating optical beam structures in nematic liquid crystals. We restrict our attention to the dipole-dipole beam arrangements. A time-dependent model for the beam propagation and the director reorientation in nematic liquid crystals is numerically treated in three spatial dimensions and time. Stable dipole beams are observed in a very narrow threshold region of control parameters. Below this region the beams diffract, above the region spatiotemporal instabilities are observed, as the input intensity is increased and also as the distance between the dipole partners is decreased. A transverse beam displacement of counterpropagating dipole beams is also found. The difference between the in-phase and out-of-phase components of the dipole is significant, but only for a smaller distance between the dipole partners.
EN
In this paper, the propagation and behavior of spatial solitons of inhomogeneous nonlinear Schrödinger equation in thermal medium will be investigated analytically. The theoretical model is established by considering the change of refractive index of medium due to heat deposition of entrance beam. The soliton like solution in such thermal medium was derived. The effect of input pump power and beam radius on the behavior of solitons will be studied finally.
EN
We investigate relations between bestselling artists in last decade on phonographic market and from perspective of listeners by using the Social Network Analyzes. Starting network is obtained from the matrix of correlations between the world's bestselling artists by considering the synchronous time evolution of weekly record sales. This method reveals the structure of phonographic market, but we claim that it has no impact on people who see relationship between artists and music genres. We compare "sale" (based on correlation of record sales) or "popularity" (based on data mining of the record charts) networks with "similarity" (obtained mainly from survey within music experts' opinion) and find no significant relations. We postulate that non-laminar phenomena on this specific market introduce turbulence to how people view relations of artists.
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