[Show abstract][Hide abstract] ABSTRACT: We discuss differences between the variational approach to solitons and the
accessible soliton approximaion in a highly nonlocal nonlinear medium. We
compare results of both approximations by considering the same system of
equations in the same spatial region, under the same boundary conditions. We
also compare these approximations with the numerical solution of the equations.
We find that the variational highly nonlocal approximation provides more
accurate results and as such is more appropriate solution than the accessible
soliton approximation. The accessible soliton model offers a radical
simplification in the treatment of highly nonlocal nonlinear media, with easy
comprehension and convenient parallels to quantum harmonic oscillator, however
with a hefty price tag: a systematic numerical discrepancy of up to 100% with
the numerical results.
[Show abstract][Hide abstract] ABSTRACT: We investigate the destructive influence of noise on the shape-invariant solitons in a three-dimensional model that includes the highly nonlocal nature of nematic liquid crystals. We first determine the fundamental shape-preserving solitons and then establish that any noise added to the medium or to the solitons induces them to breathe at short propagation distances and to disperse at long propagation distances. The characteristics of breathing solitons at short distances are well predicted by the variational calculation [Phys. Rev. A 85, 033826 (2012)]. At longer propagation distances soliton beams suddenly spread, almost without radiation losses. Their power remains almost conserved until they reach the transverse boundaries of the sample. The increase in the amount of noise accelerates beam spreading and soliton destruction. The influence of the correlation length of noise is more complex. An initial increase in the correlation length causes solitons to disperse at shorter propagation distances. However, further increase in the correlation length leads to a reversal—to prolonged stability and dispersal at longer propagation distances. We give theoretical explanation for such behavior in terms of mean-field evolution equations.
Physical Review A 04/2013; 87(4). · 3.04 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
Journal of the Optical Society of America B 04/2013; 30(4):1036-. · 2.21 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We generate perturbed fundamental solitons in three dimensional highly nonlocal uniaxial nematic liquid crystals in the presence of an externally applied bias voltage, by launching specific Gaussian beams into the liquid crystal cell. In general, launching Gaussians leads to their dispersal for low intensities and small widths, and to their instabilities for high intensities and large widths. Localized solutions in the form of well defined breathing solitons are observed only for the well defined values of the input beam intensity and width, which can be determined by a variational technique. In this case, the oscillating Gaussian beam characteristics are close to the perturbed breathing fundamental soliton solutions, with the characteristics well-predicted by the variational calculation.
[Show abstract][Hide abstract] ABSTRACT: We investigate numerically and theoretically solitons in highly nonlocal three-dimensional nematic liquid crystals. We calculate the fundamental soliton profiles using the modified Petviashvili method. We apply the variational method to the widely accepted scalar model of beam propagation in uniaxial nematic liquid crystals and compare the results with numerical simulations. To check the stability of such solutions, we propagate them in the presence of noise. We discover that the presence of any noise induces the fundamental solitons—the so-called nematicons—to breathe. Our results explain the difficulties in experimental observation of steady nematicons.
Physical Review A 03/2012; 85(3). · 3.04 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We studied electromagnetic wave transmission through layered structures that include negative index materials. The excitation of leaky guided modes leads to the formation of anomalous lateral shifts in the reflected beam with a double-peak structure and in the transmitted beam with a single-peak structure. In the absence of losses, we demonstrate that the total transparency (i.e. zero reflection) of the slab waveguide with the negative index material can be achieved under conditions in which high reflectivity is normally expected. We demonstrate the trade-off effect between the high transmission and the high lateral shift. This peculiar effect exists not only for the pure TE or the pure TM polarization of the obliquely incident radiation, but also under certain circumstances for both of them simultaneously i.e. for the nonpolarized radiation.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: In this paper, a stability analysis of the Ginzburg–Landau system is performed using a variational method. Growth rates for radially symmetric (isotropic) and asymmetric (anisotropic) perturbations of fundamental steady-state solutions of the cubic-quintic Ginzburg–Landau equation are found. The stability domain of fundamental dissipative solitons is established. Analytical results are confirmed by exhaustive numerical simulations.
[Show abstract][Hide abstract] ABSTRACT: We question physical existence of shape invariant solitons in three
dimensional nematic liquid crystals. Using modified Petviashvili's method for
finding eigenvalues and eigenfunctions, we determine shape invariant solitons
in a realistic physical model that includes the highly nonlocal nature of the
liquid crystal system. We check the stability of such solutions by propagating
them for long distances. We establish that any noise added to the medium or to
the fundamental solitons induces them to breathe, rendering them practically
[Show abstract][Hide abstract] ABSTRACT: We determine analytical extended traveling-wave and spatiotemporal solitary solutions to the generalized (3+1)-dimensional Gross-Pitaevskii equation with time-dependent coefficients, for the sinusoidally time-varying diffraction and quadratic potential strength. A number of periodic and localized solutions are obtained whose intensity does not decrease in time in the absence of externally induced gain or loss. Stability analysis of our solitary solutions is carried out, to display their modulational stability.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We study numerically the interaction of two counterpropagating (CP) optical beams near the boundary of a truncated one-dimensional photonic lattice. We demonstrate that the mutual coupling of beams suppresses the effective repulsion from the lattice edge, resulting in the formation of CP surface solitons. Such localized beams may propagate in the same, as well as in neighboring, waveguides. We also reveal that the lattice disorder reduces substantially the threshold power for the formation of CP surface states.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We study numerically the interaction of two counterpropagating (CP) optical beams near the boundary of a truncated one-dimensional photonic lattice. We demonstrate that the mutual coupling of beams suppresses the effective repulsion from the lattice edge, resulting in the formation of CP surface solitons. Such localized beams may propagate in the same, as well as in neighboring, waveguides. We also reveal that the lattice disorder reduces substantially the threshold power for the formation of CP surface states. (C) 2010 Optical Society of America
[Show abstract][Hide abstract] ABSTRACT: A generalized Ginzburg-Landau equation describing dissipative solitons dynamics in negative-refractive-index materials is derived from Maxwell equations. This equation having only real terms with opposite sign differs from the usual Ginzburg-Landau equation for positive-refractive-index media. A cross-compensation between the saturating nonlinearity excess, losses, and gain makes obtained self-organized solitons dissipationless and exceptionally robust. In the presence of such solitons medium becomes effectively dissipationless. The compensation of losses is of particular interest for media with resonant character of interactions like negative-refractive-index materials.
Physical Review A 01/2010; 81(4). · 3.04 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: General nonlinear and nonparaxial dissipative complex Helmholtz equations for magnetic and electric fields propagating in negative refractive index materials (NIMs) are derived ab initio from Maxwell equations. In order to describe nonconservative soliton dynamics in NIMs, such coupled equations are reduced into generalized Ginzburg-Landau equation. Cross-compensation between the excess of saturating nonlinearity, losses, and gain renders these self-organized solitons dissipationless and exceptionally robust. The presence of such solitons makes NIMs effectively dissipationless. Comment: 5 figures
[Show abstract][Hide abstract] ABSTRACT: 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.
Journal of Optics A Pure and Applied Optics 06/2008; 10(7):075102. · 1.92 Impact Factor