Gennadiy Burlak

Stability boundary and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity.

We introduce one- and two-dimensional (1D and 2D) models of parity-time (PT)-symmetric couplers with the mutually balanced linear gain and loss applied to the two cores and cubic-quintic (CQ) nonlinearity acting in each one. The 2D and 1D models may be realized in dual-core optical wave guides in the spatiotemporal and spatial domains, respectively. Stationary solutions for PT-symmetric solitons in these systems reduce to their counterparts in the usual coupler. The most essential problem is the stability of the solitons, which become unstable against symmetry breaking with the increase of the energy (norm) and retrieve the stability at still larger energies. The boundary value of the intercore-coupling constant, above which the solitons are completely stable, is found by means of an analytical approximation, based on the cw (zero-dimensional) counterpart of the system. The approximation demonstrates good agreement with numerical findings for the 1D and 2D solitons. Numerical results for the stability limits of the 2D solitons are obtained by means of the computation of eigenvalues for small perturbations, and verified in direct simulations. Although large parts of the soliton families are unstable, the instability is quite weak. Collisions between 2D solitons in the PT-symmetric coupler are studied by means of simulations. Outcomes of the collisions are inelastic but not destructive, as they do not break the PT symmetry.

Spectrum of Cherenkov Radiation in Dispersive Metamaterials with Negative Refraction Index

We numerically studied the spectrum of Cherenkov optical radiation by a nonrelativistic anisotropic electron bunch crossing 3D dispersive metamaterial. A practically important case when such a medium is described by Drude model is investigated in details. In our theory only parameters of a metamaterial are flxed. The frequency spectrum of internal excitations is left to be deflned as a result of the numerical simulation. It is found that a periodic fleld structure coupled to plasmonic excitations is arisen when the dispersive refractive index of a metamaterial becomes negative. In this case the reversed Cherenkov radiation is observed.

Dynamics of matter-wave solitons in a time-modulated two-dimensional optical lattice

By means of the variational approximation (VA) and systematic simulations, we study dynamics and stability boundaries for solitons in a two-dimensional (2D) self-attracting Bose-Einstein condensate (BEC), trapped in an optical lattice (OL) whose amplitude is subjected to periodic time modulation (the modulation frequency

PT-symmetric couplers with competing cubic-quintic nonlinearities

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Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources ?

may be in the range of several kHz). Regions of stability of the solitons against the collapse and decay are identified in the space of the models parameters. A noteworthy result is that the stability limit may reach the largest (100%) modulation depth, and the collapse threshold may exceed its classical value in the static lattice (which corresponds to the norm of Townes soliton). The minimum norm

CHANGE OF STRUCTURE OF THE CHERENKOV EMISSION AT MODULATED SOURCE IN DISPERSIVE METAMATERIALS

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The Electromagnetic Properties of the Generalized Cantor Stack in Spherical Multilayered Systems

necessary for the stability of the solitons is identified too. It features a strong dependence on

The Subwavelength Optical Field Confinement in a Multilayered Microsphere with Quasiperiodic Spherical Stack

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The Cherenkov Emission in Regular and Random Photonic Crystals

at low frequencies, due to a resonant decay of the soliton. Predictions of the VA are reasonably close to results of the simulations. In particular, the VA helps understand salient resonant features in the shape of the stability boundaries observed with the variation of

The Green Function and Optical Field Enhancement in a Multilayered Microsphere with Metamaterial

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