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 waveguides, in the spatiotemporal and spatial domains, respectively. Stationary solutions for PTsymmetric 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 solitons 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.

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The Classical and Quantum Dynamics of the Multispherical Nanostructures Downloaded from www.worldscientific.com by 54.213.91.117 on 05/09/18. For personal use only. PrefaceNowadays there are various emerging possibilities to produce dielectric microspheres with sizes of about 1 micron and less. The number of theoretical and experimental works on the subjects of microspheres increases every year. The most fruitful turns out to be the idea of transition from the passive use of natural volume waves to the active management by the properties of such waves by growing the necessary structures in a surface. Creation of multilayered alternating structures (a dielectric stack) in a surface of microspheres allows one to sharply reduce radiative losses in a necessary frequency range and thus effectively control the parameters of radiation from microspheres. The opportunity of localization of quantum objects (quantum points) in a small working volume of the microsphere allows for the creation of miniature quantum devices. Effects of the thin layers are especially important when the thickness of a layer becomes about a quarter wavelength of radiation. So for wavelengths of about 600 nanometers such thickness becomes 150 nanometers, and for metallo-dielectric layers it is even less. Thus in multilayered microspheres interplay of micro-nano-scales effects occurs, which determines the unique features of the coated microsphere. It has predetermined the theme of this book. The various spherical micro and nano-structures are now heightened interest with experimenters, and theorists. The reason is that a dielectric microsphere possesses a number of unique features based mainly on an opportunity of energy conservation of optical oscillations in a very small working volume. Such microspheres possess natural modes of light oscillation at characteristic frequencies corresponding to the specific size and to the wavelength ratios. Presently only a spectrum of the optical modes having the large spherical quantum numbers (whispering gallery mode -WGM) is in use, and it is possible to observe the interesting phenomena to find the various engineering applications (see [Bishop et al., [Braginsky & Ilchenko, 1987; Braginsky et al., 1989]. However all of them still remain an object of intensive researches. As a result it was possible to lower the spatial scales up to the size when interaction of fields with various quantum subsystems becomes rather effective [Artemyev et al., 2001b and references therein]. Such phenomena are already described by quantum electrodynamics. Due to an opportunity of localization of fields in such a small volume (the radius of microspheres makes about 1−2 µm and less) it is possible to observe the nonlinear effects with very low threshold [Spillane et al., 2002 and references therein]. A variety of interesting nonlinear phenomena in micro-droplets have been reported [Braunstein et al., 1996 and references therein], and finally, the creation of the ensembles of such particles allows for the creation of struct...

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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 the periodic time modulation (the modulation frequency, ω, 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 model's 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). Minimum norm N min necessary for the stability of the solitons is identified too. It features a strong dependence on ω at a 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 to understand salient resonant features in the shape of the stability boundaries observed with the variation of ω. PACS numbers: 03.75.Lm,05.45.Yv 1 arXiv:0804.3424v1 [cond-mat.other]

Abstract-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 fixed. The frequency spectrum of internal excitations is left to be defined as a result of the numerical simulation. It is found that a periodic field 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.

We introduce a one-dimensional model of the parity-time ( PT)-symmetric coupler, with mutually balanced linear gain and loss acting in the two cores, and nonlinearity represented by the combination of self-focusing cubic and defocusing quintic terms in each core. The system may be realized in optical waveguides, in the spatial and temporal domains alike. Stationary solutions for PT-symmetric solitons in the systems are tantamount to their counterparts in the ordinary coupler with the cubic-quintic nonlinearity, where the spontaneous symmetry breaking of solitons is accounted for by bifurcation loops. A novel problem is stability of the PT-symmetric solitons, which is affected by the competition of the PT symmetry, linear coupling, cubic self-focusing, and quintic defocusing. As a result, the solitons become unstable against symmetry breaking with the increase of the energy (alias integral power, in terms of the spatial-domain realization), and they retrieve the stability at still larger energies. Above a certain value of the strength of the quintic self-defocusing, the PT symmetry of the solitons becomes unbreakable. In the same system, PT-antisymmetric solitons are entirely unstable. We identify basic scenarios of the evolution of unstable solitons, which may lead to generation of additional ones, while stronger instability creates expanding quasi-turbulent patterns with limited amplitudes. Collisions between stable solitons are demonstrated to be quasi-elastic.