Lj. Hadžievski

Dynamic polarization of graphene by moving external charges: Random phase approximation

We evaluate the stopping and image forces on a charged particle moving parallel to a doped sheet of graphene by using the dielectric-response formalism for graphenes

Nonlinear localized flat-band modes with spin-orbit coupling

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Refractive properties of metamaterial composed of InGaAs layers with alternating doping densities

-electron bands in the random phase approximation (RPA). The forces are presented as functions of the particle speed and the particle distance for a broad range of charge-carrier densities in graphene. A detailed comparison with the results from a kinetic equation model reveal the importance of interband single-particle excitations in the RPA model for high particle speeds. We also consider the effects of a finite gap between graphene and a supporting substrate, as well as the effects of a finite damping rate that is included through the use of Mermins procedure. The damping rate is estimated from a tentative comparison of the Mermin loss function with a high-resolution reflection electron energy loss spectroscopy experiment. In the limit of low particle speeds, several analytical results are obtained for the friction coefficient that show an intricate relationship between the charge-carrier density, the damping rate, and the particle distance, which may be relevant to surface processes and electrochemistry involving graphene.

Soliton nanoantennas in two-dimensional arrays of quantum dots

We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flat-band network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the systems band-gap structure, and preserves the existence of CLSs at the flat-band frequency, simultaneously lowering their symmetry. Adding on-site cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies that are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.

Extreme events in two-dimensional disordered nonlinear lattices

The aspects of light propagation through a semiconductor metamaterial (SMM) which consists of two alternating differently doped In0.53Ga0.47As layers are studied analytically and numerically. A general analytical expression for the effective index of refraction of the Poynting vector is derived for periodic structure composed of two alternating layers of absorptive and dispersive semiconductors and light propagation is simulated by finite-difference-time-domain method. Negative values of the effective refractive index with low absorption are observed in the mid-infrared frequency range. The main advantage of this design is the possibility to control the frequency region with negative effective refractive index by changing the doping densities of the layers.

Coherent light propagation through multicore optical fibers with linearly coupled cores

We consider two-dimensional (2D) arrays of self-organized semiconductor quantum dots (QDs) strongly interacting with electromagnetic field in the regime of Rabi oscillations. The QD array built of two-level states is modelled by two coupled systems of discrete nonlinear Schrödinger equations. Localized modes in the form of single-peaked fundamental and vortical stationary Rabi solitons and self-trapped breathers have been found. The results for the stability, mobility and radiative properties of the Rabi modes suggest a concept of a self-assembled 2D soliton-based nano-antenna, which is stable against imperfections In particular, we discuss the implementation of such a nano-antenna in the form of surface plasmon solitons in graphene, and illustrate possibilities to control their operation by means of optical tools.

Surface solitons in trilete lattices

Abstract Spatiotemporal complexity is induced in a two dimensional nonlinear disordered lattice through the modulational instability of an initially weakly perturbed excitation. In the course of evolution we observe the formation of transient as well as persistent localized structures, some of which have extreme magnitude. We analyze the statistics of occurrence of these extreme collective events and find that the appearance of transient extreme events is more likely in the weakly nonlinear regime. We observe a transition in the extreme events recurrence time probability from exponential, in the nonlinearity dominated regime, to power law for the disordered one.

Models of spin-orbit-coupled oligomers

Multicore fibers with linearly coupled cores are considered as a means of the coherent transport needed for high-capacity communication systems and high-power fiber lasers. The conditions of the existence and stability of coherent light propagation in multicore fibers with circularly arranged cores are derived. The multicore fiber is modeled by the linear discrete complex Ginzburg–Landau equation, while its eigenvalues are found analytically. The inverse eigenvalue problem proposing the commensurability of eigenvalues is solved to find the intercore coupling coefficients that support periodic revivals of the input state. Both planar modes and vortices are considered. Effects of the central core and material loss/gain on eigenvalue commensurability conditions and mode dynamics are studied in detail.

Long-lived double periodic patterns in dipolar cigar-shaped Bose?Einstein condensates in an optical lattice

Abstract Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schrodinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter—actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss.

Extreme Events in Nonlinear Lattices

We address the stability and dynamics of eigenmodes in linearly shaped strings (dimers, trimers, tetramers, and pentamers) built of droplets in a binary Bose-Einstein condensate (BEC). The binary BEC is composed of atoms in two pseudo-spin states with attractive interactions, dressed by properly arranged laser fields, which induce the (pseudo-) spin-orbit (SO) coupling. We demonstrate that the SO-coupling terms help to create eigenmodes of particular types in the strings. Dimer, trimer, and pentamer eigenmodes of the linear system, which correspond to the zero eigenvalue (EV, alias chemical potential) extend into the nonlinear ones, keeping an exact analytical form, while tetramers do not admit such a continuation, because the respective spectrum does not contain a zero EV. Stability areas of these modes shrink with the increasing nonlinearity. Besides these modes, other types of nonlinear states, which are produced by the continuation of their linear counterparts corresponding to some nonzero EVs, are found in a numerical form (including ones for the tetramer system). They are stable in nearly entire existence regions in trimer and pentamer systems, but only in a very small area for the tetramers. Similar results are also obtained, but not displayed in detail, for hexa- and septamers.