From solitons to rogue waves in nonlinear left-handed metamaterials

Forward and backward propagating breathers in a DNA model with dipole-dipole long-range interactions

The present study explores the existence and orbital stability of discrete bright breathers through the Joyeux-Buyukdagli DNA model incorporating long-range interactions (LRIs). The nonlinear Schrödinger equation is derived from a semidiscrete approximation and subsequently used to construct the targeted initial condition for numerical computations of the discrete breather. It appears that the interplay between the carrier wave frequency and the LRI induces stationary forward or backward propagating waves. For critical values of the LRI, stationary waves can occur out of the center/edge of the first Brillouin zone. The predicted breathers differ in their robustness and mobility for specific carrier-wave frequency and LRI. In all cases, semianalytical predictions agree with numerical simulations.

Discrete vortices on spatially nonuniform two-dimensional electric networks

Two-dimensional arrays of nonlinear electric oscillators are considered theoretically where nearest neighbors are coupled by relatively small constant but nonequal capacitors. The dynamics is approximately reduced to a weakly dissipative defocusing discrete nonlinear Schrödinger equation with translationally noninvariant linear dispersive coefficients. Behavior of quantized discrete vortices in such systems is shown to depend strongly on the spatial profile of the internode coupling as well as on the ratio between time-increasing healing length and lattice spacings. In particular, vortex clusters can be stably trapped for some initial period of time by a circular barrier in the coupling profile, but then, due to gradual dissipative broadening of vortex cores, they lose stability and suddenly start to move.

Waves in hyperbolic and double negative metamaterials including rogues and solitons

The topics here deal with some current progress in electromagnetic wave propagation in a family of substances known as metamaterials. To begin with, it is discussed how a pulse can develop a leading edge that steepens and it is emphasised that such self-steepening is an important inclusion within a metamaterial environment together with Raman scattering and third-order dispersion whenever very short pulses are being investigated. It is emphasised that the self-steepening parameter is highly metamaterial-driven compared to Raman scattering, which is associated with a coefficient of the same form whether a normal positive phase, or a metamaterial waveguide is the vehicle for any soliton propagation. It is also shown that the influence of magnetooptics provides a beautiful and important control mechanism for metamaterial devices and that, in the future, this feature will have a significant impact upon the design of data control systems for optical computing. A major objective is fulfiled by the investigations of the fascinating properties of hyperbolic media that exhibit asymmetry of supported modes due to the tilt of optical axes. This is a topic that really merits elaboration because structural and optical asymmetry in optical components that end up manipulating electromagnetic waves is now the foundation of how to operate some of the most successful devices in photonics and electronics. It is pointed out, in this context, that graphene is one of the most famous plasmonic media with very low losses. It is a two-dimensional material that makes the implementation of an effective-medium approximation more feasible. Nonlinear non-stationary diffraction in active planar anisotropic hyperbolic metamaterials is discussed in detail and two approaches are compared. One of them is based on the averaging over a unit cell, while the other one does not include sort of averaging. The formation and propagation of optical spatial solitons in hyperbolic metamaterials is also considered with a model of the response of hyperbolic metamaterials in terms of the homogenisation ('effective medium') approach. The model has a macroscopic dielectric tensor encompassing at least one negative eigenvalue. It is shown that light propagating in the presence of hyperbolic dispersion undergoes negative (anomalous) diffraction. The theory is ten broadened out to include the influence of the orientation of the optical axis with respect to the propagation wave vector. Optical rogue waves are discussed in terms of how they are influenced, but not suppressed, by a metamaterial background. It is strongly discussed that metamaterials and optical rogue waves have both been making headlines in recent years and that they are, separately, large areas of research to study. A brief background of the inevitable linkage of them is considered and important new possibilities are discussed. After this background is revealed some new rogue wave configurations combining the two areas are presented alongside a discussion of the way forward for the future.