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.

Dispersion properties of nonradiating configurations: finite-difference time-domain modeling.

A finite-difference time-domain (FDTD) numerical analysis is used to demonstrate that a toroidal solenoid, coaxial with an electric dipole, is a remarkable nonradiating configuration. It can be used to measure the dielectric permittivity of any ambient matter. It becomes a directional radiator at an interface between two dielectric media, depositing energy in the material with the highest polarizability.

Excitation of vortices using linear and nonlinear magnetostatic waves.

It is shown that stationary vortex structures can be excited in a ferrite film, in the important centimeter and millimeter wavelength ranges. It is shown that both linear and nonlinear structures can be excited using a three-beam interaction created with circular antennas. These give rise to a special phase distribution created by linear and nonlinear mixing. An interesting set of three clockwise rotating vortices joined by one counter-rotating one presents itself in the linear regime: a scenario that is only qualitatively changed by the onset of nonlinearity. It is pointed out that control of the vortex structure, through parametric coupling, based upon a microwave resonator, is possible and that there are many interesting possibilities for applications.

High-order nonlinear phase shift caused by cascaded third-order processes.

We show, for the first time to our knowledge, that the fundamental beam that participates in the process of third-harmonic generation experiences an additional high-order nonlinear phase shift. The magnitude of the shift is proportional to the square of the pump intensity and the length of the sample and depends on the deviation from the exact phase-matched condition. This phase shift arises from cascaded third-order processes. Its value can exceed the value of the phase shift that originates from inherent fifth-order susceptibility of the nonlinear medium. Its sign is controllable by the sign of the phase mismatch of the third-harmonic generation process.

Exact dispersion relations for transverse magnetic polarized guided waves at a nonlinear interface.

We derive exact dispersion relations for transverse magnetic polarized guided waves at an interface between either a linear dielectric or a metal and a nonlinear dielectric. The nonlinearity is taken to be a Kerr-type nonlinearity. Numerical results are presented for the dielectric-metal case.