Neil King

Negative Refraction in Perspective

The concept of negative refraction is attracting a lot of attention. The initial ideas and the misconceptions that have arisen are discussed in sufficient detail to understand the conceptual structure that binds negative refraction to the existence of backward wave and forward wave phenomena. A presentation of the properties of isotropic media supporting backward waves is followed by a discussion of negative phase velocity media, causality, anisotropic crystals, and some connections to photonic crystals. The historical background is always coupled to a detailed presentation of all the issues. The paper is driven numerically and is illustrated with the outcomes of original FDTD simulations.

Creating stable gain in active metamaterials

The question of losses in metamaterials that are based upon magnetic resonances deriving from split-ring arrays is addressed through the use of active inclusions designed from diode arrays. A full discussion of the way in which the current-voltage characteristics of the inclusions are deployed to produce gain is given, and the question of the overall stability of the new material is investigated in a quantitative way that is linked to absolute and convective instability. It is shown that instability associated with the inclusion of negative resistance devices can be avoided through a scheme that is approximately scalable from gigahertz to at least the low terahertz regimes. Furthermore, absolute instabilities that potentially complicate any active gain media can be controlled through a suitable choice of the system parameters. The latter step reduces the working frequency window over which spatial gain is available, leading to the need for compromise. Full numerical details are given with the conclusion that construction of such arrays of diode inclusions is possible and that a practical gain window is accessible.

Circuit Model of Gain in Metamaterials

Metamaterials embody exciting prospects for a new generation of novel photonic devices. From their initial emergence as a physical construct in the GHz domain at the start of the 21st century [1–3], they have attracted a significant amount of global interest [4–13] with considerable effort being undertaken to extend their operation into the THz window and even optical regimes [14,15]. However, as they stand, early theoretical indications are that losses will cause potential problems for all possible frequencies and, in particular, kill any opportunity [16] for a useful metamaterial operating around and above 30THz. Such losses are inevitably closely linked to the resonant behaviour of the metaparticles and is addressed here by the placement of active diodes onto a form of metallic split-ring. The use of diodes to create a nonlinear magnetic response [16] and to create tunability [17] has already been discussed but active diodes [18] not only promise means of reducing losses but they can be deployed to produce an overall gain [19]. This behaviour is readily scalable from GHz to THz and even to nanowire [20] and nanoparticle-based metamaterials [21] operating in the optical frequency window. Nevertheless, it is highlighted here that instabilities could present a serious issue. From an investigation of the dispersion relation for a plane wave, a number of conditions are derived that identify the limits placed upon the system parameters, in order to ensure stable overall gain. Any examination of loss, or gain, must, however, be conducted from the perspective of the entire metamaterial, including the permittivity. Depending on the level of sophistication required in the fabrication technique, split-rings may be engineered with different shapes and deployed in a number of different arrays. The most popular have either a circular, or square shape. The term “split-ring” is treated here as a generic name and is not necessarily indicative of a specific shape.

From ‘Trapped Rainbow’ Slow Light to Spatial Solitons

The metamaterial global revolution, stimulated by the pioneering work of Pendry [1], in the year 2000, raises all kinds of questions as to what they can be used for.

Weakly and strongly nonlinear waves in negative phase metamaterials

A fundamental approach to a slowly varying amplitude formulation for nonlinear waves in metamaterials will be established. The weakly nonlinear slowly varying amplitude approach will be critically examined and some misunderstandings in the literature will be fully addressed. The extent to which negative phase behaviour has a fundamental influence upon soliton behaviour will be exposed. The method will deploy nonlinear diffraction and a special kind of diffraction-management. This is additional to a detailed modulation instability analysis. The examples given involve waveguide coupling and a nonlinear interferometer. In addition, a strongly nonlinear approach will be taken that seeks exact solutions to the nonlinear equations for a metamaterial. A boundary field amplitude approach will be developed that leads to useful eigenvalue equations that expose, in a very clear manner, the possibility that new kinds of waves can be generated.

On the possibility of gain control and special solitons in metamaterials

A discussion of gain control up to the THz frequency range is presented together with a study of diffraction-managed solitons in metamaterials. Full dynamical simulations are used at every stage to illustrate the principles being evolved. An interesting approach based upon the mapping of the complex frequency-plane onto the complex wave number-plane is given as a way of demonstrating whether the offset of loss by using gain leads to a stable material. Nonlinear behaviour is addressed through the possibility of soliton formation under the conditions for which nonlinear diffraction can play a role whenever an attempt to manage the diffraction is made with a suitable combination of left-handed and right-handed materials. All of this activity requires the modeling of curious artificial molecules but the computational outcomes inspire confidence that is exemplified with exciting illustrations. The remit of control, exercised through external influences such as an applied magnetic field, and cavity formation is briefly explored.

Progress in Negative Phase Metamaterials

A review of the state-of-the-art of negative phase metamaterials is presented for which the phase velocity and group velocity form a backward wave mode. The scenarios embraced include loss, gain, solitons and slow light.

Modeling and Theory of Nonlinear or Gyrotropic Negative Phase Velocity Metamaterials

Negative phase velocity metamaterials are engineered media that are currently enjoying a surge of interest due to their interesting properties and potential applications, such as cloaking to make things invisible. The literature is alive with papers devoted to the design of suitable metamaterials and there is a particular desire to create photonic applications that will operate at THz frequencies and above. At one level, the modeling of curious artificial molecules is straightforward. Nevertheless, the approximations involved need to be able to inspire confidence for optical frequency operation. Nonlinear behaviour is intrinsic to the Holy Grail quest for power control but this topic is only just being explored. With the introduction of power come the possibility of competition with damping, gain and the creation of auto- or dissipative solitons. Functionality comes not only through power control, however, but also through other externally imposed influences such as gyromagnetic effects and external stresses. Some novel possibilities that embrace these will be presented and a new generalized theory of metamaterial behaviour, based upon a nonlinear Lorentz lemma will be outlined. The outcomes of extensive computations will be used, throughout, to illustrate all the concepts in a dramatic fashion

Modeling and theory involving metamaterial photonic structures

The literature is alive with papers devoted to the design of metamaterials and there appears to be a particular desire to create photonic applications that will operate at THz frequencies and above. At one level the modelling of suitable artificial molecules is straightforward but nevertheless the approximations involved need to be able to inspire confidence for optical frequency operation. This presentation will set out a modelling activity that is known to be satisfactory only over certain frequency ranges. Split-ring and omega particles will be specifically investigated and the possibilities discovered will be related to the current experimental expertise. The detailed manner in which the constitutive relations can be controlled and the novel way in which an envelope equation emerges for even the most complex structure is exposed. The transmission and reflection properties of nano-structured materials will be discussed within a magneto-optic environment. Simulations of sub-wavelength transmission through holes in metallic and magneto-optic screens will be discussed using finite-difference time-domain (FDTD) methods. Modelling the interaction of light beams with metamaterials is developed, again using FDTD techniques, and it is shown that special care needs to be taken with structures that have sharp external edges. Finally, a summary of the problems surrounding efficient computations will be shown and some discussion of the role of genetic algorithms in metamaterial design will be featured.

Gyrotropic control of negative phase velocity media

A description of the fascinating coupling between gyrotropic media and negative refracting media will be presented. The article will address negative phase velocity media and particular types of dielectric-gyrotropic film-dielectric systems in which the applied magnetic field may result in a magneto-optic, or gyromagnetic, influence. The control features use a diverse family of dispersion curves.