R. C. Mitchell-Thomas

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.

It's a (meta)material world! The final frontier?

There is now a global interest in the creation of creation of electromagnetic metamaterials. The substantive early work is focused upon the GHz frequency range but almost immediately the desire to progress rapidly to the optical frequency range gathered momentum. This is a natural desire because many applications operate at optical frequencies but the THz range is also important for a range of medical applications as well. The concepts that underpin the need for metamaterials, and their special properties, are explained in this article and why the creation of exotic, artificial, molecules is required to produce material behaviour beyond any performance that could naturally be expected. It will be shown that the major key lies in adding magnetic properties to special dielectric behaviour. This leads to composites that have almost magical behaviour. This presentation will explore the current global experimental progress towards three-dimensional metamaterials and will explain, in a straightforward manner, the concept of negative refraction that is attracting such a lot of attention. The initial ideas, and even some of the early misconceptions, will be addressed and clearly illustrated in a manner that enhances any understanding of the conceptual structure will be expressed. It will be shown that even though negative refraction can be associated with both backward and forward waves, the novel metamaterial concept is to associate backward wave phenomena with isotropic media, artificially endowed with negative permittivity and permeability. The principle application shown here is to a nonlinear ring interferometer that is capable of sustaining arbitrarily thin solitons or optical needles that can also be managed by an external magnetic field.

Nonlinear and magnetooptic light control in photonic metamaterial waveguides and superfocusing

Summary form only given. The major global initiative that is addressing metamaterials in the optical frequency domain must now involve nonlinearity and must include the possibility of external control. This presentation will provide an elegant route to the inclusion of nonlinearity and waveguide complexity, through original forms of transformations and special choices of metamaterials, such as those classed as hyperbolic. All of this will be framed within a magnetooptic environment that deploys externally applied magnetic field orientations to direct light for energy capture, environmental and medical purposes. The history of optical solitons is fascinating and any theory of these has a weakly guiding foundation. Vortex generation and propagation properties have also a beautiful history, and the possibility of generating them together with magnetooptic control in plasmonic metamaterials together with diffraction-management will be discussed in detail. An emphasis will be placed on the fact that spatial solitons have a lot of application possibilities, especially when placed into the context of materials being used in a light-controlling light environment that is suitable for optical chips of the future. The dramatic advantage of using magnetooptics is emphasized and complicated structures will be examined. The general theory of magnetooptic waveguides embraces Cotton-Mouton, Polar and Faraday orientations. A nonlinear electromagnetic field (energy) concentrator is also considered, for cylindrically symmetric systems and a new method of investigation proves that superfocusing must be expected. The techniques involve complex geometrical optics and the full-wave nonlinear solutions. The superfocusing leads to a dramatic appearance of “hot spots”. A new form of switching is found when the input field intensity exceeds some “threshold” value. The control of light propagating in complex waveguides is an immensely important global topic and nonlinearity is a critical tool for ultimate device control [1]. In a nonlinear context, the use of metamaterials is seminal to the development of these new devices. It will be shown that changes to the boundary conditions, due to the presence of effective media, permit even modest amounts of power to initiate elegant control of the effective group velocity. A new dawn of integrated circuits is beginning to emerge. Magnetooptics [2,3] is a discipline that is also known, globally, in other contexts, to be a powerful mechanism for control, so it is important to add its influence to metamaterial complex systems. Through magnetooptics, many novel applications emerge but when combined with, for example, metamaterials with a permittivity designed to be near to zero, the future for nonlinear integrated systems looks very exciting. Novel techniques, involving transformations and complex geometrical optics, coupled to full-wave simulations, will be used to design completely new forms of nonlinearly controlled metamaterial energy concentrators [4] in the electromagnetic domain. It will be shown that special boundary conditions emerge that lead to the establishment of unique energy ‘hotspots’. A nonlinear energy concentrator will be demonstrated which shows that power-driven switching occurs with great precision. Finally, a full theory of nonlinear magnetooptic transformation optics will be outlined.

Advances in active and nonlinear metamaterials

Metamaterial research is an extremely important global activity that promises to change our lives in many different ways. These include making objects invisible and the dramatic impact of metamaterials upon the energy and medical sectors of society. Behind all of the applications, however, lies the business of creating metamaterials that are not going to be crippled by the kind of loss that is naturally heralded by use of resonant responses in their construction. Under the general heading of active and tunable metamaterials, an elegant route to the inclusion of nonlinearity and waveguide complexity coupled to soliton behavior suggested by forms of transformation dynamics is presented. In addition, various discussions will be framed within a magnetooptical environment that deploys externally applied magnetic field orientations. Light can then be directed to achieve energy control and be deployed for a variety of outcomes. Quite apart from the fact that the manufacture of metamaterials is attracting such a lot of global attention, the ability to control light, for example, in these materials is also immensely interesting and will lead to a new dawn of integrated circuits and computers. Recognizing the role of nonlinearity raises the possibility that dramatic manufacturing and applications are on the horizon.

Nonlinear waves in metamaterials: state of the art

Guided waves in metamaterials are attracting attention, even though, experimentally, there remain some substantial questions about the fabrication of wave guides. Nonlinear guided optical waves have always been attractive for their device potential, so the development of nonlinear waves in metamaterials is an important direction to take and this is the basis of the discussion put forward by this paper. Given an effective medium starting point, it is possible to highlight the metamaterial influences upon both exact nonlinear waves and the soliton behaviour that is characteristic of the weakly nonlinear regime. This paper progresses through a number of priorities that have been discussed in the literature. The outcomes are rapidly reviewed from the point of view of putting the field into the context of both strongly nonlinear waves and spatial solitons, since both scenarios emphasise the role of metamaterial control. Finally, the possibility of using magneto-optics as an external control to modify the metamaterial influences is briefly displayed.

Solitons, Vortices and Guided Waves in Plasmonic Metamaterials

The history of optical solitons is fascinating and any theory of these has a weakly guiding foundation. Vortex generation and propagation properties have also a beautiful history, and the possibility of generating them together with magnetooptic control in plasmonic metamaterials will be discussed in detail. An emphasis will be placed on the fact that spatial solitons have a lot of application possibilities, especially when placed into the context of materials being used in a light-controlling light environment that is suitable for optical chips of the future. In addition, temporal solitons will also be invoked. An initial emphasis will be placed upon narrow beams and extremely short pulses, but it will be pointed out very strongly that detailed control of light-packets can also be introduced by using plasmonic metamaterials in the optical frequency range. This feature requires an exact study of wave propagation in waveguides that are possibly tapered, or simply just power controlled. To any designs that are proposed can be added the advantage of using magnetooptics. The complicated structures that will be examined will include soliton-like channels near interfaces. Optically linear and nonlinear metamaterials will be discussed in this context. The applications of the outcomes should lead to a new range of optical switching.

Bright spatial solitons, nonlinear guided waves, and complex metamaterial structures

The creation of electromagnetic metamaterials is an important activity. The latter should anticipate the kind of applications in which unique metamaterial behaviour can appear. This paper addresses nonlinear wave phenomena in both the strongly and the weakly nonlinear regimes. It inevitably involves novel nonlinear guided waves and solitonic beam activities. In this context, some magnetooptic control is introduced. In addition, the kind of structural complexity that can lead to trapped rainbows will be briefly examined. Finally, some aspects are made of vortex control in a diffraction-managed metamaterial is presented.

Strongly nonlinear wave control in gyroelectric metamaterials

A fascinating review of nonlinear waves in metamaterials is presented. The usual weakly nonlinear approximation is dispensed with, and there is an emphasis upon complex waveguides. Many opportunities exist for elegant control using the deployment of magnetooptic environments.

Nonlinear gyroelectric waves in magnetooptic metamaterials

The nonlinear properties of metamaterials are going to be important for the control of new computing and sensor devices. In addition, an exciting dimension can be added through the inclusion of magnetooptical properties. Both temporal and spatial solitons will be considered for a range of metamaterials with an emphasis being placed upon bright and bright‐dark soliton interactions coupled to magnetic effects drawn from both the Voigt and the Faraday configurations. Strongly nonlinear waves will also be discussed in terms of their exciting ability to slow light and respond vigorously to both nonlinear and magnetooptic tuneability. A special emphasis will be placed upon the switching possibilities of solitons at an interface and complex waveguides, and shape effects will also be addressed.

Nonlinear guided waves in tuneable, gyrotropic, metamaterial complex structures

The creation of electromagnetic metamaterials that will operate at THz frequencies, and into the visible frequency range, is an extremely important task that points to far-reaching medical, data storage, and processing applications. It is imperative, therefore, that these properties be associated with complex systems that can sustain both guided and surface waves in the nonlinear regime, and to offer the possibility of tunability through the addition of a gyromagnetic environment. In particular, a magneto-optic part of a metamaterial guiding structure will exert a dramatic influence because it can readily take advantage of the types of nanostructured geometries that are coming into existence. If the nonlinearity is strong, the shape of the modal fields of nonlinear guided waves changes significantly with power, as demonstrated a long time ago. The investigation of spatial and temporal solitons in double negative metamaterials is important to the future of integrated optical structures which rely upon specialized data manipulation. Some examples of strongly nonlinear waves will be given and the magnetooptic influences will be reserved for soliton management.