Y. G. Rapoport

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.

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.

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 waves in hyperbolic metamaterials: focus on solitons and rogues

The investigation of hyperbolic metamaterials, shows that metal layers that are part of graphene structures, and also types I and II layered systems, are readily controlled. Since graphene is a nicely conducting sheet it can be easily managed. The literature only reveals a, limited, systematic, approach to the onset of nonlinearity, especially for the methodology based around the famous nonlinear Schrödinger equation [NLSE]. This presentation reveals nonlinear outcomes involving solitons sustained by the popular, and more straightforward to fabricate, type II hyperbolic metamaterials. The NLSE for type II metatamaterials is developed and nonlinear, non-stationary diffraction and dispersion in such important, and active, planar hyperbolic metamaterials is developed. For rogue waves in metamaterials only a few recent numerical studies exist. The basic model assumes a uniform background to which is added a time-evolving perturbation in order to witness the growth of nonlinear waves out of nowhere. This is discussed here using a new NLSE appropriate to hyperbolic metamaterials that would normally produce temporal solitons. The main conclusion is that new pathways for rogue waves can emerge in the form of Peregrine solitons (and near-Peregrines) within a nonlinear hyperbolic metamaterial, based upon double negative guidelines, and where, potentially, magnetooptic control could be practically exerted.

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.

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.

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.