P. Egan

Nonlinear surface waves in left-handed materials.

We study both linear and nonlinear surface waves localized at the interface separating a left-handed (LH) medium (i.e., a medium with both negative dielectric permittivity and negative magnetic permeability) and a conventional [or right-handed (RH)] dielectric medium. We demonstrate that the interface can support both TE- and TM-polarized surface waves-surface polaritons, and we study their properties. We describe the intensity-dependent properties of nonlinear surface waves in three different cases, i.e., when both the LH and RH media are nonlinear and when either of the media is nonlinear. In the case when both media are nonlinear, we find two types of nonlinear surface waves, one with the maximum amplitude at the interface, and the other one with two humps. In the case when one medium is nonlinear, only one type of surface wave exists, which has the maximum electric field at the interface, unlike waves in right-handed materials where the surface-wave maximum is usually shifted into a self-focusing nonlinear medium. We discuss the possibility of tuning the wave group velocity in both the linear and nonlinear cases, and show that group-velocity dispersion, which leads to pulse broadening, can be balanced by the nonlinearity of the media, so resulting in soliton propagation.

Roadmap on optical metamaterials

Optical metamaterials have redefined how we understand light in notable ways: from strong response to optical magnetic fields, negative refraction, fast and slow light propagation in zero index and trapping structures, to flat, thin and perfect lenses. Many rules of thumb regarding optics, such as mu = 1, now have an exception, and basic formulas, such as the Fresnel equations, have been expanded. The field of metamaterials has developed strongly over the past two decades. Leveraging structured materials systems to generate tailored response to a stimulus, it has grown to encompass research in optics, electromagnetics, acoustics and, increasingly, novel hybrid materials responses. This roadmap is an effort to present emerging fronts in areas of optical metamaterials that could contribute and apply to other research communities. By anchoring each contribution in current work and prospectively discussing future potential and directions, the authors are translating the work of the field in selected areas to a wider community and offering an incentive for outside researchers to engage our community where solid links do not already exist.

Novel nonlinear surface and guided TE waves in asymmetric LHM waveguides

The first comprehensive exact theory of strongly nonlinear guided waves in a double-negative planar metamaterial waveguide is developed. The theoretical consequences are that novel surface and guided waves are predicted because of the special relationship of the boundary fields to each other. The analysis leads smoothly to tunability with power and direct access to group velocity control.

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.

Advanced Solitonic Metamaterial Structures under External Magnetophotonic Control

Metamaterial research is an extremely important global activity that promises to change our lives in many different ways, including making objects invisible and having a very dramatic impact upon the energy and medical sectors of society. Behind all of the applications, however, lies the design of metamaterials and this can be led by elegant routes that include nonlinearity, waveguide complexity and structured light. The associated optical device formats often involve coupling to soliton behavior. Vortex formation is going to be a critical feature for future applications focusing attention upon the role of angular momentum in special metamaterial-driven light beams. In this context nonlinear diffraction must be assessed and some discussion of a magnetooptical environment will be included. Solitonic behavior of light beams will be mentioned, including what have now become known as Peregrine solitons.

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.