Allan D. Boardman

'Trapped rainbow' storage of light in metamaterials.

Light usually propagates inside transparent materials in well known ways. However, recent research has examined the possibility of modifying the way the light travels by taking a normal transparent dielectric and inserting tiny metallic inclusions of various shapes and arrangements. As light passes through these structures, oscillating electric currents are set up that generate electromagnetic field moments; these can lead to dramatic effects on the light propagation, such as negative refraction. Possible applications include lenses that break traditional diffraction limits and ‘invisibility cloaks’ (refs 5, 6). Significantly less research has focused on the potential of such structures for slowing, trapping and releasing light signals. Here we demonstrate theoretically that an axially varying heterostructure with a metamaterial core of negative refractive index can be used to efficiently and coherently bring light to a complete standstill. In contrast to previous approaches for decelerating and storing light, the present scheme simultaneously allows for high in-coupling efficiencies and broadband, room-temperature operation. Surprisingly, our analysis reveals a critical point at which the effective thickness of the waveguide is reduced to zero, preventing the light wave from propagating further. At this point, the light ray is permanently trapped, its trajectory forming a double light-cone that we call an ‘optical clepsydra’. Each frequency component of the wave packet is stopped at a different guide thickness, leading to the spatial separation of its spectrum and the formation of a ‘trapped rainbow’. Our results bridge the gap between two important contemporary realms of science—metamaterials and slow light. Combined investigations may lead to applications in optical data processing and storage or the realization of quantum optical memories.

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.

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.

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.

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.

Gyrotropic impact upon negatively refracting surfaces

Surface wave propagation at the interface between different types of gyrotropic materials and an isotropic negatively refracting medium, in which the relative permittivity and relative permeability are, simultaneously, negative is investigated. A general approach is taken that embraces both gyroelectric and gyromagnetic materials, permitting the possibility of operating in either the low GHz, THz or the optical frequency regimes. The classical transverse Voigt configuration is adopted and a complete analysis of non-reciprocal surface wave dispersion is presented. The impact of the surface polariton modes upon the reflection of both plane waves and beams is discussed in terms of resonances and an example of the influence upon the Goos–Hanchen shift is given.

Bright magnetostatic spin-wave envelope solitons in ferromagnetic films

Abstract The theory and simulation of the spin-wave soliton formation in thin ferromagnetic films is considered. The necessary and sufficient conditions for soliton formation are analysed and some novel numerical results for different, yet possible, physical input conditions are presented.

Nonlinear Guided Waves

Since its inception in the 1960s, nonlinear optics has led to a rich variety of wave-mixing interactions that have applications to basic materials research [1–2], to the generation of new frequencies [1], and most recently to all-optical signal processing [3]. In general, nonlinear optical interactions occur whenever the optical fields associated with one or more laser beams propagating in a material are large enough to produce polarization fields proportional to the product of two or more of the incident fields. These nonlinear polarization fields radiate electric fields at the nonlinear frequency. For some interactions, the generated fields grow linearly with propagation distance under optimum conditions of phase-matching. Typically, the efficiency of any nonlinear optical interaction depends on (1) the product of the power densities of the input and output waves, raised to some power, and (2) the interaction distance raised to some power greater than or equal to unity. Since power density is power per unit area, the efficiency of any nonlinear interaction can be enhanced by reducing the cross-sectional area of the interacting beams. For plane waves this can be achieved by focusing with a lens. There is a tradeoff, of course, because the high power density can be maintained only over the depth of focus of the lens, which limits the effective interaction length.

Nonlinear magnetostatic surface waves in ferromagnetic films

A comprehensive perturbation theory is presented, that enables the nonlinear wavenumber shift of magnetostatic surface waves (MSSW) on a thin ferromagnetic film to be calculated from first principles. The MSSW propagate, in this case, perpendicularly or obliquely to the applied magnetic field and their group-velocity dispersion is positive. Detailed calculations show that the nonlinear coefficient is also positive so that bright envelope solitons are forbidden. Nevertheless, nonlinear pulse shaping is possible so the use of the nonlinear Schrodinger equation is discussed in detail, together with the role of damping. >

TE waves at an interface between linear gyromagnetic and nonlinear dielectric media

The dispersion relations for low-frequency TE waves guided by the interface between semi-infinite non-linear and linear frequency-dependent gyromagnetic media have been investigated theoretically and numerically. It is shown that TE waves can propagate, with or without linear limits. The power dependence of the non-reciprocal behaviour of these waves is quite dramatic and, in principle, can lead to some interesting experimental applications. The variation of the wave index with the power flow, and the consequent interface nonlinearity, are found to be very frequency dependent.