S. Anantha Ramakrishna

Physics of negative refractive index materials

In the past few years, new developments in structured electromagnetic materials have given rise to negative refractive index materials which have both negative dielectric permittivity and negative magnetic permeability in some frequency ranges. The idea of a negative refractive index opens up new conceptual frontiers in photonics. One much-debated example is the concept of a perfect lens that enables imaging with sub-wavelength image resolution. Here we review the fundamental concepts and ideas of negative refractive index materials. First we present the ideas of structured materials or meta-materials that enable the design of new materials with a negative dielectric permittivity, negative magnetic permeability and negative refractive index. We discuss how a variety of resonance phenomena can be utilized to obtain these materials in various frequency ranges over the electromagnetic spectrum. The choice of the wave-vector in negative refractive index materials and the issues of dispersion, causality and energy transport are analysed. Various issues of wave propagation including nonlinear effects and surface modes in negative refractive materials (NRMs) are discussed. In the latter part of the review, we discuss the concept of a perfect lens consisting of a slab of a NRM. This perfect lens can image the far-field radiative components as well as the nearfield evanescent components, and is not subject to the traditional diffraction limit. Different aspects of this lens such as the surface modes acting as the mechanism for the imaging of the evanescent waves, the limitations imposed by dissipation and dispersion in the negative refractive media, the generalization of this lens to optically complementary media and the possibility of magnification of the near-field images are discussed. Recent experimental developments verifying these ideas are briefly covered. (Some figures in this article are in colour only in the electronic version)

Limitations on subdiffraction imaging with a negative refractive index slab

A planar slab of material, for which both the permittivity and permeability have the values of −1, can bring not only the propagating fields associated with a source to a focus, but can also refocus the nonpropagating near fields, thereby achieving resolution beyond the diffraction limit. We study the sensitivity of this subwavelength focus to the slab material properties and periodicity, and note the connection to slab surface plasmon modes. We conclude that significant subwavelength resolution is achievable with a single negative index slab, but only over a restrictive range of parameters.

Imaging the Near Field

Abstract In an earlier paper we introduced the concept of the perfect lens which focuses both near and far electromagnetic fields, hence attaining perfect resolution. Here we consider refinements of the original prescription designed to overcome the limitations of imperfect materials. In particular we show that a multilayer stack of positive- and negative-refractive-index media is less sensitive to imperfections. It has the novel property of behaving like a fibre-optic bundle but one that acts on the near field, and not just the radiative component. The effects of retardation are included and minimized by making the slabs thinner. Absorption then dominates image resolution in the near field. The deleterious effects of absorption in the metal are reduced for thinner layers.

Removal of absorption and increase in resolution in a near-field lens via optical gain

A recent paper showed how to construct a lens that focuses near field radiation and hence produce resolution unlimited by wavelength. The prescription requires lossless materials with negative refractive index: finite loss cuts off the finer details of the image. In this paper we suggest compensating for losses by introducing optical gain media into the lens design. Calculations demonstrate a dramatic improvement in performance for a silver/gain composite medium at optical frequencies.

Physics and Applications of Negative Refractive Index Materials

Introduction General historical perspective The concept of metamaterials Modeling the material response Phase velocity and group velocity Metamaterials and homogenization procedure Metamaterials and Homogenization of Composites The homogenization hypothesis Limitations and consistency conditions Forward problem Inverse problems: retrieval and constitutive parameters Homogenization from averaging the internal fields Generalization to anisotropic and bianisotropic media Designing Metamaterials with Negative Material Parameters Negative dielectric materials Metamaterials with negative magnetic permeability Metamaterials with negative refractive index Chiral metamaterials Bianisotropic metamaterials Active and nonlinear metamaterials Negative Refraction and Photonic Bandgap Materials Photonic crystals and bandgap materials Band diagrams and iso-frequency contours Negative refraction and flat lenses with photonic crystals Negative refraction versus collimation or streaming Media with e < 0 and < 0: Theory and Properties Origins of negative refraction Choice of the wave-vector and its consequences Anisotropic and chiral media Energy and Momentum in Negative Refractive Index Materials Causality and energy density in frequency dispersive media Electromagnetic energy in left-handed media Momentum density, momentum flow, and transfer in media with negative material parameters Limit of plane waves and small losses Traversal of pulses in materials with negative material parameters Plasmonics of Media with Negative Material Parameters Surface electromagnetic modes in negative refractive materials Waveguides made of negative index materials Negative refraction of surface plasmons Plasmonic properties of structured metallic surfaces Surface waves at the interfaces of nonlinear media Veselagos Lens Is a Perfect Lens Near-field information and diffraction limit Mathematical demonstration of the perfect lens Limitations due to real materials and imperfect NRMs Issues with numerical simulations and time evolution Negative stream of energy with a perfect lens configuration Effects of spatial dispersion Designing Super Lenses Overcoming the limitations of real materials Generalized perfect lens theorem The perfect lens in other geometries Brief Report on Electromagnetic Invisibility Concept of electromagnetic invisibility Excluding electromagnetic fields Cloaking with localized resonances Appendix A: The Fresnel Coefficients for Reflection and Refraction Appendix B: The Dispersion and Fresnel Coefficients for a Bianisotropic Medium Appendix C: The Reflection and Refraction of Light across a Material Slab References Index

The asymmetric lossy near-perfect lens

We extend the ideas of the perfect lens recently proposed [J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)] to an alternative structure. We show that a slab of a medium with negative refractive index bounded by media of different positive refractive index also amplifies evanescent waves and can act as a near-perfect lens. We examine the role of the surface states in the amplification of the evanescent waves. The image resolution obtained by this asymmetric lens is more robust against the effects of absorption in the lens. In particular, we study the case of a slab of silver, which has a negative dielectric constant, with air on one side and other media such as glass or GaAs on the other side as an ‘asymmetric’ lossy near-perfect lens for p-polarized waves. It is found that retardation has an adverse effect on the imaging due to the positive magnetic permeability of silver, but we conclude that subwavelength image resolution is possible in spite of it.

Design of multi-band metamaterial perfect absorbers with stacked metal–dielectric disks

Simple periodic structures of stacked metal and dielectric microdisks can display very high absorbance over multiple bands at infrared frequencies (3–10 μm wavelengths). The stack can be envisaged as intersecting tri-layers, each tri-layer composed of metal–dielectric–metal disks that form independent impedance matched resonators, and give rise to large absorbance at different frequencies. Numerical simulations show that dual-band and multi-band absorbers with near unity absorbance on all their bands can be flexibly designed whereby the dielectric materials determine the absorption band of the metamaterial. The multi-band absorber is reasonably polarization insensitive and the absorbance remains large even with large angles of incidence. This approach of multi-layered stacked metamaterials is compared and shown to be superior to another approach to multiple-band metamaterial perfect absorbers having closely packed resonators within a unit cell.

Design of highly absorbing metamaterials for Infrared frequencies

Simple designs for polarization independent, metamaterial absorbers at mid-infrared wavelengths and over wide angle of incidence are evaluated computationally. One design consists of an array of circular metallic disks separated from a continuous metallic film by a dielectric film, and shows over 99.9% peak absorbance and a resonant bandwidth of about 0.2 μm wavelengths. The effects of various geometric parameters are analyzed for this metamaterial. Another design consisting of an array of stacked metal-dielectric-metal disks is shown to have an absorbance of over 90% in a comparatively large band of over 1 μm bandwidth, although with a lower peak absorbance of 97%.

Spherical perfect lens: Solutions of Maxwell's equations for spherical geometry

It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the sub-wavelength image information contained in the evanescent modes of a source. Here we elaborate on perfect lens solutions to spherical shells of negative refractive material where magnification of the near-field images becomes possible. The negative refractive materials then need to be spatially dispersive with

Resolving the wave vector in negative refractive index media

\epsilon(r) \sim 1/r