Negative Refraction at Optical Frequencies in Nonmagnetic Two-Component Molecular Media

Abstract

The sign of the refractive index of any medium is soley determined by the requirement that the propagation of an electromagnetic wave obeys Einstein causality. Our analysis shows that this requirement predicts that the real part of the refractive index may be negative in an isotropic medium even if the electric permittivity and the magnetic permeability are both positive. Such a system may be a route to negative index media at optical frequencies. We also demonstrate that the refractive index may be positive in left-handed media that contain two molecular species where one is in its excited state.PACS numbers: 41.20.Jb,78.20.Ci,42.25.Fx In 1968 Veselago [1] considered the electrodynamic properties of isotropic media where the real part of the electric permittivity ǫ and the real part of the magnetic permeability µ are simultaneously negative. Veselago showed that if ǫ, µ < 0 then the electric field E, the magnetizing field H and the wave-vector k form a lefthanded orthogonal set, contrary to all known naturallyoccurring materials where the triplet of these vectors is right-handed. Media with both negative electric permittivity and magnetic permeability are referred to as left-handed materials (LHM) at the frequencies for which ǫ, µ < 0.A consequence of simultaneously negative ǫ and µ is that the Poynting vector S = E × H and the wave-vector k = (ω/|E|2 )E × B point in opposite directions for a monochromatic plane wave with angular frequency ω, as here the direction of the magnetic field necessarily opposes that of the magnetizing field, B = µH [1]. Veselago argued that the direction of the energy flow (S) must point away from its source and thereby reached the surprising conclusion that in LHM the wave-vector points toward the source [1]. This in turn lead to the prediction that LHM exhibit a negative refractive index, as well as reversed Doppler and Cherenkov effects [1].No naturally-occurring isotropic material is known to have ǫ, µ < 0 at the same frequency, since the underlying polarizabilities and magnetizabilities, in general, exhibit different frequency responses (resonances). Pendry et al. thus [2] suggested that structures containing metal strips and split-ring resonators could be engineered such that both ǫ and µ are negative at microwave frequencies. Shelby et al. [3] subsequently reported the observation of negative refraction at 10.5 GHz in a left-handed metamaterial. There are to date no experimental reports of homogeneous, isotropic media that exhibit a negative refractive index at optical frequencies. We note that neither photonic crystals [4,5], nor birefringent crystal assemblies [6] are isotropic and can therefore not be characterized by a single, scalar refractive index.

Resolving the wave vector and the refractive index from the coefficient of reflectance

“…[12] performs a numerical analysis of a wave-packet propagation in a system considered in [2]. Correcting errors of [3] by the same authors, [12] reconfirms the conclusion of [2] that the refractive index of the active medium considered in the latter reference has a positive imaginary part. This conclusion is in agreement with results of the present work.…”

“…For an active medium (ǫ ′′ 2 < 0) the choice of the sign of the square root in Eq. (3) is far from evident [1][2][3][4][5][6]8] while this choice strongly affects the coefficient of reflectance of Eq. (1).…”

“…Recently, there has been much of debate regarding the correct selection of the sign of the normal-to-the-interface component of the wave-vector k z of an electromagnetic wave propagating in an active medium or, equivalently for the normal incidence, of the refractive index of the active medium [1][2][3][4][5][6]. Specifically, if one considers a system of a glass prism, a metal film, and an active dielectric (the Kretschmann-Raether configuration) as schematized in Fig.…”

“…1 (a) by the finite thickness d 2 of the active dielectric and the presence of a semi-infinite passive dielectric with the dielectric constant ǫ 3 . For this system the coefficient of reflectance can be written as [9] ), in agreement with [2] and in disagreement with [1] and [3,10], where the branch cuts were taken along the negative imaginary (−π/2 ≤ φ < 3/2 π) and negative real (−π ≤ φ < π) axes, respectively. Therefore, for an active medium the refractive index n = √ ǫ has negative real part.…”

Dual-Frequency Electromagnetic Cloaks Enabled by Lc-Based Metamaterial Circuits

“…By exploiting the additional freedom introduced by these circuits, it is possible to realize the unconventional permeability at two different frequencies. Physically, this behaves similarly as a two-component system [41] and it is a metamaterial with very flexible properties.…”