Negative Refractive Index in Optics of Metal-Dielectric Composites

Abstract

Specially designed metal-dielectric composites can have a negative refractive index in the optical range. Specifically, it is shown that arrays of single and paired nanorods can provide such negative refraction. For pairs of metal rods, a negative refractive index has been observed at 1.5 micrometer. The inverted structure of paired voids in metal films may also exhibit a negative refractive index. A similar effect can be accomplished with metal strips in which the refractive index can reach -2. The refractive index retrieval procedure and the critical role of light phases in determining the refractive index is discussed. Comment: 39 pages, 17 figures, 24 equations

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Negative Refractive Index in Optics of Metal-Dielectric
Composites
A. V. Kildishev , W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev*, V. P. Drachev, and V. M. Shalaev

School of Electrical and Computer Engineering, 465 Northwestern Ave., W. Lafayette, IN 47907
* Ethertronics Inc., 9605 Scranton Road, San Diego, CA 92121

Abstract: Specially designed metal-dielectric composites can have a negative refractive
index in the optical range. Specifically, it is shown that arrays of single and paired
nanorods can provide such negative refraction. For pairs of metal rods, a negative
refractive index has been observed at 1.5 µm. The inverted structure of paired voids in
metal films may also exhibit a negative refractive index. A similar effect can be
accomplished with metal strips in which the refractive index can reach −2. The refractive
index retrieval procedure and the critical role of light phases in determining the refractive
index is discussed.

OCIS codes: 160.4760, 260.5740, 310.6860

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Introduction
In the recent few years, there has been a strong interest in novel optical media which have
become known as left-handed materials (LHMs) or negative index materials (NIMs). Such
materials have not been discovered as natural substances or crystals, but rather are artificial,
man-made materials. The optical properties of such media were considered in early papers by
two Russian physicists, Mandel’shtam1 and Veselago,2 although much earlier works on negative
phase velocity and its consequences belong to Lamb3 (in hydrodynamics) and Schuster4 (in
optics).
In NIMs, k
?
, E
?
, and H
?
form a left-handed set of vectors, and were therefore named
LHMs by Veselago. As a result of the negative index of refraction and negative phase velocity,
these artificial materials exhibit a number of extraordinary features, including an inverse Snell’s
law relationship, a reversed Doppler shift, and reversed Cherenkov radiation. These features
suggest a flexible regulation of light propagation in these media and facilitate new, fascinating
applications.
The most recent successful efforts to demonstrate negative refraction have been inspired
by Pendry’s revision5 of the Veselago lens, which renewed interest in the practical aspects of the
earlier papers. Pendry predicted that a NIM lens can act as a “superlens” by providing spatial
resolution beyond the diffraction limit. Fig. 1 compares the simplest case of refraction at a single
interface between vacuum and common, positive refractive index material (Fig. 1(a)) versus
refraction at the interface with a NIM (Fig. 1(b)). For any oblique angle of incidence
iθ , the
tangential wavevector k?
?
of an incident plane wave from the vacuum side must remain
continuous across the interface. This is the case for both positive and negative refractive indicies.
However, in contrast to a normal, positive refraction material as the light passes from vacuum

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into a NIM, the wavevector component normal to the interface (k⊥
?
) must change the sign. As a
result, the total refracted wavevector is on the same side of the normal as the incident
wavevector. Figure 1(b) illustrates this effect as the reversed Snell’s law, where the angles of
reflection (
rθ ) and transmission (
tθ ) are reversed (
rt
θθ=
) for the case of n = −1. This reversal
suggests insightful consequences for the imaging applications of NIMs, the most critical of
which is the ‘perfect lens’ as illustrated in Fig. 1(c). For refracted rays from a point source, a
planar NIM slab of sufficient thickness with n = −1 should first focus the rays inside the NIM
and then re-focus them again behind the slab. At the perfect lensing condition of n = −1, this
focusing property is extraordinary, and the resolution limit intrinsic to conventional imaging no
longer applies to imaging with a NIM slab as shown by Pendry.5 The essence of the effect is that
a NIM compensates the usual decay of the evanescent waves. Contrary to a conventional
imaging device, in a super lens these evanescent waves are recovered by the NIM and the image
is perfectly reconstructed.5 The perfect lensing requirements (
( )
n = − ,
Re1
( )
n =
Im0
) are
difficult conditions to meet. The first requirement means that n is wavelength-dependent and the
perfect lens is restricted to work at a single wavelength. The second requirement implies that
there is no absorption in the NIM. In reality, losses are always present in the NIM and can
dramatically diminish the resolution.6,7
The development of optical NIMs is closely connected to studies of periodic arrays of
elementary scatterers, where, for example, frequency selective surfaces (FSS) arranged from
those arrays have been used as narrowband filters for plane waves. The major resonant elements
of optical metal-dielectric composites (metallic spheres, disks, rods, and their inversions, i.e.
circular and elliptic holes) have been inherited from earlier FSS designs, together with evident
orthotropic properties and angular dependences. Another source of earlier expertise is found in

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the studies of artificial dielectrics (ADs), where the homogenization method and approaches to
define equivalent electromagnetic material properties have been examined under resonant
conditions. Predictions of anomalously large effective permeability and permittivity due to
resonant regimes of elementary scatterers have also been made for ADs arranged from periodic
metal-dielectric structures8.
While negative permittivity in the optical range is easy to attain for metals, there is no
magnetic response for naturally-occurring materials at such high frequencies. Recent theories
and experiments showed that a magnetic response and negative permeability can be
accomplished in the terahertz spectral ranges by using parallel rods, split-ring resonators (SRRs)
and other structures.9-14 As predicted13 and experimentally demonstrated,14 u-shaped structures
are particularly well suited for magnetism at optical frequencies. Recently, light propagation
through an interface that mimics negative refraction has also been found in two-dimensional
photonic crystals (PCs).15 It has been shown that under certain conditions, unique focusing
effects in PCs are also possible.16
Fig. 1. (a) Snell's law at an interface between
vacuum and a positive refractive index
material; (b) reversed Snell's law at the
interface with NIM (n = −1); and (c) the
superlens.
kt
kr
ki
θr
θt
kt
kr
n = −1
ki
θr
θt
(a) (b) (c)

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Up to the microwave frequencies the fabrication of metal-dielectric composites can
follow practically any pattern suggested either by human intuition or computer-aided tools with
evolutionary optimization. Yet at optical frequencies, the best possible design of metal-dielectric
composite NIM should overcome two substantial difficulties: severe fabrication constrains and
increased losses. For these reasons, this paper addresses the simplest geometries of resonant 3D
structures. Such structures include coupled metal rods in a dielectric host17-21 (fabricated, for
example, through electron-beam lithography (EBL)) and inversions of rods, i.e. coupled
dielectric holes of elliptical (spherical,22 in the limiting case) or rectangular shape23 (fabricated,
for example, by etching tri-layer metal-dielectric-metal films by ion beam etching (IBE) or
through interferometric lithography).
The first experimental realization of a negative refractive index in the optical range (at
1.5 µm) was accomplished with paired metal nanorods in a dielectric,21 and then for the inverted
system of paired dielectric voids in a metal.22,23 We note that inverted NIMs, i.e. elliptical or
rectangular dielectric voids in metal films,23 are physically equivalent to paired metal rods in a
dielectric host, in accordance with the Babinet principle.24 We also note here Ref. [25] that
considers other interesting optical properties of metal rods, although these properties are not
related directly to NIMs.
In the current paper, in addition to paired metal rods and dielectric voids, we also study
two-dimensional coupled-strip composites as a basis for further comprehensive studies of NIMs.