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121110-4 Nasir et al. Appl. Phys. Lett. 107, 121110 (2015)
FIG. 3. Effective medium parameters
of (a) metamaterial A and (b) metamaterial
B. Please note that Im(e z ) curves
in AAO and air overlap in (a) and (b).
(c) Experimentally measured and (d)
simulated reflectance dispersions of
the metamaterial B for p-polarised
light. The apparent change of contrast
in (c) is due to the change of the detector
in the measurements from the visible
(top panel) to IR (bottom panel).
The angular range corresponds to
30 –70 in glass. The light line in air
and the effective plasma frequency are
marked with solid and dashed lines,
respectively.
infrared spectral range to 1200 nm. This is related to two
simultaneous effects: an increase in the nanorod aspect ratio
which affects the CSP of the individual nanorods, and a
reduction of the coupling between the CSPs on neighbouring
nanorods.
The metamaterials’ optical properties have been modelled
using both an analytical transfer matrix method (TMM)
combined with an EMT based homogenization (Eq. (1)) as
well as full-vectorial microscopic numerical simulations
based on a finite element method (FEM). The tabulated permittivity
of Au was used 31 incorporating a correction to the
mean free path of electrons in electrochemically deposited
gold. 18 In the case of the numerical modelling, the unit cell
of a periodic square array with the periodicity given by the
inter-rod distance was modelled. The experimental data is in
good agreement with both numerical and EMT modelling,
reproducing the spectral position of the extinction peaks.
The EMT theory in particular, allows efficient extraction of
the effective medium parameters of the metamaterial and the
effective plasma frequency (Figs. 3(a) and 3(b)).
The real part of the effective permittivity components,
e x,y and e z , have the same sign for short wavelengths, where
the metamaterials operate in the elliptical dispersion regime,
while the effective plasma frequency is reached at wavelengths
around 795 nm and 1280 nm for metamaterials A and
B, respectively. For longer wavelengths, the metamaterials
are hyperbolic, supporting bulk plasmon polaritons. 11 If the
AAO matrix is removed so that the nanorods are in air, the
effective plasma frequency is shifted to shorter wavelengths
of about 625 nm and 850 nm, for metamaterials A and B,
respectively. Still the effective plasma frequency is sufficiently
away from the absorption resonance of e x,y .
The reflection spectra (Figs. 3(c) and 3(d)) show a set of
waveguided modes supported by the anisotropic metamaterial
slab in the visible spectral range where the dispersion is
elliptic in nature. The measured modes lie between light
lines of the air superstrate and the glass substrate, thus they
are leaky in the substrate and can be excited in attenuated
total internal reflection (ATR) measurements. 11 For the angle
of incidence corresponding to wavevectors smaller than the
light line in air, the modes are Fabry-Perot-type resonances
of the planar metamaterial slab. The mode structure drastically
changes in the IR spectral range below the effective
plasma frequency, where the dispersion is hyperbolic, and,
for the p-polarised light, the metamaterial has a strong metallic
behaviour supporting plasmon-polaritonic modes. 11 The
measured mode dispersions (Fig. 3(c)) are in a good agreement
with simulated dispersions (Fig. 3(d)) of the metamaterial
slab. Thus, the planar metamaterial waveguides can be
designed to support different types of modes in different dispersion
ranges using the control over the effective plasma
frequency developed here.
In conclusion, we have demonstrated hyperbolic
nanorod based metamaterials which allow improved flexibility
in designing the effective plasma frequency
throughout the visible and near-infrared ranges using
anodization in selenic acid. In particular, this approach
allows the effective plasma frequency to be designed in
the technologically important telecom wavelength range.
Such metamaterials are important for extending the spectral
reach of these versatile metamaterials and are
expected to impact applications in polarisation optics,
design of nonlinear optical response, sensing applications
and fluorescence control in the infrared.
This work was supported, in part, by EPSRC (UK)
and the ERC iPLASMM Project (No. 321268). A.Z.
acknowledges support from the Royal Society and the
Wolfson Foundation. G.W. acknowledges the support from
the EC FP7 Project No. 304179 (Marie Curie Actions).
The data access statement: all data supporting this
research are provided in full in the results section.