2015-3

Tuning the effective plasma frequency
of nanorod metamaterials from visible to
telecom wavelengths
Cite as: Appl. Phys. Lett. 107, 121110 (2015); https://doi.org/10.1063/1.4931687
Submitted: 11 June 2015 . Accepted: 13 September 2015 . Published Online: 25 September 2015
M. E. Nasir, S. Peruch, N. Vasilantonakis, W. P. Wardley, W. Dickson, G. A. Wurtz, and A. V. Zayats
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Appl. Phys. Lett. 107, 121110 (2015); https://doi.org/10.1063/1.4931687 107, 121110
© 2015 AIP Publishing LLC.

APPLIED PHYSICS LETTERS 107, 121110 (2015)
Tuning the effective plasma frequency of nanorod metamaterials
from visible to telecom wavelengths
M. E. Nasir, a) S. Peruch, N. Vasilantonakis, W. P. Wardley, W. Dickson, G. A. Wurtz,
and A. V. Zayats
Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
(Received 11 June 2015; accepted 13 September 2015; published online 25 September 2015)
Hyperbolic plasmonic metamaterials are important for designing sensing, nonlinear, and emission
functionalities, which are, to a large extent, determined by the epsilon-near-zero behaviour
observed close to an effective plasma frequency of the metamaterial. Here, we describe a method
for tuning the effective plasma frequency of a gold nanorod-based metamaterial throughout the
visible and near-infrared spectral ranges. These metamaterials, fabricated by two-step anodization
in selenic acid and chemical post-processing, consist of nanorods with diameters of around 10 nm
and interrod distances of around 100 nm and have a low effective plasma frequency down to a
wavelength range below 1200 nm. Such metamaterials open up new possibilities for a variety of
applications in the fields of bio- and chemical sensing, nonlinearity enhancement, and fluorescence
control in the infrared. VC 2015 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4931687]
The ability to design the optical properties of metamaterials
has already achieved a significant impact in a variety
of photonic, data processing, and sensing applications. 1–6
Various types of metamaterials have been explored in the
radio-frequency (RF), terahertz, infrared, and optical regions
based on split-ring resonators, nanorod pairs, coaxial structures,
fishnets, and other approaches, allowing both the electric
and magnetic resonances to be engineered, providing
control of the permittivity and permeability of the nanostructured
media. 7–9 The adaptation of the above mentioned
approaches at longer wavelengths is straightforward, while
their scaling down to the visible spectral range is difficult
due to challenging top-down fabrication required at the subwavelength
scale.
A different class of metamaterials based on arrays of
aligned plasmonic nanorods has also been studied. 10 This
type of anisotropic metamaterial has unique electromagnetic
properties determined by the electromagnetic interaction
between the rods forming the array and can be described
within the effective medium theory (EMT) via the effective
permittivity tensor components e x ¼ e y 6¼ e z , corresponding
to the direction perpendicular to (x,y) and along (z) nanorod
axes. The metamaterial behaves as an indefinite metamaterial
(Re(e z ) ¼ 1) at RFs and can exhibit hyperbolic dispersion
in the spectral range where Re[e x,y (k)] > 0 and
Re[e z (k)] < 0. For a plasmonic nanorod-based metamaterial,
the hyperbolic regime has a short-wavelength cut-off typically
in the visible spectral range, but no long-wavelength
limit. The optical properties of such anisotropic metamaterials
are governed by their ability to support bulk plasmonpolaritons
which define the behaviour of the extraordinary
modes supported by the metamaterial. 11 Both ordinary and
extraordinary modes are related to the inter-rod coupling
via cylindrical surface plasmons (CSPs) supported by the
nanorods in the array. 12,13 These peculiar dispersion properties
exhibited by the metamaterial have been used for
a) mazhar.nasir@kcl.ac.uk
negative refraction index engineering and super-resolution
applications, deep-subwavelength wave guiding, spontaneous
emission control, nonlinearity enhancement, ultrasensitive
refractive index sensing, etc. 4–6,10,11,14–16
Many of the above described properties are defined by the
ÞŠ 0) of the metamaterial,
which is the onset of hyperbolic dispersion and around
which the so-called epsilon-near-zero (ENZ) regime takes
place. In contrast to other types of metamaterials, which can
be easily fabricated at long wavelengths, but which are problematic
in the visible, control over the bulk plasma frequency
of nanorod-based metamaterials can easily be achieved in the
visible spectral range by changing the interaction between the
nanorods in the array. This can be accomplished by changing
either the period of the array or the nanorod diameter, using a
bottom-up, template-based fabrication approach. Typically,
metamaterials comprised of arrays of aligned metallic nanorods
are synthesised in a porous alumina template fabricated
using conventional electrolytes, such as sulphuric or oxalic
acid, and have an effective plasma frequency limited to the
visible spectral range of 530–650 nm (Refs. 17 and 18) for Aubased
metamaterials and to shorter wavelengths for those fabricated
using Ag. The use of other plasmonic metals results in
increased losses due to the intrinsic material properties. Thus,
in contrast to other types of metamaterials, it is not straightforward
to fabricate such nanorod-based metamaterials with an
effective plasma frequency in the infrared and telecom spectral
ranges.
In this paper, we describe the design, fabrication and
characterisation of metamaterials based on periodic arrays of
vertically aligned Au nanorods which allows the effective
plasma frequency to be tuned throughout the visible and into
the infra-red spectral range. Highly ordered nanoporous alumina
templates with 15 nm pore diameter and 120 nm
interpore spacing over large cm-sized areas are fabricated by
two-step anodization in selenic acid. The effective plasma
frequency of Au-nanorod based metamaterials obtained with
such templates can then be tuned by controlling the nanorod
effective plasma frequency (Re½e z ðx ef f
p
0003-6951/2015/107(12)/121110/5/$30.00 107, 121110-1
VC 2015 AIP Publishing LLC

121110-2 Nasir et al. Appl. Phys. Lett. 107, 121110 (2015)
diameter via post processing of the pores while keeping both
the inter-rod spacing and rod length constant.
The optical properties of plasmonic nanorod metamaterials
are determined by the coupling of cylindrical surface
plasmons supported by individual nanorods in the array. On
the macroscopic level, this is well described by the Maxwell-
Garnett type EMTs which can be validated through comparison
with the experimental and microscopic numerical modelling.
19 The effective permittivities in both the in-plane and
out of plane directions are given by
ð1 þ pÞe Au þ ð1 pÞe h
e xy ¼ e h
ð1 pÞe Au þ ð1 þ pÞe h
e z ¼ pe Au þ ð1
pÞe h ; (1)
where p ¼ p(r/d) 2 is the nanorod concentration with r being
radius of the nanorods and d being distance between the
nanorods, e Au and e h are the permittivities of Au and the host
medium (Al 2 O 3 ), respectively. This model is valid away
from the Brillouin zone edge of the nanorod array with
k 0 p d , where k 0 is the wavevector of the incident light in
the plane of the metamaterial slab. 11 The effective plasma
frequency of Au nanorod metamaterials, which is determined
by Re(e z ) ¼ 0, is affected by both the host medium properties
and the nanorod concentration. 11 This frequency separates
the elliptic dispersion regime, where the metamaterial
behaves as a strongly anisotropic dielectric, and the hyperbolic
regime where the metamaterial supports bulk plasmonpolaritons
due to its metallo-dielectric behaviour.
In order to fabricate the metamaterial, Au nanorods are
electrodeposited in porous anodic alumina oxide (AAO) templates,
synthesized by a two-step anodization process. An aluminium
film of 800 nm thickness was sputtered on a
multilayer substrate comprised of a glass slide with a 10 nm
thick adhesion layer of tantalum pentoxide and a 7 nm thick
Au film acting as a weakly conducting layer. Tantalum pentoxide
is deposited by sputtering tantalum using a 20% oxygen/80%
argon mixture. The porous alumina structures were
synthesized by a two step-anodization in 0.3 M selenic acid
at 40–48 V at 0 C. The temperature of the sample and electrolyte
was controlled throughout the anodization process.
After an initial anodization step, the porous layer formed
was removed by etching in a solution of H 3 PO 4 (3.5%) and
CrO 3 (20 g l –1 )at70 C leaving an ordered, patterned surface.
The samples were then subjected to a second anodization
step under the same conditions as in the first step and
subsequently etched in 30 mM NaOH to tune the diameters
of pores from 15 nm to 50 nm. Gold electrodeposition was
performed using a three-electrode geometry and a noncyanide
solution. The length of the nanorods was controlled
by the electrodeposition time.
In general, the geometrical parameters of the porous alumina
template used for nanorod metamaterial fabrication are
determined by the electrolyte used for anodization and by
the applied anodizing potential. The pore diameter and interpore
spacing of the porous alumina template is proportional
to the applied voltage with proportionality constants
k d ¼ 1.29 nm V 1 and k int ¼ 2.52 nm V 1 , respectively. 20–24
Therefore, for a chosen electrolyte, the diameter of the pores
can be increased in a pore widening process for a given
voltage, resulting in an increase in the nanorod concentration
p. However, due to the limitations of currently used electrolytes,
a different approach is required in order to provide
ENZ-related functionalities in the infrared, including at telecom
wavelengths.
Self-ordered porous alumina is typically obtained in
acidic electrolytes, such as sulphuric, oxalic, phosphoric,
malonic, and tartaric acids. 25–28 In these electrolytes, the diameter
of pores is determined by the applied voltage with a
proportionality constant equal to or greater than 1 nm/V and
the interpore distance determined by a proportionality constant
2.52 nm V 1 . In selenic acid, 24 the pore diameter of
the self-ordered porous alumina template has a weaker dependence
on the applied voltage (a proportionality constant
is 0.3 nm/V) while the interpore distance has about the
same dependence (proportionality constant 2.33 nm V 1 ).
Figure 1(b) shows the SEM image of the self-ordered porous
alumina template formed in 0.3 M selenic acid at 48 V,
keeping the temperature at 0 C. The regular pore arrays
have been observed within micrometre sized domains. The
diameter of the pores is 15 nm with an interpore separation
of approximately 112 nm. The porosity, determining nanorod
concentration p, of the anodic alumina obtained in selenic
acid is 3.4%, much lower than achievable with sulphuric
acid (down to 12.6%). 22,29 It is very interesting to note that
both sulphuric acid and selenic acid possess similar chemical
structures (Fig. 1(c)) but totally different anodization behaviour.
In the case of acids having similar chemical structure,
acid strength decreases as the size of the central atom
increases. The atomic size of selenium is bigger than sulphur;
therefore, selenic acid is less soluble than sulphuric acid
under the same anodization conditions. This low solubility
accounts for the much smaller pore diameter observed here.
With a decrease in anodization temperature, the solubility
of selenic acid decreases leading to the unusual selfordered
porous alumina with smaller than expected pore
diameter, while the period remains unaffected. This unique
porous alumina structure has enabled the metamaterials’
plasma frequency to be tuned throughout the visible and
near-infrared spectral ranges. Additionally, since the geometry
of the gold nanorods is determined by the porous alumina
template, the diameter of nanorods may be varied by changing
the pore diameter in a pore widening process while keeping
the inter-rod spacing the same. Alternatively, we can
also tune the pore diameter while keeping the interpore distance
constant by raising the temperature during the anodization
process. Figure 1(e) shows the effect of varying the
nanorod diameter while maintaining constant nanorod spacing
and length. With a reduction in nanorod concentration, a
monotonous long-wavelength shift of the dominating extinction
peak is observed, accompanied by a broadening of the
peak due to the red-shift of the effective plasma frequency
(as the concentration of metal becomes smaller the interaction
between the nanorods becomes weaker).
Metamaterials comprised of Au nanorods embedded in
an AAO matrix were designed with the effective plasma frequency
in the infrared spectral range (Fig. 2). The extinction
spectra show the two typical dominating resonances, which
are well separated from each other spectrally. A short wavelength
resonance is associated with plasmonic excitations by

121110-3 Nasir et al. Appl. Phys. Lett. 107, 121110 (2015)
FIG. 1. (a) Schematics of the metamaterial based on a nanorod array. (b) SEM image of porous alumina synthesized in selenic acid at 48 V (sample B). (c)
Comparison of sulphuric and selenic acid molecules. (d) SEM image of the nanorods after removal of alumina matrix (sample B). Please note that disorder is
introduced in the nanorod array after the matrix removal due to the reduced self-supporting properties of thin nanorods. (e) The effect of nanorod concentration
on the extinction of the metamaterial (the Au nanorods in AAO matrix, p-polarized light, 40 angle of incidence).
light polarised perpendicular to the nanorod axes, while the
strong long-wavelength absorption near the effective plasma
frequency takes place for incident light polarised along the
nanorod axes. 30 These two resonances, of a different nature,
remain separated even when the AAO is removed, when for
the samples with higher nanorod concentrations they typically
overlap. For smaller nanorod diameters with the same
period, the peak in the ENZ region is shifted further in the
FIG. 2. Extinction spectra of metamaterials (a–c) A (nanorods of 40 nm diameter, 115 nm period, and 200 nm height, embedded in AAO matrix) and (d–f)
B (nanorods of 25 nm diameter, 115 nm period, and 350 nm height, embedded in AAO matrix) at different angles of light incidence: (a) and (d) experiment,
(b) and (e) full-vectorial microscopic modelling, (c) and (f) EMT modelling. For sample A an electron mean free path restriction of 23 nm was used for electrochemical
Au; 18 the metamaterial has a 7 nm thick Au underlayer and a 700 nm thick AAO overlayer. For sample B, the electron mean free path restriction is
8 nm for electrochemical Au; the metamaterial has a 7 nm thick Au underlayer and a 650 nm thick AAO overlayer.

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.

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