Enhancing the Nonlinear Optical Response Using Multifrequency Gold-Nanowire Antennas
Hayk Harutyunyan,1Giorgio Volpe,2Romain Quidant,2,3and Lukas Novotny1,*
1Institute of Optics, University of Rochester, Rochester, New York 14627, USA
2ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
3ICREA-Institucio ´ Catalana de Recerca i Estudis Avanc ¸ats, 08010 Barcelona, Spain
(Received 10 November 2011; published 23 May 2012)
We introduce and experimentally demonstrate the concept of multifrequency optical antennas that are
designed for controlling the nonlinear response of materials. These antennas consist of two arms of
different lengths, each resonant with one of the incoming frequencies. They are embedded in a nonlinear
medium (indium tin oxide) that acts as a receiver. Because the two arms have different spectral
resonances, tuning of the antenna gap size has minimal effect on the linear optical properties.
However, it strongly affects the nonlinear response. Thus, by employing antenna elements with different
spectral resonances, we provide a strategy to decouple the nonlinear response of nanomaterials from their
linear optical properties.
DOI: 10.1103/PhysRevLett.108.217403 PACS numbers: 78.67.Bf, 73.20.Mf, 73.21.?b, 78.47.N?
Optical antennas provide a means to transduce localized
fields into free-propagating optical radiation, and vice
versa . So far, most of the implemented antenna struc-
tures operate in the linear regime; that is, the polarization
currents depend linearly on the excitation field. The illu-
mination of an optical antenna by an incident radiation
generates strongly enhanced localized fields governed by
distinct plasmon resonances [2–4]. These local fields can
be further enhanced and controlled by antennas made of
multiple elements. For example, gap antennas, consisting
of two arms of equal length separated by a tiny gap, have
been used to control both the linear response and the non-
linear response [5–7]. Recently, nonlinear optical antennas
have been discussed theoretically for modulation and
switching purposes [8–10]; however, the nonlinear re-
sponse can be complex and it is not a priori clear what
the best design strategies are to optimize the nonlinear
response . A figure of merit for nonlinear materials is
the strength of the nonlinear response relative to the linear
response of the material [12,13]. Typically, the nonlinear
response depends on a strong linear response . Here we
show that this is not generally the case and that we are able
to enhance the nonlinear response without increasing the
The multifrequency antenna consists of two metal arms
of different lengths and separated by a gap that is filled by a
nonlinear optical material (Fig. 1). The fields ESð!1Þ and
ESð!2Þ received by the two antenna arms overlap in the
gap region, where they simultaneously interact with the
nonlinear medium. The lengths of the metal arms are
chosen such that a half-wave resonance is established at
frequencies !1and !2, respectively [14–17]. The non-
linear medium can be viewed as a localized receiver that
converts the input signals at frequencies !1and !2into an
output signal centered at frequency !3through a third-
order nonlinear frequency mixing process referred to as
four-wave mixing (4WM) . While there is no gap
enhancement effect in the linear regime for either of the
incoming wavelengths, the nonlinear response is strongly
dependent on the gap size, proving the purely nonlinear
nature of these resonant antennas.
In our experiments the antenna structures were fabri-
cated on ITO-coated glass substrates using standard
positive-resist e-beam lithography. The samples consisted
of antenna arrays with varying antenna arm lengths and
gap sizes. As shown in Fig. 1, two ?200-fs infrared pulse
FIG. 1 (color online).
E0ð!1Þ, and E0ð!2Þ, with different near-infrared frequencies
are received by a linear gap antenna with different arm lengths.
Each arm is resonant with one of the incoming frequencies. The
antenna converts the input signals into an output signal centered
at a new frequency !3, which is subsequently recorded by a
Illustration of the resonant nonlinear
PRL 108, 217403 (2012)
PHYSICAL REVIEW LETTERS
25 MAY 2012
? 2012 American Physical Society
were focused on a single antenna structure resulting in spot
sizes comparable to the dimensions of the antennas used in
the experiments (210 to 510 nm). The distance between
adjacent antennas was set to 4 ?m to avoid any significant
coupling effects. In a typical experiment, the sample was
raster scanned through the laser focus, and the signal was
collected through the same focusing objective. For non-
linear measurements, the laser pulses were overlapped in
space and time, and the spectrum of scattered radiation was
recorded with a CCD-coupled spectrometer (Fig. 1). For
every image pixel, a full spectrum was acquired. The
spectra were then fitted with a narrow Lorentzian line
shape function and a broad polynomial, from which we
extracted the magnitudes of 4WM and two-photon excited
luminescence (TPL). For determining the linear reso-
nances of the antenna arms, dark-field linear scattering
measurements were performed by using spatial filtering
in the Fourier planeof the objective lens toreject laser light
reflected from the glass-air interface. The light scattered by
the antennas was detected by an avalanche photodiode
(APD). Because the back aperture of the objective was
underfilled for the dark-field measurements, the resulting
focal spot sizes were on the order of a few microns,
significantly larger than the diffraction limit. The polariza-
tion of both beams was aligned in direction of the antenna
arms, and the average power was on the order of
50–300 ?W (peak intensities of 0:2–1:2 GW=cm2).
Let us first theoretically analyze the behavior of the
nonlinear optical antenna. Fig. 2 shows the electromag-
netic field distribution near an optical antenna made of two
gold arms of lengths 80 and 140 nm, respectively. The
width of the antenna arms is 40 and their separation is
20 nm. The two antenna arms are embedded in a nonlinear
medium with dielectric constant " ¼ 2:89 (ITO) and third-
order susceptibility ?ð3Þ¼ 2:16 ? 10?18m2=V2, giving
rise to an instantaneous nonlinear response . As shown
in Fig. 2(a), the field at wavelength ?1¼ 780 nm is reso-
nant with the short antenna arm and gives rise to an
enhanced field that is localized near the short antenna
arm. On the other hand, the field at wavelength ?2¼
1100 nm is resonant with and localized near the long
antenna arm [cf. Fig. 2(b)]. The two enhanced fields over-
lap in the gap region where they induce a nonlinear polar-
Pð3Þð!3Þ ¼ "o?ð3Þð?!3;!1;!1;?!2ÞE1E1E?
which in turn gives rise to radiation at the frequency !3¼
2!1? !2. Fig. 2(c) depicts jPð3Þj2near the optical antenna
for an isotropic nonlinear material. The line cut in the
figure shows that nonlinear signal generation is mostly
localized to the gap region. We neglect the nonlinear
response of the two gold arms because the exciting
fields penetrate only weakly into the material [cf.
Figs. 2(a) and 2(b)] and, therefore, predominantly interact
with the nonlinear medium surrounding the antenna arms.
Thus, due to the asymmetry of the antenna design, the
near-fields contributing to the linear [Figs. 2(a) and 2(b)]
and nonlinear [Fig. 2(c)] optical response have different
spatial distribution. This allows independent tuning of the
The linear spectral dependence of the multifrequency
antenna is rendered in Fig. 3. The three curves show the
square modulus of the electric field (E2) normalized by the
incident field intensity (E2
0) for the short antenna arm alone
(dashed line), the long antenna arm alone (dotted curve),
and for both antenna arms (solid curve). For the two
isolated antenna arms the field is evaluated at a distance
of 1 nm from the endpoints of the antenna arms, and for the
FIG. 2 (color online).
made of two gold arms of lengths 80 and 140 nm, respectively,
embedded in a nonlinear medium with dielectric constant " ¼
2:89 (ITO). (a),(b) Square modulus of electric field (E2). The
antenna is irradiated by plane waves of frequencies !1¼
2?c=?1and !2¼ 2?c=?2, respectively. (c) Square modulus
of nonlinear polarization jPð3Þj2at the frequency !3¼ 2!1?
!2. The white curve is a line cut along the axis of the antenna,
showing that the nonlinear signal is almost entirely generated in
the gap of the antenna.
Field distribution near an optical antenna
PRL 108, 217403 (2012)
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antenna consisting of both arms, the field is evaluated in
the gap at the midpoint between the arms. The curves
reveal that the short and long antenna arms exhibit half-
wave resonances at ?1¼ 780 and ?2¼ 1100 nm, respec-
tively. The interaction between the two antenna arms
slightly shifts the two resonances and increases the fre-
quency splitting . However, it is evident that the inter-
action is weak and that the spectral dependence of the two
antenna arms is not significantly affected. To experimen-
tally verify this observation, we have performed linear
scattering measurements on antennas. First, the lengths
of antenna arms resonant with our excitation wavelengths
at ?1¼ 800 and ?1¼ 1150 nm were identified by dark-
field imaging of antennas of different arm lengths (data
not shown). Then, the linear response of structures with
fixed arm lengths, but varying gap size, was measured.
Figures 3(b) and 3(c) show the dark-field linear scattering
of thesameresonant antennas whenonlythe sizeofthegap
is varied from 20 to 80 nm in 10-nm steps. In both images
the scattering amplitude is nearly constant, proving that the
linear interaction is virtually absent in far-field measure-
ments. Higher order plasmonic modes are not expected to
play a major role under current experimental conditions
due to the relatively small size of the antenna elements .
This was verified by linear scattering measurements at
633 nm, close to 4WM emission wavelength (615 nm),
where no measurable gap dependence of the scattered
signal was observed.
We next evaluate the efficiency of frequency conversion
as a function of the two incident wavelengths ?1and ?2.
For simplicity we assume that the ?ð3Þis frequency inde-
pendent. The frequency conversion efficiency is propor-
tional to the square modulus of the nonlinear polarization
and is shown in Fig. 4. The nonlinear spectral response
from composite materials can be complex due to the strong
coupling between the plasmonic modes . However,
from Fig. 4 it is evident that in the case of spectrally
detuned antenna elements, the overall nonlinear response
is still governed by the plasmonic resonances of the indi-
vidual elements, and the frequency conversion efficiency is
the highest if the two incident wavelengths are resonant
with the two antenna arms.
To test if the nonlinear response of the antennas indeed
shows different behavior as compared to their linear re-
sponse as predicted by the theoretical calculations shown
in Fig. 2, we carried out experiments of frequency conver-
sion with different antenna geometries (Fig. 5). Here each
arm length was chosen according to the linear measure-
ments to be in resonance with one of the excitation wave-
lengths, and the gap size was again varied from 20 to
80 nm. In difference to our linear scattering experiments,
the 4WM signal strongly depends on the size of the gap.
The signal is strongest for the smallest gap size and van-
ishes for large gaps (Fig. 5). On the other hand, if the
antenna arms are not resonant with the excitation wave-
lengths, we find that the 4WM signal reduces significantly
and no longer depends on the gap size (data not shown).
Thus, by employing antenna elements with different spec-
tral resonances, we provide a strategy to tune the nonlinear
response independent of the linear properties. This behav-
ior is expected to break down in the quasistatic regime,
where the resonances are no longer size-dependent .
The results shown in Fig. 5 have been verified for different
antenna arrays. While there are slight variations among the
data points due to fabrication uncertainties (see inset of
800 1000 12001400
E2 / Eo
FIG. 3 (color online).
frequency antenna. (a) Dashed curve: short antenna arm alone;
dotted curve: long antenna arm alone; solid curve: both antenna
arms. The dashed and dotted curves correspond to the square
modulus of the field (E2) evaluated at a distance of 1 nm from the
endpoints of the antenna arms. The solid curve corresponds to
the E2evaluated at the midpoint between the two antenna arms.
(b) and (c) dark-field scattering images of antennas with fixed
arm lengths of 110 and 210 nm, at the two excitation wave-
lengths ?1¼ 800 and ?2¼ 1150 nm.
Linear spectral dependence of the multi-
characterized in Fig. 3 as a function of input wavelengths. The
figure shows contours of jPð3Þð?1;?2Þj2, which is proportional to
the frequency conversion efficiency.
Efficiency of frequency conversion of the antenna
PRL 108, 217403 (2012)
25 MAY 2012
Fig. 5), the above-mentioned trends were consistently ob-
served for all measured antenna arrays. See Supplemental
In our experiments the antennas were resting on a non-
linear substrate rather than being embedded in it as in the
calculations presented above. This difference, however,
has proven to have little or no influence on the nonlinear
response of very similar nanoantenna-ITO hybrid systems
. Thus, while embedding our samples in ITO or any
other highly nonlinear medium might have increased the
efficiency of frequency conversion, we do not expect any
qualitative changes in the behavior of the nonlinear signal.
The gap dependence of the 4WM signal in resonant anten-
nas is a direct evidence that the signal is generated in the
nonlinear material in the gap region, i.e., the nonlinear
substrate and the end facets of the antenna arms. It is
also interesting to note that we did not measure any repro-
ducible gap dependence of the emitted two-photon excited
luminescence (TPL) signal. TPL is a nonlinear process that
does not require multifrequency excitation and therefore is
expected to be significantly less sensitive to the relative
positions of the antenna elements. Similarly, if the two
antenna arms are excited nonresonantly, most of the resid-
ual 4WM signal originates from the individual antenna
arms and hence does not depend on the gap size.
In conclusion, we have introduced the concept of reso-
nant nonlinear antennas and have experimentally demon-
strated its realization at optical frequencies. The use of
nonlinear materials in combination with traditional noble
metal nanostructures provides a framework for nonlinear
optical signal generation. The approach developed here
holds promise for applications such as on-chip optical
frequency conversion and design of metamaterials with
enhanced nonlinear response.
This research was funded by the U.S. Department of
Energy (Grant No. DE-FG02-01ER15204), the National
Science Foundation (Grant No. ECCS-0918416), ERC-
2010-StG Plasmolight (Grant No: 259196), and Fundacio ´
Privada CELLEX. We thank Pieter Kik, Palash Bharadwaj,
and Zack Lapin for valuable input and fruitful discussions.
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1020 30 405060 708090
Normalized 4WM intensity
FIG. 5 (color online).
(a) 4WM images of a sequence of antennas with fixed arm
lengths (110 and 210 nm) and varying gap size d. The gap is
varied from 20 (left) to 80 nm (right). Scale bar 1 ?m. (b) Total
4WM signal normalized to the linear response shown in
Figs. 3(b) and 3(c) . The solid line is an exponential fitting
function. The inset shows a SEM image of an asymmetric gold
antenna. Scale bar 100 nm.
Dependence of 4WM on antenna gap.
PRL 108, 217403 (2012)
25 MAY 2012