Departmento de Física, Universidade Federal de Pernambuco, Recife-PE
50670-901, Brazil The Blackett Laboratory, Department of Physics, Imperial
College London, London SW7 2BW, United Kingdom 1 The authors contributed
equally to this work.

# Nonlinear dielectric epsilon near-zero hybrid nanogap antennas

Romain Tirole1<EMAIL_ADDRESS>The Blackett Laboratory,
Department of Physics, Imperial College London, London SW7 2BW, United Kingdom
Benjamin Tilmann1 Chair in Hybrid Nanosystems, Nanoinstitut München, Ludwig-
Maximilians-Universität München, 80539 München, Germany  Leonardo de S.
Menezes  Chair in Hybrid Nanosystems, Nanoinstitut München, Ludwig-
Maximilians-Universität München, 80539 München, Germany  Stefano Vezzoli  The
Blackett Laboratory, Department of Physics, Imperial College London, London
SW7 2BW, United Kingdom  Riccardo Sapienza<EMAIL_ADDRESS>The
Blackett Laboratory, Department of Physics, Imperial College London, London
SW7 2BW, United Kingdom  Stefan A. Maier  School of Physics and Astronomy,
Monash University, Clayton, Victoria 3800, Australia

###### Abstract

High-index Mie-resonant dielectric nanostructures provide a new framework to
manipulate light at the nanoscale. In particular their local field confinement
together with their inherently low losses at frequencies below their band-gap
energy allows to efficiently boost and control linear and nonlinear optical
processes. Here, we investigate nanoantennas composed of a thin indium-tin
oxide layer in the center of a dielectric Gallium Phosphide nanodisk. While
the linear response is similar to that of a pure GaP nanodisk, we show that
the second and third-harmonic signals of the nanogap antenna are boosted at
resonance. Linear and nonlinear finite-difference time-domain simulations show
that the high refractive index contrast leads to strong field confinement
inside the antenna’s ITO layer. Measurement of ITO and GaP nonlinear
susceptibilities deliver insight on how to engineer nonlinear nanogap antennas
for higher efficiencies for future nanoscale devices.

##  1 Introduction

The implementation of nonlinear optics at the nanoscale and at visible to
near-infrared (near-IR) wavelengths is of great interest for technical
applications such as quantum light sources, optical circuits and frequency
control or biophotonics. Although nanoantennas provide a gateway to
efficiently couple incident light into structures at the nanoscale, other
aspects such as small interaction volume or low damage threshold remain
challenging. In particular, the latter limits the possible usage of plasmonic
structures made of (noble) metals, together with their significant Ohmic
losses. Hence, all-dielectric materials have proven to be a promising
alternative platform for nanophotonics. Of particular interest are group IV
and III-V semiconductors that generally have large refractive indices, high
nonlinear susceptibilities as well as a high transparency for light energies
below their electronic band gap, making them excellent candidates for
nonlinear nanoscale applications 1, 2, 3. Similar characteristics appear in
two-dimensional materials and more specifically transition metal
dichalcogenides, however, their naturally small interaction volume yields only
low absolute signal and lowers the damage threshold due to high excitation
intensities 4.

All-dielectric nanoantennas have shown efficient harmonic generation 5, 6, 7,
8, 9, 10, 11, 12, 13 and ultrafast nonlinear optical switching 14, 15, 16, 17
in various materials such as Silicon, (Aluminum) Gallium Arsenide, Gallium
Phosphide or Germanium. By acting as nanocavities they open the path to larger
interaction volumes while maintaining strong resonant behavior with a high
tolerance to incident field intensities. Particularly the magnetic dipole 8,
9, 13, 7 and anapole resonances 6, 5 of nanodisks have been exploited for
harmonic generation given their characteristic strong field confinement within
the medium. These single-particle modes can also be used as building blocks
for collective resonances: dielectric metasurfaces with various geometries
were shown to exhibit high quality factors 18, 19, 20, 21, emerging from bound
states in the continuum or constructive interference between single-antenna
modes and lattice resonances.

In addition to mode engineering by changing the geometry of nanostructures, an
alternative approach is based on the integration of multiple materials in a
single antenna 22, 23, 24, 25, 26. In particular, creating a gap inside a
high-index dielectric structure in the lateral direction, filled either with
air or a low-index material has the potential to have great impact on the
linear and nonlinear properties of the system 27. Given the optical contrast
between dielectric $n_{d}$ and gap $n_{s}$, the field intensity scales as
$n_{d}^{4}/n_{s}^{4}$ from the continuity of the electric displacement field
at an interface, where $n_{d},n_{s}$ are the respective refractive indices 28.
Moreover, as long as the slot’s dimensions are significantly smaller than that
of the the effective wavelength, the far field optical properties of the
antenna are retained as well as its resonant behavior, as determined by the
effective refractive index. This makes these nanogap antennas promising
candidates for nonlinear nanophotonic applications 29, however, the
experimental realization of different materials in a single nanostructure
remains challenging. Only recently, a nanogap using a low index material,
Indium Tin Oxide (ITO), slotted in silicon was demonstrated and used for
enhanced harmonic generation 30. ITO shows a zero-crossing of the real part of
the dielectric function in the near-infrared (near-IR), allowing for the
realisation of a nanogap with high optical contrast. It was also shown that
ITO exhibits large optical nonlinearities in the vicinity of this so-called
epsilon-near-zero (ENZ) regime 31, 32, 33.

In this work, we realize and characterize a nanogap antenna made of high-
refractive index Gallium Phosphide (GaP) and a nanolayer of ITO and compare it
to a pure GaP antenna of similar dimensions. We design the nanostructures to
exhibit strong optical resonances in the ENZ region, dominated by magnetic
dipole (MD) and electric (ED) contributions. Under illumination with near-IR
light, we observe strong second- and third-harmonic generation (SHG, THG),
whereas the nanogap antenna exceeds the efficiency of the GaP-only case
particularly for excitation at the ED resonance. We show that this enhancement
appears over a broad wavelength range, exceeding the ENZ regime of ITO. To
explain this result, we perform a thorough analysis of the nonlinear
coefficients of both materials and conduct nonlinear scattering simulations.
Our results proposes the concept of nanogap antennas as a new and flexible
platform with a wide range of possible applications in nonlinear optics.
Furthermore, it opens the path of integrating ITO or other ENZ materials into
dielectric structures to enhance specific optical resonances of the
directivity of emission, as well as time-modulated antennas for frequency
control and holography 34, 35.

##  2 Design and fabrication

Figure 1: GaP and nanogap antennas for nonlinear light generation. a
Refractive index spectrum of ITO: real (blue curve) and imaginary (orange
curve) parts. The ENZ region is highlighted with the red-shaded area. b Sketch
of the nanogap antenna concept. The displacement field is represented by the
white double-ended arrow. c Diagram of the expected field intensity
distribution (pink) as a function of the centered antenna depth, resulting
from the permittivity contrast (light blue). d Scanning electron microscopy
images of the sample, taken at angles of 60 and 75 degrees (tilted). e FDTD
simulation of the scattering cross section of a GaP antenna as a function of
pump wavelength and antenna radius. The ED, MD and EQ modes are highlighted
with the black dashed curves. f,g Simulated field intensity profile in
logarithmic scale, the XZ plane for a radius of 200 nm and 1160 nm wavelength
for the GaP (f) and nanogap (g) antennas. White dashed lines show the contour
of the different materials.

GaP-ITO-GaP films are fabricated by a multi-step sputtering process at
elevated temperature, more details can be found in the Supplementary
materials. The materials where chosen such that a high optical contrast
between the two layers is achieved, confirmed by the measured refractive
indices shown in Figure 1a, while maintaining losses low at $\omega$ and
$2\omega$. The ENZ point of the ITO layer lies around 1300 nm, a regime where
GaP shows a high refractive index and virtually no optical losses. In a
nanodisc with an ITO film located in the center, as sketched in Fig. 1b, the
contrast of the permittivity at the ENZ wavelength reaches a maximum of more
than ten, which leads to a strong confinement of the electric field inside the
ITO layer (see Fig. 1c. The fabrication of the nanostructures is carried out
by electron-beam lithography (EBL) and subsequent reactive ion etching (RIE),
more details can be found in the Supplementary Information. The distance
between individual antennas is kept at $3\,\upmu\text{m}$ to prevent cross-
antenna coupling. GaP-only nanodisks with identical dimensions were fabricated
following the same process. A scanning electron microscopy (SEM) image of the
nanogap discs with varying radii is shown in Fig. 1d (left). Looking at the
tilted SEM image in the right hand side of Fig. 1d, one can clearly observe
the three distinct layers which confirms the successful fabrication of the
nanogap antennas.

We perform finite-difference time-domain (FDTD) simulations to investigate the
scattering properties of the fabricated structures. Fig. 1e shows the
evaluated scattering cross section for GaP-only structures, in dependence of
the excitation wavelength and nanodisc radius. Clearly, a set of distinct
resonances can be identified. By comparison with a multipole decomposition
shown in the Supplementary Information, three main contributions can be
identified as indicated in Fig. 1e. At larger radii, higher order as the
electric quadrupole (EQ) dominate the scattering spectrum, whereas smaller
radii are dominated by MD and ED. A similar simulation carried out for the
hybrid nanodiscs is shown in Supplementary Information and confirms that the
far-field response is only marginally affected by the presence of the ITO
layer (which makes only 7.5% of the volume of the antenna). However, the
continuity of the displacement field vector D requires a change in the
electric near-field distribution and consequently strongly confines the
electric near-field into the low-index region (pink-shaded area in Figure 1c).
This is even more pronounced when comparing the simulated near field
distributions of the GaP-only nanodisc in Fig. 1f and of the nanogap antenna
in Fig. 1g, for a wavelength of 1160 nm and an antenna with a radius of 200
nm. For the latter, the field is clearly highly concentrated within the 20 nm
thin ITO layer with distribution towards the edges of the disc. Contrarily,
the near field of a GaP-only antenna under similar conditions has a field
broadly confined over the antenna’s volume, with maximum intensity values one
order of magnitude smaller.

##  3 Harmonic measurements

The GaP and nanogap discs are investigated with respect to their nonlinear
optical response by using a nonlinear microscopy setup, based on a tunable
wavelength laser with 100 kHz repetition rate and 225 fs (FWHM) pulses. The
generated nonlinear signal is collected in reflection geometry (see Fig. 2a)
and then either sent to a single photon detector or a spectrometer to
respectively map the resonances as a function of radius and illuminating
wavelength, or measure the light’s spectrum. To calculate the intensity at
each wavelength, average excitation power and beam size are measured at the
focal position. More details of the experimental setup can be found in the
Supplementary Information.

For an excitation wavelength of $\lambda_{0}=1350$ nm and a nanogap disc
radius of $\sim$ 330 nm, the corresponding SHG and THG spectrum are shown in
Fig. 2b. The collected light is indeed harmonic centered at
$\lambda_{SHG}=675\,\text{nm}=1350\,\text{nm}/2$ and
$\lambda_{THG}=450\,\text{nm}=1350\,\text{nm}/3$, with no evidence for
photoluminescence. Furthermore, the nonlinear character of the observed signal
is confirmed by power dependence measurements (see Supplementary Information).
Measurements on a GaP-only disc yield similar results, however, from the
amorphous nature of the GaP it is expected that the SHG is largely generated
by surface instead of bulk contributions 36.

Figure 2: Measurement of harmonic generated light from nanodisks. a
Experimental microscopy setup for the spectral characterisation of antennas.
The reflected harmonic from the sample can be sent for detection either by a
single photon detector or CCD camera spectrometer. b Second and third harmonic
spectra from a nanogap antenna of radius of 330 nm and illumination wavelength
of 1350 nm. c Comparison of THG (top) and SHG (bottom) efficiency dependence
on radius between the nanogap (purple and blue curves) and the GaP-only
(yellow and red curves) nanodisks, for a wavelength of 1350 nm.

Fig. 2c shows the SHG and THG signal at a fixed excitation wavelength of 1350
nm in dependence of radius for GaP-only and GaP-ITO antennas. In the case of
THG (upper panel), the enhancement of the nanogap (purple) against GaP (dark
yellow) is limited at the visible ED and MD modes, with only an enhancement by
a factor of 1.3 (respective values of 10.45 and 8.01 kHz.cm2/GW). Yet, the
resonances are significantly broadened over a range of radii, with THG counts
staying at a constant level between 230 and 300 nm radius. For SHG on the
other hand, the nonlinear signal is enhanced over a broad range of radii (blue
against red line, lower panel). This can be explained by the added amount of
interfaces between layers, essential in the generation of the second harmonic
as it increases the surface area where SHG occurs 37, along with a potential
higher second order nonlinear susceptibility from the surface of ITO.

Next, we characterise the spectral dependence of the harmonic generation and
the evolution of the nanodisc resonances by varying the incident light pulse
wavelength. Fig. 3a shows the measured THG counts per unit intensity for
antennas without the ITO layer, in dependence of radius and excitation
wavelength. Three distinct resonances are clearly visible, and can be
associated to the scattering simulation in Figure 1e. It follows that the
lower resonances is caused by the scattering peak that was associated with the
ED resonances, whereas the second follows the course of the MD scattering dip.
The resonance that is visible at the largest radii can be assign to the higher
order electric quadrupole (EQ). The THG signal that is generated from the MD
is more than one order of magnitude larger than for ED and EQ. This can be
explained by near field simulations (see Supplementary Material), where the MD
strongly concentrates the electric field inside the volume of the
nanostructures. Furthermore, this is confirmed by nonlinear scattering
simulations that are shown in the Supplementary Material and which
qualitatively reproduce the measured THG signal with good agreement.

Following the same procedure, THG was measured for the hybrid GaP-ITO
nanostructures, with the spectral and radial dependence shown in Figure 3b.
Again, the previous three resonances can clearly be seen, with the ED, MD and
EQ appearing at similar radii and wavelengths as for the GaP-only structures.
One can see the MD mode yields less signal further in the IR, around 1650 nm
wavelength, but presents a higher generation efficiency in range near its ENZ
wavelength (1300-1400 nm). Furthermore, the mode is spectrally broader, and
the nanogap antenna exhibits a higher THG efficiency off resonance compared to
the GaP-only case.

Figure 3: Characterisation of the nanodisk’s nonlinear signals. a,b
Experimentally measured THG signal in counts per second per unit intensity as
a function of disk radius and pump wavelength for GaP (a) and nanogap (b)
disks. c Extracted resonant wavelength for the ED, MD and EQ modes as a
function of radius for the nanogap antenna (blue diamonds), GaP antenna (red
diamonds)

The nanogap antenna shows a distinctive feature in mode evolution when
compared to the GaP antenna in its ED resonance. Fig. 3c represents the
extracted resonant radii of the disks for each excitation wavelength. Each
diamond corresponds to a mode’s most efficient radius for THG for a given
wavelength. All three modes are clearly visible for GaP (light red), and as
expected the optimal antenna resonant radius increases with wavelength for
each mode as the GaP antenna is a cavity. This is verified by nonlinear
scattering simulations (see Supporting Information), which agrees very well
with the experimental measurement. For the GaP-ITO antenna, a similar behavior
can be observed for the MD and EQ resonances, agreeing well with the course of
the GaP-only case and the simulations. For the ED however, a particular dip in
the resonant wavelength can be observed for the ED mode, that happens around
the ENZ region. Here, the resonant radius drops by $\sim$ 50 nm when the
illuminating pump wavelength is increased by the same amount.

##  4 Nonlinear susceptibility and field distribution

Although an enhancement of the nonlinear signal of a factor up to 2 at
resonance from the nanogap compared to the GaP-only antennas could be
observed, the effects is not comparable to 100$\times$ field enhancement
reported in 30. To address this discrepancy, we measure and compare the
$\chi^{(3)}$ of GaP and ITO in the following. This is done by measuring the
samples under weakly focused illumination after which the THG light is
collected. Then, the measured harmonic power is processed and compared to the
illuminating power to extract a value of the nonlinear susceptibility (see
Supplementary Information). A 400 nm thick GaP thin film as well as three thin
films of ITO with various thicknesses (40, 100 and 310 nm) are investigated.
Note that an additional 20 nm ITO thin film was measured, but yielded too weak
harmonic signal in the present configuration to give an accurate value for the
nonlinear susceptibility. The resulting third harmonic nonlinear
susceptibility spectra are presented in Fig. 4a. As can be seen, GaP (in red)
has a $\chi^{(3)}$ an order of magnitude above that of ITO (in blue), with a
value of 6.95 $\times 10^{-19}$ m2/V2 at $1350\,\text{nm}$ wavelength. All
three ITO samples, with various thicknesses and different ENZ wavelengths in
the near-infrared region, have comparable third harmonic susceptibilities. For
this reason, we assume the nonlinear susceptibility of the $21\,\text{nm}$
layer of ITO within the nanogap antennas to be equal to that of the
$40\,\text{nm}$ layer. The reason that the measured $\chi^{(3)}$ is lower than
previous reports using Z-scan or pump-probe spectroscopy 38, 32 is the
following. These techniques are efficient at estimating third order
nonlinearities for the Kerr effect, corresponding to a nonlinear
susceptibility tensor of taking the form of
$\chi^{(3)}(\omega,\omega,\omega,-\omega)$ where the first frequency refers to
the outgoing wave and the following ones to the waves interacting via the
nonlinearity. For THG, the nonlinear susceptibility is evaluated for different
frequencies of $\chi^{(3)}(3\omega,\omega,\omega,\omega)$ and can thus take a
different value. Thus, observing strong Kerr nonlinearities in ITO does not
guarantee observing efficient THG.

We further investigate the contributions of the ITO and GaP layers within the
antenna by looking at FDTD simulations, more precisely at the average field
enhancement (normalised to the illuminating field intensity), shown in Fig. 4b
for a radius of 320 nm, at the MD resonant wavelength of 1285 nm. Clearly, the
field is highly concentrated into the ITO layer (light blue box), with a
predicted average enhancement of 13.17. From this, the contribution of the ITO
layer to the generated THG signal could be approximated to be $13.17^{3}$
larger than that of the GaP layers. But evidently, this did not lead to an
increase of the total THG signal in the experiment, which we explain by three
contributing factors.

Figure 4: Mechanisms reducing harmonic generation from the ITO layer. a
Measured $\chi^{(3)}$ of various ITO thin films, with 40 nm (dark blue curve),
100 nm (blue curve) and 310 nm (light blue curve) thicknesses, and of GaP (red
curve). The nonlinear susceptibilities of ITO are multiplied by 10 for
comparison. b Average intensity enhancement with regards to the incoming beam,
in the ITO (light blue bar) and GaP (red bar), layers as well as over the
entire antenna (purple bar), simulated using FDTD for a 320 nm nanodisk at the
MD resonant frequency of 1285 nm. c Corresponding intensity enhancement
integrated normalised by the volume of the layers or antenna: the
comparatively small size of the ITO layer reduces its contribution to the THG
signal. d THG prediction using FDTD, setting
$\chi^{(3)}_{\textrm{GaP}}=\chi^{(3)}_{\textrm{ITO}}$: a poor overlap with the
harmonic field profile reduces the ITO layer’s contribution even further in
comparison to the GaP layers. Note that constructive interference between the
ITO and GaP layers enhances the harmonic signal. e THG prediction using FDTD
and the experimentally measured nonlinear susceptibility of the materials: the
ITO contribution to THG is greatly reduced in comparison to the average
intensity enhancement presented in panel b.

First, the ITO layers occupies only 7.5% of the total. This explains the low
shift in the overall antenna resonant radius, but as Fig. 4c shows it also
plays against the third harmonic enhancement from the nanogap effect.
Multiplying the average field enhancement by the relative volume logically
reduces the contribution of the ITO to the total THG by a factor of 10, on a
now similar scale to that of GaP.

Second, the antenna’s resonance at the harmonic wavelength plays an important
role in the harmonic generation process 3, 39. In order to enhance the
generated signal, the nanodisk needs to provide good overlap between the
resonances at the fundamental and the harmonic. Nonlinear FDTD simulations
(see Supplementary Information) in Fig. 4d shows this is not the case in the
ITO layer, which suffers from this constraint in comparison to the GaP layers.
Nevertheless, constructive interference between the THG signal generated by
the ITO and GaP layers can enhance the resulting harmonic signal.

Finally, with the additional effect of the nonlinear susceptibility, the
contribution of the ITO layer to the total harmonic generated signal then
becomes modest, as shown in Fig. 4e.

We have thus shown that the insertion of an ITO nanogap in a high-index
dielectric antenna brings little advantage in third harmonic enhancement if
the base material shows high nonlinearities. Similar results are expected to
hold for Al-GaAs, Ge, or LiNbO3, with ITO or AZO as a nanogap layer. Second
harmonic generation, on the other hand, is enhanced, which we attribute to the
fact it is not generated in the bulk of centrosymmetric materials such as
a-GaP or ITO 40, 37, and is proportional to area and not volume, thus
mitigating the limited height of ITO. Furthermore, the field distribution is
enhanced at the surface of the ITO, while for GaP the field is more evenly
distributed throughout the volume.

Instead, we suggest an alternative application for nonlinear nanogap antennas.
To take advantage of the strong Kerr effect and field enhancement within the
ITO layer, the nanogap antennas could be used for ultrafast switching and
frequency modulation via time-varying effects. By experiencing a strong and
swift change in permittivity under pumping at the resonant wavelength, a probe
beam at the same wavelength should undergo changes in carrier frequency 41 and
spectral width 42. Then, factors such as overlap and interference of the
harmonic field are ruled out, while making use of the strong Kerr nonlinearity
of ITO.

##  5 Conclusion

In summary, we have characterised the crossing between the resonances of a GaP
high-index dielectric antenna and the nanogap effect from an ITO thin film, by
measuring a broadband enhancement of SHG and THG signal from the nanodiscs.
The comparison to a GaP-only antenna shows the conservation of the mode
resonances and a significantly increased second harmonic signal across all
nanogap antenna radii, while the third harmonic, though slightly enhanced,
shows a limited increase in efficiency. We attribute this to a combination of
lowered parametric nonlinearities in ITO in comparison to GaP, as well as the
limitations of volume and field overlap affecting the overall signal generated
by the nanogap layer. This demonstrates that engineered antennas with ENZ
nanolayers can be used for nonlinear light generation. Further development of
these nanodisks could leverage the exceptional properties of ITO and other
transparent conducting oxides for ultrafast switching or time-varying effects
31, 43.

The authors acknowledge funding from the Engineering and Physical Sciences
Research Council (EP/V048880). S.A.M. additionally acknowledges the Australian
Research Council and the Lee-Lucas Chair in Physics.

Supporting Information is available from the Wiley Online Library or from the
author.

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