# Hybrid Dielectric-Plasmonic Nanoantenna with Multi-Resonances for
Subwavelength Photon Sources

Pavel A. Dmitriev  [  Emmanuel Lassalle  [
<EMAIL_ADDRESS>Lu Ding  [  Zhenying Pan  [  Darren C. J.
Neo  [  Vytautas Valuckas  [  Ramón Paniagua-Dominguez  [  Joel K. W. Yang  [
Hilmi Volkan Demir  [  Arseniy I. Kuznetsov  [
<EMAIL_ADDRESS>
###### Abstract

The enhancement of the photoluminescence of quantum dots induced by an optical
nanoantenna has been studied considerably, but there is still significant
interest in optimizing and miniaturizing such structures, especially when
accompanied with an experimental demonstration. Most of the realizations use
plasmonic platforms, and some also use all-dielectric nanoantennas, but hybrid
dielectric-plasmonic (subwavelength) nanostructures have been very little
explored. In this paper, we propose and demonstrate single subwavelength
hybrid dielectric-plasmonic optical nanoantennas coupled to localised quantum
dot emitters that constitute efficient and bright unidirectional photon
sources under optical pumping. To achieve this, we devised a silicon nanoring
sitting on a gold mirror with a $10\,$nm gap in-between, where an assembly of
colloidal quantum dots is embedded. Such a structure supports both (radiative)
antenna mode and (non-radiative) gap mode resonances, that we exploit for the
dual purpose of out-coupling the light emitted by the quantum dots into the
far-field with out-of-plane directivity, and for enhancing the excitation of
the dots by the optical pump. Moreover, almost independent control of the
resonance spectral positions can be achieved by simple tuning of geometrical
parameters such as the ring inner and outer diameters, allowing to
conveniently adjust these resonances with respect to the quantum dots emission
and absorption wavelengths. Using the proposed architecture, we obtain
experimentally average fluorescence enhancement factors up to $654\times$
folds mainly due to high radiation efficiencies, and associated to a
directional emission of the photoluminescence into a cone of $\pm 17\degree$
in the direction normal to the sample plane. We believe the solution presented
here to be viable and relevant for the next-generation of light-emitting
devices.

imre]Institute of Materials Research and Engineering, A*STAR (Agency for
Science, Technology and Research), 2 Fusionopolis Way, $\\#$08-03 Innovis,
138634 Singapore [ntu]LUMINOUS! Centre of Excellence for Semiconductor
Lighting and Displays, School of Electrical and Electronic Engineering, School
of Physical and Mathematical Sciences, School of Materials Science and
Engineering, Nanyang Technological University, Singapore 639798, Singapore
imre]Institute of Materials Research and Engineering, A*STAR (Agency for
Science, Technology and Research), 2 Fusionopolis Way, $\\#$08-03 Innovis,
138634 Singapore imre]Institute of Materials Research and Engineering, A*STAR
(Agency for Science, Technology and Research), 2 Fusionopolis Way, $\\#$08-03
Innovis, 138634 Singapore imre]Institute of Materials Research and
Engineering, A*STAR (Agency for Science, Technology and Research), 2
Fusionopolis Way, $\\#$08-03 Innovis, 138634 Singapore imre]Institute of
Materials Research and Engineering, A*STAR (Agency for Science, Technology and
Research), 2 Fusionopolis Way, $\\#$08-03 Innovis, 138634 Singapore
imre]Institute of Materials Research and Engineering, A*STAR (Agency for
Science, Technology and Research), 2 Fusionopolis Way, $\\#$08-03 Innovis,
138634 Singapore imre]Institute of Materials Research and Engineering, A*STAR
(Agency for Science, Technology and Research), 2 Fusionopolis Way, $\\#$08-03
Innovis, 138634 Singapore sutd]Singapore University of Technology and Design,
8 Somapah Road, 487372, Singapore [imre]Institute of Materials Research and
Engineering, A*STAR (Agency for Science, Technology and Research), 2
Fusionopolis Way, $\\#$08-03 Innovis, 138634 Singapore ntu]LUMINOUS! Centre of
Excellence for Semiconductor Lighting and Displays, School of Electrical and
Electronic Engineering, School of Physical and Mathematical Sciences, School
of Materials Science and Engineering, Nanyang Technological University,
Singapore 639798, Singapore [bilkent]Department of Electrical and Electronics
Engineering, Department of Physics, UNAM – Institute of Materials Science and
Nanotechnology, Bilkent University, Ankara 06800, Turkey imre]Institute of
Materials Research and Engineering, A*STAR (Agency for Science, Technology and
Research), 2 Fusionopolis Way, $\\#$08-03 Innovis, 138634 Singapore

##  1 Keywords

fluorescence enhancement, Purcell effect, optical nanoantenna, nanoparticle-
on-mirror, nanopatch antenna, quasi-normal modes

##  2 Introduction

With the constant effort for miniaturizing light-emitting devices, new
nanoscale light-emitting diodes (also known as "nano-LEDs") and on-chip single
photon sources with subwavelength dimensions, typically below $1\,\mu$m in the
visible range, are more and more on-demand, for applications like advanced
display, optical communications or quantum technologies. A promising way to
create efficient and bright photon sources is to enhance the photoluminescence
(fluorescence) of quantum emitters (such as quantum dots) with optical
nanoantennas, which are optically resonant nanostructures designed to control
and boost the light-matter interactions at the nanoscale through extreme
confinement of the light field 1. This process is otherwise very inefficient
due to impedance mismatch between the optical cross-sections of quantum
emitters and the wavelength of light 2.

In general, fluorescence enhancement can be achieved via three different
mechanisms 1, such as local enhancement of the pump field intensity to enhance
the excitation of the fluorescent emitters by the incident pump, modifying the
electromagnetic environment via the local density of optical states (also
known as “Purcell effect”) to make the light emission process faster and/or
more efficient, and shaping the emitted fluorescence towards the collection
system to increase the collected signal. The optical nanoantennas used for
fluorescence enhancement usually aim to leverage on combining part of — if not
all — these mechanisms.

To date, the platforms that provide the highest fluorescence enhancements are
plasmonic nanoparticle-on-mirror (also known as nanopatch optical antennas)3,
in which the quantum emitters are embedded in the narrow gap formed between a
subwavelength plasmonic nanoparticle and a metallic mirror. This architecture
was first pinpointed theoretically for the large Purcell factor they can
provide 4, in order to dramatically accelerate the spontaneous emission
process of the quantum emitters. It was later realized experimentally 5, with
many subsequent realizations 6, 7, 8, 9, 10. However, these plasmonic
nanopatch antennas work best for sub-$10\,$nm gap, which is suitable for the
purpose of enhancing the fluorescent signal from small molecules, but not for
e.g. modern colloidal quantum dots which are much more relevant for the
creation of photon sources due to their stability, but are also much bigger
with typical diameters $\sim 10\,$nm, and thus cannot be integrated in such
small gaps 2. Moreover, they suffer from absorption losses of their metal
parts, that ideally must be reduced in order to improve the radiative
efficiency of these nanoantennas (also called quantum efficiency or quantum
yield), defined as the probability that the excitation of the quantum emitters
results in a photon emitted in the far-field, which is estimated between
$20-50\,\%$ 1.

As an alternative solution, all-dielectric nanoantennas, made of low-loss and
high-refractive index materials, ensure higher radiative efficiencies and more
flexibility for controlling the emission directivity and enhancing the
emission of magnetic emitters11. Nevertheless, despite providing in theory
relatively high enhancement factors in comparison with plasmonic antennas for
larger gaps 12, these realizations are usually far from the record-breaking
performances of plasmonic nanopatch antennas 13, 14. This field has also
mainly been driven by single molecule microscopy rather than photonic
integration.

Hybrid dielectric-plasmonic structures aim to take the best of both worlds,
that is the field enhancement and confinement of plasmonic structures and the
low losses and greater flexibility of dielectric structures to tune the
resonances and shape the directivity15, 16. Most of them typically involve
micron-scaled hybrid bullseye antennas17, 18, 19, 20 to demonstrate high
directivity, but such systems cannot be shrunk down to subwavelength sizes by
nature. More recently, a particularly interesting design was put forward in
the context of nanoparticle-on-mirror antennas with subwavelength size,
consisting in a dielectric nanodisk sitting on top of a metallic mirror, with,
in theory, high Purcell factor, quantum efficiency, and directional emission
21. Two subsequent experimental works demonstrated the relevance and potential
of such a hybrid platform by enhancing the photoluminescence of quantum dots
located in the gap formed between a silicon nanosphere and a gold mirror 22,
23, essentially leveraging on the Purcell effect to boost the emission
process, but without considering directivity control. The absence of more
experimental demonstrations with subwavelength nanoantennas could be because
the integration of emitters with the nanoantenna is on its own a very complex
problem, usually requiring either precise manipulation24, 25, 26, 27, 28, 29
or precise measurement of existing emitters location30.

In this work, we design a silicon hollow disk (i.e. a nanoring) antenna
sitting on top of a gold mirror, forming a nanogap of about $\sim 10\,$nm,
within which colloidal quantum dots are embedded. We thus obtained self-
localised emitters, present underneath the nanoantenna only, alleviating the
problem of quantum emitters localisation. Silicon nanorings present strong
scattering properties, with geometrically tunable resonances (also called “Mie
resonances”) that provide control over the scattering strength and
directivity, with potential ability to tailor the emission of electric or
magnetic dipole emitters31, 32, 33, 34, but it is generally difficult to
efficiently couple an assembly of emitters. Our hybrid nanopatch antenna
allows us to achieve an efficient coupling due to the presence of two classes
of resonant modes: strongly radiative modes that also provide out-of-plane
directivity (called "antenna modes" hereafter), similar to the standalone
nanoring resonances but with much better coupling strengths with the QDs due
to the presence of the mirror; and weakly radiative modes confined in the gap
between the particle and the mirror35, 21 (called "gap modes" hereafter; these
two classes of modes are also discussed in related configurations, see e.g.
36). We also find that these two types of modes can be spectrally tuned,
almost independently from each other, by simply varying the nanoring
geometrical parameters, such as its inner and outer diameters. By carefully
designing these parameters to match the antenna mode and gap mode resonances
with the emission wavelength of our quantum dots and the excitation wavelength
of the pump laser, respectively, we demonstrate experimentally a directional
fluorescence enhancement over $650$ into a cone of $\pm 17\degree$ in the
direction normal to the surface, compared to the rather isotropic emission of
quantum dots on gold film. We clearly identify the main mechanisms responsible
for the total enhancement, by the use of analytical and quasi-normal mode
frameworks in conjunction with full-waves simulations, to be a combination of
radiative, excitation, and directivity enhancements. Overall, the hybrid
dielectric-plasmonic nanoantenna reported here presents multi-resonances with
strong local field confinement, scattering and directivity properties, that
can be used with the association of an active medium (e.g. quantum dots) to
create efficient, bright and directional photon sources.

##  3 Design and fabrication

The nanoantenna design, as shown schematically in Fig. 1a, consists of an
amorphous silicon (aSi) nanoring sitting on a gold (Au) mirror substrate, with
an alumina (Al2O3) spacer in between where the quantum emitters are embedded.
Scanning electron microscopy (SEM) image of a fabricated sample is shown in
Fig. 1b. We use CdSe/ZnS quantum dots (QDs) as quantum emitters, which have a
strong electric dipole transition, with an emission centered around
$650\,$nm37. A transmission electron microscope image of the QDs is shown in
Fig. 1c, with QD sizes of the order of $\sim 10\,$nm. Their photoluminescence
and absorption spectra measured in solution or on top of a glass substrate are
given in Supp. Info. Section 1, Fig. S1.

A basic model of their energy levels can be found in Supp. Info. Section 1,
Fig. S2, which constitutes the fluorescence model used to interpret our
experimental results, and the basis on which most fluorescence experiments are
analysed. In a reference configuration (chosen to be e.g. QDs deposited on a
substrate), we associate a rate to each transition between different energy
levels, namely an excitation rate $\gamma_{\text{exc}}^{0}$ induced by the
excitation from a laser pump at the excitation wavelength
$\lambda_{\text{exc}}$ (and directly proportional to its intensity), an
intrinsic non-radiative decay rate $\gamma_{\text{nr}}^{0}$ due to non-
radiative decay channels present in the emitter (such as vibrations or other
non-radiative relaxation channels) and a radiative decay rate
$\gamma_{\text{r}}^{0}$ associated to the spontaneous emission of a photon of
emission wavelength $\lambda_{\text{em}}$ (Fig. S2a). One can then
characterize the emitter by its intrinsic quantum yield, defined as
$\text{QY}^{0}\equiv\gamma_{\text{r}}^{0}/(\gamma_{\text{r}}^{0}+\gamma_{\text{nr}}^{0})$,
which quantifies the radiation efficiency (i.e. the probability that the
excitation of the emitter actually results in the emission of a photon in the
far field). In the nanoantenna configuration, we assume that its presence does
not modify the intrinsic non-radiative decay rate $\gamma_{\text{nr}}^{0}$,
but does modify the other rates, which becomes
$\gamma_{\text{exc}}^{0}\rightarrow\gamma_{\text{exc}}(\mathbf{r})$ for the
excitation rate and
$\gamma_{\text{r}}^{0}\rightarrow\gamma_{\text{r}}(\mathbf{r})$ for the
radiative decay rate (Fig. S2b). In addition, the nanoantenna introduces a new
decay channel (highlighted by the dashed line in Fig. S2b), which is the
possibility that the emitted photon gets absorbed by the nanoantenna and lost
in terms of heat, for which we associate an absorption decay rate
$\gamma_{\text{abs}}(\mathbf{r})$. Note that the $\mathbf{r}$ dependence
meaning that these rates now depend on the spatial location of the emitter —
while in the reference configuration they are usually not position-dependent.
For a low-loss dielectric nanoantenna as the one used in this work, this
absorption channel is expected to be small. The quantum yield of the emitter
is thus modified as
$\text{QY}(\mathbf{r})=\gamma_{\text{r}}(\mathbf{r})/[\gamma_{\text{r}}(\mathbf{r})+\gamma_{\text{nr}}^{0}+\gamma_{\text{abs}}(\mathbf{r})]$.

The reference configuration considered in this work consists in a monolayer of
QDs deposited on the gold mirror; we call it the “Reference” hereafter. An SEM
image of the relatively homogeneous distribution of QDs after spin-coating can
be seen in Fig. 1d. Note that in order to prevent quenching by the gold mirror
and to protect from the subsequent CVD deposition of the aSi nanoantenna (see
Methods section), the QDs were sandwiched between two ultra-thin layers of
Al2O3 (we denote this configuration by Au/Al2O3/QDs/Al2O3). The overall
thickness of the three layers is $\sim 10\,$nm. Importantly, the quantum yield
of the QDs in the Reference situation was found to be $\text{QY}^{0}=3.8\times
10^{-3}$, drastically decreased compared to the value for QDs in solution
($\text{QY}^{0}=0.29$). This observation is similar to what has been reported
in Ref. 38, however in our case the decrease is not due to quenching by the
gold mirror, but instead to some degradation that happens during the
deposition of the second protective layer of Al2O3 (more details are given in
Methods section). Finally, all the QDs which were not precisely located
between the Au mirror and aSi nanoantenna were etched out; hence, we managed
to create spatially self-aligned and localized QDs in a nanogap of $g\approx
10\,$nm, without requiring any complex emitter manipulation or
characterization, similar to what was previously reported38.

We first simulated the near-field optical response of our nanoantenna in Fig.
1e, which shows the norm of electric field $|\mathbf{E}|$ average in the
middle plane of the nanogap (see Methods section for the simulation details),
for a nanodisk with varying outer diameter $D_{\text{out}}$ (lower half), and
for a nanoring with varying inner diameter (or hole diameter) $D_{\text{in}}$
(upper half). In both cases the height of the nanoantenna is fixed at
$H=230\,$nm. One can see that while all modes are red-shifted as
$D_{\text{out}}$ increases, the modes labelled by $\alpha_{i}$ are blue-
shifted as $D_{\text{in}}$ increases, while the modes labelled by $n_{i}$ do
not vary. As discussed in more details later, these modes pertained to two
distinct classes: the modes $\alpha_{i}$ correspond to "antenna modes", which
have strong radiative properties, and the modes $n_{i}$ correspond to "gap
modes", mostly confined in the gap between the nanoantenna and the gold
mirror, and much less radiative. As we will see in the following, because of
the presence of these two classes of modes — the antenna modes which are
strongly sensitive to $D_{\text{in}}$, and the gap modes which are mostly
sensitive to $D_{\text{out}}$ — we are able to almost independently control
the spectral positions of both types of resonances, allowing us to adapt the
design to match the emission and excitation wavelengths of the QDs and the
pump laser, respectively. Another route towards independent control these two
types of resonances is to vary the height $H$ of the nanoantenna, as shown in
Supp. Info. Section 2, Fig. S3 (for a closely related configuration, also see
36). In this work, we choose to set the height at $H=230\,$nm and the outer
diameter $D_{\text{out}}=380\,$nm to have one main strongly radiative antenna
mode around the QD emission wavelength of $650\,$nm (mode $\alpha_{1}$ in Fig.
1e) and a gap mode resonance that can be exploited for excitation enhancement
around $570\,$nm (mode $n_{3}$ in Fig. 1e), while $D_{\text{in}}$ is used as
"node" to spectrally tune the antenna resonances with respect to the gap mode
resonances (as can be seen in the upper half of Fig. 1e).

We next designed and fabricated the aSi nanorings to have a fixed outer
diameter of $D_{\text{out}}\approx 380\,$nm and a fixed height of $H\approx
230\,$nm, and varying inner diameters $D_{\text{in}}$ (ring hole) between
$D_{\text{in}}\approx 60\,$nm to $D_{\text{in}}\approx 140\,$nm (SEM images of
the nanorings are shown as insets in Fig. 1f). We characterized their far-
field optical response by dark-field scattering measurements (see Methods
section). Experimental scattering intensity spectra are shown in Fig. 1f and
reveal that the scattering features are blue-shifted with increasing
$D_{\text{in}}$, in agreement with the antenna modes behavior (while the gap
modes are not really seen in the far-field as they do not radiate much).

##  4 Quasi-normal mode analysis of the antenna modes

In order to better understand the features appearing in the near-field spectra
of Fig. 1e, we computed the resonant modes $\mathbf{E}_{\alpha}$ of the system
as well as their complex eigenwavelengths
$\lambda_{\alpha}=\lambda_{\alpha}^{\prime}+\mathrm{i}\,\lambda_{\alpha}^{\prime\prime}$,
with $\alpha$ labelling the mode, using quasi-normal mode (QNM) calculations
39 (see Methods section for the calculation details). We identified that the
main features appearing in the near-field spectra are associated to the
excitation of three particular antenna modes, labelled $\alpha_{1}$,
$\alpha_{2}$ and $\alpha_{3}$ (the real part of their eigenwavelengths
$\lambda_{\alpha}^{\prime}$, called resonance wavelength, is shown in Fig. 1e
by olive green dashed lines).

For the nanoring, the mode $\alpha_{1}$ presents a higher $Q$-factor of about
$Q\sim 30$ compared to the modes $\alpha_{2}$ and $\alpha_{3}$ with $Q\sim 10$
and $Q\sim 20$, respectively (calculated as
$Q=\lambda_{\alpha}^{\prime}/(2\lambda_{\alpha}^{\prime\prime})$). Moreover,
its spectral position is more shifted as with $D_{\text{in}}$ varies than for
the two other QNMs, as can be seen in Fig. 1e, allowing for a higher degree of
tunability. For these reasons, we choose the antenna mode resonance
$\alpha_{1}$ for the purpose of enhancing the emission of the QDs. The field
profile of this mode $|\mathbf{E}_{\alpha}|$, shown as insets in Fig. 2a,
reveals that most of the electric field is located inside the hole of the
nanoring, which explains why this mode is highly sensitive to the parameter
$D_{\text{in}}$, which is not the case for the other modes $\alpha_{2}$ and
$\alpha_{3}$ (not shown here).

It is interesting to make a comparison with the case of a standalone nanoring
in free space; Fig. 2a shows the resonance wavelength vs $D_{\text{in}}$ in
the case of the nanoring in free space (green dots).One can see that that the
presence of the metallic mirror (red dots, same as $\alpha_{1}$ in Fig. 1e),
in addition to contributing to slightly blue-shifting its spectral position
compared to the standalone case (green dots), contributes to more than
doubling the $Q$-factor of the mode $\alpha_{1}$ (see inset in Fig. 2a with
same color code). We also calculated the Purcell factor associated to this
mode (called "modal Purcell factor"), for the nanoring in free space and in
the presence of the metallic mirror, according to the formula:

$F_{\alpha}(\mathbf{r})=\frac{6\pi c^{3}}{\omega^{\prime
3}_{\alpha}}Q_{\alpha}\text{Re}\left(\frac{1}{V_{\alpha}(\mathbf{r})}\right)$
(1)

with $c$ being the speed of light in vacuum. The modal Purcell factor
quantifies the coupling of an emitter located at position $\mathbf{r}$ with
QNM $\alpha$, and corresponds to the decay rate enhancement due to this mode
compared to a homogeneous background (free space is considered here), for a
perfect matching of the emission frequency of the emitter with the (real part
of the) QNM eigenfrequency. The mode volume $V_{\alpha}(\mathbf{r})$
associated with this QNM, and appearing in Eq. (1), is given by the relation
40, 39:

$V_{\alpha}(\mathbf{r})=\frac{1}{2\epsilon_{0}\left(\mathbf{E}_{\alpha}(\mathbf{r})\cdot\mathbf{u}\right)^{2}}$
(2)

with $\epsilon_{0}$ being the vacuum permittivity. One can see from Eq. 2 that
the volume quantifies the interaction between electric dipole emitters with
dipole orientation along unit vector $\mathbf{u}$ and the QNM field
$\mathbf{E}_{\alpha}(\mathbf{r})$ at the position of the emitter
$\mathbf{r}=(x,y,z)$. The smaller the mode volume, the stronger the
interaction40, 39.

Figs. 2b and c show the spatial distribution of the modal Purcell factor
associated with the antenna mode $\alpha_{1}$, across the horizontal plane
located $5\,$nm underneath the ring, in the case of a nanoring with
$D_{\text{in}}=60\,$nm (which is the case discussed hereafter in the main
text), for dipoles oriented out-of-plane (i.e. perpendicular to the plane,
denoted by the symbol $\perp$) and dipoles oriented in-plane (i.e. parallel to
the plane, denoted by the symbol $\parallel$).

One can see that in the presence of the mirror (Fig. 2b), it is the _out-of-
plane_ dipoles that mostly couple to this mode, within a much larger area
(that forms a circular “band” surrounding the hole of the nanoring as seen in
the left panel of Fig. 2b), with a maximum modal Purcell factor reaching a
value of $F_{\alpha}=27.4$. For the standalone nanoring case (Fig. 2c), it is
mostly the _in-plane_ dipoles that couple to this mode, and only within a
small area (located right underneath the hole of the nanoring as seen in the
right panel of Fig. 2c). In practice, since it is very challenging to control
the position and orientation of the emitters precisely, the PL signal coming
from the assembly of emitters is averaged out over emitters spatially
distributed over the nanoantenna area with random dipole orientations.
Therefore, QDs coupled to a nanoring on top of a metallic mirror is expected
to give a significantly higher PL enhancement compared to the case of a
standalone nanoantenna, due to higher coupling strengths and the more
spatially “extended” coupling.

##  5 Theoretical analysis of the gap modes

It is not very convenient to identify the gap modes using QNM computations
because in the spectral region around and below $600\,$nm, the number of QNMs
is very large and they are not spectrally well separated, which makes their
analysis quite tedious. Instead, we use a more intuitive analytical approach
to find the gap mode resonances, based on geometrical considerations only. As
mentionned in Yang et al. 21, the gap resonances of our system can be
understood as “the surface plasmon of a planar multilayer metal-dielectric
system restricted to specific quantized wavectors”. The cylindrical symmetry
of our system implies that resonances can be labeled with indices $(n,m)$,
enumerating field variations in the radial and azimuthal directions,
respectively. The wavevectors $k_{mn}$ are “quantized” due to the geometry of
the nanoantenna, which reflects the surface plasmon at its boundary, similarly
to the modes of a Fabry-Perot type resonator41, 35, 42, 43.

The resonance wavelengths, denoted $\lambda_{mn}$, thus have a geometric
origin and read (in the case of a disk)35:

$\lambda_{mn}=\frac{2\pi}{k_{mn}}\quad\text{with}\quad
k_{mn}D_{\text{out}}+\phi=2J_{mn}$ (3)

where $k_{mn}$ is the real part of the surface plasmon polariton wavevector
$k$ (whose multilayer dispersion relation is given in Supp. Info. Section S3),
$D_{\text{out}}$ is the diameter of the disk, $J_{mn}$ is the $n^{\text{th}}$
zero of the Bessel’s function of the first kind of order $m$ with $m$ the
azimuthal number, and $\phi$ is a reflection phase that depends upon the
structural and material parameters41. These gap mode resonances are thus
spectrally tunable by simply varying the diameter of the particle
$D_{\text{out}}$. Moreover, since these gap modes are strongly confined inside
the nanogap, they can be exploited for local enhancement of the pump field
intensity, and hence for excitation enhancement of the QDs.

We make use of Eq. (3) in the case of the ring as a first approximation — even
if it strictly holds for a plain disk only — to calculate the gap resonance
wavelengths in our system. Due to the symmetry of the pump field that we will
use in this work (normal incidence and linearly polarized), only the modes
with $m=1$ can be excited. In Fig. 1e, we show the resonance wavelengths
$\lambda_{12}$ and $\lambda_{13}$ (dashed lines in white color and labelled
$n_{2}$ and $n_{3}$, respectively — the mode $n=1$ being outside of the
wavelength range of interest), obtained by applying Eq. (3) with $\phi=-\pi/2$
and $\phi=0$, respectively (reflection phase values were chosen to closely
match these analytically calculated resonance wavelengths with the features
appearing in the near-field spectra simulations of Fig. 1e; also, since these
reflection phases are related to the extension of the plasmon field beyond the
particle terminations41, it should not be too surprising that different modes
pick up different reflection phases). One can see indeed that there is almost
no changes when increasing the inner diameter of the ring $D_{\text{in}}$,
which justify the use of this equation even in the case of a ring (especially
as inner diameter remains small). In particular, for $D_{\text{out}}=380\,$nm,
we have the following resonance wavelengths: $\lambda_{12}=625\,$nm and
$\lambda_{13}=574\,$nm. In the following, we use $n_{3}$ mode to enhance the
excitation of the QDs, because the spectral position of $n_{2}$ overlaps with
the emission of the QDs (see Supp. Info. Fig. S1), making it difficult to
distinguish the emission from the pump in the PL signal.

##  6 Fluorescence enhancement results

In the following, we present the results obtained for the selected nanoring
with $D_{\text{in}}=60\,$nm (shown by blue arrows line in Fig. 1e), which we
call “Antenna” hereafter, for which we obtained the highest total fluorescence
enhancement experimentally. To characterize the total fluorescence enhancement
of the QDs in the Antenna situation compared to the Reference one (denoted by
the superscript “0” hereafter), we use the well established fact that, in the
low excitation regime, the fluorescence enhancement per emitter (located at
position $\mathbf{r}$) is proportional to the gains in excitation rate,
collection efficiency and quantum yield 44, 5, 1, 45:

$\text{EF}_{\text{th}}(\mathbf{r})=\frac{\gamma_{\text{exc}}(\mathbf{r})}{\gamma_{\text{exc}}^{0}}\frac{\text{D}_{\text{em}}(\mathbf{r})}{\text{D}_{\text{em}}^{0}}\frac{\text{QY}(\mathbf{r})}{\text{QY}^{0}}$
(4)

The excitation rate $\gamma_{\text{exc}}$ (previously introduced) is directly
proportional to the local enhancement of the pump intensity at the position of
the emitter $\mathbf{r}$, and depends therefore on the wavelength used for the
pump laser $\lambda_{\text{exc}}$. The directivity (or collection efficiency)
$\text{D}_{\text{em}}$, which corresponds to the collected signal into a given
numerical aperture (NA), thus depends on the collection NA, denoted by
$\text{NA}_{\text{col}}$, and also on the wavelength of fluorescent emission
$\lambda_{\text{em}}$. Finally, the emitter quantum yield QY (previously
introduced) also depends on the emission wavelength $\lambda_{\text{em}}$.
Note that all of these quantities are defined for a single electric dipole
emitter at a given position $\mathbf{r}$ and also having a fixed orientation
of its dipole moment along the unit vector $\mathbf{u}$, but for the sake of
readability, we omit the dependence on the parameter $\mathbf{u}$ in the above
quantities. Also, it is interesting to note from Eq. (4) that the total
fluorescence enhancement $\text{EF}_{\text{th}}$ depends on the type of
emitter used in the Reference situation through its intrinsic quantum yield
$\text{QY}^{0}$, and is thus not an absolute figure-of-merit to characterize
the performance of a given antenna.

However, in our case where the QDs have a very small intrinsic quantum yield
$\text{QY}^{0}\ll 1$, we have $\gamma_{\text{r}}^{0}\ll\gamma_{\text{nr}}^{0}$
(here $\gamma_{\text{r}}^{0}\sim 10^{-3}\,\gamma_{\text{nr}}^{0}$), and
further assuming that the that the decay rate enhancement in the presence of
the nanoantenna is such that
$\gamma_{\text{r}}(\mathbf{r})+\gamma_{\text{abs}}(\mathbf{r})\ll\gamma_{\text{nr}}^{0}$,
we have $\tau(\mathbf{r})/\tau^{0}\approx 1$, where we further introduce the
fluorescence lifetimes defined as $\tau(\mathbf{r})\equiv
1/[\gamma_{\text{r}}(\mathbf{r})+\gamma_{\text{nr}}^{0}+\gamma_{\text{abs}}(\mathbf{r})]$
and $\tau^{0}\equiv 1/(\gamma_{\text{r}}^{0}+\gamma_{\text{nr}}^{0})$ in the
nanoantenna and reference situations, respectively. Using the fact that
$\text{QY}(\mathbf{r})/\text{QY}^{0}=[\gamma_{\text{r}}(\mathbf{r})/\gamma_{\text{r}}^{0}][\tau(\mathbf{r})/\tau^{0}]$,
we thus have
$\text{QY}(\mathbf{r})/\text{QY}^{0}\approx\gamma_{\text{r}}(\mathbf{r})/\gamma_{\text{r}}^{0}$,
and Eq. (4) can be recast into the following form, which is independent of the
type of emitter and will be more convenient for our purpose of characterising
the underlying mechanisms at play in our nanoantenna44:

$\text{EF}_{\text{th}}(\mathbf{r})\approx\eta_{\text{exc}}(\mathbf{r},\lambda_{\text{exc}})\times\eta_{\text{em}}(\mathbf{r},\lambda_{\text{em}},\text{NA}_{\text{col}})$
(5)

In Eq. (5), we defined the quantities
$\eta_{\text{exc}}\equiv\gamma_{\text{exc}}/\gamma_{\text{exc}}^{0}$ and
$\eta_{\text{em}}\equiv(\text{D}_{\text{em}}/\text{D}_{\text{em}}^{0})(\gamma_{\text{r}}/\gamma_{\text{r}}^{0})$,
which quantify the enhancements in excitation and emission, respectively, and
we made the dependence in terms of $\lambda_{\text{exc}}$,
$\lambda_{\text{em}}$ and $\text{NA}_{\text{col}}$ of the terms
$\eta_{\text{exc}}$ and $\eta_{\text{em}}$ explicit. Applying Eq. (5) to the
case of our Antenna to each QD and averaging over QDs positions and
orientations gives a theoretical fluorescence enhancement factor of
$\left<\text{EF}_{\text{th}}\right>=1263$, for an excitation source coming at
normal incidence and linearly polarized, and for a collection in a single
direction, i.e. the upward direction (see Methods section and Supp. Info.
Section S4 for more details). The excitation and emission wavelengths used in
the simulations, that is $\lambda_{\text{exc}}=583\,$nm and
$\lambda_{\text{em}}=680\,$nm, were obtained by optimizing the excitation and
emission separately (see next sections).

_Excitation enhancement and gap resonance._ Experimentally, we first searched
for the excitation wavelength $\lambda_{\text{exc}}$ that maximizes the PL.
For that, we recorded the PL signal as we varied the pump wavelength
$\lambda_{\text{exc}}$ from $488\,$ to $588\,$nm, while maintaining a constant
pump power, by collecting the light radiated into air using an objective lens
with $\text{NA}=0.9$. Even though the QDs absorb shorter wavelength light more
efficiently (as shown in Supp. Info. Section S1), optimal pumping conditions
for PL enhancement in the Antenna case were found to be at approximately
$\lambda_{\text{exc}}=570\,$nm, as shown in Fig. 3a. In all subsequent
measurements, we therefore fix the pump wavelength at
$\lambda_{\text{exc}}=570\,$nm.

We confirmed with full-wave simulations that there is a maximum for the local
field intensity around $570\,$nm (exactly at $583\,$nm), as shown in Fig. 3b
(see Methods section for details about the full-wave simulations), which gives
an excitation enhancement factor
$\left<\eta_{\text{exc}}\right>_{\text{th}}=7.3$ — the bracket denoting
position and orientation averaging of the QDs. The spectral position of the
maximum is in fair agreement with the third order gap mode resonance labelled
$n_{3}$ predicted by the theory at $574\,$nm (vertical dashed line in Fig.
3b). Moreover, the field intensity in the horizontal cross-section located in
the middle of the gap, and in vertical cross-section passing through the
middle of the nanoring, shown in Figs 3c, d, respectively, reveal that
intensity “hot spots” are formed within the nanogap. To better appreciate the
match with the theory, we show in the Supp. Info. Section S3, Fig. S5 the
vertical field component $E_{z}$, which matches the field profile of the gap
mode expected in theory with symmetry $(n=3,m=1)$ (see Supp. Info. Section S3,
Fig. S4a). This corroborates the fact that it is a gap mode resonance that is
responsible for the excitation enhancement. Finally, note that the intensity
distribution of this gap mode presents a rather good spatial overlap with the
area within which the mostly coupled emitters to the antenna mode (exploited
for _emission_ enhancement) shown in Fig. 2b.

_Emission enhancement and antenna resonance._ We quantify hereafter the
emission enhancement in the upward direction, since our nanoantennas radiate
mostly in the upward (out-of-plane) direction (see directivity patterns which
are given later). For that, we choose to integrate the experimental angle-
resolved PL (raw angle-resolved PL spectra can be found in Supp. Info. Section
5 Fig. S7), obtained using back focal plane imaging technique (see Methods
section), over a collection $\text{NA}_{\text{col}}=0.3$, which corresponds
approximately to $\pm 17\degree$. Note that we make the choice to integrate
over this collection NA (instead of considering strictly a single direction,
i.e. the upward direction, like in the simulations) in order to average the
noise present in the collection channel. Moreover, in order to obtain the
experimental total fluorescence enhancement from these PL spectra, we
deconvoluted the PL signal of the nanoantenna with the Reference PL, according
to the formula:

$\left<\text{EF}_{\text{exp}}\right>=\frac{I}{I_{0}}\frac{\mathcal{A}_{0}}{\mathcal{A}}$
(6)

where $I$ (resp. $I_{0}$) is the PL intensity collected in the nanoantenna
situation (resp. in the Reference situation) and $\mathcal{A}$ (resp.
$\mathcal{A}_{0}$) is the area corresponding to the ring horizontal cross-
section that reads $\mathcal{A}=\pi(D_{\text{out}}/2)^{2}$ with
$D_{\text{out}}=380\,$nm where the QDs are located (resp. the area of the
excitation spot $\mathcal{A}_{0}=\pi(D_{\text{spot}}/2)^{2}$ which is
estimated to $D_{\text{spot}}\simeq 1.37\,\mu$m; see Supp. Info. Section S6,
Fig. S8). The obtained experimental total fluorescence enhancement spectrum is
plotted in Fig. 4a. One can see one main peak around the central emission
wavelength of the QDs which is around $650\,$nm, at which we get a maximum
total fluorescence enhancement factor of
$\left<\text{EF}_{\text{exp}}\right>=654$. One can also see a secondary peak
around $720\,$nm.

We corroborated this experimental total fluorescence enhancement spectrum with
full-wave simulations of the emission enhancement
$\left<\eta_{\text{em}}\right>$ in the upward direction (using reciprocity,
see Methods section), because it corresponds to the direction of maximum
directivity, and where the bracket denotes once again position and orientation
averaging of the QDs. The simulated spectrum is shown in Fig. 4b. One can see
a fair agreement with the experiment, with also the presence of two main
peaks, at $680\,$nm and $725\,$nm in the simulations. The shift of the
resonances in the simulations compared to the experiment can be attributed to
slight size variations in the height and outer diameter of the ring. Moreover,
from the previous mode analysis shown in Fig. 1e, we identify these two
resonances with the antenna modes $\alpha_{1}$ and $\alpha_{3}$, respectively,
as highlighted in Fig. 4b by vertical dashed lines. One can even see a weaker
third resonance in-between the main two peaks, which we identify with the
antenna mode $\alpha_{2}$ from Fig. 1e, as highlighted in Fig. 4b. The maximum
emission enhancement at the main peak is
$\left<\eta_{\text{em}}\right>_{\text{th}}=206.2$. Note that the value of the
averaged total enhancement $\left<\text{EF}_{\text{th}}\right>=1263$ is not
strictly equal to the average excitation enhancement
$\left<\eta_{\text{exc}}\right>_{\text{th}}=7.3$ times the average emission
enhancement $\left<\eta_{\text{em}}\right>_{\text{th}}=206.2$, which is
totally normal and is due to the averaging process. Indeed,
$\left<\text{EF}_{\text{th}}\right>\neq\left<\eta_{\text{exc}}\right>_{\text{th}}\times\left<\eta_{\text{em}}\right>_{\text{th}}$
in general for spatially inhomogeneous couplings.

We show in Fig. 4c (left panel) the experimental back focal plane image of the
PL intensity at the wavelength $650\,$nm, coming from the main peak and
associated to the QNM $\alpha_{1}$ (see Methods section for experimental
details). One can see some directivity, compared to the rather isotropic
emission from the Reference (right panel). It becomes even clearer when
plotting the experimental angular radiation patterns — obtained as a
horizontal cut of Fig. 4c — in Fig. 4d (left panel), where one can clearly see
that the Antenna reshapes the emission into a main lobe oriented in the upward
direction (dark lines), in contrast with the rather isotropic emission in the
Reference case (light blue lines). The directivity enhancement at this
wavelength is calculated to be
$\left<\text{D}_{\text{em}}/\text{D}_{\text{em}}^{0}\right>_{\text{exp}}=1.43$
within $\text{NA}_{\text{col}}=0.3$ (see Eq. (9) in Methods section for the
formula used).

We also computed the radiation patterns (using reciprocity, see Methods
section for more details), shown in Fig. 4d (right panel). One can see a good
qualitative agreement between experiment and simulation, showing out-of-plane
directivity. These simulation results give a simulated directivity enhancement
of
$\left<\text{D}_{\text{em}}/\text{D}_{\text{em}}^{0}\right>_{\text{th}}=1.31$
in the upward direction, which matches relatively well with the value
extracted from the experimental measurements. We thus deduced by applying the
relation (non-rigorous)
$\left<\eta_{\text{em}}\right>_{\text{th}}\approx\left<\text{D}_{\text{em}}/\text{D}_{\text{em}}^{0}\right>_{\text{th}}\left<\gamma_{\text{r}}/\gamma_{\text{r}}^{0}\right>_{\text{th}}$
that the theoretical average radiative decay rate enhancement (i.e. radiative
yield) is
$\left<\gamma_{\text{r}}/\gamma_{\text{r}}^{0}\right>_{\text{th}}=157.4$.

##  7 Discussion

The theoretical average enhancement factor
$\left<\text{EF}_{\text{th}}\right>=1263$ calculated from Eq. (5)
overestimates the experimental average enhancement factor
$\left<\text{EF}_{\text{exp}}\right>=654$. However, this can be expected if
one remembers that Eq. (5) used to estimate the theoretical enhancement factor
is valid under the approximation that $\tau/\tau^{0}\approx 1$. Based on the
experimentally obtained value from the measured lifetimes with a time-resolved
PL setup (see Methods section), we obtain, after fitting the experimental data
(see Supp. Info. Section S7), a lifetime reduction of
$\left<\tau/\tau^{0}\right>_{\text{exp}}^{-1}\approx 2.19$, that is
$\left<\tau/\tau^{0}\right>_{\text{exp}}\approx 0.46$. Therefore, Eq. (5) will
overestimate the experimental enhancement factor of roughly a factor of two
(non-rigorous), which we found to be the case. A more quantitative estimation
of the theoretical average enhancement factor that takes into account the
value of the intrinsic quantum yield $\text{QY}^{0}$ provides
$\left<\text{EF}_{\text{th}}\right>=790$, in better agreement with the
experimental value (see Supp. Info. Section S8). Note that another factor that
may contribute to overestimate the experimental enhancement factor is that in
theory we calculate it in a single direction, i.e. the upward direction, where
the emission is maximum, while in the experiment we average over a
$\text{NA}_{\text{col}}=0.3$ (chosen to average out noise present in the
optical setup).

We also analyse in Supp. Info. Section S7 the results obtained for two other
nanoantennas, called Antenna B and C (the one shown in the main text being
called Antenna A in Supp. Info.), having approximately identical outer
diameters and heights, but larger inner diameters, namely
$D_{\text{in}}=80\,$nm and $D_{\text{in}}=110\,$nm, respectively. We found
similarly that the theoretical calculations of the total enhancement factors
overestimates the one found in experiment, by roughly the factor corresponding
to the lifetime reduction. Moreover, this comparative study between Antennas
A, B and C highlights that one can tune (blue-shift) the resonance exploited
for emission by varying (increasing) $D_{\text{in}}$ with respect to the
resonance exploited for absorption, as already anticipated from the mode study
in Fig. 1e. We also note that as the inner diameter $D_{\text{in}}$ increases,
the total emission decreases, in agreement with the calculation of the modal
Purcell factor which decreases as well (shown in Supp. Info. and which we
recall quantify the coupling of the QDs with the strongly radiative antenna
mode).

Finally, in order to check if our design can accomodate different QDs sizes
and types, we simulated the average emission enhancement factor
$\left<\eta_{\text{em}}\right>_{\text{th}}$ for different nanogap sizes and
refractive index of the spacer layer. The results (see Supp. Info. Section S9)
reveal that despite variation in terms of resonance strength, the spectral
position of the resonances are not really affected, which was also reported in
22, in constrast will all-plasmonic nanopatch antenna for which the resonances
are more sensitive, making this hybrid system quite robust for a diversity of
active materials.

##  8 Conclusion

In this work, we experimentally demonstrated an efficient and multi-resonance
silicon nanoring on gold mirror nanoantenna coupled to localised quantum dots
in a nanogap of $\sim 10\,$nm, which transformed very poor emitters (with an
intrinsic quantum yield of $\text{QY}^{0}=3.8\times 10^{-3}$) into bright and
directional sources. A total fluorescence enhancement factor of $654\times$
was measured, coming from different mechanisms that contributed to increase
the brightness of our Antenna. We calculated in theory average enhancements of
$\left<\gamma_{\text{r}}/\gamma_{\text{r}}^{0}\right>_{\text{th}}=157.4$,
$\left<\gamma_{\text{exc}}/\gamma_{\text{exc}}^{0}\right>_{\text{th}}=7.3$ and
$\left<\text{D}_{\text{em}}/\text{D}_{\text{em}}^{0}\right>_{\text{th}}=1.31$,
for the radiative yield, excitation and directionality, respectively, and we
experimentally obtained an average lifetime reduction of
$\left<\tau/\tau_{0}\right>_{\text{exp}}^{-1}=2.19$. One can infer from this
analysis that the radiative emission enhancement is the main mechanism
responsible for the total fluorescence enhancement observed here, with also
non-negligible contribution of the excitation enhancement, and modest
collection efficiency gain and lifetime reduction.

One particularity of the nanoring antenna is that it supports several
resonances with strong scattering properties — the antenna mode resonances to
which the emitters are efficiently coupled — that increase the radiative rates
of emitters and reshape the directionality of emission within a main lobe
pointing in the upward direction. These resonance wavelengths can be easily
tuned using the ring _inner diameter_ to match with the emission wavelength of
the emitters. Furthermore, the metallic mirror creates a nanogap that supports
localized modes (gap mode resonances)35, 21, whose resonance wavelength mostly
depends on the ring _outer diameter_ and therefore can be easily tuned using
this parameter, in an almost independent way from the resonances exploited for
the emission enhancement. These were used to create intensity “hot spots” in
the nanogap, leading to an overall gain in the excitation efficiency of the
QDs.

Among the future improvements that should be carried out on these types of
nanoantennas, we would like to mention a few here. First of all, there is a
need to pay attention to ensure that the QDs are protected and not degraded by
the fabrication process (i.e. not as reported in this work and in Ref. 22), in
order to guarantee the integrity of the quantum emitters. Secondly, by
exploiting lower order gap mode resonances, one could increase the excitation
enhancement (by a factor 4 if one makes use of the second order according to
our simulations — not shown here), to potentially bring the total fluorescence
to 3 orders of magnitude enhancement, figures reported so far only in all-
plasmonic nanopatch antennas. It was not possible in this work because the
second order gap mode could not be well separated spectrally from the emission
of the QDs, and therefore we exploited a higher order gap mode (third order),
which provided more modest excitation enhancement.

Among the advantages and potentials of such hybrid structures, we would like
to highlight that they could accommodate different QD sizes and could easily
be enlarged or shrunk to shift the resonances to near-IR or UV wavelengths.
Shifting to near-IR wavelengths would, in principle, be easier because of
lower losses in the silicon at those wavelengths, while shifting to UV
wavelengths might require using a different material with lower losses in the
wavelength range for the ring structure.

The experimental demonstration provided in this paper confirms the relevance
of nanorings in hybrid dielectric-plasmonic nanostructures as highly tunable
nanoantennas with subwavelength size, to create efficient, bright and
directional photon sources in the visible spectral range, that can be of
foremost importance for the next-generation of light-emitting devices.

##  9 Methods

###  9.1 Fabrication

To fabricate the nanoantenna structure, we deposited a $100\,$nm thick film of
gold onto a silicon substrate with a $5$ nm titanium adhesion layer by
Electron-beam Physical Vapor Deposition (EBPVD, Denton Explorer) at a rate of
$0.1\text{\AA}/s$.

Next, we deposited a first layer of alumina (Al2O3) with thickness of $\approx
3\,$nm on the gold using Atomic Layer Deposition (ALD, Beneq TFS 200) 46, from
trimethylaluminum and H2O precursors at $120\degree$C. After that, a layer of
CdSe/ZnS alloyed quantum dots, synthesized according to 37, were spin-coated
at $2000$ rpm for $1$ minute from a solution of $5$ mg QDs per ml in toluene.
The quantum dots were then covered by another $\approx 3$ nm thick layer of
alumina, this time using ALD at a temperature of $80\degree$C. The final
Al2O3/QDs/Al2O3 sandwich structure has a total thickness of approximately
$10-15\,$nm (ellipsometry measurements estimated the thickness, assuming a
homogeneous alumina layer, of $13\,$nm), prior to patterning the silicon (Si)
ring nanoantenna.

For the ring structure, we deposited a $230$ nm thick film of amorphous
silicon by Induction-Coupled Plasma Chemical Vapor Deposition (ICP-CVD, Oxford
PlasmaPro 100) at $80\degree$C from a SiH4 precursor. Hydrogen silsesquioxane
e-beam resist (Dow Corning XR-1541-06), spin coated at $5000$ rpm for $1$
minute and a change dissipation layer (Espacer 300AX01), spin coated at $1500$
rpm for $1$ minute were used for the Electron Beam Lithography (EBL) writing
(Exlionix ELS-7000), with a dose of $\approx 300$ mC/cm2. The sample was then
developed by a NaOH/NaCl salty solution ($1\%$ wt. $/4\%$ wt. in de-ionized
water) for $60$ s and then rinsed by de-ionized water to stop the development.
The final structures was created by Induction-Coupled Plasma Reactive Ion
Etching (ICP-RIE, Oxford Plasmalab 100) using chlorine gas, with a slight over
etch to etch any quantum dots not protected by the silicon structures. A
fabrication process flow schematics can be found in Supp. Info. Section S10,
Fig. S14.

Since the fabrication process exerts thermal and chemical stress that can
potentially degrade the QDs 47, we characterized optically the QD layer at all
steps of the fabrication process to quantify the changes in photoluminescence
(PL) and fluorescence lifetimes (see Supp. Info. Section S10, Fig. S15). While
we observed that the quenching is successfully overcome by the presence of the
first layer of Al2O3, the intensity of the PL is reduced by almost $98\%$
after depositing the second layer of Al2O3, that is in the configuration
Au/Al2O3/QDs/Al2O3 (keeping the same excitation power). Moreover, the time-
resolved PL experiments revealed that this drop in PL is correlated with a
reduction of the QDs lifetime from $\tau_{0}=5.00\,$ns to $\tau_{0}=0.65\,$ns.
From these observations, we estimated that the intrinsic quantum yield drops
from $\text{QY}^{0}=0.29$ to $\text{QY}^{0}=3.8\times 10^{-3}$, and concluded
that the QDs are degrading because of thermal stress during the atomic layer
deposition process used to deposit the second alumina layer 47.

###  9.2 Optical characterization

All optical measurements were performed in a microspectrometer setup, based on
an inverted microscope (Nikon Ti-U) and a spectrometer system (Andor SR-303i
spectrograph with a $150$ lines/mm grating coupled to a $400\times 1600$ pixel
Andor Newton 971 EMCCD). Incident light was focused on the sample by a
$100\times$ objective lens with a $0.9$NA (Nikon LU Plan Fluor). Signal
collected by the same objective lens was then projected onto the spectrograph
entrance slit with a width of $250\,\mu$m.

  * •

_Dark-field scattering measurements:_ For dark-field scattering, white light
from a halogen lamp was used to excite the sample, with the central
low-$\vec{k}$ portion of the beam blocked from entering the objective lens,
meaning only light scattered by the nanoantennas was collected and sent to the
spectrograph. Reflectance of an silver mirror was used as the Reference.

  * •

_Photoluminescence spectroscopy:_ For photoluminescence measurements, a
supercontinuum source (SuperK Power, NKT Photonics) with band-pass filter
(SuperK Varia, NKT Photonics), pulse duration $70$ ps, $78$ MHz repetition
rate was used to excite PL. The band-pass filter was used to scan the pump
wavelength from $488$ to $588$ nm with a $10$ nm bandwidth. Average pump power
was maintained at $\approx 250\,\mu$W. The pump laser was focused onto the
sample substrate by the same $100\times$ $0.9$ NA objective lens, resulting in
an approximately $1.37\,\mu$m diameter laser spot (see Supp. Info. Section S6
for details on the method used to estimate the laser spot size). A $610$ nm
long pass filter was used to cut off any pump laser light in the collection
beam path, the $610$ nm cut-off can be clearly seen in all the
photoluminescence curves in Supp. Info. Fig. S1b.

  * •

_Back-focal-plane imaging:_ To capture back-focal-plane images, the same
$100\times$ $0.9$NA objective lens was used to collect light emitted by the
nanoantennas, except that, instead of the image plane, the back focal plane of
the objective was projected onto a CCD. The maximum collected angle, according
to $NA=n\sin{\theta}$, and in our case, $n=1$ (air), is about
$\theta=64.2\degree$.

  * •

_Back-focal-plane spectroscopy:_ To measure angle-resolved PL spectra, the
same $100\times$ $0.9$NA objective lens was used to collect light emitted by
the nanoantennas, except that, instead of the image plane, the back focal
plane of the objective was projected onto the spectrograph entrance slit. The
maximum collected angle, according to $NA=n\sin{\theta}$, and in our case,
$n=1$ (air), is about $\theta=64.2\degree$.

  * •

_Lifetime measurements:_ Time-resolved photoluminescence was studied using a
Picoquant Microtime 200 TCSPC system coupled to our microspectometer setup.
The same supercontinuum source was used to excite the sample. Spectrally
integrated PL in a narrow $5$ nm range, centered at $650$ nm was collected
using a Si single photon avalanche photodiode. The instrument response
function (IRF) was recorded using excitation light scattered from the sample,
where the IRF was measured to be $77$ ps. PL decay measurements were fit using
reconvolution with the measured IRF by a bi-exponential function48.

###  9.3 Numerical simulations

  * •

_Quasi-normal mode calculations:_ The quasi-normal modes (QNMs), denoted
$\mathbf{E}_{\alpha}(\mathbf{r})$, can be defined as an eigenvalue problem of
the solution of Maxwell equations in the absence of sources:

$\nabla\times\frac{1}{\mu_{0}}\nabla\times\mathbf{E}_{\alpha}(\mathbf{r})=\omega^{2}_{\alpha}\varepsilon(\mathbf{r},\omega_{\alpha})\mathbf{E}_{\alpha}(\mathbf{r})$
(7)

where
$\omega_{\alpha}=\omega_{\alpha}^{\prime}+\mathrm{i}\,\omega_{\alpha}^{\prime\prime}$
denotes the complex eigenfrequency associated with the eigenmode
$\mathbf{E}_{\alpha}(\mathbf{r})$, and supplemented by outgoing boundary
conditions (also known as the Sommerfeld radiation condition as
$|\mathbf{r}|\rightarrow\infty$). Note that $\omega_{\alpha}^{\prime\prime}<0$
due to the convention “$\text{e}^{-\mathrm{i}\omega t}$” used for the time-
harmonic fields. Here, the system is considered nonmagnetic with a vacuum
permeability $\mu_{0}$, and $\varepsilon(\mathbf{r},\omega)$ denotes the
relative permeability of the medium. the complex eigenwavelengths are defined
as $\lambda_{\alpha}\equiv 2\pi c/\omega_{\alpha}$.

In order to solve Eq. (7) and obtain the eigenmodes and eigenfrequencies in
the configurations shown in Fig. 1e, we employed the “QNMEig solver”,
developped by IOGS-CNRS49, which, computes and normalizes the QNMs of
plasmonic and photonic resonators, implemented using COMSOL Multiphysics. The
QNMEig solver needs all dispersive material permittivities to be modelled by a
$N$-pole Lorentz-Drude model, in order to reformulate Eq. (7) into a linear
eigenvalue problem (see, for example, Yan et al. 49). The parameters of the
Lorentz-Drude model that we used for the dispersive permittivities of
amorphous silicon (nanoantenna) and gold (substrate) can be found in Supp.
Info. Fig. S11.

  * •

_Near-field simulations:_ To compute the near-field, we used the finite-
difference time-domain (FDTD) method in Ansys Lumerical FDTD. The Si particle
(nanoantenna) in the presence of Au mirror was surrounded by a Total-Field
Scattered-Field (TFSF) source, which simulates a plane wave excitation. The
distance between the TFSF box and nanoantenna was set to be larger than
$100\,$nm. The incident wave was chosen to be linearly polarized and coming at
normal incidence from the top of the nanoantenna. The norm of the electric
field was recorded in the plane located in the middle of the gap between the
silicon nanoring and the gold mirror and then spatially averaged. We
considered that the gap was filled with a homogeneous medium of refractive
index corresponding to the one of alumina, i.e. $n=1.77$.

  * •

_Excitation enhancement simulations:_

To compute the term $\eta_{\text{exc}}(\mathbf{r},\lambda_{\text{exc}})$ in
Eq. (5) shown in Fig. 3, we use the fact that the excitation rate is
proportional to the local intensity of the electric field and therefore
$\eta_{\text{exc}}(\mathbf{r},\lambda_{\text{exc}})$ can be readily expressed
as50:

$\eta_{\text{exc}}(\mathbf{r},\lambda_{\text{exc}})=\left|\frac{\mathbf{u}\cdot\mathbf{E}(\mathbf{r},\lambda_{\text{exc}})}{\mathbf{u}\cdot\mathbf{E}_{0}(\mathbf{r},\lambda_{\text{exc}})}\right|^{2}$
(8)

where we recall that $\mathbf{u}$ is a unit vector showing the orientation of
the emitter dipole moment, $\mathbf{r}$ is the position of the emitter, and
$\mathbf{E}(\mathbf{r})$ (resp. $\mathbf{E}_{0}(\mathbf{r})$) is the electric
field at the emitter position $\mathbf{r}$ for a given excitation source in
the nanoantenna case (resp. in the Reference case). We computed, using Ansys
Lumerical FDTD, and considering as incident illumination a _linearly_
polarized planewave coming at _normal incidence_ from the top of the
nanoantenna, the electric field intensity in the horizontal plane (i.e.
parallel to the substrate) and located in the middle of the nanogap over an
area corresponding to the ring horizontal cross-section. The averaged
excitation enhancement $\left<\eta_{\text{exc}}\right>$ was obtained after
averaging over all directions to account for randomly distributed and oriented
dipole emitters, and normalizing by the case without Si nanoantenna.

  * •

_Emission enhancement simulations:_ The computation of the radiative emission
enhancement $\eta_{\text{em}}(\mathbf{r},\lambda_{\text{em}})$ from Eq. (5)
and shown in Fig. 4 were carried out using the reciprocity principle51,
following the method well described in Ref. 52. This method was implemented in
Ansys Lumerical FDTD, where planewave sources were used with two orthogonal
linear polarizations and at normal incidence to excite the nanoantenna, using
the TFSF source tool. Then, the near-field response was recorded in a plane
located in the middle of the gap by point monitors, distributed in an area
with the same size as the nanoantenna cross-section, and with a density of
$3\,600\,\mu\text{m}^{-2}$ (i.e. we use approximately $400$ point monitors
homogeneously distributed below the ring within an area of $\pi R^{2}$ with
$R=D_{\text{out}}/2=190\,$nm). By reciprocity, the power recorded in each
point monitor and calculated from the projection of the electric field along
axis $i$ ($i=x$, $y$ or $z$) is equal to the emission power of light with the
same polarization as the source from a point electric dipole oriented along
$i$ and located at the same position as the monitor. To obtain the averaged
emission enhancement $\left<\eta_{\text{em}}\right>$ of the assembly of
electric dipoles randomly oriented and distributed uniformly under the
nanoantenna, the power over all orientations $i$ and over the spatial
distribution of monitors was integrated, averaged over two orthogonal linear
polarizations, and normalized to the case without nanoantenna.

  * •

_Directional enhancement simulations:_

To obtain the directivity patterns shown in Fig. 4d, we use the same
reciprocal simulations as for the emission enhancement simulations, and made a
sweep over all angles of incidence. In Fig. 4d, we show the emission angular
power distribution (averaged over two orthogonal linear polarizations).

In order to quantify the percentage of light that can be collected in the
upward direction with given collection NA $\text{NA}_{\text{col}}$, we use the
relation (see e.g. 53):

$\text{D}_{\text{em}}=\frac{\int_{0}^{2\pi}\,\int_{0}^{\theta_{\text{col}}}p(\theta,\phi)\,\text{sin}(\theta)\text{d}\theta\text{d}\phi}{\int_{0}^{2\pi}\int_{0}^{\pi}p(\theta,\phi)\,\text{sin}(\theta)\text{d}\theta\text{d}\phi}$
(9)

with $p(\theta,\phi)$ being the angular power radiated into a certain solid
angle (parametrized by $\theta$ and $\phi$), and $\theta_{\text{col}}$ is
defined as $\theta_{\text{col}}=\text{sin}^{-1}(\text{NA}_{\text{col}})$. We
consider only a single direction for the calculated radiation patterns, which
is the upward direction, to be consistent with the enhancement spectra shown
in Fig. 4b, that is we set $\theta_{\text{col}}=0$ in Eq. (9) (corresponding
strictly speaking to $\text{NA}_{\text{col}}=0.0$). For the experimental
directivity measurements, we choose to perform the integration over
$\text{NA}_{\text{col}}=0.3$ in order to average the noise present in the
collection channel, as explained in the main text.

The authors would like to thank Sergey Gorelik and Zhaogang Dong for helpful
discussions regarding the fluorescence lifetime measurements. P.D. would also
like to thank Jinfa Ho for assistance with nanofabrication. E.L. would like to
acknowledge Christophe Sauvan for valuable advise regarding the quasi-normal
mode analysis. The authors would like to acknowledge the Facility for
Analysis, Characterisation, Testing and Simulation, Nanyang Technological
University, Singapore, which provided their electron microscopy facilities.
Finally, we would like to thank the anonymous reviewers for their greatly
detailed reviews which would have definitely contributed to bring significant
improvements to our manuscript clarity and quality.

##  10 Funding Sources

This work was supported by the A*STAR SERC Pharos program (grant number
1527300025) and MTC Programmatic Grant No. M21J9b0085.

##  11 Author contributions

P.D., E.L., R.P.-D., H.V.D. and A.I.K. developed the concept. R.P.-D.,
J.K.W.Y., H.V.D. and A.I.K supervised and coordinated the work. P.D.
fabricated all the nanostructures and performed the SEM and all the optical
measurements of the fabricated structures. E.L. designed the nanoantenna and
developed the code based on reciprocity principle used for the emission
calculations and performed the numerical simulations of the near-field color
maps, radiative emission spectra and emission angular patterns. E.L. also
performed the quasi-normal mode analysis. P.D. also performed the calculations
of the field enhancement in excitation configuration as well as some emission
spectra and emission patterns calculations. L.D. provided support and
supervised some of the optical measurements. Z.D. developed part of the
fabrication process and supervised some of the fabrication. D.C.J.N.
synthesized the QDs and helped to spin coat them onto the samples. V.V. helped
with SEM measurements. P.D. and E.L. wrote the manuscript, and all co-authors
participated in results interpretation and read and reviewed the manuscript.

Quantum dot emission/absorption spectra and fluorescence model; Resonance
dependence on disk height; Gap mode resonance; Simulations of total
fluorescence enhancement; Angle-resolved PL spectra; Laser spot size
estimation; Comparison between antennas A, B and C; Enhancement dependence on
QD quantum yield; Enhancement dependence on gap size; Nanoantenna fabrication
process flow; Optical constants of amorphous silicon and gold.

Figure 1: _Design and fabrication of hybrid dielectric-plasmonic
nanoantennas._ a. Artist’s impression of the aSi nanoring of height $H$, outer
diameter $D_{\text{out}}$ and inner diameter $D_{\text{in}}$, placed on a Au
substrate, with a Al2O3 spacer layer containing the embedded QDs (represented
by the red dots). b. Tilted SEM image of a typical fabricated nanoantenna. The
scale bar represents $400\,$nm. c. TEM image of the CdSe/ZnS QDs. The scale
bar represents $10\,$nm. d. SEM image of the Au substrate coated by a thin
layer of Al2O3 itself covered with spin-coated QDs. The scale bar represents
$400\,$nm. e. Simulated electric field in nanoantenna gap, for varying
$D_{\text{out}}$ with fixed $D_{\text{in}}=0\,$nm (disk case, lower half) or
varying $D_{\text{in}}$ with fixed $D_{\text{out}}=380\,$nm (ring case, upper
half). In all cases $H=230\,$nm. Olive green dashed lines show calculated
resonance wavelengths of three antenna modes labelled $\alpha_{1}$,
$\alpha_{2}$, $\alpha_{3}$. White dashed lines show calculated resonance
wavelengths of second and third order gap plasmon modes labelled $n_{2}$,
$n_{3}$. Blue arrows on the sides show the case $D_{\text{in}}=60\,$nm (chosen
to be discussed in the rest of this work and called "Antenna"). f.
Experimental scattering intensity spectra measured for different nanoantennas
having approximately same $D_{\text{out}}=380\,$nm and $H=230\,$nm, but
increasing $D_{\text{in}}$ (from bottom to top). The insets show the
corresponding SEM images of the fabricated nanoantennas. The scale bars
represent $100\,$nm. The scattering of the "Antenna" (case
$D_{\text{in}}=60\,$nm) is highlighted by a thicker line. Dashed black line is
a guide-to-the-eye showing the evolution of one of the resonances with
changing inner hole diameter.  Figure 2: _Quasi-Normal Mode analysis of the
nanopatch antenna mode $\alpha_{1}$ and comparison with an identical nanoring
in free space._ a. Inner (hole) diameter $D_{\text{in}}$ vs. resonance
wavelength $\lambda_{\alpha}^{\prime}$ of the QNM $\alpha_{1}$ for the
nanoring on top of gold mirror (red dots, same as in Fig. 1e) and identical
nanoring standing in free space (green dots). The top right inset shows the
inner diameter $D_{\text{in}}$ vs. $Q$-factor of the mode $\alpha_{1}$ in the
two cases (same color code). The case of $D_{\text{in}}=60$ (chosen to be
discussed in the rest of this work and called "Antenna") is also highlighted
(horizontal black dashed lines). The two insets in the left side represent the
norm of the QNM field $\alpha_{1}$ $|\mathbf{E}_{\alpha}|$ (in the vertical
plane passing through the middle of the nanoantenna) for the nanoring with
$D_{\text{in}}=60\,$nm on gold mirror (upper inset) and in free space (lower
inset). Redder (bluer) colors represent high (low) values. b. Spatial
distribution of the modal Purcell factor associated to the QNM $\alpha_{1}$,
computed according to Eq. (1) in the horizontal plane located $5\,$nm below
the nanoring, in the case of the nanoring on gold mirror with
$D_{\text{in}}=60\,$nm (Antenna case). We discriminate between the out-of-
plane oriented dipoles (symbol $\perp$) and the in-plane oriented dipoles
(symbol $\parallel$, where in this case the Purcell factor is averaged over
two orthogonal orientations). c. Same for nanoring in free space. The dotted
white lines in b. and c. represent the projection of the outer and inner
diameters of the nanoring in the horizontal plane. Figure 3: _Excitation
enhancement._ a. Experimental spectra of PL counts (cts) in Antenna case,
showing their dependence on the pump excitation wavelength
$\lambda_{\text{exc}}$. The maximum emission peak is obtained for
$\lambda_{\text{exc}}=570\,$nm. b. Simulated average excitation enhancement
$\left<\eta_{\text{exc}}\right>_{\text{th}}$ for Antenna case as a function of
the excitation wavelength $\lambda_{\text{exc}}$, computed according to Eq.
(8) (see Methods section). The vertical dashed line denotes the theoretical
resonance wavelength of the gap mode at $\lambda_{\text{exc}}=574\,$nm (third
harmonic). The inset shows the maxima of the PL spectra of a. (same color
code) as a function of $\lambda_{\text{exc}}$, for better comparison with the
simulation result (the dashed line connecting the points is guide-to-the-eye).
c. and d. Simulated pump field intensity distribution in the horizontal cross-
section passing through the middle of the nanogap (c.) and in the vertical
cross-section passing through the middle of the nanoring (d.), respectively,
at the maximum of excitation enhancement. In the simulations, the excitation
source has its electric field linearly polarized along the $x$-direction, and
comes at normal incidence, like in the experiment. Figure 4:  _Emission
enhancement._ a. Experimental average enhancement factor
$\left<\text{EF}_{\text{exp}}\right>$ spectrum obtained after deconvoluting
the Antenna PL from the Reference PL, according to Eq. (6), and restricting
the PL integration over $\text{NA}_{\text{col}}=0.3$ (to quantify the
directional emission enhancement). b. Simulated emission enhancement
$\left<\eta_{\text{em}}\right>_{\text{th}}$ spectrum for Antenna computed in
the upward direction. The vertical dashed lines denotes the resonance
wavelengths of QNMs $\alpha_{1}$, $\alpha_{2}$ and $\alpha_{3}$ computed in
Fig. 1f, enabling us to identify the main peaks with these resonances. c.
Experimental back focal plane (BFP) images of the emission PL of Antenna
(left) and Reference (right) cases taken with a bandpass filter centered
around $\lambda_{\text{em}}=650\,$nm (with a $30\,$nm bandwidth). The dotted
circles represent $\text{NA}=0.3$. The intensities are not normalized. d.
Left: Experimental angular radiation patterns obtained as a linear cut of the
BFP images in the Antenna (dark curve) and Reference cases (light blue curve)
in c.. The grey dashed lines show the maximum collection angle corresponding
to $\theta=\pm 64.2\degree$. Right: Simulated angular radiation patterns in
the Antenna (dark curve) and Reference cases (light blue curve), computed at
the wavelength corresponding to the maximum peak ($\alpha_{1}$) in b.. The
intensities are normalized such that the integration over all angles gives a
value of $2\pi$.

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