As mentioned in the theoretical framework section, to extract $\Theta$ from $\delta$, many parameters need to be included in the calculation. While the experimental configuration (collection NA, optical index, substrate, etc) is easily defined, the dipolar nature of the nanoparticles is not always straightforward to confirm. Besides, an ambiguous dipole dimension of nanoparticles might lead to a significant uncertainty of obtained $\Theta$. In fact, the calculation showed that for the specific experimental situation like our study, at a given value of $\delta$, depending on 1D or 2D dipolar particles, the corresponding values of $\Theta$ can be different by up to more than 50°[79]. Some previous works need to combine polarization analysis with a supporting measurement to address the nature of the radiation. For example, Fourier plane imaging has been performed to confirm the 2D dipolar nature of the CdSe/CdS nanoplatelets for the orientation determination [76].

It turns out that the fit of many measured $\delta$ on the curve $\delta(NA)$ in the Fig 4.9a is a good way to validate the dimension of dipole that should be included inside the calculation. Furthermore, from this curve, $\Theta$ is also able to be extracted. The AuBP in Fig 4.9 for instance, the fit of 1D dipole model follows very well the measured data and gives an out-of-plane orientation $\Theta_{fit} = 69^\circ$ with $\pm2^\circ$ of precision $^2$. This value is nearly equal to the orientation obtained from the curve $\delta(\Theta)$ (see Figure 4.6), however, holding a greater confidence. This is due to the fact that the curve $\delta(\Theta)$ is calculated for a fixed collection NA = 1.49 which is only one point on the curve $\delta(NA)$. Besides, the minor different between $\Theta$ and $\Theta_{fit}$ here is because of the AuBP behaves very similar to a 1D dipole, thus, the fits of the two curves should give the same orientation. In conclusion, from the measurement of $\delta(NA)$, we are more certain about the choice of dipolar nature of the particle for the simulation as well as extraction of its associated orientation.

### Which NA is optimal for the measurement of $\Theta$?

The strong dependence $\delta(NA)$ raises a fundamental question about which objective numerical aperture should be used for the polarimetric measurement. The best NA of an objective to precisely determine a dipole orientation is a compromise between two factors: (i) a strong $\delta(\Theta)$ dependence, and (ii) a good intensity collection efficiency. Let us discuss two extreme cases of nearly parallel or vertical dipoles (as opposed to the substrate surface).

<footnote>$^2\Theta_{fit}$ denotes for orientations extracted from $\delta(NA)$, to distinguish with $\Theta$ obtained from $\delta(\Theta)$</footnote>
In the case of elongated nanoparticles that are nearly horizontally deposited (Θ > 70°) such as bipyramids or nanorods, it can be seen clearly in Fig 4.8 that a very narrow NA is not appropriate for the measurement because δ is always unity for every orientations in this region. On the contrary, a large collection NA is favorable results from a minor change in orientation leading to a significant variation of δ. Furthermore, when a dipole is located near a glass-air interface, the most perpetuated polarization and concentrated emission are located around the critical angle, and thus, the collection objective with NA falls inside this region might be the best choice for orientation measurement.

To strengthen our hypothesis, we extract Θ at every collection NA ∈ [0.6; 1.49] from the curve δ(Θ) for the same AuBP. The accuracy of Θ at an associated NA is evaluated based on its quantitative difference with the most precise value - Θ<sub>fit</sub> extracted from the curve δ(NA), defined by ΔΘ = Θ<sub>fit</sub> - Θ/Θ<sub>fit</sub> (%). Figure 4.10 displays the obtained results of ΔΘ at different NA and the error of Θ<sub>fit</sub> is taken as a reference (grey bar). We clearly see that ΔΘ = 0 at NA = 1-1.1 for all the presented AuBPs with the exception of the last AuBP (Θ<sub>fit</sub> = 85°). In addition, the errors increase when the AuBPs orient more parallel to the substrate surface. Actually, the polarization analysis is the least sensitive to probe Θ in the range between 80-90° because δ is nearly constant for every collection NA [79].

<figure><img src="image_48.png" /><figcaption>Figure 4.10: Relative different between Θ and Θ<sub>fit</sub> as a function of NA measured for 4 AuBPs (red dots). Grey bars display the errors of measured Θ<sub>fit</sub></figcaption></figure>

In the case of a nearly vertical dipole (Θ < 10°), a small NA objective allows a more accurate determination of Θ than a large NA objective because the Θ increases very quickly when the dipole slightly leaves the vertical position. However, the collection efficiency needs to take into consideration to obtain an adequate signal-to-noise ratio.
4.5 Conclusion

A dark-field scattering polarization analysis has been developed to measure the 3D orienta-
tion of AuBPs at the individual level. The out-of-plane component was precisely determined
by taking advantage of the angular collection at the wide numerical aperture. We experiment
tally demonstrated that the more scattered light is collected, the more degree of polarization
is decreased. In particular, the contribution of the evanescent wave is especially important
in the orientation measurements. It is worth noting that the out-of-plane orientation can
also be extracted from the evolution of the degree of polarization with the numerical aper-
ture. Compared to other polarimetric methods, where the dipole orientation is determined
from the degree of polarization only for one numerical aperture, our method combined with
theoretical analysis strengthens our confidence in the determined orientation. The experi-
mental technique that we have proposed here may be applied to more complex systems such
as nanoparticle assembly where our method can discriminate polarization behaviors with the
numerical aperture.

The investigation of the orientations of the AuBPs in this Chapter is very important to
interpret the optical responses of the nanopatch in the following chapters when the AuBPs
are deposited on more complex substrates. On the other hand, in further work, surface
treatment by silanization is expected to be done in order to improve the deposition of the
AuBPs. More details of this work presented in this chapter can be found in [72].
# Chapter 5

## Opening-gap nanopatch antennas

We introduce a plasmonic nanopatch antenna consisting of a gold bipyramid nanoparticle separated from a gold film by a sub-10nm TiO₂ gap. In a first step, we show (experimentally confirmed with simulations) that placing a AuBP with contact facet on a high index substrate reveals the hidden quadrupolar mode. In a second step, we demonstrate that the hybrid structure supports a rich optical response that possesses distinctive characteristics of each plasmonic individual: strong field localization inside the metal-insulator-metal gap and radiative nature induced by localized surface plasmon resonance of the particle. This only can be achieved when a crucial condition of the bipyramid's orientation is satisfied: a tip and a facet of the particle touch the surface, forming a nanogap with an opening mouth. In addition, the structure also provides the degree of freedom in the design of geometrical parameters that allow engineering the optical response. Here, we show how the modes are constructed by adjusting the gap thickness. Our investigation establishes a basis for the understanding of the coupling of the nanopatch to emitters.
# Contents

<table><tr><td>5.1 Introduction to opening-gap nanopatch antennas</td><td>106</td></tr><tr><td>5.2 Characterization methods</td><td>113</td></tr><tr><td>5.3 Gold bipyramids on a high refractive index substrate</td><td>116</td></tr><tr><td>5.4 Gold bipyramids on the gold film</td><td>122</td></tr><tr><td>5.4.1 Scattering spectra</td><td>122</td></tr><tr><td>5.4.2 Physical formation of the modes</td><td>126</td></tr><tr><td>5.5 The complexity of the AuBP nanopatch antenna</td><td>129</td></tr><tr><td>5.6 Conclusion</td><td>131</td></tr></table>

## 5.1 Introduction to opening-gap nanopatch antennas

Recalling the main characteristics of the gap plasmon of planar MIM waveguides

When two insulator-metal interfaces are brought closer to each other, the SPPs on either side of the dielectric medium hybridize and split into high and low-energy modes. When insulator gap thickness reduces to below the diffraction limit ~ λ/2, due to the matching of the field symmetry, only the low-energy mode (symmetry) is excited [38]. We refer to this mode as “gap plasmon”. The detailed theoretical descriptions of the planar MIM waveguide can be found in Chapters 1 and 2. Here, we recall two main characteristics of the gap plasmon that would be very beneficial for boosting light-matter interactions:

* large in-plane wavevector $k_{||}$ for tight confinement of light
<figure><img src="image_49.png" /><figcaption>Figure 5.1: Dispersion relation of gap plasmon and LDOS enhancement of an planar MIM structure. (a) Geometry of the MIM device: Au/TiO₂/Au. Here the dielectric function of gold ε<sub>Au</sub> is taken from [11], and of the gap ε<sub>TiO2</sub> = (2.4)². A dipole is placed in the middle of gap as a source to excite the optical modes. (b) Calculated dispersion relation of gap plasmon mode of the MIM structure at g = 4nm and compare to dispersion relation of SPPs on a single interface (c) LDOS enhancement (is proportion to the normalised dissipated power of the dipole) of total system, MIM and quenching and the leakage waves (in the air) as a function of the gap thickness g.</figcaption></figure>

* huge local density of state (LDOS), which overcome the quenching (i.e. lossy surface waves that do not couple to the radiation but undergo heating of the metal).

For example, we calculate the dispersion relation of the gap plasmon and its LDOS
enhancement (i.e. Purcell factor) restricted to planar Au/TiO₂/Au structure, as shown in
Figure 5.1. We use the same technique as described in Chapter 2, using a point dipole
buried in the middle of the gap to excite the optical modes. The dispersion is obtained by
calculating the spatial spectrum of the power dissipated by the dipole at each wavelength.
As can be seen in Figure 5.1b, the *k*<sub>||</sub> corresponding to the gap plasmon is approximately
1 order of magnitude higher than the free-space plane waves of photons or SPPs, provided
by a TiO<sub>2</sub> gap thickness of 4nm. This large in-plane wavevector is associated with a small
plasmon wavelength λ<sub>p</sub> = 2π/*k*<sub>||</sub> on the order of 10nm, for the free-space wavelength of
excitation ranging from visible to near-infrared. On the other hand, the dispersion of the MIM waveguide in the very thin gap limit $g < 10$nm also can be approximated as [52, 103]:

$$k_{\parallel} = k_0 \sqrt{\varepsilon_d + 2\xi(1 + \sqrt{1 + \frac{\varepsilon_d - \varepsilon_m}{\xi}})} \quad (5.1)$$

where $\xi = \sqrt{\frac{k_0 g \varepsilon_m}{\varepsilon_d}}$ and $k_0 = \frac{2\pi}{\lambda}$. Here, $\varepsilon_d$ and $\varepsilon_m(\omega)$ are the dielectric functions of the dielectric and metal, respectively. The equation 5.1 also indicates that the in-plane $k_{\parallel}$ increases significantly as the gap thickness is reduced.

In terms of LDOS, we can equalize the LDOS enhancement of the MIM waveguide as compared to the vacuum to the normalized power dissipated by the dipole. Figure 5.1c displays the value of LDOS enhancement of the gap plasmon mode, the quenching, and the total system as a function of gap thickness between 1-10nm. We can see that all the values of LDOS rapidly enhanced ~ $10^4$ as the gap thickness decreased. Especially, the LDOS of the gap plasmon largely surpasses the quenching despite the sub-10nm proximity to the metal of the dipole. The work of P. Lalanne et al [104] also found that for vanishing gap thickness, both the gap plasmon mode and the quenching have identical $g^{-3}$ scaling; however, there is also a significant decrease in the group velocity of the gap plasmon thus largely enhancing its optical density. Interestingly, the quenching of the MIM planar system calculated here can be valid for associated nanopatch antennas (see configuration below) of sizes larger than a few nanometers [51, 105].

## Gap plasmon antennas based on the MIM waveguide

Practically, to benefit from the full potential of the MIM waveguide, the gap thickness has to be smaller than 10nm [22, 66, 106]. Besides, the gap plasmon has a very short propagation length at this very thin gap thickness, which is around a few ten nanometers, and thus can be completely lost before reaching the end facets of the MIM waveguide-based devices. Therefore, the lateral dimension of these devices is essential close to the propagation length of the gap plasmon. Recent advances in nanofabrication allow producing sub-nm-scale plasmonic dimensions, from which gap plasmon devices can be classified into two main configurations: (i) dimers consisting of two closely-space colloidal metallic nanoparticles [107,
108, 109] or (ii) nanopatch antennas using nanoparticle-on-mirror (NPoM) geometry [22, 53, 105, 110, 111], where a metallic nanoparticle is placed on top of a flat metallic film (mirror), which is predeposited with a thin dielectric spacer to prevent conductive contact.

## The attractiveness of plasmonic nanopatch antennas

<figure><img src="image_50.png" /><figcaption>Figure 5.2: **Gap plasmon in a nanopatch antenna.** Gap plasmon in a nanopatch antenna assembles transverse stationary modes in a Fabry-Pérot cavity. The light confinement inside the gap can be evaluated through the effective index and the group index of the modes ($n_g = n_{eff} - \lambda \frac{\partial n_{eff}}{\partial \lambda}$). The indices are simulated at $\lambda = 700$nm.</figcaption></figure>

* **Fabrication:** Roughly, the gap plasmon produced by a dimer or by coupling a particle to its mirror image in the metallic film is equivalent [53, 112]. However, a particular reproducible, controllable with nanometric precision, and scalable plasmon gap can be constructed for nanopatch antennas by using nanolithography [113], atomic layer deposition (ALD), or self-assembled monolayer molecules [114]. For instance, a gap size below 2nm can be routinely achieved by monolayers of $MoS_2$, which is identical across large areas over $100\text{cm}^2$ [54].

* **A Fabry-Pérot liked cavity:** Due to the limited lateral dimension and reflection at the
nanoparticle edges, the MIM gap plasmon modes can resonantly bounce back and forth below the patch (defined by dielectric spacer embedded between the particle's facet and the metallic film) and can generate stationary gap plasmon waves, as illustrated in Figure 5.2. In other words, a nanopatch antenna works as a resonator and is analog to a Fabry-Pérot cavity [38, 51].

The nanopatch antennas take full profits from the planar MIM waveguide but further boost its properties. At an optimal configuration, an LDOS enhancement is greater than 2 orders of magnitude as compared to the associated MIM planar waveguide can be achieved by the nanopatch antenna [104], from which the quenching becomes negligible. This can be achieved firstly because the mode volume is shrunk into a deep subwavelength scale $V \sim (\lambda/2n_{eff})^3$ with $n_{eff} = Re(k_{||})/k_0$ is the effective refractive index of the gap plasmon mode. The second reason is that there is an increase of the quality factor Q even at very proximity to the metal surfaces where its absorption is considerable. Intuitively, the gap plasmon mode is slowed down (i.e., its group velocity is reduced) due to the bouncing back and forth between the patch's edges, which is very similar to the light trapping for a long time inside photonic crystal cavities [115]. It is worth mentioning that for an extremely thin gap < 10nm, the Fabry-Pérot cavity model has been proven that it is still valid to describe the resonance of gap plasmon mode; however, the quality factor provided by the nanopatch antennas is limited by the value in the quasi-static limit $Q_s \sim 10^2$ [51] (with $Q_s \propto \omega_0/Im(\epsilon_m)$ [116], the imaginary part implies that the loss is purely induced by the intrinsic loss of the metals).

## Opening gap nanopatch antennas

Despite holding many advantages as presented above, the conversion of gap plasmon modes in the nanopatch antennas into desired output channels such as free-space radiation or SPPs is relatively inefficient. This is because of the large mismatch between in-plane $k_{||}$ of the plasmon gap mode and $k_0$ in free space, the resonant hotspots in the gap typically emit into high angles for thin gap thickness, which is nearly inaccessible by using the conventional phase-matching devices such as gratings or prism couplers. This loss is usually referred to as “coupling loss”. Recent works [51, 117] have shown that engineering the facets of
<figure><img src="image_51.png" /><figcaption>**Figure 5.3: Classification of gap plasmon antennas based on its facet reflectivity**
Left: Tapered-nanogap antennas with low facet reflectivity $R \approx 0$. Right: nanocube-patch antennas with large facet reflectivity. Source: R. Faggiani et.al., [104].</figcaption></figure>

the nanoparticles could mitigate reflectivity at the end of the nanopatch and thus reduce the coupling loss. For example, two configurations are presented in Figure 5.3. A tapered antenna implements no reflectivity at the “mouth” of its curve edges yielding significantly large photon-radiation conversion above 70%, which is ~ 4 times higher than its counterpart, e.g. the state-of-art nanocube antennas, with a large facet reflectivity. In turn, the tapered antenna offers a smaller LDOS of gap plasmon mode (around 1 order of magnitude at the same gap thickness). Therefore, a nanopatch antenna design that provides a better balance between the large gap mode density and high photon-radiation efficiency is necessary.

In this context, we propose a new structure of gap plasmonic antenna with delicate engineering of facets, which is expected to offer a better balance between the large gap mode density and high photon-radiation efficiency. The antenna consists of a colloidal synthesized gold bipyramid nanoparticle (AuBP) placed over a gold film, separated by a well-controlled nanoscale dielectric gap (Figure 5.4). The interesting feature of this antenna design comes from the geometry of the AuBPs when they lie on the metallic surface, each plays a role as a nanopatch antenna with an “opening-mouth”. The cavity volume is determined by the space between the bipyramid and the underlying gold film. This volume consists of two parts: (i) the dielectric spacer with a fixed thickness embedded between a triangular facet of AuBP and the gold surface (flat gap) and (ii) the mixing of air/dielectric gap resulting from the inclination of the bipyramid (“opening-mouth”).

To intuitively understand the different behavior of each component gap induced by their geometry, we calculate the effective refractive index $n_{eff} = Re(k_{\|})/k_0$ of the MIM mode inside each gap. While a full simulation that takes into account the geometry of the nanoparticle's
<figure><img src="image_52.png" /><figcaption>Figure 5.4: Opening-gap nanopatch antenna of gold bipyramid. Left: Geometry of the patch antenna with gap is made from TiO$_{2}$. Right: effective index of gap plasmon associating to the flat gap ($g$ is fixed at 4nm) and opening-mouth gap ($g = 4 - 20$nm).</figcaption></figure>

facets is needed to find the exact value of $n_{eff}$, an approximation to the planar MIM structure of infinite width is possible for the extremely small gaps used here. Indeed, for a small gap situation $g/\lambda \to 0$, the effective index $n_{eff}$ can be given from equation 5.1 with an assumption that $\xi \gg \varepsilon_m, \varepsilon_d$

$$n_{eff} = -\frac{2\varepsilon_d}{\varepsilon_m(gk_0)} \qquad (5.2)$$

For vanishing gap thickness, the $n_{eff}$ becomes independent of the width. This can be thought of as the mode confinement caused by reducing the gap thickness between two metallic surfaces is considerably stronger than those induced by dielectric walls at the end facets. For any given value of the lateral width $w$, we can have $w \gg \lambda/(2n_{eff})$ as the gap thickness is reduced.

Here, we deduce the $n_{eff}$ of the gap plasmon mode of the bipyramid nanopatch antenna from the in-plane $k_{||}$, which is computed from an equivalent planar MIM structure. Figure 5.4b shows the evolution of the calculated $n_{eff}$ with the lateral position $x$. The $n_{eff}$ is sufficiently large and constant inside the flat gap region. However, along the opening-mouth gap, $n_{eff}$ is gradually reduced as the gap thickness increases, thus paving the way for the light escape to the free space. In other words, while the flat gap offers a platform for effectively supporting the MIM plasmon modes, the opening-mouth gap can play a role in efficiently
converting these modes into outgoing SPPs/photons.

## 5.2 Characterization methods

**Experimental methods:** In our experiments, the substrate is prepared by evaporating a 45nm gold film with a 5nm Cr adhesion layer onto a clean glass coverslip via electron-beam evaporation. A sub-10 nm dielectric spacer layer of TiO₂ is grown on the Au film via atomic layer deposition. The thickness of the TiO₂ spacer is well-controlled by the number of deposition cycles. Finally, a diluted solution of 30nm-width and 80nm-length gold bipyramids is dropped onto the TiO₂ surface. The concentration of the colloids in the solution and the time that the surface is exposed to the colloidal solution are controlled to ensure a low bipyramid surface coverage for single-nanoparticle measurements. It is worth noting that the AuBPs have been subtly synthesized with not sharp, but curved end edges (by controlling the growing time of the seeds [89, 90]) to mitigate the reflectivity and avoid the point effect of charge accumulation.

The optical index of gold film and TiO₂ spacer is measured by a spectroscopic ellipsometer. Below 10nm thickness, the TiO₂ film has refractive index $n_{TiO_2}$ = 2.4. Above this, the deposited film's optical index might vary due to the changing in the crystal structure of TiO₂. The thicknesses of each layer are determined optically from SPPs dispersion shifting via leakage radiation microscopy (see Chapter 3). Atomic force microscopy is also performed to measure the thickness and gives the same results as the optical measurement.

To identify the optical modes of the system, we characterize the scattering of white lamps from individual AuBPs on the substrate via dark-field spectroscopy. Figure 5.5 depicts a schematic of the experiment and the structure of the nano patch antenna with a bipyramid situated on a gold film. The experimental setup of dark-field microscopy was described in detail in Chapter 3. Briefly, an unpolarized white light beam is focused onto the sample using a 40X objective with NA = 0.25 so that the sample is uniformly illuminated from small angles of incidence $\theta_i$ = 0 – 15°. Forward scattering is then collected in transmission by an oil immersion objective (NA = 1.49) while the excitation beam is omitted from the detection by a beam stop (NA<sub>BS</sub> = 0.5) installed at the back focal plane of the oil objective. With
<figure><img src="image_53.png" /><figcaption>Figure 5.5: **Nanoatch antenna scattering.** (a) Experimental scheme. (b-c) Dark-field images of one excitation spot on the surface of TiO₂/gold film before (b) and after (c) depositing AuBPs.</figcaption></figure>

this configuration, the collection angles take place between $\theta_c = 20 - 80^{\circ}$.

In a dark-field image, any object that scatters light appears as bright spots on a dark background. Because of the limit of diffraction, it is not straightforward to distinguish the AuBPs from other objects that might be present on the substrate such as dust or holes (observed in the AFM images). This is easier for AuBPs deposited on a glass substrate where a single particle can be well identified based on its distinctive longitudinal LSPR on the scattering spectrum. In the situation of AuBPs on the TiO₂/gold film, the interaction between the particle and the substrate can induce unpredictable scattering resonances (see later). To locate AuBPs on the dark-field images, we correlate images of the substrate before and after depositing AuBPs. Figure 5.5b shows a dark-field image of the bare TiO₂/gold substrate with some dust/holes appearing as extremely bright spots due to its big sizes. Subsequently, an image at the same excitation area but after dropping the diluted solution of AuBPs. By correlating the two images, we can identify the scattering from AuBPs that are marked as gold circles in Figure 5.5c. The dilution can be done in ethanol that rapidly evaporates (~15 minutes, room temperature), and thus allows a fast acquisition time of two correlated images without changing the excitation spot's position on the sample stage.

**Method of calculation:** COMSOL simulation has been performed to calculate the optical cross-section spectra, associated charge distributions, and near-field distribution of the
<figure><img src="image_54.png" /><figcaption>Figure 5.6: Configurations of the COMSOL simulation for calculating scattering cross-section. The AuBP is deposited on (a) 4nm-TiO₂/glass substrate and (b) 4nm-TiO₂/45nm-gold/glass substrate. The excitation of a plane wave in the normal direction and polarized along the long axis of the AuBP takes place in air. The integration sphere defines the surface for calculating the scattered power in the near-field.</figcaption></figure>

nanopatch. The geometrical dimensions and features of the bipyramids (i.e., the truncated tips and a pentagonal base) are given by the TEM measurement (see Chapter 3). Two configurations are simulated: the AuBP is either placed on a TiO₂ film (Figure 5.6a) or a TiO₂ film over a gold film (Figure 5.6b), both supported by the glass substrate. Here, the dielectric function of gold $\epsilon_m(\omega)$ is taken from the Johnson and Christy's table [11]; and for the spacer, we use a refractive index $n_{TiO_2} = 2.4$, which is obtained from the ellipsometry measurement. The background fields in each media are those resulting from the excitation by an incoming plane wave normal to the substrates, in the absence of the AuBP. The incoming electric field is linearly polarized along the long axis of the particle. The scattered power (or scattering cross-section) is calculated in the near field by integrating the corresponding Poynting vector over a sphere enclosing the AuBP (see Figure 5.6), which accounts for contributions in air and glass semi-infinite media as well as in the supporting films. The COMSOL simulations in this Thesis are done by Michel Pellarin.
## 5.3 Gold bipyramids on a high refractive index substrate

The nanopatch substrate consists of multilayers that are both absorbing (gold) and dielectric (TiO₂ and glass) materials. Since the TiO₂ spacer has a high refractive index of 2.4, it might have certain impacts on the optical response of the deposited AuBP. To support the interpretation of scattering from AuBPs on nanopatch structure later, we first perform the dark-field scattering measurement of AuBP on a 4nm-TiO₂/glass substrate.

<figure><img src="image_55.png" /><figcaption>Figure 5.7: Scattering of AuBPs on 4nm-TiO₂/glass substrate. Left: Two selected spectra represent two kinds of spectra measured. Right: Resonance wavelength and spectral width of many particles</figcaption></figure>

We observed two kinds of scattering spectra as shown in Figure 5.7. The first one exhibits single-mode resonance at around $\lambda_{\parallel}^{D} = 680$ nm, which is associated with the longitudinal LSPR of AuBPs. In the second, the longitudinal mode is red-shifted by ~ 30 nm ($\lambda_{i}^{D}$) and interestingly, a small additional mode arises in the shorter wavelength at $\lambda_{i}^{Q} = 640$ nm. We emphasize that these spectral features are reproducibly observed across many AuBPs. We present their resonance wavelengths and associated spectra widths in Figure 5.7b. The single-mode particles (black dots), all show a narrow FWHM ~ 50 nm that is nearly equal to that of AuBPs on the bulk glass substrate, suggesting the presence of the very thin TiO₂
layer merely leads to an additional mode broadening. In terms of the center position of resonance, a dispersion of $\Delta\lambda \approx 50$nm is observed for different single-mode AuBPs.

## Orientation effects on the optical response: Qualitative description

As we will show in the simulation below, the appearance of two sets of scattering modes is induced by the orientation of the AuBPs on the substrates. Due to the elongated morphology, the plasmon resonance of AuBPs is mostly sensitive to the local properties of the external medium near its “hot-spot” tips, where the field is strongest enhanced (around 2 orders of magnitudes [68, 5]). Therefore, for a given distance of the particle from the surface, the interaction strength of AuBPs and underneath substrate is expected to strongly depend on the tip-substrate separation, which is governed by the orientation of the AuBPs. Our previous measurement indicated that the inclination of AuBPs on the flat substrate ranges between 0 – 30° (see Chapter 3) corresponding to the tip-substrate distances of 0 – 15nm. Therefore, there are situations in which the AuBPs incline with a tip touching the substrate, the particle-substrate interaction is significant yielding to the red-shifted of the longitudinal plasmon resonance and the birth of a new optical mode. In contrast, there are bipyramids that lie flat along the surface so that the presence of the substrate weakly impacts their scattering.

## Simulation observation

To examine the orientation effects on the optical responses of the particles, we calculate the scattering cross-section spectra in two situations: (i) AuBP lies horizontally to the substrate and (ii) tilting AuBP by 20° to lie one tip against the surface and the other raised in the air (see Figure 5.8). The simulation of surface charge distribution has been also performed to understand the origin of the modes.

As expected, the two orientations induce different optical responses as observed in the experiment. The horizontal bipyramid exhibits single resonance with center wavelength and the spectra width is almost identical to AuBPs deposited on the glass substrate without the presence of the TiO₂ film (Figure 5.8 above). The inset of simulated charge distribution also confirms its longitudinal dipolar nature. Since the tips are separated far from the substrate, the localized charges around the tip mostly feel the homogeneous medium of air resulting in
<figure><img src="image_56.png" /><figcaption>Figure 5.8: Calculation of scattering cross-section of the AuBPs on 4nm-TiO2/glass substrate. Two orientations of the AuBPs are simulated: horizontal to the substrate or tilted with a tip touching the surface.</figcaption></figure>

negligible modification of the longitudinal plasmon mode in the far-field scattering. On the other hand, when one tip of the inclined AuBP touches the surface, it strongly senses the inhomogeneous of the local optical index induced by the underneath layered substrate. As the result, the dipolar longitudinal plasmon is propelled to the higher wavelengths ($\lambda_i^D$) and gives rise to the new mode at the lower wavelength ($\lambda_i^Q$). The separation of these two modes is around 100nm, which is nearly equal to the value observed in the experiment.

We note that this double-resonance response does not occur for intermediate orientations of AuBPs (i.e. tip is separated from the surface), suggesting the effect of lateral surface contact. Tilting AuBPs by a maximum inclined angle not only minimizes the tip-substrate distance but also allows a facet of the particle contacting to the surface and thus results in stronger interaction. On the other hand, the intermediate orientations are responsible for the dispersion of scattering resonance as observed in Figure 5.7b. However, the resonance wavelength is only dispersed in the range of the spectra width ($\Delta\lambda < 2FWHM$). This means that as long as the tips are separated from the surface, the orientation only plays a
minor role in the optical response of the AuBPs, its effect cannot compete with broadening
induced by the intrinsic losses of the metallic particle.

The mode $\lambda_i^Q$ has an even symmetry in the charge distribution, which resembles a longitudinal quadrupole. One possible explanation for the birth of this mode $\lambda_i^Q$ is the result of its coupling to the dipolar mode. The work of P. Nordanler et al [92] about the nanocubes showed that the “dark quadrupolar mode” can reveal itself in the scattering spectra through coupling to the “bright dipolar mode”. This interaction is mediated when a facet of the nanocube contacts the substrate. This interaction is especially pronounced for a large dielectric constant substrate and a small particle-substrate separation. In the case of bipyramid, because of the more complicated geometry, further calculation and study are needed to fully understand. Nevertheless, all the features are in good agreement between the experiment and simulation.

**Estimation of the penetration depth of the field around the AuBP's tip.**

Above we have seen the important role of the orientation effect on the interaction of the AuBPs and the substrate. Now at an optimal tilting configuration that completely omits the spacing between the tip and the surface, we want to estimate the thicknesses of the TiO₂ spacer at which the “hot spot” of AuBPs still “feels” the glass substrate underneath it. This can be done by tracing the resonance shift of the dipolar longitudinal mode when the TiO₂ thickness increases gradually. Roughly, the change of TiO₂ film thickness induces the change of the effective index of the layered substrate ($n_{glass} < n_{eff} < n_{TiO2}$), and thus yields the shift of the localized plasmon resonance.

Figure 5.9 shows the calculation of the scattering spectra of an AuBP inclined on the TiO₂ film/glass substrate, considering the TiO₂ thickness as an adjustable parameter $t = 0-20$nm. The resonance wavelength of the associated dipolar mode is also reported in the Figure 5.9 as a function of $t$. There is no surprise that the plasmon mode is red-shifted when the TiO₂ film thickness increases, by more than 100nm. At $t = 0$ (i.e., without TiO₂ film), the plasmon resonance is identical to that of AuBP on the bulk glass substrate. When the TiO₂ film thickness increases, $\lambda_i^D$ is rapidly red-shifted for small thicknesses; then becomes saturated and asymptote to the resonance of the AuBP on the bulk TiO₂ substrate when $t > 10$nm. Especially, this evolution follows very well a fitted exponential function
<figure><img src="image_57.png" /><figcaption>Figure 5.9: Calculation of scattering cross-section spectra of AuBPs on TiO2/glass substrate with varying TiO₂ film thickness. The longitudinal dipolar plasmon resonance $\lambda_i^D$ is plotted as a function of the TiO₂ film thickness $t$ (black dots) and fitted with an exponential function (red line).</figcaption></figure>

$$ \frac{\Delta\lambda_i^D}{\Delta\lambda_0} \propto e^{-t/\tau} \qquad (5.3) $$

where $\Delta\lambda_i^D = \lambda_{TiO2} - \lambda_i^D$ and $\Delta\lambda_0 = \lambda_{TiO2} - \lambda_{glass}$, within $\lambda_{TiO2} = 770$nm and $\lambda_{glass} = 690$nm are the longitudinal dipolar plasmon resonance wavelength of the AuBP on the bulk TiO₂ and glass substrate, respectively. The exponential decay of the resonance shift here resembles the "universal" scaling behavior of the interparticle plasmon coupling, which can be explained by the dipole-dipole coupling model [118]. In this work, the authors show that the exponential decay can be approximated nearly the scaling of the near field of the plasmon particle or the coupling strength as $D^{-3}$, with D is the interparticle distance.

We assign $\tau$ to the critical thickness of TiO₂ film (i.e., decay length) that for $t < \tau$, the localized plasmon field of AuBPs can significantly penetrate the glass substrate and feel its impact. Here, the fit gives $\tau = 5$nm, which means that if we want the AuBP to interact effectively with the underneath substrate, the thickness of TiO₂ should be smaller than 5nm.
Therefore, in the following measurement of AuBPs on the gold film configuration, we choose
TiO₂ spacer thickness below 5nm.
## 5.4 Gold bipyramids on the gold film

### 5.4.1 Scattering spectra

**Experimental results.** Figure 5.10 presents the scattering spectra of AuBPs deposited on the 4nm-TiO₂/45nm-gold/glass substrate. From the dark-field measurements, we also recorded two categories of spectra: single mode and multimode.

<figure><img src="image_58.png" /><figcaption>Figure 5.10: Scattering spectra of the AuBPs on gold film measured by the dark-field microscope. The measured spectra are classified in two kinds: single-peak spectra and multiple-peak spectra corresponding to the orientations of the AuBP (insets).</figcaption></figure>

For single-mode spectra, the resonance wavelength is not far from the associated position of horizontal AuBPs placed on the TiO₂ film/glass substrate at ~680nm. Based on the previous discussion, we correlate these single-mode spectra to longitudinal dipolar plasmon resonance of the AuBPs oriented *without* tip-touching the surface (inset), in which the localized plasmon is weakly affected by the underneath substrate. However, the absorption of the gold film induces a large dispersion of the resonance wavelength from 600nm to 700nm accompanied by a broadening of ~100nm, which is 2 times larger than the spectra width of
AuBPs on the bare glass substrate. Besides, in some scattering spectra, there is a shoulder arising at the blue side of the main dipolar resonance.

For the multimode spectra, many modes are excited that expand the spectrum from the visible to the near-infrared regime. The center wavelength positions of the three main peaks in Figure 5.10 (below) take place at approximately 530nm, 700nm, and 1000nm, respectively. In which, the two first peaks share a dip at around 600nm. We note that visible resonance was measured by the 1st grating of the spectrometer (Andor, Kimera 193i model), whereas the 1000nm-resonance was recorded by the 2nd grating in order to obtain better detection efficiency.

**Simulation results.** We simulated the scattering spectra of AuBPs on 4nm-TiO₂/45nm-gold/glass substrate by the COMSOL calculation, particularly focused on the two orientation configurations: horizontal (Figure 5.11) and maximum incline (Figure 5.12).

<figure><img src="image_59.png" /><figcaption>Figure 5.11: Calculation of scattering cross-section spectrum and associated charge distribution of the AuBP lying parallel to the gold film</figcaption></figure>

As expected, the optical response of the flat AuBP (Figure 5.11) is nearly unaffected by the presence of the absorbing substrate of gold: only dipolar longitudinal plasmon resonance is exhibited with negligible spectral shift and broadening, as compared to the previous situation without gold film. In contrast, tilting the AuBPs yields a distinctive optical response with a rich structure of modes. We can see a series of peaks that appear in the simulated scattering
<figure><img src="image_60.png" /><figcaption>Figure 5.12: Calculation of scattering cross-section spectrum and associated charge distributions of the inclined bipyramid on gold film. The particle is rotated to display the charge distribution in the bottom facet that contacts the gold film. The charge distribution of the weak resonance $\lambda_t$ is also displayed in saturation. The longitudinal and the transverse axis of the AuBP are denoted as $l$ and $t$.</figcaption></figure>

spectrum in Figure 5.12, labeled as $\lambda_t = 530\text{nm}$, $\lambda_l^+ = 670\text{nm}$, $\lambda_l^- = 720\text{nm}$, and $\lambda_l^D = 930\text{nm}$. In which, the $l$ resonances dominate the scattering spectrum while the $t$ resonance only exhibits a weak contribution. Besides, the two resonances $\lambda_l^+$ and $\lambda_l^-$ share a dip at around 700nm. In the following, we restrict our discussion on the configuration of the AuBP tilted on the surface.

## Identification of the modes from the charge distributions

To support the understanding of the nature of the modes, we first simulate the charge distribution of the modes, as presented in Figure 5.12 (below). Here, there is symmetry breaking in the charge distributions induced by the substrate. As we can see in all the presented modes that the charges on the AuBP are mostly modified in the region that contacts the substrate (flat gap) while elsewhere it remains nearly unchanged (opening mouth). We classify the modes into two categories: $t$ and $l$ modes, since their charges mainly vary in
the transverse or longitudinal axis of the system, respectively.

*   **The *t* mode:** The weak and resonance below 600nm is a broad distribution of hybridized modes. Here, we only display the charge distribution of the center position at $\lambda_t$ = 530nm. In fact, the nearby wavelengths (still inside this resonance) are varied in the charge distribution, which is not shown here for clarity. The mode decomposition of this low-wavelength resonance can be found in [119], where the authors also show this broad resonance as a spectral overlapping of many higher-order quasi-normal modes. Although the charge configuration is complex due to the interaction with the substrate, it can be considered close to the transverse mode of the system as observed in the saturated image (Figure 5.12 below). Because of the very weak far-field optical response, in the following, we only focus on the three dominant radiative modes of the longitudinal *l* category.

*   **The *l* modes:** The mode $\lambda_l^D$ shows its longitudinal dipolar character of the AuBP as the opposite charges are distributed on the two sides of the particle. On the other hand, for the modes $\lambda_l^+$ and $\lambda_l^-$, it is not straightforward to fully interpret the nature of these modes owning their complicated charge configuration. However, we still point out some main features that can be observed here. For example, both displays an intense charge distribution with many nodes on the facet of the AuBP that contact to the underlying gold film. Besides, unlike the mode $\lambda_l^D$ which has a nodal line at the middle of the facet, the modes $\lambda_l^+$ and $\lambda_l^-$ have maximum charge accumulation in the middle and two edges of the bottom facet.

**Correlation of the experiment and simulation spectra**

Qualitatively, the simulation covers all the resonance that appears in the measured spectra, except for the resonance at $\lambda_l^+$ = 670nm which we believe is spectrally overlapped by resonance $\lambda_t$. However, we insist that the scattered power, as it is calculated here, accounts for contributions in air and glass semi-infinite media as well as in the supporting films (which is defined by the integration sphere in Figure 5.6). It cannot be directly compared to the power scattered at very large distances (far field) in the collection angle defined by the immersion oil objective used in experiments (glass/oil media). Actually, the simulated power
in Figure 5.12 (integrated in the near-field) is close to the sum of the powers scattered at large distances in the air and in the glass media (over a solid angle of $2\pi$ sr). However, the corresponding spectra would be shown to be different, not in the location but rather in the intensity of resonances.

Moreover, the scattered light collected experimentally depends on: (i) the far-field scattering diagram in the forward direction and (ii) the numerical aperture of the collection objective. Corresponding far-field spectra can be determined but they were not calculated during this thesis. As a consequence, it must be bear in mind that a comparison between experiment and near-field calculations will be relevant only in discussing the positions of the plasmon resonances that are independent of such considerations.

### 5.4.2 Physical formation of the modes

In order to further understand the nature and the formation of the plasmon modes of the AuBP nanopatch, we investigate the spectral evolution of the modes with the dielectric gap thickness. Figure 5.13 shows the calculation of scattering cross-section spectra, considering the gap thickness as a varying parameter. The gap thicknesses are set smaller than $\tau = 6$nm, i.e., the thickness of TiO$_2$ film at which, the bipyramid still interacts effectively with the underlying film (as shown in Figure 5.9). When the g decreases, the mode $\lambda_l^D$ is seen to rapidly redshift. This shift is mostly induced by the mirror effect, i.e., the interaction between the longitudinal dipolar mode of the AuBP and its charge image in the underlying gold mirror, which resembles a dimer configuration [112, 120, 107].

The most remarkable aspect of the dispersion curves in Figure 5.13 is that the two modes $\lambda_l^+$ and $\lambda_l^-$ display the distinctive feature of the mode hybridization with an anti-crossing evolution. The green and red lines are plotted to guide the interaction between fundamental modes, which we denote as $\lambda_l^Q$ and $\lambda_l^G$. At $g = \tau = 6$nm, only mode $\lambda_l^Q$ displays a strong scattering resonance at around 680nm. We assign the mode $\lambda_l^Q$ to the longitudinal quadrupolar mode of the AuBP which is similar to the one that has been observed in the case of the AuBP placed on the TiO$_2$ film/ glass substrate (see Figure 5.8). On the other hand, the mode $\lambda_l^G$ just weakly appears as a shoulder of the $\lambda_l^Q$ on the blue side at the beginning. When the gap thickness is reduced, the resonance of $\lambda_l^G$ becomes prominent, which correlates
<figure><img src="image_61.png" /><figcaption>Figure 5.13: **Spectral evolution of the modes with the gap thickness.** Scattering spectra of the AuBP on gold film calculated for different gap thickness g. The evolution of the *l* resonances is guided by the black line. The interaction between the two fundamental mode $\lambda_l^Q$ and $\lambda_l^G$ is also illustrated in red and green lines.</figcaption></figure>

with the characteristic of the MIM gap plasmon mode. Variation of the gap thickness allows these two fundamental modes to approach spectrally, they interact and open a wavelength gap, forming the hybrid modes. As shown in Figure 5.13, the strongest interaction can be observed at around g = 3-4 nm. This is consistent with the results of the charge distribution of the hybrid $\lambda_l^+$ and $\lambda_l^-$ modes found previously at g = 4nm, where we can see at the facet that forms the MIM waveguide with the gold film, they share the same symmetry and the charges oscillate in the opposite phase (see Figure 5.12).

To further understand the symmetry rules that are responsible for the mode hybridization, we simulate the near-field distribution of the *l* modes. Figure 5.14 displays the simulation of the normalized total electric-field distribution $|E|^2/|E_0|^2$ (in the yz plane normal to the substrate) and its scattering field components along the z-axis Re($E_z$) and y-axis Re($E_y$),
<figure><img src="image_62.png" /><figcaption>Figure 5.14: Calculation of near-field distribution of the AuBP on the gold film. Normalized total field distribution $|E|^2/|E_0|^2$ and the component field $Re(E_z(y, z))$ and $Re(E_y(y, z))$ in the Oyz plane. The red and black rings highlight the field distribution in the middle of the gap.</figcaption></figure>

focusing on the three main resonances $\lambda_l^+$, $\lambda_l^-$, and $\lambda_l^D$. Generally, we see that these modes exhibit strong field localization at the tip-ends and within the flat gap; the maximum near-field intensity enhancement is found around $|E|^2/|E_0|^2 = 30$. On the other hand, the field enhancement in the space of the opening-mouth gap is negligible as compared to that in the flat gap due to the less confinement. In addition, it appears in all three modes that the resonant electric fields in the flat gap are mostly polarized along the transverse direction to the metal's surface. As can be seen in the simulation in Figure 5.14, the transverse field component $Re(E_z)$ is the predominant field in the gap, while the longitudinal field component $Re(E_y)$ is negligible. This confirms the MIM gap plasmon characteristic of the modes of the system [38, 121].

The field distribution of the whole system is complex, but if we paid attention only to the gap region at this stage, we once again can see the hybrid modes $\lambda_l^+$ and $\lambda_l^-$ possess similar near-field distributions that are concentric at the center of the flat gap (red rings). As opposed, the mode $\lambda_l^D$, which does not show the anti-crossing feature with the other
mode, is maximized at both ends and null in the middle (black rings).

Although the modes $\lambda_l^+$ and $\lambda_l^-$ are at the mixed state, here we can still see the signatures of their origins. The formation of the field distribution inside the gap of the mode $\lambda_l^+$ can be interpreted as the finite MIM gap plasmon like Fabry-Pérot resonance induced by the interaction between the flat metal surface at the bottom facet of the AuBP and the gold film. Due to the finite dimension of the MIM waveguide defined by the lateral facet of the AuBP, the transverse gap plasmon is bounced back and forth inside the gap due to the reflection at the gap terminal and displays stationary nodes [38, 111, 88, 121]. As shown in the field distribution of this mode, the electric field is localized in the core and largest at both ends, which resembles the character of the standing wave. On the other hand, the field inside the gap of the mode $\lambda_l^-$ is formed by the interaction of the particle with its mirror image in the gold film, similar to the situation in a plasmonic nanoparticle dimer [103, 112, 107]. As shown by the charge distribution (Figure 5.12), the mode $\lambda_l^-$ originates from the quadrupole, which is also concordant with Figure 5.13. Indeed, in this Figure we see that at g=4nm, the modes of these are not completely hybridized so that the quadrupolar mode $\lambda_l^Q$ is still dominant in the mode $\lambda_l^-$.

## 5.5 The complexity of the AuBP nanopatch antenna

In the previous discussion, we presented the most remarkable features of the AuBP nanopatch. However, due to the geometry of the bipyramid, the structure is in fact really complicated in terms of the plasmonic effects that contribute to the formation of the modes and subsequent difficulties in the interpretation of the results.

### A complex plasmon structure

Here, we see the structure in three aspects, respectively are:

* An *elongated plasmonic nanoparticle* that strongly supports the localized plasmon resonance along its longitudinal axis rather than the transverse one. In addition, the tip effect of the AuBP is also significant resulting in the strong field localization in the near-field around the tip ends.
* A MIM waveguide with finite lateral dimension: Tilting AuBP introduces a facet of the particle in contact with the surface. The dielectric space embedded between the particle's facet and the underlying gold film (i.e., a nanopatch) can now be seen as a MIM waveguide with a finite lateral dimension, which resembles a Fabry-Pérot cavity. As the result, the stationary wave of the transverse gap plasmon can be observed within the gap region.

* A dimer induced by the mirror effect: When the metallic nanoparticle is brought close to the gold film, the charge distribution on the particle induces image charges in the underlying conducting layer. This configuration can be thought of as a nanoparticle interacting with its mirror image that is equivalent to plasmonic nanoparticle dimers. As the result, the dipolar mode can be repelled to higher wavelengths and gives birth to new resonances of the higher-order modes in the lower region.

Because many effects involve the formation of the mode, it is not straightforward to identify the nature of the mode clearly. Usually, the nanopatch of more symmetric nanoparticles such as spheres and cubes [122, 110, 103, 53], where the modes of the structure can be clearly classified into two families: antenna mode and gap plasmon cavity mode, based on their most significant features, either strongly radiate or tightly confined field. However, in the case of the AuBP, both the gap plasmon, and especially the tip effect exhibit in all the modes, which are not predominantly by the other.

In terms of the hybridization of the modes $\lambda_l^+$ and $\lambda_l^-$, it is also perturbed by the effects mediated by the gold film. Roughly, for a perfect coupling system at the strongest interaction, the splitting of the hybrid modes possesses a mirror symmetry in terms of phase, spectral position, and intensity [123]. In addition, the spectral separation of the modes in the anti-crossing branches should be in the opposite direction, which is red-shifted for bonding mode and blue-shifted for anti-bonding one [123, 124]. However, the anti-crossing of the hybrid modes, as observed in Figure 5.13, presents an imbalance of intensities of the two resonances at the strongest hybridization $g = 3-4$nm. Moreover, the spectral evolutions of their fundamental modes are both pulled towards the red as the gap thickness decreases (green and red lines in Figure 5.13). Here, the very weak shift of the mode $\lambda_l^Q$ is caused by the
cancelation of the red shift due to the mirror effect and the blue shift induced by the mode
hybridization.

Geometry imposes the selection rule on the excitation

Because of the elongated shape and the tilting AuBP with one facet contacting with the
surface, the illumination is necessary to be in the normal direction, as we have done above,
in order to optimize the power introduced to the structure. This makes it difficult to inter-
pret the formation of the gap mode. Usually, the gap plasmon mode of the more symmetric
nanoparticle-on-mirror configuration (e.g., spheres or cubes) can be directly excited by the
plane wave in the high-angle illumination that induces more electric field components po-
larized perpendicular to the metal surface [110, 125]. On the other hand, in the case of the
AuBP nanopatch, the excitation of the gap plasmon mode is not directly from the plane
wave illumination but rather from multiple processes. First involves the longitudinal local-
ized plasmon of the AuBP is excited by the plane wave and then localized the field around its
lower tip will be responsible for excitation of the gap mode. This can be seen in the near-field
distribution in Figure 5.14, the near field around the lower tip that touches the surface is
more distributed inside the gap as the nodes in the gap increase.

**5.6 Conclusion**

In conclusion, we have studied the optical response of the AuBP on the high-index substrate and on the gold film. We first highlighted the important role of the orientation of the particle on the surface in terms of increasing the interaction strength of the particle and the substrate. Bringing an inclined AuBP in proximity to the gold film yields a rich optical response, where the modes have hybrid behavior of the localized surface plasmon of elongated particle, in an isolated structure and a liked-dimer, and gap plasmon in the finite MIM waveguide. Each possesses distinctive features such as strong dipolar and multipolar far-field radiation or strong field confinement. In addition, these resonances are tunable by varying the geometrical parameter of the system, which makes the structure can be very beneficial for sensing, photochemistry, and optoelectronics. However, there are still remaining questions,
for instance: a mechanism of the high index dielectric substrate induced the higher order
mode of the AuBP, a rigorous calculation of the reflectivity at the patch terminals, from
this the role of the opening-mouth gap in terms of enhancing radiation conversion can be
evaluated quantitatively.
# Chapter 6

## Optically launching of Surface Plasmon Polaritons by Bipyramid Nanopatch Antennas

Surface plasmon polaritons (SPPs) offer great potential for various present-day photonic applications, thanks to their ability to concentrate light in space and time. SPPs can be excited optically by a diffraction-limited beam [85, 34] or electrically using inelastic tunneling as a light source [126, 127, 128]. By any means of generating SPPs, the nanopatch antennas based on a metal-insulator-metal (MIM) structure have been shown their comprehensive capability to mediate SPP emission efficiently. Due to the ability to squeeze and tailor the light at the nanoscale, the nanopatch antennas provide degrees of freedom in the design of the structure that would allow us to properly engineer the properties of SPP emission, including the emission spectrum, polarization, and emission efficiency [78].

In this Chapter, we employ the light scattering from the bipyramid nanopatch antennas to excite SPPs propagating along a dielectric/gold interface. We firstly demonstrate the SPP emission launched by the antenna in the visible regime, which is possibly extended to the near-infrared wavelengths thanks to the rich optical-mode structure of the antennas. We also report the angular emission pattern of SPPs induced by the scattered light. Finally, we measure the SPP emission efficiency of the antenna and compare it with SiO2 nanobeads. The physical mechanisms involved in generating SPPs also will be discussed.
# Contents

<table><tr><td>6.1 SPP emission spectrum</td><td>134</td></tr><tr><td>6.2 Spatial and angular emission of SPPs</td><td>136</td></tr><tr><td>6.3 SPP emission efficiency</td><td>139</td></tr><tr><td>6.4 Role of nanopatch antenna in SPP emission</td><td>144</td></tr><tr><td>6.5 Conclusion</td><td>148</td></tr></table>

## 6.1 SPP emission spectrum

To fully profit from the rich optical response of bipyramid nanopatch antennas, we only pay attention to tip-touching-surface AuBPs (inclined AuBPs) deposited on 4nm-TiO₂/45nm-Au/glass substrate. We use the white lamp focused by 0.25-NA objective to excite the antenna in the air and measure the forward scattering on the glass side by the 1.49-NA objective in the dark-field configuration (see Chapter 3). Roughly, the collection consists of both the leakage in the substrate through the thin gold film of excited SPPs and the residual scattering, which does not excite SPPs. To accurately identify the SPP emission spectrum, it is necessary to disperse the scattered light spectrally and spatially. We first measure the scattering spectrum of an antenna, as shown in Figure 6.1a. As clarified in the previous chapter, the inclined AuBPs can produce a multiple-resonance spectrum ranging from 500 – 1200nm. Because of the higher noise for $λ > 1000$nm arising from the low detection efficiency of the spectrometer, here we concentrate on the resonances in the visible regime.

For the spatial distribution, we record a Fourier-plane image corresponding to the visible spectrum of the single antenna, as shown in Figure 6.1b. The leakage of SPPs appears in
<figure><img src="image_63.png" /><figcaption>Figure 6.1: **SPP emission spectrum.** (a) Dark-field scattering spectrum of inclined AuBP on 4nm-TiO₂/45nm-Au/glass substrate (inset). Here, only the visible regime is displayed. (b) Fourier-plane image of scattering in (a). (c) Dispersion relation of selected direction on the Fourier-plane (white lines in (b)). Dotted line is the calculated dispersion relation. In-plane wavevector: $k_{\|} = \sqrt{k_x^2 + k_y^2}$</figcaption></figure>

the Fourier-plane as a bright ring of radius just above $k_{\|} = k_0$ (where $k_0 = 2\pi/\lambda_0$ is the light wavevector in vacuum). The SPP ring is composed of surface plasmon propagating at different wavelengths associated with the scattered light of the antenna. To see the part of the scattering coupling to SPPs, we measure the dispersion relation between the in-plane wavevector ($k_{\|}$) and the wavelengths by making an image of one selected direction in the Fourier-plane (white bars) on the vertical entrance slit of the spectrometer. Figure 6.1c displays the collected image, from which the SPP emission appears as a bright trace above the light line of the vacuum ($k_{\|} = k_0$). The SPP dispersion closely follows the dispersion curve (dotted line) calculated for SPPs propagating on the similar multilayer substrate, except for
the regime below 600nm. Qualitatively, two main factors drive SPP emission here: resonant
scattering of the antenna and the intrinsic loss owing to the absorption of gold. Below $\lambda$ =
600nm, the influence of the interband transition of gold is dominant, resulting in the negligible
appearance of the SPP emission. As far from this regime, the scattering resonance weakly
suffers from this loss and generates SPPs as the bright trace on the dispersion image. Besides,
the most intense region in the SPP dispersion is at around $\lambda$ = 700nm, which is associated
with the second resonance on the scattering spectrum, suggesting the SPP emission by this
mode is driven mainly by the scattering resonance.

**6.2 Spatial and angular emission of SPPs**

We now present the spatial and angular emission of the surface plasmon excited by the
scattered light from the antenna, using a SuperK supercontinuum laser for excitation. The
supercontinuum laser can provide a beam-quality laser with a white-lamp spectra range of
400-980nm. Technically, the super-wide continuous spectrum is produced by sending intense
light pulses through a nonlinear medium. A slit is used to select the wavelength, making
a laser beam with the smallest spectra width of 10nm. For example, Figure 6.2 shows a
real-space image in the dark field and its corresponding Fourier-plane images of an antenna
excited by a 650nm± 5nm laser beam.

In the real-space image, we see an intensity maximum at the center enclosed by concentric
interference rings propagating away from the antenna. These rings are interpreted as the
interference of leakage radiation of SPPs propagating in opposite directions. In addition,
there are other rings with longer periodicity resulting from the diffraction-limited image of
residual scattering collected by the finite numerical aperture of the objective [129]. To access
the SPPs propagation, we plot the intensity along with a cross-section through the center of
the real-space image as a function of the distance to the antenna on the x-axis, as shown in
Figure 6.2b. Note that we used a linear polarizer oriented along the x-axis (white arrow) to
select surface plasmon propagation in this direction. An exponential decay profile is observed
with a propagation length estimated to be 1.5 ± 0.03µm, which is shorter by ~ 3µm than
what we predicted theoretically for the SPPs launching on the similar thin TiO₂ film over
<figure><img src="image_64.png" /><figcaption>Figure 6.2: **Spatial and angular emission of SPPs.** (a) Real-space image of the antenna measured by the dark-field imaging. (b) Cross-section profile along the x-axis of polarized real-space image (inset). The black dots are the experimental data, the red line is exponential decay fit. (c) Fourier-plane images of (a), from left to right: unpolarize, linear polarize along y-axis, linear polarizer along x-axis. BS: Beam Stop. (d) Intensity of SPPs extracted from the image (c) (no polarize) as a function of the angle $\varphi$. The measured data is fitted to dipolar model (i.e., considering the AuBP as a dipole placed near the substrate.)</figcaption></figure>
the gold film. We attribute this difference to the film’s surface roughness, which is highly dependent on the deposition procedure [130]. In our experiment, the surface roughness is ~30% of the TiO₂ film thickness deposited by the ALD.

The angular radiation pattern of the leakage SPPs can be observed in the Fourier-plane image with the overwhelming excitation omitted by the beam stop (BS). As shown in Figure 6.2c, SPPs emerge as a circular pattern with a bright and narrow ring whose radius corresponds to the wavevector of 1.07k₀, a signature of SPPs propagating along an air/4nm-TiO₂/gold interface.

To analyze the spatial polarization distribution of the scattering, we place a linear polarizer along the x-axis and y-axis behind the objective’s back focal plane. Figure 6.2c shows the Fourier-plane images for two orientations of the polarizer. We can see that the field along the polarizer orientation is transmitted, whereas the field along the orthogonal direction is filtered out. In other words, the photons in the ring are almost polarized radially with respect to the origin formed by the position of the antenna (p polarization), which shows the characteristic of the leakage radiation of SPPs.

In terms of the directionality, we can see a non-uniform intensity distribution in the circular ring of the Fourier-plane image. In Figure 6.2d we plot the maximum intensities of the SPPs $I_{SPP}^{max}$ (extracted from the bright ring in Figure 6.2c) as a function of the polar coordinate $\varphi$ corresponding to the direction of SPP’s propagation. The AuBP is modelled as a linear dipole, which is place near the substrate with its 3D orientations ($\Theta, \Phi$) as a adjustable parameter. We see that the measured $I_{SPP}^{max}(\varphi)$ follows very well the cosine square function of the dipolar simulation. The best fit is given at an out-of-plane orientation $\Theta \approx 70^\circ$, corresponding to the AuBP is tiltled by around 20° on the surface (the dipolar axis is along the longitudinal axis of the AuBP). Interestingly, this orientation is in a good agreement with the values estimated from the geometrical dimensions of the AuBP ~ 75 ± 5° (see Figure 4.7c), suggesting that the directivity of launching SPPs is mostly controlled by the dipolar character of the AuBP. Besides, we also observe that the SPPs mainly propagate in the direction along the longitudinal axis of the bipyramid (i.e., $I_{SPP}^{max}(\phi)$ peaks at $\Phi \sim 0^{\circ}$; $180^{\circ}$). Thanks to the SuperK supercontinuum laser, we also can measure the angular emission of SPPs of other resonance; however, it is complicated to go into detail of interpretation.
## 6.3 SPP emission efficiency

An important figure of merit of a source for launching surface plasmon is the SPP emission efficiency, which depends on both the system that is used to excite SPPs (e.g., prism, grating, local scatters) and the collection efficiency of the experiment. In the case of the bipyramid nanopatch antenna, the structure plays a role in harvesting the power from the light source and delivering it to the surface plasmon. This involves multiple processes that will be discussed later. Here, we first present how we measure the SPP emission efficiency using leakage radiation microscopy.

Briefly, the excited SPPs and the transmission of the excitation can be extracted spatially in the Fourier-plane image of the leakage radiation microscope. This method has been employed in previous studies to characterize the SPP coupling efficiency of the local sub-wavelength scatterers. For instance, A. Baudrion et al., [32] have used a single hold of variable size ~ 100-500nm milled in a gold film to generate SPPs. The SPP emission efficiency is defined as a ratio of the total leakage power of the SPPs and the incident power of the laser, taking into account only the part that arrive on the hole area. However, some ambiguities, e.g., the transmission of the SPPs through the gold film or the total power that the hole received from the excitation beam, have remained. Similar work has been studied by T. Ebbesen et al., [31], in which the SPPs are generated by a sub-wavelength slit. The work was more rigorous in the quantification of the leakage SPPs on the Fourier plane by introducing the leakage transmission factor for the SPPs. In our work, we combine the advantages of both presented work to measure SPP emission efficiency of the AuBP nanopatch antenna.

Following the previous works [32, 131, 84], we also define the antenna efficiency to generate SPPs as the ratio of the excited SPP power $P_{SPP}$ to the incident power $P_0$:

$$E_{SPP} = \frac{P_{SPP}}{P_0} \qquad (6.1)$$

Here, $P_0 = P_{beam} \frac{A_{BP}}{A_{beam}}$ is the partial power of the laser beam $P_{beam}$, taking into account only the part that impinges onto the surface over the geometrical cross-section area of the bipyramid (see Figure 6.3). Here, the size of laser beam $A_{beam}$ is measured directly in the
image for each wavelength (e.g. $\lambda = 650$nm, diameter ~ 3.3µm) that is also approximately to the Airy function with diameter of $d \approx 1.22 \frac{\lambda}{NA}$. The $A_{BP} = L/2 \cdot W/2$ is the geometrical cross-section area of the AuBP, with L = 70nm and W = 25 nm are average sizes of AuBPs obtained for TEM measurement (see Chapter 4).

<figure><img src="image_65.png" /><figcaption>Figure 6.3: Measuring the SPP emission efficiency by leakage radiation microscope. Schematic illustration of a focused laser beam excite the nanopatch to generate the SPPs. The red circle beam represents the beam spot ($A_{beam} \sim \lambda^2$), $A_{BP}$ is the geometrical area of the AuBP. The experiment allows to measure (a) the leakage power of the SPPs $P_{SPP}$ and (b) the transmitted power of laser $P_T$.</figcaption></figure>

## Powers measured from leakage radiation experiments

Since the gold slab has a finite thickness, the surface plasmon propagating away from the antenna in the air is a leaky wave that radiates energy into the higher-index side of the glass substrate. Suppose we neglect the scattering loss into the air due to the surface roughness. In that case, the total excited SPP power $P_{SPP}$ can be deduced from the leakage surface plasmon $P_{LK}$ (i.e., the quantity that we can measure) taking into account the leakage transmission factor $\tau_{LK}$ [31, 35] and is given by:

$$P_{SPP} = \frac{P_{LK}}{\tau_{LK}} \qquad (6.2)$$

The leakage transmission of the surface plasmon through a finite gold layer is calculated as $\tau_{LK} = e^{-2|k_z|d_{Au}}$ with $d_{Au} = 45$nm as the thickness of the gold slab and $k_z =$
<table><caption>Table 6.1: Parameters need for calculation of SPP coupling efficiency. Values of transmission are calculated the multilayer substrate of air ($ε_{air}=1$)/4nm-TiO$_2$ ($ε_{TiO2}=2.4$)/45nm-Au ($ε_{Au}$)/glass ($ε_{glass}=1.5$).</caption><thead><tr><th>λ(nm)</th><th>ε<sub>Au</sub></th><th>T</th><th>k<sub>spp</sub>/k<sub>0</sub></th><th>Δk<sub>spp</sub>/k<sub>0</sub></th><th>τ<sub>LK</sub></th><th>A<sub>beam</sub>/A<sub>AuBP</sub></th></tr></thead><tbody><tr><td>600</td><td>-9.38+1.39i</td><td>14%</td><td>1.1</td><td>0.10</td><td>6.5%</td><td>100</td></tr><tr><td>650</td><td>-12.90+1.04i</td><td>9.7%</td><td>1.072</td><td>0.03</td><td>5.5%</td><td>120</td></tr><tr><td>700</td><td>16.54+1.00i</td><td>7.0%</td><td>1.056</td><td>0.02</td><td>4.9%</td><td>140</td></tr><tr><td>750</td><td>-20.36+1.17i</td><td>5.3%</td><td>1.044</td><td>0.02</td><td>4.5%</td><td>160</td></tr></tbody></table>

$\sqrt{k_{spp}^2 - ε_{Au}(2π/λ_0)^2}$ is the wavevector of the SPPs in the normal direction to the surface. The SPP wavevector $k_{spp}$ for each wavelength is deduced from the angular distribution of SPP emission in the Fourier-plane image (see below). The dielectric function $ε_{Au}$ of gold is taken from the data obtained by Johnson and Christy [11].

Similarly, the incident power $P_0$ is measured from the transmitted power $P_T$ of the laser through the substrate, illuminating at the position without the presence of antenna as $P_0 = \frac{P_T}{T} \cdot \frac{A_{beam}}{A_{BP}}$. Here, T is the direct transmission of the laser at the normal incident through the multilayer substrate (see Figure 6.3b), which is calculated from the matrix transfer formalism [48].

Finally, we can display the SPP coupling efficiency of the antenna as a function of the parameters that we can measure from the experiment as

$$E_{SPP} = \frac{P_{LK}}{P_T} \cdot \frac{T}{\tau_{LK}} \cdot \frac{A_{beam}}{A_{BP}} \qquad (6.3)$$

In which, the leakage and transmitted powers $P_{LK}$ and $P_T$ are extracted from Fourier-plane images, while the other parameters are measured at four different wavelengths and displayed in Table 6.1.

The parameters needed for calculation of SPP coupling efficiency at four different wavelengths are displayed in Table 6.1.

## Measuring $P_{LK}$ and $P_T$

To remove the artifact of the attenuation due to the optical elements, both transmitted powers are measured by integrating all the corresponding signals from the images recorded at the same laser input power related to the surface area of the particle ($P_0$). When the antenna
<figure><img src="image_66.png" /><figcaption>Figure 6.4: **Measuring SPP emission efficiency.** (a) Schematic of the measurement. $P_0$: in-put power of laser over the geometrical cross-section area of bipyramid. $P_{spp}$: power excited SPPs. $P_T$: transmitted power of $P_0$ through substrate in the absence of the antenna. $P_{LK}$: leakage power of SPPs. (b) Fourier-plane image of laser’s transmission (1). (c) Fourier-plane image of antenna’s scattering (2). White ring is the region of the beam stop. Red rings enclosed the region of SPPs. (d) Intensity profile of a line cut on the scattering pattern (white line) as a function of $k_x/k_0$. Black line is the experimental curve, red line is the Lorentzian fit.</figcaption></figure>
is excited, the leakage SPPs can be extracted from the dark-field scattering pattern in the Fourier-plane image (see (1) in Figure 6.4a). On the other hand, the laser's transmission is also measured on the Fourier plane. Still, the excitation is in the absence of the bipyramids, taking only the transmission due to the multilayer substrate (see (2) in Figure 6.4a. In Figure 6.4b, the laser transmission is observed as a disk with a radius ~ 0.25 k₀ associated with the numerical aperture of the excitation objective. The power P_T can be determined by integrating all the signals from this Fourier-plane image.

Figure 6.4c shows the scattering pattern of the antenna in the Fourier-plane image, which can be interpreted as a superposition of the leakage SPPs on the scattered light background of the antenna (i.e., residual scattering that does not excite SPPs). To quantify the leakage SPPs, we integrate the Fourier plane between ($k_{spp} - \Delta k_{spp}$) and ($k_{spp} + \Delta k_{spp}$), which is enclosed by red rings in Figure 6.4c. The SPP wavevector $k_{spp}$ and the width $\Delta k_{spp}$ are given from the Lorentzian fit of an intensity profile of a radial cross-cut along the $k_x$-axis as shown in Figure 6.4d. The contribution of surface plasmon is defined approximately by an area under the Lorentzian curve, whereas the area that does not fit within the Lorentzian function is attributed to the residual scattering. Here, the leakage SPPs account for around 60% of the total detected emission (all the signals in Figure 6.4c) and 10% of the transmission of the laser ($P_{spp}/P_T = 10\%$). Taking into account the transmission factors ($T$ and $\tau_{LK}$) at $\lambda = 650$nm, we obtain an SPP coupling efficiency $E_{SPP} = 20$. We repeat the measurement of the SPP coupling efficiency at three other wavelengths (600nm, 700nm, and 750nm) displayed in Figure 6.5(focusing on the second resonance at around 700nm).

In Figure 6.5, we correlate the measured SPP emission efficiency to the scattering spectrum, focusing on the second resonance at around 700nm. We see that the efficiency is also resonantly enhanced following the plasmon resonance of the considered mode. The efficiency at center resonance wavelength (700nm) is larger by ~ 4 times as compared to those at off-resonances. However, the measured values of $E_{SPP}$ here all far more exceeds unity, implying that more light than is incident upon the geometrical cross-section of the bipyramid is converted into SPPs. This will be discussed in more detail in the following section.
<figure><img src="image_67.png" /><figcaption>Figure 6.5: The SPP emission efficiency of the AuBP nanopatch measured. The efficiency is measured at four wavelengths and correlated to the scattering spectrum.</figcaption></figure>

## 6.4 Role of nanopatch antenna in SPP emission

An optical antenna, as the name implied its analogy to the microwave and radio wave antennas, is an optical element that converts localized energy into propagating radiation, and vice versa. Discussing the SPP generation, the nanopatch antenna plays both roles as a receiver (i.e., a resonator that harvests the light from the free space and confines in its body) and a transducer (i.e., a strong scatterer) [1]. Based on this concept, we define the SPP emission efficiency of the nanopatch antenna as

$$E_{SPP} = \frac{P_{SPP}}{P_0} = \eta_{ext} \cdot \beta_{SPP} \qquad (6.4)$$

which is composed of the extinction efficiency ($\eta_{ext}$), which defines the total power of the excitation that is delivered by the antenna, and the SPP conversion efficiency ($\beta_{SPP}$) that determines the proportion of the receiving power indeed excites SPPs. Figure 6.6 illustrates these two steps and details will be discussed in the following.

### Total power delivered by the antenna

As the total power that the antenna carried away from the excitation light is either
<figure><img src="image_68.png" /><figcaption>Figure 6.6: The SPP generation by the AuBP nanopatch antenna. The total power that antenna received from the excitation is defined by the extinction efficiency $\eta_{ext}$, which is later converted into SPPs, given by the conversion efficiency $\beta_{SPP}$.</figcaption></figure>

scattered or absorbed and dissipated, we attribute the “lost” power to the extinction cross-section. We thus define the extinction efficiency as the fraction of the power that is received in the cases of with ($P_{total}$) and without antenna ($P_0$):

$$ \eta_{SPP} = \frac{P_{total}}{P_0} = \frac{\sigma_{ext}}{A_{BP}} \qquad (6.5) $$

where $\sigma_{ext}$ is the extinction cross-section of the antenna and $A_{BP}$ is the geometrical cross-section area of the bipyramid. We have known that at the resonance condition of the plasmonic structure, the $\sigma_{ext}$ is resonantly enhanced, and thus the total power that the antenna receives $P_{total}$ can be far more exceed the power incident the AuBP area $P_0$. This explains why the measured SPP emission efficiency in Figure 6.5 can be larger than 1. The over-unity efficiency was also predicted for SPPs launching by scattering from a rectangular metallic hole etched in a metal substrate [131]. The author showed that an SPPs generation efficiency of 5 can be achieved at an optimal hole depth.

To support the above statements, we seek a comparison to SPPs launched by a dielectric nanobead of SiO₂ (diameter ~ 120nm, $\epsilon_{SiO2}$ = 2.25). In a homogeneous medium, the elastic scattering is fully responsible for the optical response of the “lossless” SiO2 bead to the visible illumination [55]. For the particle near the gold film, it is affected by the field components reflected from the surface resulting in an additional absorption cross-section in the extinction cross-section. When the nanobead is illuminated, its near-field scattering can excite SPPs
<figure><img src="image_69.png" /><figcaption>Figure 6.7: Enhancing SPP emission efficiency due to extinction efficiency. (a) Extinction cross-sections are calculated for a SiO₂ nanobead on 45nm-gold/glass substrate as compared to the AuBP nanopatch. (b) Associated SPP emission efficiency is measured at the same experimental conditions.</figcaption></figure>

on the gold film.

Figure 6.7 shows the calculation of the extinction cross-section of the SiO₂ bead deposited on 45nm-gold film/glass substrate in response to the plane wave excitation. The presence of the gold film near the bead yields to the rising of the extinction cross-section below 600nm, which is mainly contributed by the absorption cross-section (not shown here for clarity). We can see that at the resonance wavelengths above 600nm, the extinction cross-section of the nanopatch is significantly larger than that of the SiO₂ bead by around 1 order of magnitude. This means that at the resonance, the total power delivered by the nanopatch is ~10 times larger than the power harvested by the nanobead (Figure 6.7a). Taking into account the geometrical cross-sectional areas, we can deduce the fraction of the extinction efficiency of the two structures is $\eta_{ext}^{BP}/\eta_{ext}^{SiO2} \approx 60$, indicating the important role of plasmon modes supported by the antenna in the SPP emission in term of harvesting light and also SPP generation.

Subsequently, we measure the SPP emission efficiency of the bead, as shown in Figure 6.7, keeping the same experimental conditions as for the nanopatch. We can see that all the measured efficiency of the patch is larger than those measured for the bead, which is the most significant at the resonance $\lambda = 700$nm: $E_{SPP}^{BP}/E_{SPP}^{SiO2} \approx 7$. As mentioned above, to arrive at
the final value of the SPP emission efficiency, both extinction efficiency $\eta_{ext}$ and conversion efficiency $\beta_{SPP}$ are necessarily quantified. Unfortunately, it still requires further work for us to determine the conversion efficiency of the system (details below). However, by connecting both figures we can see the important contribution of the nanopatch antenna as a resonator in converting light into SPP emission.

## Conversion of the total power delivered by the antenna into SPPs

The next step is to ensure that a significant part of the total power received by the antenna indeed excites SPPs, which can be defined by the SPP conversion efficiency as

$$ \beta_{SPP} = \frac{P_{SPP}}{P_{total}} \qquad (6.6) $$

Roughly, this conversion efficiency closely depends on the nature of the optical modes that are excited, including the modal local density of state (LDOS) and the modal absorption. The total power $P_{total}$ of the nanopatch can be funneled into the optical modes (e.g., $\lambda_l^{(1,2,Q)}$) or dissipated in the losses of the metal, Chapter 5). Therefore, the mode of large LDOS has more advantages in receiving the total power. As shown at the beginning of Chapter 5, the gap plasmon mode can provide a significant LDOS tight field confinement inside MIM nanogap, which largely overcomes the quenching even for very thin gap thickness when the structure is excited by an emitter (see Figure 5.1). However, the strong confinement of the gap plasmon comes with the price of low modal conversion to the free-space radiation owning its large modal absorption. The resonant hotspots in the gap are typically reflected back inside the gap or emitted into high angles because of their large in-plane $k_{\parallel}$.

It is worth insisting that this modal absorption is different from the losses of the metal mentioned above, which are higher-order modes outside the spectra ranges of interest or heating the metal. If the structure is excited by an emitter, the modal absorption can be thought of as a nonradiative channel, while the losses are the quenching of the emitter. However, unlike quenching which is intrinsically determined by the proximity to the metal, the absorption depends on the nanoantenna design [122, 110, 105]. For example, a low absorption is favored by the antenna with curve edges (e.g., sphere or tie-bow) that implement
small reflectivity at the facet edges [104, 1]. Another strategy is to optimize the geometrical parameters of the nanopatch antenna in order to couple the tightly confined gap plasmon mode to the antenna mode of strong radiating [105, 132]. The resulting hybrid modes will possess both the large LDOS and the high modal SPP conversion efficiency.

In the case of the AuBP nanopatch antenna, the structure can be a promising class of
nanogap antenna with the facet edge's reflectivity gradually decreasing in the opening mouth.
From this, an efficient SPP emission can be achieved through balancing between the large
LDOS and the low modal absorption. However, in order to address the SPP conversion
efficiency $\beta_{SPP}$ of the nanopatch and also of the modes, further works, using for example a
rigorous modal formalism [110, 119], are required to separate the contribution of each mode.
In turn, it is useful to show a simple and intuitive picture, as presented here, to understand
the role of the nanopatch antenna in the SPP emission process. Although without accessing
to the conversion efficiency $\beta_{SPP}$ of the nanopatch, based on the resonant evolution of the
SPP emission efficiency $E_{SPP}$ (Figure 6.5), which strictly follows the scattering resonance,
we can anticipate that the $\beta_{SPP}$ might be independent of the wavelengths in this resonance.

**6.5 Conclusion**

In summary, we have shown that the SPP emission in the AuBP nanopatch antenna can be generated in a wide range of spectra with achievable directionality. Here, the nanopatch antenna plays both roles as a receiver that harvests the light in the far field into its plasmonic modes, and a scatter that can excite SPPs. We have demonstrated that the SPP emission efficiency can be resonantly enhanced by the nanopatch by around 1 order of magnitude as compared to the dielectric local scatters. This enhancement is contributed by both extinction efficiency $\eta_{ext}$ and the conversion efficiency $\beta_{SPP}$. Here, the extinction efficiency is estimated through the calculation of the extinction cross-section. However, the SPP conversion efficiency $\beta_{SPP}$ of the total system and the specific mode still remains unknown. In the perspective, an emitter or a dipole can be placed inside the structure as a probe to extract $\beta_{SPP}$ efficiency.
Conclusion and Perspectives

In this Thesis, we have investigated analytically the dipole coupling in the weak regime to different planar plasmonic structures, from a single interface, and a three-layer device to multilayer structures. By using dipole as a probe, figures of merit of the plasmonic structure have been identified, including spatial distribution and profile of the modes, propagation length of the delocalized surface plasmon, and coupling efficiency to the modes. This provided part of the necessary groundwork for understanding the plasmonic properties in more complicated structures. In addition, the configuration studied here may be interesting for multimode integrated devices such as single photons on a chip, quantum entanglement, or optical communications.

The main task of this Thesis was to investigate the optical properties of the gold bipyramid
nanopatch antennas in a nanoparticle-on-mirror configuration. We have demonstrated that
the orientation of the AuBPs on the substrate plays a crucial role in yielding the interactions
of the particle and the underneath gold film. Only when the AuBP is tilted with one facet
contacting the surface, the nanopatch can be formed, from which a rich optical mode structure
is produced. We identified experimentally and theoretically the set of plasmonic modes
supported by the structure, which possesses both radiating characteristics and strong field
confinement. Especially, we have shown there is a hybridization between the modes that
share similar symmetry of the charges (and field) distribution inside the finite MIM gap.
We assign this as the interaction between the quadrupolar mode and the gap plasmon liked
Fabry-Pérot cavity mode. Moreover, the complexity of the structure induced by the geometry
of the AuBP, as compared to the other nanopatch antennas of more symmetric geometry, has
been discussed thoroughly. In the last chapter, we have employed the nanopatch as a source
for launching surface plasmon on the gold film surrounding the structure, which has proven
to control the properties of SPPs emission, including the emission spectrum, polarization, and emission efficiency. The understanding of the properties of such a complex structure that has been explored in this Thesis set the important groundwork for coupling the AuBP nanopatch antenna to the other systems (i.e., emitters or other metallic nanoparticles) in further work.

## Perspectives

### Stabilization of the AuBP by silanization

In this Thesis, the substrate's surface is cleaned basically by a nitrogen pump and the AuBPs are deposited randomly on the surface without surface treatment or control. In the following work, we want to improve the quality of the surface of the substrate and make the particles more stable on the substrate. This can be done by silanization -a technique for immobilizing nanoparticles on a substrate, which has been used previously to graft the AuBPs on the glass substrate [68]. In addition to attaching the objects to the surface, the silanes also stabilize the morphology of anisotropic gold nanoparticles. Fortunately, the silanization process tends to make the AuBPs oriented in a good direction (i.e., one facet of the particle contacts the underlying surface). An overview of the silanization protocol can be seen in Figure C1.

<figure><img src="image_70.png" /><figcaption>Figure C1: Schematic illustrates the silanization protocol to graft bipyramid on the substrate. Source [5]</figcaption></figure>
## Correlation between the orientation and the spectral shift

As shown in Chapters 3 and 4, the orientation of the AuBP on the substrate, especially high index substrate, can induce the spectral shift of the longitudinal dipolar localized surface plasmon resonances. In further work, we want to make a correlation between these two parameters and compare the results to the orientations measured by the polarization analysis. This can be particularly useful for biosensing applications.

## Coupling to emitters

Owning the hybrid plasmon properties, both radiative nature and tightly field confinement, coupling to emitters is the most potential application of the nanopatch antennas. In our work, we expect to couple the AuBP nanopatch to fluorescent molecules or quantum dots. As we can see in the near field distribution of the plasmon modes, we have many positions to place a single emitter in close proximity to the structure, where the choice depends on the properties that we want to enhance. For example, a large spontaneous decay rate enhancement can be achieved when the emitter is buried in the gap or placed near the lower tip. In addition, the directionality and the emission spectra of the emitters are also possibly controlled by coupling to the plasmonic modes of the structure.

## Energy transfer over the surface

<figure><img src="image_71.png" /><figcaption>Figure C2: Interference of SPPs generated by two AuBPs deposited in the proximity on the 4nm-TIO₂/gold film.</figcaption></figure>

Another exciting perspective is to employ the ability of SPP generation of the AuBP
nanopatch to induce the interaction between the particles on the surface. Figure C2 shows
an image of the interference of SPPs produced by two bipyramid particles on the nanopatch
substrate. Here, although the two bipyramid nanoparticle are separated at a micrometer
distance, they still can “talk” to each other thanks to the coherent and long propagation of
the SPPs.
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