## Nanoantennas Thesis Statements

Let us now consider a configuration where the *DA* is used as optical nano-tweezers. It is supposed to be illuminated by a linearly polarized plane wave impinging from a glass substrate on which it is deposited. As commonly used, the superstrate medium, which contains the particles to be trapped, must be a liquid (for instance water with *n* = 1.315) in order to compensate their weight by the Archimedes’ buoyancy. First, we calculated the near-field electric and magnetic enhancement factors as in Fig. 2 measured at 5 nm above the *DA* center. Results are plotted in Fig. 5 and show that the resonance properties (both resonance wavelength and enhancement factors) of the *DA* are affected by the presence of the substrate. This phenomenon was already pointed out for another kind of nano-antennas, such as a bowtie nano-antenna^{11} or the bowtie nano-aperture antenna (*BNA*) for which the resonance properties were examined as a function of the antenna-to-substrate distance^{24,25}. In the latter cases, a shift as large as Δ*λ* = 500 *nm* of the resonance wavelength of a *BNA* occurs when the latter moves up over 10 *nm* from the substrate interface. In the present case, the shift is smaller (only Δ*λ* = 70 *nm*) due to the small contrast of the optical index between the substrate (*n* = 1.49) and the superstrate (*n* = 1.315) compared to the case of InP (*n* = 3.17) and air (*n* = 1) considered in the study of ref.^{25}. Nevertheless, we should take into account this shift especially if we aim to operate at a given value of the wavelength.

At first glance and compared to the enhancement of the electric field generated at the vicinity of a *BNA*^{13}, the *DA* seems to be more efficient to act as a nano-tweezers. Unfortunately, there is a major discrepancy between the two nano-antennas: contrarily to the *BNA* where the optical force is due to the light passing through it, a predominant part of the force generated on a *NP* placed in front of the *DA* consists on a radiation pressure. This is particulary valid when the *NP* is far from the nano-antenna and/or when it exhibits a large radius. Thus, stable and efficient trapping is only expected for small *DA*-to-*NP* distances and small *NP*s. Nevertheless, the effect of this background illumination may lead, according to the *NP* dimension, to a trapping position without contact (compensation of the radiation pressure by the gradient force). To investigate all these assumptions, we have made extensive simulations to quantify the force exerted on dielectric *NP*s. We present here three different studies where only the *NP* position along the vertical axis passing by the *DA* center (perpendicular to the substrate plane) is considered. The calculated vertical force *F*_{z} (the only non zero component of the force) is normalized by the total energy impinging the *DA*. In all simulations, the dielectric permittivity of the *NP* is modeled with a subgriding technique in order to accurately describe its spherical geometry.

In the first study, the radius of the *NP* is fixed while its position varies together with the illumination wavelength. In the second study, the distance *S* is fixed and the two other parameters vary (*R* and *λ*). Last study is done when fixing the wavelength and varying *R* and *S*. The corresponding results are shown on Figs 6, 7 and 9 respectively. For each study, attractive and repulsive zones are indicated on the corresponding figure together with the colored separation line (*F*_{z} = 0) that corresponds to the optical trapping of the *NP*. According to the coordinate system in Fig. 1, a negative value of *F*_{z} corresponds to an attractive force while positive one leads to push the *NP* away from the *DA*.

In Fig. 6a, we recall the geometric parameters of the studied configuration and we depict the 11 force spectra for values of the *NP* radius varying from *R* = 30 nm to *R* = 80 nm by 5 nm step. The solid line on all the sub-figures corresponds to *F*_{z} = 0 i.e. a possible trapping position far from the *DA* (trapping at distance). For *R* = 30; 35; 75 and 80 nm (see Fig. 6b,c,k,l) attractive force occurs at small distances *S* < 140 nm and at wavelength values ranging from *λ* = *λ*_{res} = 1528 nm to *λ* = 1800 nm. One notes that when trapping occurs, it corresponds necessarily to a contact between the *DA* and the *NP*. The white solid lines correspond then to an unstable trapping characterized by a maximum of the potential instead of a minimum (potential well).

Nevertheless, for radius value from *R* = 40 nm to 70 nm, the attractive zone becomes limited to smaller wavelength values than *λ*_{res} = 1528 nm. In fact, as shown on Fig. 6d, *F*_{z} vanishes in the vicinity of the resonance. This is probably due to the fact that the radiation pressure becomes larger while the gradient force is almost kept the same. According to the insets of the Fig. 2b,c, the force is mainly due to the the magnetic field confinement that occurs at the *DA* center. We have verified that the contribution of the magnetic field to the force is generally of the order of magnitude of the electric field one. Nevertheless, these two contributions have an opposite sign and thus can compensate each other. For (see Fig. 6e–j), a very interesting phenomenon appears where the attractive zone is preceded by a repulsive one when *S* increases. This corresponds to a stable trapping without contact between *NA* and *NP* as depicted by the blue lines in Fig. 6g,h.

We have verified that this trapping at distance is only obtained for *NP*s with . Nonetheless, the wavelength intervals, where this regime occurs, vary with the radius value as it will be shown in the following. When the *NP* radius increases (see Fig. 6k,l), the attractive zone shifts toward larger values of the wavelength due to the efficient overlap between the *NP* and the electric field of the *DA* generated at its corners. By the way, another value of *R* exists for which the vertical force vanishes at resonance (here *R* = 75 nm as seen on Fig. 6k).

In Fig. 7, four values of the *DA*-to-*NP* distance are considered: *S* = 15; 55; 95 and 155 nm. For *S* = 15 nm, Fig. 7a shows that attractive force occurs at small distance *S* for all *NP* radius and small values of the wavelength (). The attractive and repulsive zones are separated by white lines. The dashed blue line on the figure corresponds to the *DA* resonance wavelength. Along this line, when we increase the distance *S* from 55 nm to 95 nm, the attractive zone becomes smaller and it is globally blue-shifted as shown on Fig. 7b,c. The maximum of the repulsive force always appears nearby the resonance wavelength due to the funnel effect (see Fig. 3c) induced by the *DA* leading to increase the radiation pressure on the *NP*. For larger distance values *S* (>155 nm), the attractive zone almost vanishes in the considered wavelength range and the *NP* is pushed away from the *DA* as shown in Fig. 7d. This phenomena, as expected, occurs as a result of the background illumination that becomes predominant when the *NP* is far from the *DA*.

To get more physical insight on the *DA*-*NP* interaction at the resonance wavelength, we plot on Fig. 8 a cross-section made on the result of Fig. 7a at *λ*_{res} (vertical dashed blue line). This plot gives the optical force exerted on the *NP* as a function of its radius (*R*) when it is placed in front of a resonant *DA* (*λ* = *λ*_{res} = 1528 nm) and at a fixed distance *S* = 15 nm. This allows direct determination of the *NP* radii (here two values) for which trapping occurs (zero vertical force) at this specific distance. The first value (see red vertical arrow on Fig. 8) is *R* = 40 nm and it almost corresponds to quarter of the *DA* length. For this *NP* dimension, only the field confinement that occurs at the *DA* center is felt by the *NP* and seems to compensate the radiation pressure exerted on the *NP* parts that are out of the *DA* shadow. The second value (see the blue vertical arrow on Fig. 8) is *R* = 70 nm corresponding to a *NP* size that is almost equal to the *DA* one (*D* = 135 nm). In this case, the trapping is obtained thanks to the effect of the electric field confinement at the *DA* corner that acts together with the field confinement at the *DA* center to compensate the radiation pressure growth.

Experimentally, it is more adequate to operate at a fixed wavelength value. Figure 9 shows the variations of the vertical force for three different values of the wavelength when both *R* and *S* vary. Figure 9a corresponds to a wavelength smaller than the resonance one. In this case, a stable trapping at distance (white solid line) may occur for providing initial *DA*-to-*NP* distance smaller than 100 nm. This can be obtained by increasing the concentration of *NP*s in the liquid. The black line corresponds to an unstable trapping as mentioned above. At the resonance wavelength, the repulsive zone spreads over almost the total window and two small attractive areas remain for *R* > 70 nm and *R* < 40 nm only if *S* < 90 nm. At this peculiar wavelength, only trapping with contact may occur and *NP*s such are never trapped as seen on Fig. 9b. This configuration can be exploited to make a *NP* sorting with respect to their dimensions. For larger wavelength value (here *λ* = 1800 *nm*), only repulsive zone exists due to the absence of any light confinement. The radiation pressure is then predominant and only pushing force acts on the *NP* as shown in Fig. 9c.

In order to point out how to manipulate *NP* within a *DA*, we extract three different scenarios that correspond to pushing, trapping at distance or trapping at contact that can exist for a given *NP* (fixed *R* value) only by changing the operation wavelength. We only consider four values of the *NP* radius (*R* = 50; 55; 60 and 65 nm) for which trapping at distance can occur. As shown in Fig. 10 where the potential is plotted as a function of *S*, one can always find a wavelength value that corresponds to one of the three scenarios. In all cases, the trapping at distance exhibits a potential well larger than 10 *kT* providing an illumination power larger than 5 *mw*. In all figures, the red curves represent the trapping without contact regime where a potential well exists for *S* ≠ 0 while green curves correspond to the case of trapping with contact where the potential well occurs for S < 15 nm. Due to the symmetry of the configuration, there is no lateral components of the force and only the vertical one is non zero along the *z*-axis. On the contrary, the blue curves correspond to wavelength values for which the *NP* is pushed away from the *DA* (no trapping). Finally, a sorting process can be envisaged at this wavelength value where all *NP*s with are pushed away from the *DA* and other *NP* radii (<150 nm) are trapped.

Plasmonic nanoantennas that a support localized surface plasmon resonance (LSPR) are capable of confining visible light to subwavelength dimensions due to strong electromagnetic field enhancement at the probe tip. Nanoantenna enable optical methods such as tip-enhanced Raman spectroscopy (TERS), a technique that uses scanning probe microscopy tips to provide chemical information with nanoscale spatial resolution and single-molecule sensitivities. The LSPR supported by the probe tip is extremely sensitive to the nanoscale morphology of the nanoantenna. Control of nanoscale morphology is notoriously difficult to achieve, resulting in TERS probes with poor reproducibility. In my thesis, I demonstrate high-performance, predictable, and broadband nanospectroscopy probes that are fabricated by self-assembly. Shaped metal nanoparticles are organized into dense layers and deposited onto scanning probe tips. When coupled to a metal substrate, these probes support a strong optical resonance in the gap between the substrate and the probe, producing dramatic field enhancements. I show through experiment and electromagnetic modeling that close-packed but electrically isolated nanoparticles are electromagnetically coupled. Hybridized LSPRs supported by self-assembled nanoparticles with a broadband optical response, giving colloidal nanoantenna a high tolerance for geometric variation resulting from fabrication. I find that coupled nanoparticles act as a waveguide, transferring energy from many neighboring nanoparticles towards the active TERS apex. I also use surface-enhanced Raman spectroscopy (SERS) to characterize the effects of nanoparticle polydispersity and gap height on the Raman enhancement. These colloidal probes have consistently achieved dramatic Raman enhancements in the range of 108–109 with sub-50 nm spatial resolution. Furthermore, in contrast to other nanospectroscopy probes, these colloidal probes can be fabricated in a scalable fashion with a batch-to-batch reproducibility of ~80%. This body of work serves as an important demonstration that bottom-up engineering can be used for batch fabricatation of high-performance and high-reliability devices using inexpensive equipment and materials.

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