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Broadside Nanoantennas Made of Single Silver Nanorods Xiaolu Zhuo, Hang Kuen Yip, Qifeng Ruan, Tiankai Zhang, Xingzhong Zhu, Jianfang Wang, Hai-qing Lin, Jian-Bin Xu, and Zhi Yang ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b08423 • Publication Date (Web): 06 Feb 2018 Downloaded from http://pubs.acs.org on February 6, 2018

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Broadside Nanoantennas Made of Single Silver Nanorods Xiaolu Zhuo,† Hang Kuen Yip,† Qifeng Ruan,† Tiankai Zhang,§ Xingzhong Zhu,†,# Jianfang Wang,*,† Hai-Qing Lin,‡ Jian-Bin Xu,§ and Zhi Yang# †

Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China

‡

Beijing Computational Science Research Center, Beijing 100193, China

§

Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin, Hong

Kong SAR, China #

Key Laboratory for Thin Film and Microfabrication of Ministry of Education, Department of

Micro/Nano Electronics, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

ABSTRACT

Directional optical nanoantennas are often realized by nanostructured systems with ingenious or complex designs. Herein we report on the realization of directional scattering of visible light from a simple configuration made of single Ag nanorods supported on Si substrates, where the incident light can be routed towards the two flanks of each nanorod. Such an intriguing far-field scattering behavior, which has not been investigated so far, is proved to result from the near-field

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coupling between high-aspect-ratio Ag nanorods and high-refractive-index Si substrates. A simple and intuitive model is proposed, where the complicated plasmon resonance is found to be equivalent to several vertically aligned electric dipoles oscillating in phase, to understand the farfield properties of the system. The interference among the electric dipoles results in wavefront reshaping and sidewise light routing in a similar manner to the broadside antenna described in the traditional antenna theory, allowing for the naming of these Si-supported Ag nanorods as “broadside nanoantennas”. We have carried out comprehensive experiments to understand the physical origins behind and the affecting factors on the directional scattering behavior of such broadside nanoantennas.

KEYWORDS: broadside nanoantennas, dielectric substrates, directional light scattering, gap plasmon, plasmon resonance, silver nanorods

The interaction between light and plasmonic nanostructures, which is governed by collective electron oscillations known as localized surface plasmon resonance (LSPR), enables nanoscale antennas working at optical frequencies.1–4 Plasmonic nanoantennas have been intensively studied as light concentrators to generate strong optical near-fields below the diffraction limit, which has led to breakthroughs in surface-enhanced spectroscopies,5,6 sensing,7,8 fluorescence enhancement,9,10 particle trapping and manipulation,11 nonlinear frequency conversion,12 and quantum optics.13 Recently, growing attention has been paid to the design of nanoantennas for directional control of light,14–31 which is of fundamental importance for achieving efficient single-photon sources, nanolasers, color routing, holograms, quantum information processing, and integrated on-chip photonic devices.


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Directional nanoantennas require judicious wavefront reshaping through phase modulation at the subwavelength scale. Wavefront reshaping has been demonstrated mainly in two types of schemes. One relies on the interference of two or more electric dipoles with specific phase retardation, that is, plasmonic nanoparticles that support dipolar LSPR modes respectively and interact with each other through wavefront reshaping. Examples include Yagi-Uda nanoantennas,14–16 bimetallic nanodisk dimers,17,18 coupled nanoholes,19,20 nanoparticle arrays,21,22 and various metasurfaces.23 Since the performances of these nanoantennas strongly depend on the positions and geometrical parameters of the antenna elements, all of these schemes require precise top-down nanofabrication techniques. The other type of schemes relies on nanostructures that enable interference between electric and magnetic dipolar modes, such as plasmonic split rings,24 nanocups,25 nanoparticle clusters,26 and dielectric nanostructures with high or moderate refractive indexes.27,28 When the electric and magnetic dipolar modes have very close resonance wavelengths and nearly the same intensity, unidirectional forward light scattering can be achieved. Some of these nanostructures can be synthesized chemically25–28 and therefore have lower requirement on the nanofabrication technique. The main difficulty lies in balancing the strengths of the electric and magnetic dipoles at desired and tunable working wavelengths, because any geometric changes of a nanostructure would simultaneously affect the intensities and resonance wavelengths of its magnetic and electric dipoles. Taken together, although tremendous progresses have been made in both types of schemes, most of the previous works on directional nanoantennas have been devoted to their electric and/or magnetic dipolar modes. Not much attention has been paid to other LSPR modes even though they possess nearfield and far-field properties that are largely different from the dipolar ones.29–31


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In this work, we investigate the far-field behavior of single high-aspect-ratio Ag nanorods supported on Si substrates and demonstrate a LSPR mode, called broadside mode, that allows for light scattering towards the two flanks of each Ag nanorod. These Si-supported Ag nanorods are named as “broadside nanoantennas”. In the traditional antenna theory, a broadside antenna is described as an array of half-wave vertically aligned antenna elements with uniform spacing and in-phase current feeding.32 Our broadside nanoantennas exhibit a similar directional feature and operation principle to their radiowave analogues but do not require multiple elements, which avoids large geometric footprint and the need of precise top-down nanofabrication techniques. Moreover, an electric dipole array model is presented to understand the broadside LSPR mode and the resultant sidewise scattering behavior of our broadside nanoantennas in a simple and intuitive picture. Our systematic study on the sidewise scattering behavior of individual highaspect-ratio plasmonic metal nanoantennas supported on high-refractive-index (~3 and above) substrates suggests an intriguing operation principle of directional plasmonic nanoantennas. Our results are also applicable for understanding the charge oscillations and far-field properties of other similar systems consisting of high-aspect-ratio plasmonic metal nanostructures supported on strongly polarizable substrates. They will open possibilities for the design of functional nanoantennas, and create opportunities for nanoscale light manipulation, fluorescence control, and quantum-information processing.

RESULTS AND DISCUSSION We first investigated the dark-field scattering patterns of the individual high-aspect-ratio Ag nanorods deposited on Si substrates. Silicon was chosen as the substrate because it is the most commonly used material in semiconductor and nanophotonic devices and previous studies have


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revealed the pronounced substrate effect of Si on the LSPRs of metal nanocrystals.33–35 The highly uniform Ag nanorods were synthesized by a wet-chemistry method (Figure 1a and Figure S1, see the Methods for the synthesis details).36 They were randomly deposited on Si substrates at low surface number densities for single-particle scattering measurements. We utilized a pattern-matching method to correlate the dark-field image of each Ag nanorod with its scanning electron microscope (SEM) image (Figure 1b). On the focal plane (Figure S2), each singleparticle dark-field image exhibits a double-lobe pattern, where two bright spots can be clearly seen at the two flanks of the Ag nanorod (Figure 1c). The double-lobe pattern clearly reflects the orientation of the corresponding Ag nanorod. Although some high-order longitudinal modes also show multiple lobes in the far-field, all of these lobes should be rotationally symmetric about the length axis of each nanorod, due to the geometrical symmetry of the nanorod.31 In this regard, the double-lobe patterns observed in our experiments, which do not have a rotational symmetry about the length axis of each nanorod, should not result from the scattering of those high-order longitudinal modes. In addition, similar double-lobe images were also observed from chemically synthesized high-aspect-ratio Au nanorods and some of lithographically fabricated Ag nanorods supported on Si substrates (Figures S3–S5). Therefore, the double-lobe scattering pattern is believed to be a universal phenomenon of high-aspect-ratio metal nanostructures supported on high-refractive-index substrates, which is fundamentally important but has not been fully understood so far.


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Figure 1. Single Ag nanorods supported on Si substrates. (a) SEM image of a typical Ag nanorod sample. The average length and diameter are 390 ± 46 nm and 64 ± 3 nm, respectively. (b) Comparison of the SEM (left) and dark-field (right) images of the single Ag nanorods supported on a Si substrate. The orientation of each Ag nanorod can be effectively identified from its double-lobe dark-field image. These images were recorded with a monochrome camera and reproduced with color scale for clear presentation. (c) Magnified SEM (first and third) and dark-field (second and fourth) images of two typical Ag nanorods in different orientations. (d) Schematic of the 3D intensity distribution of the dark-field image with respect to the orientation of the supported plasmonic nanorod.


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Figure 1d shows the three-dimensional (3D) intensity distribution of a dark-field scattering image with respect to the orientation of the supported plasmonic nanorod. Prior studies on similar systems, such as nanospheres,37 nanorods33 and nanocubes38 sitting on metallic films, namely the “particle-on-film” geometry, typically show doughnut-shaped far-field scattering patterns due to the vertical dipole resonances supported by the nanoparticles. We also note that unidirectional broadband light emission has been demonstrated on micrometer-scale Ag nanowires, where surface plasmon polaritons are excited from one end of the nanowire and they emit from the other end.39,40 However, to our knowledge, current studies on plasmonics cannot provide straightforward explanation for the appearance of these double-lobe images. On the other hand, this phenomenon naturally provides a facile route to the identification of the orientations of individual high-aspect-ratio plasmonic nanorods, which is traditionally challenging without the assistance of fluorescent molecules,41 polarization analysis,42–44 highorder laser modes,45 or defocusing.46,47 Furthermore, regarding each Ag nanorod as a nanoscale scattering object, the double-lobe image probably suggests that the excitation light is redirected by the Ag nanorod to its side directions, which is very different from the scattering behaviors of other metal nanostructures. Driven by the aforementioned motivations, we carried out a series of experiments to investigate the plasmonic properties of the Si-supported Ag nanorods and the physical origin of the double-lobe dark-field images. To determine the factors that affect the scattering properties of the Ag nanorods, we performed single-particle dark-field scattering measurements using (i) different substrates, (ii) Ag nanorods with different sizes, and (iii) optical configurations with different excitation schemes. Unless otherwise specified, the typical Ag nanorod sample shown in Figure 1a was employed in most of our experiments. We first measured and compared the dark-field scattering spectra of the Ag


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nanorods supported on SiO2, indium tin oxide (ITO), SiC, Si and Ge substrates (Figure S6), whose refractive indexes are approximately 1.5, 1.9, 2.7, 3.6 and 4.3 in the visible region. The four conductive ones (ITO, SiC, Si and Ge) allowed us to correlate the dark-field scattering spectrum and image of each individual Ag nanorod with its SEM image by the pattern-matching method (Figure 2a). When deposited on low-refractive-index substrates such as SiO2 and ITO, these Ag nanorods exhibit multiple peaks in the spectral range from 450 nm to 850 nm, owing to the excitation of the longitudinal multipolar plasmon modes of different orders.36 In these cases, their dark-field images appear as solid bright spots. When the substrate is changed to SiC, the longitudinal multipolar plasmon modes are suppressed and a broader peak emerges at ~500 nm. We attribute this peak to a transverse-like LSPR mode because of its high-energy feature and weak dependence on the nanorod length (Figure S6). When the Ag nanorods are deposited on high-refractive-index substrates such as Si and Ge, the short-wavelength peak becomes dominant and the dark-field images of the single Ag nanorods turn into double-lobe patterns. These changes indicate that the LSPR properties of the supported Ag nanorods, as well as their far-field scattering behaviors, are dramatically altered because of the substrate effect.33–35 According to our results, the refractive index value needed for the observation of the double-lobe patterns is ~3 and above.


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Figure 2. Effects of the substrate and the gap distance. (a) Representative dark-field scattering spectra (left column), SEM (middle column) and scattering (right column) images of the single Ag nanorods supported on ITO, SiC, Si and Ge substrates (from top to bottom). (b) Representative dark-field scattering spectra (left column), SEM (middle column) and scattering (right column) images of the single Ag nanorods supported on the Si substrates coated with mesostructured silica layers of different thicknesses.

To further examine the substrate effect, we chose Si substrates as the model system and created a gap between the Ag nanorods and the substrate by using a mesostructured silica layer with different thicknesses. The mesostructured silica layer, whose refractive index is lower than that of SiO2, was used for varying the gap distance and therefore the coupling strength between the Ag nanorods and the Si substrate. Figure 2b shows the representative dark-field scattering spectra and images of the Ag nanorods supported on the Si substrates with mesostructured silica layers of three different thicknesses, 7.5 ± 0.6 nm, 29.7 ± 0.9 nm and 120.8 ± 7.9 nm, respectively. In the absence of the mesostructured silica layer, the scattering spectrum in the


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visible region is dominated by the transverse-like mode, while the multipolar longitudinal plasmon modes are either strongly suppressed or redshifted to the near-infrared region (see the simulation results in Supporting Text I). As the gap distance is increased, the transverse-like mode weakens gradually, accompanied by the recurrence of the multipolar longitudinal plasmon modes. At the same time, the scattering image evolves from the double-lobe pattern to a solid bright spot and then to an elongated solid bright spot. When the gap distance reaches 120.8 nm, the scattering spectrum is finally dominated by the multipolar longitudinal plasmon modes, similar to those of the Ag nanorods supported on SiO2 substrates, suggesting that the coupling between the Ag nanorod and the Si substrate becomes negligible. A similar trend was also observed from another system made of (Ag nanorod core)@(mesostructured silica shell) nanostructures supported on Si substrates (Figures S7 and S8). These results demonstrate that a high-refractive-index substrate in close proximity to the high-aspect-ratio plasmonic nanorods is indispensable for the observation of the double-lobe image. Moreover, the appearance of the double-lobe image is always accompanied by the transverse-like mode on the scattering spectrum. We next studied the effect of the nanocrystal geometry on the scattering behavior. For the purpose of simplicity and conciseness, we focused on the Ag nanorods and Ag nanowires with a fixed diameter of ~65 nm for the length-dependent measurements. Ag nanospheres and Ag nanocubes with similar sizes were also examined accordingly (Figure S9). All of these Ag nanocrystals were chemically synthesized and then deposited on Si substrates for single-particle dark-field scattering measurements. As shown in Figure 3a, doughnut-shaped images with circular symmetry are seen from the Ag nanosphere, Ag nanocube and the shortest Ag nanorod. The double-lobe images become distinct when the lengths of the Ag nanorods reach ~300 nm.


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The intensity anisotropy can be clearly seen from the longitudinal and transverse intensity profiles (Figure 3b). Such a transformation from the doughnut-shaped to double-lobe image suggests that the far-field scattering behavior of the Si-supported Ag nanorods strongly depends on the nanorod length. Similar transformations were also observed from the Ag nanorods with diameters of 30 nm and 45 nm, indicating that the diameter of the Ag nanorod is not a determining factor for the double-lobe scattering pattern (Figure S10). When the Ag nanorods are longer than ~500 nm, which is above the diffraction limit, the geometric anisotropy of the Ag nanorods starts to show up in the dark-field images, that is, the double-lobe image changes from a nearly circular into an elliptic shape. Still, the double-lobe feature remains similar with increasing nanorod lengths. Interestingly, even for the Ag nanowires with lengths of several micrometers, their dark-field images still display double-track patterns. One can expect similar double-track patterns for very long nanowires of any length.


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Figure 3. Effect of the nanorod length. (a) SEM (first and third rows) and corresponding darkfield (second and fourth rows) images of the Ag nanospheres, Ag nanocubes and Ag nanorods supported on Si substrates. (b) Scattering intensity profiles along the longitudinal (blue) and transverse (green) directions of a Si-supported Ag nanorod carrying the double-lobe image. Top left: SEM image. Bottom left: scattering image. The dashed lines indicate where the intensity profiles are extracted. Right: extracted intensity profiles. (c) Dependences of IAF and SAF on the nanorod length.

For a quantitative analysis of the evolution of the dark-field image, two parameters, which are called the intensity anisotropy factor (IAF) and shape anisotropy factor (SAF), are defined as


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IAF = SAF =

∥ ∥

× 100%

∥ ∥

(1)

× 100%

(2)

where ,∥ and ,∥ are the maximal intensities and widths of the two intensity profiles along the transverse (⊥) and longitudinal (||) directions (Figure S11). We carried out dark-field scattering measurements on ~100 Ag nanorods and calculated their IAFs and SAFs, as well as on a few Ag nanospheres and nanocubes, which are regarded as Ag nanorods with aspect ratios of 1 (Figure S12). The results are plotted as functions of length in Figure 3c. The IAFs and SAFs obtained from the Ag nanospheres and nanocubes are both low, due to the nearly circular symmetry of the images. For the Ag nanorods with lengths of ~200–500 nm, the IAFs increase from 15% to 30% while the SAFs remain close to zero, indicating that the double-lobe patterns become more distinct while the outlines remain approximately circular. As the Ag nanorods become even longer, the IAFs drop down to ~10% because of the high intensities of the overall images, while the SAFs dramatically increase owing to the elongation of the images. A combination of IAF and SAF enables the quantitative identification among the doughnut-shaped, circular double-lobe and elliptic double-lobe images, providing a facile route for estimating the lengths of the Ag nanorods. Polarization-controlled excitation was imposed to examine if the scattering properties of the Ag nanorods on Si is dependent on the electric field direction of the excitation light. Figure 4a and b show the dark-field scattering images and spectra of a typical Ag nanorod under four excitation schemes called Lp, Ls, Tp and Ts (Figure S13), at a fixed incidence angle of 64° relative to the surface normal, according to the numerical aperture (NA) value (0.9) of the employed dark-field objective. Lp and Ls (Tp and Ts) refer to the p- and s-polarized excitations with the wavevector aligned in the plane that is determined by the long (short) axis of the


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nanorod and the surface normal of the substrate. For the p-polarized excitation, the incident electric field is dominated by the component that is perpendicular to the substrate plane due to the relatively large incidence angle. The electric field of the s-polarized excitation is parallel to the substrate plane. As a result, the four excitation schemes represent the four most typical excitation components of the incident light at a given incidence angle. By comparing the scattering spectra and images under the Lp, Ls, Tp and Ts excitation schemes with those obtained under the unpolarized excitation condition, we found that in our experiments the Tp component of the excitation light contributes dominantly to the transverse-like mode as well as the double-lobe images.

Figure 4. Effects of the polarization and incidence angle of the excitation light. (a) Dark-field scattering images obtained from a single Ag nanorod supported on Si under the unpolarized, Lp, Ls, Tp and Ts excitations, respectively. At the top left corner is the SEM image of the nanorod. The orientation of the Ag nanorod was adjusted deliberately to facilitate the excitation polarization-dependent measurements. (b) Scattering spectra of the Ag nanorod in (a) acquired


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under the Lp, Ls, Tp and Ts excitation schemes. (c) Dark-field scattering images obtained from a single Ag nanorod supported on Si with three objectives having different NAs. At the top left corner is the SEM image of the nanorod. (d) Scattering spectra of the Ag nanorod in (c) recorded with the three different objectives. Each spectrum has been normalized by its maximal value to eliminate the collecting efficiency differences of the objectives.

To examine the dependence of the incidence angle on the scattering behavior of the Ag nanorods, three dark-field objectives (50×, NA 0.5; 50×, NA 0.75; 100×, NA 0.9) were used to measure the scattering images and spectra of the Ag nanorods supported on Si. The incidence angles relative to the surface normal for the three objectives are 30°, 49° and 64°, respectively. Unpolarized excitation light was employed. When the objective with the incidence angle of 30° was employed, a solid bright spot image accompanied by a sharp peak at 620 nm on the scattering spectrum was observed (Figure 4c and d). The scattering peak can be attributed to a longitudinal octupolar LSPR mode.36 When the objective with the incidence angle of 49° was employed, however, the double-lobe scattering pattern was barely observable and the longitudinal multipolar plasmon mode was diminished. Only when the objective with the incidence angle of 64° was utilized, can the longitudinal multipolar plasmon mode be completely suppressed and the double-lobe image be clearly seen. The results obtained from the polarization- and incidence angle-dependent measurements show that the double-lobe scattering patterns can only be effectively excited under the Tp excitation scheme at a large incidence angle. From this, we can infer that the double-lobe patterns are produced by the collective charge oscillations in the direction perpendicular to the substrate, which will be further verified by numerical simulations below. For comparison, we also carried out the same experiments on an


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individual Ag nanocube supported on Si (Figures S14 and S15), furthering verifying the importance of the Tp excitation and a high NA for the occurrence of the double-lobe pattern. We have revealed the major requisites for the experimental observation of the double-lobe scattering images: (i) a dielectric substrate with a high refractive index; (ii) a small gap distance between the nanorods and the high-refractive-index substrate; (iii) high-aspect-ratio Ag nanorods with rod lengths above 300 nm; (iv) excitation light at a large incidence angle; and (v) excitation light with a strong Tp component. We have also found that the diameter of the Ag nanorod is not a determining factor for the formation of the double-lobe pattern. To further understand the physical origin of the observed far-field scattering behaviors, we performed finite-difference time-domain (FDTD) simulations on the Ag nanorods supported on Si (Supporting Text I). Since the chemically synthesized Ag nanorods are capped by a surfactant bilayer, a 1-nm gap was set between the Ag nanorod and the Si substrate in our simulations.48 For a typical Ag nanorod, the Lp and Tp excitations give rise to strong scattering peaks around 500 nm (Figure S16). The peak position and shape agree well with those of the transverse-like mode observed experimentally. Therefore, we will focus on the Lp and Tp excitations in the following simulations. To confirm the length-dependent far-field scattering behaviors, we calculated the two-dimensional (2D) farfield scattering patterns of seven Ag nanorods with a fixed diameter of 66 nm and varied lengths from 66 nm to 350 nm (Figure 5). Each simulated 2D far-field scattering pattern can be understood as the far-field light intensity distributed on a hemispherical surface viewed above, with an individual Ag nanorod lying on a Si substrate beneath. Figure 5a and b show the simulated far-field patterns under the Tp and Lp excitations, respectively. These far-field patterns are asymmetric in intensity because the incoming plane wave is from one side at an incidence angle of 64° in the simulation model. In most of our experiments, however, the white excitation


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light symmetrically illuminates the individual Ag nanorods from different directions along an inverted hollow light cone. Even in the polarization-dependent experiments, the white light illuminates the individual Ag nanorods from opposite directions symmetrically. For better comparison with the experimental results obtained under the unpolarizied excitation, the far-field patterns simulated with the p-polarized excitations from the four incidence directions for each Ag nanorod were added up to give the far-field pattern (Figures S17 and S18). The simulated farfield patterns shown in Figure 5c were calculated in this manner. In Figure 5c, the simulated farfield scattering patterns of the Ag nanosphere (66 nm × 66 nm) and the shortest Ag nanorod (100 nm × 66 nm) are doughnut-shaped, while the longer nanorods exhibit more and more distinct double-lobe patterns, with the two bright spots located at the two flanks of each Ag nanorod. By comparing the far-field patterns under the Lp and Tp excitations and the overall far-field patterns, we found that the double-lobe pattern is mainly induced by the Tp excitation.

Figure 5. Simulated 2D far-field scattering patterns. (a) For the Ag nanorods with different lengths under the single-sided Tp excitation scheme. The numbers above each pattern are the


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length and diameter of the simulated nanorod. (b) For the same Ag nanorods under the singlesided Lp excitation scheme. (c) 2D far-field patterns obtained by summing up the contributions of the Tp and Lp excitation light. The 2D far-field patterns are the angular intensity distributions of the scattered light. The horizontal and vertical polar axes are along the longitudinal and transverse directions of the Ag nanorods, respectively. The radial axes, including the central point and the four circles from inside to outside, represent 0°, 10°, 30°, 60° and 90° relative to the surface normal from the top view, respectively. We also note that the simulated far-field patterns are the angular distributions of the scattered light, which should correspond to the images taken through Fourier back-focal-plane imaging. The dark-field scattering images in our experiments, however, are obtained through real-space imaging. Nevertheless, our discussion mainly focuses on the Ag nanorods with sizes smaller than one visible wavelength. Therefore, each Ag nanorod can be approximately regarded as a point source in real-space imaging, which also provides information on the angular light intensity distribution. In this regard, the simulated far-field scattering patterns are still useful for understanding our experimental results. In general, the simulated results agree qualitatively well with the dark-field scattering images observed experimentally. Moreover, the simulations provide the theoretical evidence for the scattering directionality of the Si-supported Ag nanorods. For example, the doughnut-shaped pattern suggests that most light is evenly scattered in the horizontal directions, with very little light scattered in the vertical direction. On the other hand, the double-lobe pattern implies that most light is directed into the two flanks of each Ag nanorod, which can be controlled by the orientations of the individual Ag nanorods. Compared to the unidirectional nanoantennas with complicated designs, such as Yagi-Uda nanoantennas,14–16 the broadside nanoantennas do not show advantages in the directionality. However, their


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directionality is still better than that of other systems that are constructed in a similar way, such as nanosphere-on-substrate and nanocube-on-substrate systems. Such sidewise light scattering can find interesting applications in some particular nanophotonic systems, such as the generation of collimated light beams along two opposite directions, transmission of entangled photon pairs, and light coupling from free space to planar circuits. Figure 6a shows the charge distribution contours of the seven Ag nanorods with different lengths under the Tp excitation (see Figure S19 for the corresponding results under the Lp excitation). For the Ag nanosphere and the shortest Ag nanorod, their transverse dipolar mode is excited, manifesting as the charge oscillation in the direction perpendicular to the substrate. At a certain moment, for instance, the upper surface of the nanoparticle is positively charged and the lower surface is negatively charged. Due to the charge induction effect, positive charges are induced at the surface of the Si substrate, resulting in a strong local electric field at the nanoparticle–substrate interface. The longer Ag nanorods, however, support a cavity-like resonance with the charges strongly localized in a few segments at the lower surface of the nanorods, and the opposite charges distributed evenly on the top surface. Accordingly, the induced charges at the surface of the Si substrate are also distributed in a few segments. Notably, once the cavity-like resonance appears, the double-lobe pattern starts to show up on the simulated far-field scattering pattern. Such a LSPR mode still belongs to a transverse plasmon mode but no longer a dipolar mode. Since this mode strongly depends on the gap distance and the refractive index of the underlying substrate, we ascribe this mode to the gap plasmon resonance. The concept of gap plasmon resonances has been frequently used to describe LSPR modes tightly confined within ultra-small metal nanogaps.13,38,49 The gap plasmon in our case is slightly different. Nevertheless, since Si has a high dielectric constant in the visible region, we


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believe that the gap plasmon resonances supported by metal–metal nanogaps and those by metal–silicon nanogaps should have some common features.

Figure 6. Side-by-side electric dipole array model. (a) Simulated charge distribution contours corresponding to the seven nanorods in Figure 5 under the Tp excitation. (b) Schematics of the charge oscillations simplified as a single dipole or multiple side-by-side aligned electric dipoles. Each pair of the real dipole within the Ag nanorod and the corresponding image dipole within the Si substrate is considered as a single electric dipole with a larger strength. (c) Schematic of the model for the side-by-side dipole array. The side-by-side aligned electric dipole array contains N elements. The red spots represent the single electric dipoles oriented normal to the x-y plane with a uniform spacing s. The blue arrows denote the distances from the electric dipoles to an observation point in the far-field.


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To provide a deep insight into the far-field radiation behaviors of the Ag nanorods in the presence of a gap plasmon resonance, we simplified the charge oscillations as arrays of individual side-by-side aligned electric dipoles that oscillate vertically in phase with each other (Figure 6b). The induced charges at the Si surface can be regarded as image dipoles having the same orientation as the real ones. Since the real dipole and image dipole oscillate nearly in phase, each pair of the real dipole and corresponding image dipole can be combined into a single electric dipole with a larger strength.33 As a result, the gap plasmon mode and the induced charge oscillation can be simplified to a side-by-side electric dipole array with a length-dependent number of dipole elements. Under the condition that all of the electric dipoles oscillate in phase with a uniform spacing s and a unit amplitude, the 3D angular far-field radiation of a dipole array with N elements can be analytically expressed as (Supporting Text II) sin (!⁄)$%&'()

| | ∝ sin sin (*⁄)$%&'()

(3)

where θ and φ are the polar and azimuthal angle based on a spherical coordinate system (Figure 6c), and k = ω/c is the wavenumber. In the derivation of eq 3, we assumed that there is no nearfield coupling between the adjacent dipoles. However, since each electric dipole is immersed in the electromagnetic field generated by the other electric dipoles, their radiation behavior might be modified due to the Purcell effect or other near-field interactions among the electric dipoles. To confirm the validity of our theoretical derivation, we further performed FDTD simulations to calculate the far-field angular radiations of the electric dipole arrays, where the inter-dipole coupling was taken into account. According to the simulated charge distribution contours, all of the dipoles were set to oscillate in-phase at the plasmon resonance wavelength λ = 500 nm with a uniform spacing of s = 100 nm (Supporting Text III). Therefore, the inter-dipole spacing is much smaller than the resonance wavelength. The theoretical and simulated results are in good


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agreement with each other (Figure 7a), suggesting that the near-field inter-dipole coupling is negligible. The 3D far-field patterns of these electric dipole arrays can be mainly attributed to the wavefront interference among the electric dipoles. When N = 1, | | ∝ sin . The 3D farfield pattern shows a doughnut shape, corresponding to the cases of the Ag nanosphere and the 100-nm Ag nanorod. For the array consisting of two electric dipoles, the 3D far-field pattern turns into an elongated shape like a rubber dinghy, whose top view is similar to the simulated 2D far-field patterns of the 150-nm- and 200-nm-long Ag nanorods. When the dipole number is increased to three and four, the 3D far-field patterns become dumbbell-shaped, implying that most energy is radiated from the electric dipole array along the two side directions. Viewing from top, the double-lobe patterns can be clearly seen, similar to the simulated 2D far-field patterns of the 250-nm-, 300-nm-, and 350-nm-long Ag nanorods. The interference among the radiated waves from the in-phase oscillating electric dipoles is similar to the picture described by the Huygens-Fresnel principle, as illustrated in Figure 7b. Once the number of the dipoles is more than one, the superposition of the waves from each individual dipole forms wavefronts that propagate perpendicularly away toward the two sides of the array. For the two end directions of the array, the waves from different dipoles can partially cancel each other because of the interdipole spacing and the resultant phase differences. The overall effect is that the radiations along the two side directions are always stronger than that along the two end directions.


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Figure 7. Far-field radiation of the side-by-side electric dipole arrays. (a) Theoretically calculated far-field radiation patterns (first column), schematics (second column) of the side-byside electric dipole arrays, FDTD-simulated 3D (third column) and 2D (fourth column) far-field radiation patterns of the dipole arrays. All of the dipoles were set to be oscillating in-phase with a uniform spacing of 100 nm in a homogenous medium. (b) Schematic showing the interference among the wavefronts of the electromagnetic field waves radiated from the individual electric dipoles. The gray solid lines represent the radiation from each single dipole source and the gray dashed lines represent the projected wavefront after interference. (c) Schematic of the sidewise scattering of a broadside nanoantenna made of a single Ag nanorod supported on a Si substrate.


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According to this model, the single electric dipole and the N-element array (N > 1) should possess different polarization characteristics of the radiated light in the far-field (Figure 8a). As described in the electrodynamics theory, the electric field wave radiated from a single electric dipole is radially polarized. Therefore, if a polarization analyzer is inserted in front of the detection camera, we expect to see two bright spots along the analyzer direction while the rest scattering light is filtered off. Moreover, the two bright spots should rotate together with the analyzer direction, but the spacing between the two bright spots should remain unchanged during the rotation, owing to the circular symmetry of the doughnut-shaped far-field pattern. For the electric dipole array, on the other hand, the radiated electric field wave should be radially polarized owing to the superposition phenomenon of the electric dipoles. However, when the polarization analyzer is inserted, the spacing of the two bright spots is expected to change as the analyzer direction is varied. In particular, when the analyzer direction is perpendicular to the array axis, the spacing between the two bright spots should be maximized due to the dumbbellshaped 3D far-field pattern. When the analyzer direction is parallel with the array axis, the spacing between the two bright spots should be minimized.


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Figure 8. Emission polarization characteristics. (a) Theoretical prediction of the polarization characteristics of the dark-field images of a single electric dipole and the N-element array (N > 1). (b) Experimental dark-field images measured from a Si-supported Ag nanocube (upper row) and a Si-supported Ag nanorod (lower row) in the absence of an analyzer (leftmost) and in the presence of an analyzer with varied polarization directions. The analyzer directions are indicated


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with numbers and differently oriented double-headed arrows. The Ag nanorod is horizontally oriented, as indicated above the image without the analyzer. (c) Polarization dependences of the spacing between the two bright spots measured from the Si-supported Ag nanocube and Ag nanorod. (d) Scattering spectra of the Si-supported Ag nanocube (left) and Ag nanorod (right) acquired when the analyzer direction was varied. "NC" and "NR" refer to nanocube and nanorod, respectively.

To verify this prediction, we examined the polarization characteristics of the dark-field images experimentally, using a Si-supported Ag nanocube as an analogue of the single electric dipole and a Si-supported Ag nanorod as the N-element array (Figure 8b–d and Figure S21). Unpolarized white light was used for excitation. Although the scattering off a plasmonic nanorod has been well known to be polarization-dependent,42–44 the scattering off the Si-supported Ag nanorods is not simply linearly polarized along the length axis. This point is evidenced by the dark-field images and spectra acquired as a function of the analyzer direction. The leftmost images in Figure 8b show the dark-field scattering images of the Ag nanocube and Ag nanorod in the absence of the analyzer. From the double-lobe image of the Ag nanorod, we can identify that the Ag nanorod is horizontally oriented in the image. The other images were obtained when the analyzer was inserted in front of the detection camera, with the analyzer direction being rotated. As mentioned above, the spacing between the two bright spots can be a good parameter for distinguishing the scattering from a single electric dipole and that from a side-by-side electric dipole array. We measured the spacing between the two bright spots for both cases and plotted them as functions of the analyzer direction (Figure 8c). The experimental results agree well with the theoretical predictions in both cases. More examples of the Si-supported Ag nanorods are


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provided in Figure S21. In addition, the scattering spectrum of the Ag nanocube remains nearly unchanged as the analyzer direction is varied, while the 500-nm peak of the Ag nanorod shows back-and-forth shifts as the analyzer direction is varied, which has not been fully understood yet (Figure 8d). These results demonstrate that the charge oscillations of the Si-supported Ag nanorods can be effectively described by the side-by-side electric dipole array model. Intriguingly, we found a similar design, called "broadside antenna", in the traditional antenna theory.32 Broadside antennas are bidirectional in radiation. A broadside antenna is typically composed of several half-wave elements with a uniform spacing and in-phase current feeding. From the perspective of wave interference, the sidewise directionality is caused by wavefront reshaping through the constructive interference between the dipole elements (Figure 7b). The same mechanism can be employed to understand the sidewise scattering of the Si-supported single Ag nanorods, which results from the interference in the plasmonic dipole array. Therefore, we name these Sisupported Ag nanorods as "broadside nanoantennas" after their radiowave analogues. The direction of the scattered light can be readily tailored by controlling the orientations of the broadside nanoantennas (Figure 7c). However, it is challenging to place a single Ag nanorod at a desired position in a specific orientation on a substrate by drop-casting, or to arrange the colloidal Ag nanorods into a desired geometry. In this regard, we used the trench-directed alignment approach to demonstrate the control over the position, orientation, and spacing of the colloidal Ag nanorods (see the Method section for the alignment details). Several examples with different geometries are provided in Figure S22. After the removal of the photoresist, arrays of the double-lobe far-field images were obtained from the Ag nanorod arrays, indicating that the plasmonic properties of the Ag


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nanorods were not affected by the assembly process. Reliable trench-directed alignment requires extremely high monodispersity of the Ag nanorod sample as well as deep understanding of the underlying forces involved in the alignment process. Although it is not the intention in this work to provide a technical route to the fabrication of large-scale ordered nanoantenna arrays, our preliminary attempt points out the possibility for controlling the positions and orientations of these colloidal nanoantennas for future applications, such as metasurfaces, color display, and light beam manipulation. Although most of our experiments are based on Ag nanorods and Si substrates, we believe that the broadside scattering effect, the electric dipole array model and the related understanding can be extended to other similar systems consisting of strongly polarizable substrates and highaspect-ratio plasmonic metal nanorods/nanowires.61–63 For comparison, we performed FDTD simulations to examine two typical systems, a single Ag nanorod supported on Ag and a single Si nanorod supported on Ag (Figure S23). The charge distribution contours and the corresponding far-field scattering patterns indicate that the broadside mode can be supported by both systems. In particular, the Ag-supported Ag nanorod shows a double-lobe far-field scattering pattern that is very similar to that of the Si-supported Ag nanorod. One can expect that similar systems based on Au, Ag and other plasmonic metals can also possess the same effect. For the Ag-supported Si nanorod, however, the sidewise far-field scattering appears relatively weaker, which might be caused by some other coexisting effects that have not been understood. More efforts are needed for the corresponding experimental demonstrations and further understanding.

CONCLUSION


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In summary, we have demonstrated experimentally and confirmed theoretically a type of optical nanoantennas made of single Ag nanorods supported on Si substrates. Our nanoantennas can be regarded as a scale-down single-element version of the broadside antenna described in the traditional antenna theory. The operation principle of our nanoantennas is conceptually different from those of widely reported directional nanoantennas that employ dipolar plasmon resonance modes or dipolar magnetic modes. The sidewise scattering behavior of the broadside nanoantennas is caused by the collective charge oscillations that are equivalent to several vertically aligned side-by-side electric dipoles oscillating in phase. The side-by-side dipole arrays originate from the excitation of the gap plasmon resonance tightly confined within the nanoscale gap between the Ag nanorod and the Si substrate. Using the electric dipole array model, we have described the sidewise scattering behavior in a simple and intuitive picture. Although Ag nanorods and Si substrates are used in our work for the ease of experimental demonstration, we believe that the formation of the broadside nanoantennas is a universal phenomenon of high-aspect-ratio metal nanostructures supported on strongly polarizable substrates with refractive indexes higher than ~3. Our study not only holds the prospect of gaining insight into nanoantenna design, but also offers potential for the rational use of directional nanoantennas for a variety of optical applications.

METHODS Chemicals. HAuCl4·3H2O (99%), NaBH4 (98%), trisodium citrate (99%), ascorbic acid (99%), AgNO3 (99%), tetraethyl orthosilicate (TEOS, 99.999%) were purchased from Sigma-Aldrich. HCl (5 M) and NaOH (96%) were ordered from Scharlab and Farco Chemical Supplies, respectively. Cetyltrimethylammonium bromide (CTAB, 98%) and cetyltrimethylammonium


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chloride (CTAC, 97%) were obtained from Alfa Aesar and Aladdin Chemicals, respectively. Poly(methyl methacrylate) (PMMA, molecular weight: 950,000) were purchased from MicroChem. Deionized water with a resistivity of 18.2 MΩ cm obtained from a Direct-Q 5 UV water purification system was used in all experiments. Synthesis of the Ag Nanorods and Ag Nanocubes. The Ag nanorod samples were prepared using the Au nanobipyramid-directed growth method according to our previous work.36 Typically, the Ag nanorod sample (average length: 390 ± 46 nm, average diameter: 64 ± 3 nm) used most frequently in our experiments was synthesized following the steps below. First, a freshly prepared, ice-cold NaBH4 solution (0.01 M, 0.15 mL) was mixed with an aqueous solution composed of HAuCl4 (0.01 M, 0.125 mL), trisodium citrate (0.01 M, 0.25 mL) and water (9.625 mL) under vigorous stirring. The resultant seed solution was kept at room temperature for 2 h. The solution for the growth of Au nanobipyramids was prepared by mixing together CTAB (0.1 M, 80 mL), HAuCl4 (0.01 M, 4 mL), AgNO3 (0.01 M, 0.8 mL), HCl (1 M, 1.6 mL) and ascorbic acid (0.1 M, 0.64 mL). The as-prepared seed solution (0.12 mL) was injected into the growth solution, followed by gentle inversion mixing for 10 s. The reaction solution was left undisturbed for 6 h at room temperature. The as-prepared Au nanobipyramid solution was centrifuged at 4,000 rpm for 15 min and redispersed in CTAC (0.08 M, 20 mL) , followed by subsequent addition and mixing of AgNO3 (0.01 M, 8 mL) and ascorbic acid (0.1 M, 4 mL). The mixture solution was placed in an air-bath shaker (60 °C, 120 revolutions per minute) and kept for 4.5 h, during which Ag was overgrown on the Au nanobipyramids to form Ag nanorods. The resultant solution was centrifuged at 1,800 rpm for 15 min. The precipitate was redispersed in CTAB (0.025 M, 20 mL) and left undisturbed overnight at room temperature, during which the Ag nanorods agglomerated together and precipitated to the bottom of the


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container, while the spherical impurities remained in the supernatant. The supernatant was thereafter carefully discarded. The precipitate was redispersed in water (15 mL) for further use. The Ag nanorod samples with different sizes were prepared following the same procedure. The rod diameter and length were controlled by selecting differently-sized Au nanobipyramids50 and varying the amount of the Ag precursor, respectively. The Ag nanocubes were obtained as the by-product during the synthesis of Ag nanorods when the Ag precursor was supplied in excess during the Ag overgrowth process. Synthesis of the Ag Nanospheres. The Ag nanospheres were prepared through Ag overgrowth on Au seeds, modified from a previous report.51 Briefly, a HAuCl4 solution (0.01 M, 0.25 mL) was first mixed with a CTAB solution (0.1 M, 9.75 mL), followed by the rapid injection of a freshly-prepared, ice-cold NaBH4 solution (0.01 M, 0.60 mL) under vigorous stirring. The resultant solution was kept under gentle stirring for 3 h at room temperature. A portion (1 mL) of the as-prepared seed solution was injected into a growth solution made of CTAC (0.08 M, 5 mL), AgNO3 (0.01 M, 4 mL) and ascorbic acid (0.1 M, 2 mL) in advance. The reaction mixture was then placed in an air-bath shaker (60 °C, 120 revolutions per minute) and kept for 6 h. Additional AgNO3 (0.01 M, 4 mL) and ascorbic acid (0.1 M, 2 mL) were added into the growth solution every 2 h for twice. The resultant solution was centrifuged at 5,000 rpm for 15 min. The precipitate was redispersed in water (10 mL) for further use. Synthesis of the Au Nanorods. The Au nanorod sample was grown by a three-step seedmediated method modified from a reported procedure.52,53 To obtain Au nanorods with diameters of ~60 nm, we used purified Au nanobipyramids with the longitudinal dipolar plasmon wavelength at 700 nm as the seeds instead of those described in the reference works. The extinction value at 700 nm was adjusted to be ~8 per 1 cm. Three flasks with the capacities of 10,


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50, and 400 mL were used to prepare growth solutions A, B, and C in advance, respectively. The growth solution A was made of CTAB (0.1 M, 9 mL), HAuCl4 (0.01 M, 0.225 mL) and ascorbic acid (0.1 M, 0.05 mL). The growth solution B was made of CTAB (0.1 M, 28 mL), HAuCl4 (0.01 M, 0.7 mL) and ascorbic acid (0.1 M, 1.514 mL). The growth solution C was made of CTAB (0.1 M, 325 mL), HAuCl4 (0.01 M, 8.125 mL) and ascorbic acid (0.1 M, 1.75 mL). All of the three growth solutions became colorless after gentle stirring. The Au nanobipyramid solution (3.65 mL) was added to the flask A and gently mixed. A portion (3.54 mL) of the resultant mixture was immediately transferred from the flask A to the flask B within 3 s, and all of the mixture solution from the flask B was transferred into the flask C immediately within 3 s. The solution in the flask C was then left undisturbed overnight at room temperature. The as-prepared Au nanorods were centrifuged at 1,500 rpm for 15 min and redispersed in water (15 mL) for further use. Silica Coating of the Ag Nanorods. Mesostructured silica coating on the Ag nanorods was carried out according to the previous report.41,54 Briefly, the as-grown Ag nanorod solution (1 mL) was sequentially mixed with water (4 mL), CTAB (0.1 M, 0.1 mL), TEOS (20 wt% in ethanol, 10 µL) and NaOH (0.1 M, 0.05 mL). The silica-coated Ag nanorod samples with different silica shell thicknesses were similarly prepared by repeating the coating process for several times. The as-prepared samples were kept in the growth solution for further use. Preparation of the Substrates. Glass slides (Ted Pella), ITO substrates (SPI Supplies), SiC wafers of orientation, Ge wafers of orientation, and Si wafers of orientation (Semiconductor Wafer) were obtained commercially. Mesostructured silica thin films of different thicknesses on the Si wafers were fabricated by dip-coating according to our previous work.55


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Lithographical Fabrication of the Ag and Au Nanorods. Ag nanorods of different sizes were fabricated by the standard electron beam lithography (EBL) technique. PMMA (2 wt% in anisole), which was employed as the electron beam resist, was spin-coated onto a cleaned Si substrate at 6,400 rpm for 80 s to form a 400-nm-thick resist layer. After a post-bake (200 °C, 2 min), the PMMA-coated Si substrate was subjected under electron beam exposure at a dosage of 3,000 µC cm–2. The written pattern was developed in a mixture solution of methyl isobutyl ketone and isopropyl alcohol (1:3, v/v) at a temperature of –18 °C for 60 s, followed by washing in isopropyl alcohol at room temperature for another 60 s. The substrate was then blown dry with N2. Subsequently, a silver layer (60 nm) was thermally evaporated onto the substrate, with the metal film thickness monitored with a quartz crystal microbalance. The chamber pressure of the thermal evaporator was below 1 × 10–6 torr during evaporation. The evaporation rate was 0.6 nm min–1. The PMMA layer was finally removed by a lift-off process in acetone at room temperature for 10 h to produce Ag nanorods. Au nanorods of different sizes were also fabricated following the same procedure, except for the thermal evaporation step. For the fabrication of Au nanorods, an adhesive Cr layer (4 nm) and a gold layer (60 nm) were sequentially thermally evaporated onto the Si substrate with the pre-written pattern. The chamber pressure of the thermal evaporator was below 4 × 10–6 torr during evaporation. The evaporation rate was 0.4 nm min–1. Trench-Directed Positioning and Alignment. Rectangular trenches of 370 nm in length and 90 nm in width in different orientations and spacings were utilized as the templates. The templates were fabricated on Si substrates by the standard EBL technique with PMMA as the electron beam resist, following the procedure described above. To obtain patterns of aligned Ag nanorods, a droplet of an aqueous dispersion of the Ag nanorods with an average length/diameter


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of 390 ± 46 nm/64 ± 3 nm and stabilized by CTAB was cast on the template, followed by water solvent evaporation at room temperature in a loosely covered Petri dish in the ambient environment.56–58 The Ag nanorods were pulled into the rectangular trenches by the capillary force. Finally, the PMMA layer was removed by a lift-off process in acetone at room temperature for 10 h. Instrumentation. SEM imaging was performed on an FEI Quanta 400 FEG microscope operated at 20 kV. Single-particle dark-field scattering spectra and grey images were recorded on an upright optical microscope (Olympus, BX60) that was integrated with a quartz–tungsten– halogen lamp (100 W), a monochromator (Acton, SpectraPro 2360i), and a monochrome chargecoupled device camera (Princeton Instruments, Pixis 400, cooled to –70 °C). In most of the measurements, a dark-field objective (100×, NA 0.9) was employed for both exciting the individual nanostructures with the white light and collecting the scattered light. Another two dark-field objectives (50×, NA 0.75; 50×, NA 0.5) were employed for varying the incidence angle of the excitation light. The polarization of the excitation light was controlled using a combination of a pair of pinholes and a linear polarizer (U-AN360, Olympus). The polarizer was placed in the optical path right after the white-light source, with the polarization axis aligned either horizontally or vertically, to obtain s- or p-polarized incident light relative to the substrate plane. In order to obtain a clean polarization at the substrate plane, a mask with two symmetrical pinholes of ~5 mm in diameter was inserted in the optical path right after the polarizer. The pinholes were used to select two portions of the white-light beam that were then reflected at two diametrically opposite positions of the circular mirror. The L- and T- incident light were then realized by adjusting the positions of the pinholes. To make the polarization of the excitation light as clean as possible, the Ag nanorods were aligned along either the left-and-right or the


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front-and-back direction relative to an observer looking into the eyepieces during the excitation polarization-dependent measurements. The polarization analyzer (U-AN360, Olympus) was placed in front of the camera. We utilized a pattern-matching method59,60 to correlate the geometrical structure of the nanoantennas from SEM imaging with the single-particle dark-field scattering characterization. An Elionix ELS7800 EBL system was used for the fabrication of the EBL-based metal nanostructures. The thicknesses of the mesostructured thin films were measured by an atomic force microscope (AFM, Model No. 920-006-101, Veeco Metrology) that was operated at the contact mode using a super-sharp Si3N4 tip (Nanoprobes). Finite-Difference Time-Domain Simulations. The finite-difference time-domain (FDTD) simulations were performed using FDTD Solutions 8.7 developed by Lumerical Solutions. In the simulations of a silver nanorod supported on a substrate, an electromagnetic plane wave in the wavelength range from 400 nm to 800 nm was launched into a box containing the target Ag nanorod. A mesh size of 1 nm was employed in calculating the scattering spectra, charge distribution contours and far-field scattering patterns of the differently-sized Ag nanorods. The refractive index of the medium in the top and side regions was set at 1.00 and that in the bottom was set according to the dielectric function of the Si wafer. For Si and Ag, the refractive indexes were calculated from the dielectric functions fitted from the measured data of Palik. Each Ag nanorod was modeled as a cylinder with two hemispherical ends, with a spacing distance of 1 nm from the substrate owing to the CTAB-capping layer. A power monitor was placed right above the Ag nanorod to calculate the far-field scattering pattern through the near- to far-field projection. In the simulations of the electric dipole array, the electric dipoles were set as singlefrequency point sources aligned in a line at certain spacing from each other. A monitor box surrounding the electric dipole array was employed to record the electromagnetic field on a


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closed surface. The 3D far-field radiation pattern was thereafter calculated through the near- to far-field projection.

ASSOCIATED CONTENT The authors declare no competing financial interest. Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: xxxxxx. Additional simulation results, additional theoretical model details, additional experimental results on the polarization dependence of the broadside nanoantennas, supporting text, figures and references (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. ACKNOWLEDGMENTS J.F.W. acknowledges support from Hong Kong Research Grants Council (Theme-based Research Scheme, T23-407-13N; General Research Fund, 14305314). H.Q.L. acknowledges support from NSAF Joint Fund (U1530401) between National Natural Science Foundation of China and Chinese Academy of Engineering Physics, and computational resources from Beijing Computational Science Research Center. REFERENCES


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ACS Nano

(1)

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ACS Nano

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ACS Nano

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