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Near-Field Imaging of Infrared Nanoantenna Modes Under Oblique Illumination Shingo Usui,† Shuta Kitade,‡ Ikki Morichika,‡ Kensuke Kohmura,† Fumiya Kusa,†,‡ and Satoshi Ashihara*,†,‡ †

Department of Applied Physics, Tokyo University of Agriculture and Technology, 2-24-16, Nakacho, Koganei, Tokyo 184-8588, Japan ‡ Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan S Supporting Information *

ABSTRACT: Plasmonic nanoantennas provide powerful tools in enhancing light−matter interactions by linking propagating far fields with localized near fields. Microscopic understanding on the enhancements of light−matter interactions requires precise knowledges on the near-field distributions upon nanoantenna excitations. In this article, we study nearfield distributions of nanoantennas under oblique illumination. We acquire the amplitude- and phase-resolved images of the near fields on Au nanorods in the infrared range, by use of the scattering-type scanning nearfield optical microscopy and the interferometric homodyne detection. Asymmetric near-field distributions are experimentally visualized and theoretically reproduced. The asymmetry in the near-field distributions is attributed to the preferential excitation of the surface plasmon polariton in one direction and the finite loss of the surface plasmon polariton inside the cavity. Furthermore, we organize the excitation conditions of the nanoantenna modes under oblique illumination as two formulas, each of which illustrates the cavity resonance condition and the phase matching condition for surface plasmon polariton excitation, respectively. The findings will form the basis for novel near-field engineering with inhomogeneous or spatially structured illumination.

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INTRODUCTION Plasmonic nanoantennas for the visible and infrared (IR) range enhance light−matter interactions by linking propagating far fields with localized near fields.1 Nanoantennas resonating at mid-IR frequencies2−5 are gaining increasing attention because of their attractive potential for surface-enhanced vibrational spectroscopy,6−9 chemical/biosensing,10,11 photodetectors,12,13 nonlinear light−matter interactions,14−17 etc. Fundamental properties of nanorod antennas resonating at mid-IR frequencies have been theoretically studied with electromagnetic analysis and experimentally studied often with far-field extinction/scattering measurements.2−5 In the past decade, spatial distributions of the plasmonic near fields on IR nanoantennas have been observed with the scattering-type scanning near-field optical microscopy (s-SNOM).18−21 The Raschke group18,19 obtained the amplitude- and phase-resolved images of the IR antenna modes by the s-SNOM with interferometric homodyne detection. Here the antennas were excited by the linearly polarized laser light at oblique incidence, and the light scattered by the nanotip is detected. With spolarized illumination, the antennas were excited homogeneously along their longer axes, and the odd-order multipole modes were successfully imaged.18 The Hillenbrand group20,21 obtained the amplitude- and phase-resolved images of the IR antenna modes by the transmission-mode s-SNOM and the pseudoheterodyne detection. Here the authors achieved © XXXX American Chemical Society

homogeneous antenna excitation by employing the normal illumination geometry. In practical applications, antenna excitation may be spatially inhomogeneous because of oblique illumination, structured wavefront, etc. For a deeper understanding of the enhancements of light−matter interactions under inhomogeneous excitations, it is of critical importance to elucidate excitation properties and near-field distributions of nanoantenna modes for such excitation conditions. Based on this knowledge, one would be able to further engineer the near fields by structuring the excitation light field.22 In this paper, we study excitation properties and near-field distributions of surface plasmon modes on Au nanorods for oblique illumination. We obtain amplitude- and phase-resolved images of the near fields in the mid-IR range by using our developed s-SNOM and the interferometric homodyne detection.23 Resonant excitation of the first-order (dipole) mode and that of the second-order (quadrupole) mode are observed for the nanorods with different lengths. Asymmetric near-field distributions are experimentally visualized and numerically reproduced. The asymmetry in the near-field distributions is attributed to the preferential excitation of the Received: August 24, 2017 Revised: October 22, 2017

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DOI: 10.1021/acs.jpcc.7b08465 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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surface plasmon polariton (SPP) in one direction and the finite loss of the SPP inside the cavity. Furthermore, we organize the excitation conditions of the nanoantenna modes as two formulas, each of which illustrates the cavity resonance condition and the phase matching condition for the SPP excitation within the nanorod length, respectively. So far, even-order antenna modes excited under oblique illumination have been observed in the visible/near-IR range by the far-field extinction/scattering measurements,24,25 the photoemission electron microscopy,26 and the s-SNOM.27 In the present study, we investigate the excitation properties of the dipole and the quadrupole modes in the mid-IR range, reveal their asymmetric near-field distributions, and present the physics underlying the nanoantenna excitations and the asymmetry.

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EXPERIMENTAL RESULTS The atomic force microscope (AFM) topographic images and s-SNOM amplitude images of the nanorods are shown in Figure 2(a) and (b), respectively (acquired with a relatively

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EXPERIMENTAL METHODS The IR-resonant Au nanorods are fabricated on a SiO2-glass substrate by the electron beam lithography and the lift-off process. The electron-beam resist (FEP-171, Fujifilm Corp.) is spin-coated, exposed by the electron beam (F5112, Advantest Corp.), and developed by tetramethylammonium hydroxide. The desired mass thickness of Au is thermally evaporated at room temperature with a few nanometer-thick Cr adhesion layer and is lifted off (Stripper 104, Tokyo Ohka Kogyo Co., Ltd.). The nanorods have a common width of 200 nm, a common height of about 70 nm, and varied lengths L’s of 2.2, 2.8, 3.4, 4.0, 4.6, 5.2, and 5.8 μm. The nanoantennas are illuminated at oblique incidence (an incidence angle of 60°) and with p-polarization (incident electric field has a component both along and perpendicular to the nanorod longer axis), as shown in Figure 1. Amplitude- and phase-resolved images are

Figure 2. (a) AFM topographic images and (b) s-SNOM amplitude images of Au nanorods with varied lengths. The scale bars indicate 2 μm. Bright regions are observed for the nanorods of L = 2.2, 2.8, 5.2, and 5.8 μm.

large scanning step of 156 nm and the fast scanning direction being perpendicular to the longer axes of the nanorods). In Figure 2(b), we find bright regions for the nanorods of L = 2.2, 2.8, 5.2, and 5.8 μm, suggesting resonant excitation of some antenna modes. We also find that near-field distributions are asymmetric, which will be analyzed further in the following. Figure 3 summarizes the measurements for the nanorod of L = 2.8 μm, namely, (a) the AFM topographic image, (b) the amplitude image, (c) its line profile, (d) the phase image, and (e) its line profile (acquired with a scanning step of 23 nm and the fast scanning direction being parallel to the longer axis of the nanorod). The line profiles are taken along the longer axis at the middle of the nanorod. Note that the excitation laser is incident from the left side of the figures. One can find that there are two bright regions separated by a dark region (a single node) and that the phase has a stepwise profile with a jump of π at the node. Such amplitude and phase distributions indicate the first-order (or dipole) antenna mode. One can clearly see that the amplitude profile is spatially asymmetric; the hot spot is brighter at the “rear” end of the nanorod, expressed from the incidence point of view. Figure 4 summarizes the measurements for the nanorod of L = 5.8 μm, namely, (a) the AFM topographic image, (b) the amplitude image, (c) its line profile, (d) the phase image, and (e) its line profile (acquired with a scanning step of 31 nm and the fast scanning direction being parallel to the longer axis of the nanorod). The line profiles are taken along the longer axis at the middle of the nanorod. One can find that there are three bright regions separated by two nodes and that the phase has a stepwise profile with two jumps of π. Such amplitude and phase distributions indicate the second-order (quadrupole) antenna

Figure 1. Geometry for nanoantenna excitation and near-field detection: nanoantennas are illuminated by the p-polarized laser at the incidence angle of 60°, and the near fields of the antenna modes are scattered into far field by the Si tip.

obtained by our developed s-SNOM with interferometric homodyne detection23 (see Supporting Information for the detailed description). In principle, the nanoantennas may be excited either directly by the far field or indirectly by the tipenhanced near field. We believe, however, that optical excitation is made predominantly by the far field because the Si tip is dielectric and Au nanorods have large polarizabilities at their resonances. The Si tip works to scatter the near fields of the nanoantenna modes into the far field. We set the polarizer so that the p-polarized component of the scattered light is detected. Combined with the scattering properties of the Si tip, the z-component of the near field is predominantly detected (see Figure 1 for the definitions of x-, y-, and z-axes). B

DOI: 10.1021/acs.jpcc.7b08465 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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NUMERICAL SIMULATIONS Electromagnetic field distribution around Au nanorods upon linearly polarized plane-wave illumination at the wavelength of 10.6 μm is numerically simulated by the finite-difference timedomain (FDTD) method. In the simulations, each nanorod is placed on a SiO2-glass substrate (refractive index of 2.1) and modeled using a rectangular cross-section and two halfcylinders at both ends. Incident electric field is set to be parallel to the nanorod longer axis in the normal incidence case and to be p-polarization in the oblique incidence case. Figure 5 shows the simulated electric-field amplitude distribution of the z-component (perpendicular to the substrate

Figure 3. Measured data for the Au nanorod of L = 2.8 μm: (a) the AFM topographic image, (b) the amplitude image, (c) its line profile, (d) the phase image, and (e) its line profile. The scale bar indicates 1 μm.

Figure 5. Simulated electric-field amplitude distribution (z-component) around Au nanorods with varied lengths L of 2.2, 2.8, 3.4, 4.0, 4.6, 5.2, and 5.8 μm, upon plane-wave illumination (a) at normal incidence and (b) at oblique incidence with an incidence angle of 60°. The scale bar indicates 2 μm.

surface, evaluated within an x−y plane just above the upper surfaces of the nanorods) for optical excitation (a) at normal incidence and (b) at oblique incidence with an incidence angle of 60°. Here the dimensions of each nanorod are set to be similar to those used in the experiments: a common width of 200 nm, a common height of 30 nm, and varied lengths L’s of 2.2, 2.8, 3.4, 4.0, 4.6, 5.2, and 5.8 μm. Some deviation in height (∼70 nm in the experiments) is not an issue here because it does not cause any essential difference in near-field distributions in an x−y plane. Under the normal incidence conditions, the first-order mode is resonantly excited for L = 2.2 and 2.8 μm, whereas the second-order (quadrupole) mode is not excited for any L. The spatial distribution of the near field is symmetric along the xaxis regardless of the nanorod length. Under the oblique incidence conditions, in contrast, resonant excitation is observed not only for the first-order mode (L = 2.2 and 2.8 μm) but also for the second-order mode (L = 5.2 and 5.8 μm), and the spatial distribution is asymmetric along the x-axis. These key features, namely, the resonant excitation properties and the asymmetric near-field distributions, are in excellent agreement with the experimental results found in Figure 2(b).

Figure 4. Measured data of the Au nanorod of L = 5.8 μm: (a) the AFM topographic image, (b) the amplitude image, (c) its line profile, (d) the phase image, and (e) its line profile. The scale bar indicates 1 μm.

mode. Again, asymmetry in the spatial distribution with a brighter spot on the rear end of the nanorod is clearly observed. In our experiments, different nanorods of the same length give very similar asymmetric near-field distributions. For example, the nanorod of L = 2.8 μm in Figure 2 and that in Figure 3 are nonidentical, but the asymmetric character of the near-field distribution is common. Similarly, the nanorod of L = 5.8 μm in Figure 2 and that in Figure 4 are nonidentical, but the asymmetric character is again common. Therefore, it is quite likely that the asymmetric characters of the SNOM signals originate from oblique illumination, whereas the possible asymmetry of the topographic profiles is ruled out as the origin. In fact, there is no noticeable asymmetry in the AFM topographic images shown in Figures 3(a) and 4(a) (see Supporting Information for the detailed analyses). C

DOI: 10.1021/acs.jpcc.7b08465 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 6. Simulated near-field distributions (z-component) for the Au nanorod of L = 2.8 μm (a−d) under the normal incidence and (e−h) under the oblique incidence with an incidence angle of 60°: (a, e) the amplitude images, (b, f) their line profiles, (c, g) the phase images, and (d, h) their line profiles.

Figure 7. Simulated near-field distributions (z-component) for the Au nanorod of L = 5.8 μm (a−d) under the normal incidence and (e−h) under the oblique incidence with an incidence angle of 60°: (a, e) the amplitude images, (b, f) their line profiles, (c, g) the phase images, and (d, h) their line profiles.

origin of the asymmetric near-field distributions. Resonant behaviors of nanoantenna modes on metal nanorods have been explained by considering nanorods as Fabry−Pérot cavities for SPP’s.24−29 It is known that only odd-order modes can be excited under normal illumination, and even-order modes may be excited at oblique incidence. Though the incidence-angle dependences of scattering/extinction efficiencies of nanoantennas have been observed,24−29 a systematic explanation on them has rarely been made. Here we organize the conditions of nanoantenna excitations as two formulas and show that they systematically explain the antenna excitation properties for varied illumination angles. We consider that an incident wave with a wave vector k0 and ppolarization illuminates a nanorod antenna at incidence angle of α (0 ≤ α < π/2), as shown in Figure 8. A nanorod is viewed to be divided into short segments in the direction of the nanorod longer axis. In each segment, the incident wave excites an SPP propagating in the forward direction and that propagating in the backward direction (a wave vector of an SPP is defined as kp). The excited SPPs travel along the nanorod and experience reflections at the ends. If the round-trip distance 2Leff is multiples of the SPP wavelength λp, where the effective cavity length Leff is the physical length L added by the spatial extent of evanescent fields, an SPP generated in a segment travels the round-trip distance to interfere constructively with a “fresh” SPP generated in the same segment (see Figure 8). This is nothing but the cavity resonance condition and is expressed as

We now investigate the simulated near-field distributions in more detail. Figure 6 displays (a, e) the amplitude images, (b, f) their line profiles, (c, g) the phase images, and (d, h) their line profiles, upon optical excitation (a−d) at normal incidence and (e−h) at oblique incidence for the nanorod with L = 2.8 μm (zcomponent). Here the line profiles are taken along the longer axis at the middle of the nanorod. Regardless of the incidence angle, the nanorod exhibits two bright regions separated by a single node and a stepwise phase profile with a jump of π, indicating the excitation of the first-order (dipole) mode. The near-field distribution is symmetric along the x-axis for the normal incidence, but the symmetry is broken for the oblique incidence. The amplitude- and phase-resolved images show excellent agreement with the experimental results shown in Figure 3. Figure 7 displays the same set of the numerical results for the nanorod with L = 5.8 μm (z-component). The nanorod exhibits no resonant excitation for the normal incidence, whereas it exhibits resonant excitation of the second-order (quadrupole) mode (characterized by three bright regions separated by two nodes and by a stepwise phase profile with two jumps of π) for the oblique incidence. Spatial asymmetry is clearly observed for the oblique incidence, similar to the case of L = 2.8 μm. Again, the amplitude- and phase-resolved images show excellent agreement with the experimental results shown in Figure 4.

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DISCUSSION Based on our experimental/numerical findings, we (i) organize the conditions for nanoantenna excitations and (ii) discuss the

k p = mK D

(1) DOI: 10.1021/acs.jpcc.7b08465 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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however, there are only two independent variables of Leff and α. Therefore, only two of the above three conditions are independent. In fact, one can check that eq 1 automatically holds if eq 2 holds for both the forward and backward directions. Let us first apply eqs 1 and 2 to the normal incidence case (α = 0). When eq 1 holds with an odd integer m (or Leff satisfies the odd-order cavity resonance), eq 2 is automatically satisfied. When eq 1 holds with an even integer m (or Leff satisfies the even-order cavity resonance), eq 2 is inevitably violated. In this way, the two formulas explain the well-known fact that only odd-order modes can be excited under normal illumination. Now we apply them to the oblique illumination case (α ≠ 0). In principle, the above-mentioned three conditions can be satisfied simultaneously with an appropriate set of Leff and α. Even so, the SPP propagating in the forward direction is excited more efficiently than that propagating in the backward direction. This is because the “intrinsic” wavenumber mismatch kp − k∥ is smaller for the forward direction: elementary SPPs generated in different segments add up to form an SPP with larger amplitude if the “intrinsic” wavenumber mismatch is smaller. In Table 1, we present the calculated phase mismatches of Δkcav·2Leff and ΔkSPPLeff for our experimental conditions, where

Figure 8. Illustration of the nanoantenna excitation mechanism. A nanorod is viewed to be divided into short segments. In each segment, the incident wave excites an SPP propagating in the forward direction and that propagating in the backward direction. When the cavity resonance condition holds, an SPP generated in a segment travels the round-trip distance to interfere constructively with a “fresh” SPP generated in the same segment. Elementary SPPs generated from different segments add up with phase relationships determined by the “intrinsic” wavenumber mismatch kp − k∥. When the phase matching condition for one-way SPP excitation holds, the “intrinsic” wavenumber mismatch is compensated by the odd-multiples of the grating wavenumber K. The interferences are illustrated only for the forwardpropagating SPPs, but similar interferences exist for the backwardpropagating SPPs as well.

Table 1. Characteristic Phase Mismatches of Δkcav·2Leff and ΔkSPP·Leff, Regarding the Cavity Resonance and the OneWay SPP Excitation, Respectively, for Varied Nanorod Lengths (in Units of π) Δkcav·2Leff

where m is a positive integer indicating the order of the antenna mode and K = π/Leff may be interpreted as a wavenumber of the grating with a period of 2Leff. For fixed excitation frequency (and therefore for fixed λp), this cavity resonance condition holds for an appropriate Leff, independent of α. Excitation of a nanoantenna mode requires, in addition to the cavity resonance condition, an efficient excitation of an SPP within the interaction length of Leff. In a word, SPPs excited in different segments should add up constructively (see Figure 8). For that, the phase mismatch between the exciting optical field and the excited SPP field, accumulated in the interaction length of Leff, (kp − k∥)Leff, should be odd-multiples of π. Here we define the wave vector of the exciting light projected onto the nanorod longer axis as k∥ ≡ k0·(kp/kp) = ± k0 sin α, in which the positive (negative) sign corresponds to the SPP propagating in the forward (backward) direction. The propagation direction of the SPP is expressed as forward or backward from the incidence point of view. This condition may be termed as the phase matching for one-way SPP excitation and is described as k p − k − (2n − 1)K = 0

ΔkSPP·Leff

L (μm)

m=1

m=2

forward, n = 1

2.2 2.8 3.4 4.0 4.6 5.2 5.8

−0.3 0.1 0.6 1.0 1.4 1.9 2.3

−2.3 −1.9 −1.4 −1.0 −0.6 −0.1 0.3

−0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.2

Δkcav = kp − mK and ΔkSPP = kp − k∥ − (2n − 1)K. Here we use the value of λp ∼ 5.6 μm, deduced from the FDTD simulations. The effective length Leff is set to be the physical length L added by 200 nm, referring to the simulated decay length of the near field along the longer axis. In our experiments, the incidence angle α is fixed at 60°, and only L (and therefore Leff) is varied. Then Δkcav·2Leff and ΔkSPPLeff vary with L. In Table 1, Δkcav·2Leff is evaluated for the firstorder (m = 1) and the second-order (m = 2) modes, and ΔkSPPLeff is evaluated for the case of maximum efficiency (forward direction, n = 1). We find from Table 1 that the cavity resonance for the m = 1 mode is nearly satisfied for L = 2.2 and 2.8 μm, but the one-way SPP excitation is phase-mismatched for these lengths. Therefore, the m = 1 mode would be excited with reduced efficiency, compared with the normal incidence case. For the nanorods of L = 5.2 and 5.8 μm, the cavity resonance for the m = 2 mode is nearly satisfied, and at the same time, one-way SPP excitation is nearly phase-matched. Therefore, the m = 2 mode would be efficiently excited. In this way, the experimentally/numerically observed excitation properties of the first-order (dipole) and the second-order (quadrupole) modes are reasonably explained by the two formulas. It is noteworthy that eq 2 is identical to

(2)

where n is a positive integer. This phase matching condition exists for each of the forward and the backward directions and can be satisfied with an appropriate set of Leff and α. Equation 2 is also understood as the condition that the “intrinsic” wavenumber mismatch kp − k∥ is compensated by the oddmultiples of the grating wavenumber K. Now we have three equations of eq 1 and eq 2 for the forward direction (k∥ = +k0 sin α) and eq 2 for the backward direction (k∥ = −k0 sin α). For a fixed excitation frequency, E

DOI: 10.1021/acs.jpcc.7b08465 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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the one found to describe angular distribution of radiation from a nanorod antenna.30,31 This is not surprising from the viewpoint of the reciprocity, but it is meaningful that the same formula is derived from a physically solid picture. Finally we discuss the origin of the asymmetric near-field distributions, based on the physics behind nanoantenna excitations described above. As shown in Figures 2(b) and 5(b), a bright spot exists at the rear end of the nanorod, accompanied by a dark region at the position ∼λp/2 away from the rear end, regardless of the nanorod length. An additional bright spot appears at the front end, when the cavity resonance is nearly satisfied. We confirm by numerical simulations that these features exist not only for the z-component but also for the x-component (see Supporting Information). The standingwave pattern should be the result of the interference between an excited SPP and its reflected wave. Because an SPP is more efficiently excited for the forward direction than for the backward direction and because SPPs have finite loss upon propagation and reflection, the standing-wave pattern becomes more evident on the rear end (note that absorption of the substrate and radiative damping at nanorod ends would attenuate SPPs inside the cavity, although the propagation length of an SPP at a Au/air interface lies around 10 mm in the mid-IR range32). In this way, the asymmetry in the near-field distributions is attributed to preferential excitation of SPP in one direction and its finite loss inside the cavity.

Satoshi Ashihara: 0000-0001-6697-2513 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by the Japan Society for the Promotion of Science (MEXT KAKENHI 16K13694) is gratefully acknowledged. The authors acknowledge the financial and technical support by Interdisciplinary Research Unit in Photon-Nano Science in Tokyo University of Agriculture and Technology (TUAT) and by Prof. Kazuhiko Misawa in TUAT. The sample was fabricated at VLSI Design and Education Center (VDEC), the University of Tokyo.

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CONCLUSIONS In summary, we study excitation properties and near-field distributions of plasmonic nanoantenna modes on Au nanorods in the mid-IR range for oblique illumination. We obtain amplitude- and phase-resolved images of the near fields by using our developed s-SNOM and the interferometric homodyne detection. Resonant excitation of the first-order (dipole) mode and that of the second-order (quadrupole) mode are observed for the nanorods with different lengths. Asymmetric near-field distributions are experimentally visualized and numerically reproduced. The asymmetry in the nearfield distributions is attributed to the preferential excitation of the SPP in one direction and the finite loss of the SPP inside the cavity. We organize the excitation conditions of the nanoantenna modes as two formulas, each of which illustrates the cavity resonance condition and the phase matching condition for SPP excitation within the nanorod length, respectively, and show that the two formulas systematically explain the nanoantenna excitation properties. The findings are highly relevant to the properties of nanoantennas in enhancing light−matter interactions and will form the basis for novel nearfield engineering with inhomogeneous or spatially structured illumination.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b08465. Detailed description on the s-SNOM setup and the simulated electric-field components along the nanorod longer axes (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-3-5452-6136. F

DOI: 10.1021/acs.jpcc.7b08465 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.7b08465 J. Phys. Chem. C XXXX, XXX, XXX−XXX