Characterization of Overlapped Plasmon Modes in a Gold Hexagonal

Letter Cite This: J. Phys. Chem. Lett. 2019, 10, 819−824

pubs.acs.org/JPCL

Characterization of Overlapped Plasmon Modes in a Gold Hexagonal Plate Revealed by Three-Dimensional Near-Field Optical Microscopy Takuya Matsuura,† Keisuke Imaeda,‡ Seiju Hasegawa,† Hiromasa Suzuki,† and Kohei Imura*,†,‡ †

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Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan ‡ Research Institute for Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan S Supporting Information *

ABSTRACT: A detailed characterization of plasmon modes is important not only for a deeper understanding of plasmons but also for their practical applications. In this study, we investigated the three-dimensional near-field characteristics of high-order plasmon modes excited in a gold hexagonal nanoplate. From the near-field spectroscopic images, we found that both in-plane and out-of-plane plasmon modes observed near 900 nm were spectrally and spatially overlapped. We performed three-dimensional near-field measurement to reveal the optical characteristics of the overlapped modes in detail. We found that the steric near-field distribution near the nanoplate strongly depended on the plasmon mode, and the out-of-plane mode confines electromagnetic fields more tightly than the in-plane mode. We also found that the in-plane mode was dominantly visualized as the probe tip−sample distance increased. These findings demonstrate that the three-dimensional near-field technique enables selective visualization of a single plasmon mode even if multiple modes are spatially and spectrally overlapped.

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Two-dimensional nanoplates, such as nanotriangles and nanodisks, have also been investigated actively by various research groups.23−32 Nevertheless, a comprehensive interpretation of the high-order plasmon modes in the nanoplate still remains to be solved because of their complicated spatial and spectral characteristics. Due to the dimensionality of the nanoplate, multiple plasmon modes, including in-plane and out-of-plane polarized modes, can be excited, and the spatial patterns of these modes exhibit much more complex features than those in the one-dimensional case. In addition, because the volume damping effect should be large in a plate,33 the spectral overlaps between the nearby plasmon modes become very significant.34 Because of the spatial and spectral overlaps of numerous plasmon resonances, identification of a single plasmon mode among the overlapped modes is extremely difficult, even when using STEM-EELS imaging methods. In this study, we examined the three-dimensional near-field characteristics of plasmon modes in a gold hexagonal nanoplate by combining conventional near-field optical microscopy with a precise distance regulation between the tip of the near-field probe and sample surface. Several research groups have reported a similar method to visualize a threedimensional SNOM image.35−37 The observed near-field images show that the near-field distributions near the nanoplate strongly depend on the plasmon modes excited.

ocalized surface plasmon resonances excited in metallic nanostructures confine light fields into nanospaces and generate amplified fields in the vicinity of the nanostructures.1−3 The enhanced fields have been extensively investigated for their promising applications, such as surfaceenhanced spectroscopies,4,5 nonlinear optics,6 and photochemical reaction fields.7,8 The spatial distributions of plasmon-enhanced fields near the nanostructures are directly related to the spatial characteristics of plasmons (plasmon mode); thus, visualization of the plasmon modes is essentially important for the practical applications of plasmonic fields. In particular, visualization of high-order plasmon modes is more attractive compared with that of the lowest dipolar mode because high-order plasmon modes exhibit notable optical characteristics, such as a longer dephasing time,9 multipolar radiation,10,11 and Fano resonance.12 The spatial scale of highorder plasmon modes excited in the nanostructures is smaller than that of the diffraction limit of light, and hence, far-field imaging techniques cannot spatially resolve the plasmon modes. Advanced microscopic methods, including scanning transmission electron microscopy with electron energy loss spectroscopy (STEM-EELS)13−16 and scanning near-field optical microscopy (SNOM),17−19 have been developed to visualize high-order plasmon modes with a high spatial resolution. Using these microscopic methods, visualization of high-order plasmon modes excited in various nanostructures have been reported. Among them, metallic nanorods have been studied systematically, and it has been reported that the highorder plasmon modes are interpreted as one-dimensional Fabry−Pérot modes.20−22 © XXXX American Chemical Society

Received: November 28, 2018 Accepted: January 14, 2019

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DOI: 10.1021/acs.jpclett.8b03578 J. Phys. Chem. Lett. 2019, 10, 819−824

Letter

The Journal of Physical Chemistry Letters

1a). The vertical scale becomes large as the intensity of the transmitted light decreases due to the light scattering and absorption of the sample. This spectrum exhibited multiple extinction peaks observed near 620, 700, 815, and 900 nm. These peaks are assignable to the plasmon resonances excited on the hexagonal nanoplate, as discussed later. To visualize the plasmon modes at the resonance wavelengths, we obtained near-field transmission images by detecting the transmitted light intensity over the sample substrate. Figure 1c,d shows near-field transmission images taken near 900 and 815 nm, respectively. White dotted lines represent the approximate dimensions of the nanoplate. Bright parts in the near-field image indicate a reduction of the transmitted light, indicating that the excitation probability of the plasmon was high at this position. As evident in Figure 1c,d, the extinction intensity varied depending on the excitation position on the plate, and consequently, two-dimensional oscillating patterns were observed in the near-field images. The spatial distribution of these images did not show perfect six-fold symmetry because the sample was slightly distorted from a perfect hexagonal shape. We found that these spatial patterns were highly dependent on the observation wavelength. The remarkable wavelength dependency was particularly observed at the center of the plate; a bright spot was observed in Figure 1c, whereas a dark spot was observed in Figure 1d. In this study, multiple plasmon modes are excited in a narrow spectral range, and thus, spectral overlap among the modes should be significant. Consequently, electromagnetic simulation based on Maxwell’s equations cannot provide detailed characteristics of each plasmon mode. The simulated spectrum reproduces the observed spectral features very well (Figure S1 in the Supporting Information), while most of the resonance features are hidden in the broad spectral bands. To explore the physical origin of the spatial patterns in the nearfield images, we discuss the observed results based on the eigenmodes calculated by Schrödinger’s equation (Figure S2 in the Supporting Information).39 We have reported previously and also revealed in this study that in a limited spectral range (650−900 nm) there is a one-by-one correspondence between the eigenenergy obtained by Schrödinger’s equation and the experimentally observed resonance energy (Figure S3 in Supporting Information).34 We should also emphasize here

By analyzing the steric characteristics of the plasmon modes, we selectively visualized a single plasmon mode among the overlapped ones. Hexagonal gold nanoplates were chemically synthesized following a previously reported method.38 The nanoplate was dispersed on a glass substrate and used as a SNOM sample. Figure 1a shows a scanning electron microscopy (SEM) image

Figure 1. (a) Scanning electron micrograph of a gold hexagonal nanoplate (edge length: 400 ± 20 nm; thickness: 40 ± 5 nm). (b) Near-field extinction spectrum observed at the center of the nanoplate (the red point in (a)). (c,d) Near-field transmission images taken near 900 and 815 nm, respectively. The white dotted lines represent the approximate shape of the hexagonal nanoplate. Scale bars are 200 nm.

of single gold hexagonal nanoplate (side length: 400 ± 20 nm; thickness: 40 ± 5 nm). We performed near-field transmission measurements of the sample to reveal the optical properties of the single nanoplates. Figure 1b shows a near-field extinction spectrum taken at the center of the plate (red point in Figure

Figure 2. (a,b) Near-field transmission images of the hexagonal nanoplate taken near 900 and 815 nm, respectively. (c−f) Squared moduli of the eigenfunctions calculated for a particle confined in a two-dimensional hexagonal potential well. Eigenenergy: (c) 5.25E0, (d) 6.66E0, (e) 8.40E0, and (f) 9.81E0. E0 represents the eigenenergy of the lowest eigenmode. The corresponding irreducible representation is provided for each eigenmode. (g) Superposition of the eigenmodes shown in (c,d). (h) Superposition of the eigenmodes shown in (e,f). 820


Letter

The Journal of Physical Chemistry Letters Table 1. Character Table for the C6v Point Group C6v

E

2C6

2C3

C2

3σv

3σd

A1 A2 B1 B2 E1 E2

1 1 1 1 2 2

1 1 −1 −1 1 −1

1 1 1 1 −1 −1

1 1 −1 −1 −2 2

1 −1 1 −1 0 0

1 −1 −1 1 0 0

that the SNOM predominantly visualizes the photonic local density of states (LDOS) of the sample.20 The LDOS can be approximated to the square moduli of the eigenfunctions of the elementary excitations under the resonance condition. For these reasons, we discuss and analyze the characteristics of the near-field image based on the calculated eigenmode. Figure 2c−f shows the squared moduli of eigenfunctions calculated for various eigenenergies, (c) 5.25E0, (d) 6.66E0, (e) 8.40E0, and (f) 9.81E0, where E0 represents the eigenenergy of the lowest eigenmode. A bright area in the image indicates that the probability for finding a particle is high. We should emphasize that the calculated eigenenergies do not provide quantitative plasmon energies but qualitative ones among the observed plasmon modes (Figure S3 in the Supporting Information). We also conducted a group theory analysis to determine the irreducible representations of the calculated eigenmodes. A hexagonal nanoplate on a glass substrate belongs to the C6v point group (Table 1). The surface plane of the nanoplate was taken as the xy-plane of the Cartesian coordinates (Figure S4 in the Supporting Information). We assigned each eigenmode to an irreducible representation of the C6v point group based on its spatial characteristics, as shown in Figure 2c−f. As previously reported, these irreducible representations provide the polarization characteristics of the plasmon modes.32,40 Because the A1 mode shown in Figure 2c has the same symmetry with a z vector component, this mode is assignable to the out-of-plane mode (plasmon polarized in the out-ofplane direction). On the other hand, because B1, E1, and E2 do not possess a z vector component, the eigenmodes in Figure 2d−f are assigned to the in-plane plasmon mode (plasmon polarized in the in-plane direction). We stress here that not all plasmon modes in Figure 2d−f can be optically excited by normally incident far-field light. According to the optical selection rule under the dipolar approximation with plane wave illumination, the E1 mode shown in Figure 2e is optically allowed, whereas the B1 and E2 modes in Figure 2d,f are dipole-forbidden and are only accessible by near-field local illumination. As evident in Figure 2a−f, the spatial distributions of the near-field images are partially reproduced by the calculated eigenmodes. This fact indicates that the spatial distributions in the near-field images are hardly attributed to a single eigenmode but a superposition of eigenmodes with similar eigenenergies. We simulated the superposition of two possible eigenmodes with close eigenenergies, as shown in Figure 2g,h. The spatial distributions in these images show qualitative agreement with those of the near-field images in Figure 2a,b. These agreements indicate that two plasmonic eigenmodes overlapped spectrally; consequently, the spatial superpositions of these modes were visualized in the near-field images in Figure 2a,b. This result strongly indicates that direct visualization of a single plasmon mode was extremely difficult when multiple plasmon modes were spectrally overlapped.

z

(x, y)

(x2+y2, z2)

z3

(xz, yz) (xy, x2−y2)

x(x2−3y2) y(3x2−y2) (xz2, yz2) {z(x2−y2), xyz}

To characterize the plasmon modes in detail, we performed three-dimensional near-field imaging on the hexagonal nanoplate. In this imaging technique, two-dimensional near-field imaging was performed at various near-field probe tip-tosample surface distances, d. Figure 3a−c shows near-field

Figure 3. (a−c) Near-field transmission images of the hexagonal nanoplate observed at a near-field probe tip−sample distance d = 20, 40, and 90 nm, respectively. Scale bars are 200 nm. (d) Tip−sample distance dependence of the extinction intensity at the vertex (square) and center (circle) of the hexagonal plate. The vertical axis is plotted on a logarithmic scale. The plots at the center were divided into two regions and were fitted in each region (20−50 and 50−90 nm).

transmission images of the hexagonal nanoplate taken at d = 20, 40, and 90 nm, respectively. The images were observed near a wavelength of 900 nm. As was evident in these images, the distinct extinction spot observed at the center of the nanoplate vanished as the distance d increased from 20 to 90 nm. On the other hand, the periodically oscillating spots observed along the edges remained nearly the same regardless of d. As mentioned above, the spatial features in Figure 3a can be reproduced by the superposition of the out-of-plane and inplane eigenmodes shown in Figure 2c,d. The spatial distribution of the image represents that the out-of-plane mode (Figure 2c) was dominantly excited at the center of the nanoplate, whereas the in-plane mode (Figure 2d) was dominantly excited near the vertices of the plate. From the position-dependent excitation probability of these eigenmodes, the near-field transmission image observed at d = 90 nm (Figure 3c) is attributable to the in-plane eigenmode shown in Figure 2d. This result clearly demonstrates that threedimensional near-field imaging enables us to selectively visualize a single plasmon mode even if multiple plasmon modes overlap spectrally and spatially. To elucidate the mode-dependent three-dimensional spatial characteristics in detail, we examined the distance dependence of the extinction intensity at the center and vertex, as shown in 821


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The Journal of Physical Chemistry Letters Figure 3d. The vertical scale in this figure was normalized by the extinction intensity observed at d = 20 nm. We found from the figure that the extinction intensity at the vertex decayed exponentially with a single component, whereas that at the center decayed with two components. Decay lengths at the center (red lines) were analyzed to be 160 and 700 nm, while at the vertex (blue line), the decay length was 520 nm. These results indicate that the out-of-plane mode (Figure 2c) confined the optical near field in a narrower area compared with that of the in-plane mode (Figure 2d). To confirm the plasmon-mode-dependent light confinement capability, we evaluated the dephasing times of the individual plasmon modes from the near-field extinction spectra of the nanoplate. The black lines in Figure 4a,b show experimental

to the in-plane mode. Table 2 summarizes the observed peak wavelengths, spectral bandwidths, and dephasing times of these Table 2. Summary of Peak Wavelengths, Bandwidths, and Dephasing Times of the In-Plane and Out-of-Plane Plasmon Modes Excited in a Gold Nanoplate (875 and 905 nm)

in-plane mode out-of-plane mode

central wavelength/ nm

bandwidth/ nm

dephasing time/ fs

875 905

80 60

10 14

modes. The dephasing times for the out-of-plane and in-plane modes were estimated to be approximately 14 and 10 fs, respectively. Because the dephasing time is directly related to the quality factor of the plasmon modes,33 this result indicates that the out-of-plane plasmon mode exhibits stronger field confinement than that in-plane mode, which is consistent with the conclusions drawn from the three-dimensional near-field imaging. In conclusion, we investigated the spectral and spatial characteristics of the plasmon modes excited in a gold hexagonal nanoplate by aperture-type near-field optical microscopy. In the near-field transmission spectrum, multiple plasmon resonance peaks were observed in the visible to nearinfrared region. Near-field transmission images taken at these resonance wavelengths showed periodically oscillating patterns inside of the nanoplate. The images were mostly ascribable to the superposition of eigenmodes with similar eigenenergies. We performed a three-dimensional near-field measurement on the nanoplate to elucidate the spatial and spectral properties of the overlapped modes. We revealed from the three-dimensional imaging that the out-of-plane plasmon mode confined optical fields more tightly than the in-plane mode. We demonstrated that three-dimensional near-field imaging is promising for the characterization of plasmons even in spectrally overlapping systems. We are currently developing a three-dimensional reconstruction system by improving the performances of the scanning stage and the detector in the apparatus.

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Figure 4. (a,b) Near-field extinction spectra observed at the center and vertex of the hexagonal nanoplate, respectively. The spectra were fitted by Lorentzian curves (red: A1; blue: B1; green: E1; orange: E2). Irreducible representations are given in Figure 2c−f. The spatial distributions of the A1 (out-of-plane) and B1 (in-plane) modes are provided in the right panels of (a,b), respectively.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b03578. Experimental methods, far-field scattering spectrum of the hexagonal gold nanoplate, calculation of eigenfunctions confined in a two-dimensional hexagonal potential well, relationship between the experimental plasmon energy and the calculated eigenenergy, and Cartesian coordinates for a gold hexagonal plate on a glass substrate (PDF)

near-field extinction spectra taken at the center and vertex of the nanoplate, respectively. The individual peaks were fitted by a Lorentzian function, as shown in Figure 4. The number of resonances was determined by taking the mode assignments of the near-field images and the observed spectral features into account. As discussed so far, the extinction near 900 nm was attributable to the out-of-plane and in-plane eigenmodes shown in Figure 2c,d. Contribution from these modes to the extinction should be strongly dependent on the internal position on the nanoplate. From their spatial characteristics, the out-of-plane and in-plane modes contributed to extinction at the center and vertices of the nanoplate, respectively. Therefore, the resonance bands observed near 900 nm in Figure 4a were assignable to the out-of-plane plasmon mode, whereas the band in Figure 4b was considered to be assignable

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Keisuke Imaeda: 0000-0001-8877-1085 Kohei Imura: 0000-0002-7180-9339 Notes

The authors declare no competing financial interest. 822


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The Journal of Physical Chemistry Letters

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ACKNOWLEDGMENTS This work was supported in part by JSPS KAKENHI Grant Nos. JP26107001, JP26107003, JP15K21725, JP16K13939, and JP16H04100 in Scientific Research on Innovative Areas “Photosynergetics” from the Japan Society for the Promotion of Science.

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Characterization of Overlapped Plasmon Modes in a Gold Hexagonal

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