Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 4075−4081
pubs.acs.org/JPCL
Static and Dynamic Near-Field Measurements of High-Order Plasmon Modes Induced in a Gold Triangular Nanoplate Keisuke Imaeda,† Seiju Hasegawa,‡ and Kohei Imura*,†,‡ †
Research Institute for Science and Engineering, and ‡Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan
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S Supporting Information *
ABSTRACT: Precise understanding of the spatiotemporal characteristics of plasmons is essential for the development of applications of plasmonic nanoparticles. In this study, we investigated the spatiotemporal properties of high-order plasmon modes induced in a gold triangular nanoplate by static and dynamic near-field measurements. The near-field transmission measurements revealed that in-plane and out-of-plane polarized plasmon modes were simultaneously excited and these modes spectroscopically and spatially overlapped. The superposition of these modes was visualized in the near-field two-photon excitation image of the nanoplate. We performed time-resolved autocorrelation measurements on the nanoplate and found that the correlation width was broader than the excitation pulse due to the plasmon dephasing process. From the correlation width map of the nanoplate, we experimentally demonstrated that the out-of-plane plasmon mode exhibits a longer dephasing time than the in-plane plasmon mode. These findings indicate that the outof-plane mode is desirable for improving the performance of plasmons in various applications.
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the other hand, the plasmon dephasing time in gold nanoparticles is reported to be less than 20 fs,17 and hence, direct measurements of the dephasing time are extremely difficult.22−24 Information about the dephasing time can also be obtained from the spectral width of the plasmon resonance band, and some groups have reported the dephasing time of gold nanoparticles from single-particle scattering spectra.17,25 However, this method is only valid when a single-plasmon resonance band is clearly observable in the scattering spectrum, such as a dipole mode in a small nanoparticle or a single highorder mode induced in one-dimensional nanorods. In two-dimensional nanostructures such as a nanoplate, because of their dimensionality plasmon modes becomes more complex spatially as well as spectroscopically compared with those in one-dimensional nanorods.20,26−29 In addition, plasmons are polarized in both the in-plane and out-of-plane directions with respect to the surface plane of the nanoplates. Furthermore, because the radiative damping effect becomes significant in large particles,17,25 the dephasing time in the nanoplates should be shorter than that in nanorods, resulting in broadening of the plasmon resonance band. Because of these unique spatial and spectral characteristics, plasmons induced in the nanoplates overlap both in space and in spectral domain. Therefore, the nanoplates are useful for investigating the spatiotemporal dynamics of multiple plasmons simultaneously excited, which would provide fundamental knowledge for the coherent control of plasmons. To observe the space-
oble metal nanoparticles have been extensively investigated due to their unique optical properties supported by the collective oscillation of free electrons, called surface plasmon resonances.1,2 Plasmon resonances generate intense local fields and dramatically enhance light−matter interactions.3 For example, plasmonic fields strongly interact with molecules near the nanoparticle and amplify various optical processes, such as fluorescence,4,5 Raman scattering,6 and infrared absorption.7 In particular, when the plasmons resonantly couple to the molecules, new hybrid states arise and result in the spectral splitting of the plasmon resonance band.8−11 Recently, strong coupling in plasmon−molecule hybrid systems has been actively explored due to its great potential for controlling the chemical reaction12 and tuning of the work function.13 These plasmon-enhanced light−matter interactions are closely related to the spatial and temporal characteristics of plasmons. For instance, the spatial characteristics of plasmons (plasmon modes), which reflect spatial distributions of the local density of states (LDOS) in the vicinity of the nanoparticle,14,15 govern the relaxation time of the emitter near the nanoparticle.4,16 In addition, the plasmon lifetime (dephasing time) is directly related to the quality factor of the nanoparticle, which represents local field enhancement near the particle.17,18 Therefore, detailed knowledge of the spatiotemporal properties of plasmons is indispensable for further enhancement of plasmon-enhanced light−matter interactions. Because the spatial scale of plasmon modes is smaller than that of the diffraction limit of light, conventional optical microscopy cannot directly visualize plasmon modes. Nonlinear optical microscopy15,19 and scanning near-field optical microscopy (SNOM)14,20,21 are often utilized to visualize plasmon modes in nanoparticles. On © XXXX American Chemical Society
Received: May 30, 2018 Accepted: July 5, 2018
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DOI: 10.1021/acs.jpclett.8b01671 J. Phys. Chem. Lett. 2018, 9, 4075−4081
Letter
The Journal of Physical Chemistry Letters
spots were observed along each side of the nanoplate, and consequently, unique spatial patterns were visualized. Very recently, we reported that the spatial features visualized in the near-field transmission images were qualitatively reproduced by the square amplitude of eigenfunctions of a particle confined inside of the geometrical shapes of the nanoparticles, regardless of their sizes and dielectric functions.35 In the present study, we calculated the eigenfunctions and eigenenergies of the triangular nanoplate by solving the Schrödinger equation for a particle confined in a two-dimensional triangular potential well.36 We note here that the calculated eigenenergies provide qualitative spectroscopic features of elementary excitations. We found that the spatial feature observed in Figure 2c is similar to that previously reported for a plasmonic quadrupole,20,37,38 and thus, we calculated the square moduli of the quadrupolar eigenfunction, as shown in Figure 2d. The calculated image shows three local maxima along each edge of the triangle. This spatial feature qualitatively reproduces that of the near-field image shown in Figure 2c, which suggests that the plasmon resonance observed at ∼800 nm is attributed to the plasmonic quadrupole. However, careful observation reveals that a notable difference exists between the spatial distributions in Figure 2c,d. The calculated eigenmode shown in Figure 2d exhibits a much higher intensity at the centers of the edges of the triangle, whereas the near-field image shown in Figure 2c shows strong extinctions not only at the centers of the edges but also near the apexes of the nanoplate. This mismatch suggests that the spatial distribution of the near-field image cannot be completely reproduced using only the quadrupolar eigenmode. We calculated eigenmodes with various eigenenergies and found that another eigenmode, shown in Figure 2e, exists in energetically close proximity to the quadrupolar eigenmode. The eigenmodes in Figure 2d,e were assignable to in-plane and out-of-plane modes, respectively, from their irreducible representations obtained by group theory analysis.35 It should be noted that the out-ofplane mode in Figure 2e has a dipolar forbidden character from the normal incidence and is only accessible by near-field light because of its longitudinal polarization character. The eigenenergies of the modes in Figure 2d,e were 4.33E0 and 4E0, respectively, where E0 represents the eigenenergy of the lowest mode. We estimated the correlation between the calculated eigenenergy and the observed resonance energy (Supporting Information section S1). From this analysis, we estimated the difference between the resonance wavelengths of the eigenmodes in Figure 2d,e to be approximately 10 nm, which is smaller than the commonly reported bandwidth of the plasmon resonance. This analysis implies that the two eigenmodes shown in Figure 2d,e should overlap not only spectrally but also spatially. Figure 2f shows the spatial superposition of the eigenmodes in Figure 2d,e. We found that the spatial distribution of this image reproduces well that of the near-field image in Figure 2c, indicating that the spatial feature in Figure 2c is assignable to the superposition of the two eigenmodes in Figure 2d,e. Figure 3a shows the two-photon-induced photoluminescence (TPI-PL) spectrum of the nanoplate excited by a modelocked Ti:sapphire laser (center wavelength: 810 nm; repetition rate: 80 MHz; pulse width:
