Exotic Mode Suppression in Plasmonic Heterotrimer System - The

Dec 3, 2018 - We investigate the far- and near-field properties of plasmonic heterotrimers with small detuning of the eigenfrequency numerically, theo...
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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Exotic Mode Suppression in Plasmonic Heterotrimer System Hanfa Song, Quan Sun, Jie Li, Fan Yang, Jinghuan Yang, Yaolong Li, Kosei Ueno, Qihuang Gong, and Hiroaki Misawa J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10263 • Publication Date (Web): 03 Dec 2018 Downloaded from http://pubs.acs.org on December 11, 2018

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The Journal of Physical Chemistry

Exotic Mode Suppression in Plasmonic Heterotrimer System Hanfa Song1,2, Quan Sun2, Jie Li2, Fan Yang3,Jinghuan Yang1,2, Yaolong Li1,2, Kosei Ueno2, Qihuang Gong1,4*, and Hiroaki Misawa2,5* 1State

Key Laboratory for Mesoscopic Physics and Collaborative Innovation Center

of Quantum Matter, Department of Physics, Peking University, Beijing 100871, China 2Research

Institute for Electronic Science, Hokkaido University, Sapporo 001-0021, Japan

3State

Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China

4Collaborative

Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China

5Center

for Emergent Functional Matter Science, National Chiao Tung University, Hsinchu 30010, Taiwan

*Corresponding authors’ e-mail: [email protected], [email protected]

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Abstract

We investigate the far- and near-field properties of plasmonic heterotrimers with small detuning of the eigenfrequency numerically, theoretically, and experimentally. In our simulations, we find that the dipolar mode of the middle nanorod in the trimer system is greatly suppressed in both the far and near fields. This phenomenon is confirmed by our subsequent experiments. The far-field suppression can be interpreted by the destructive interference due to the anti-phase dipolar response of the respective nanorod. To deeply understand the underlying physics, an analytical model considering both the near-field-mediated direct coupling and radiative-field-mediated indirect coupling is adopted. We determine that the radiative field coupling, which is stronger in the trimer system with smaller detuning, takes an essential role in mode suppression in the near field. Our work will provide new thoughts on the fundamental mechanisms of plasmon coupling and plasmon-based applications.

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Introduction Noble metal nanoparticles (NPs) can confine light at deep subwavelength with large near-field enhancement 1, resulted from localized surface plasmon resonance (LSPR). A number of applications have been proposed based on the strong enhancement and localization of LSPR including ultra-small optical circuits 2, photocurrent generation 3-4,

surface-enhanced Raman spectroscopy 5-6, artificial photosynthesis 7, and so on. The

optical properties of LSPRs can be tailored by the size, shape, material, and refractive index of the surrounding medium for the desired applications

8–10.

The LSPRs of

individual NPs can couple with each other when two or more NPs are placed in proximity. The plasmonic dimer, composed of two identical NPs with deep subwavelength separation, is the simplest and most typical plasmon-coupling system. The optical properties and their dependence on the separation of the plasmonic dimers have been intensively investigated in terms of far-field spectroscopy and numerical simulations 8-9. In particular, the bonding dipole plasmon mode can be formed, and it redshifts as the separation decreases, which has been well explained by the plasmon hybridization theory 10. The linearly aligned trimer or chain structures have been further investigated and exhibit a similar optical property to that of dimers. It has been explored that in all the dimers, trimers, and chain structures, the redshift of the longitudinal mode caused by the end-to-end coupling (dipolar modes of individual NPs are aligned end to end) is much larger than the blue shift of the transverse mode caused by the side-byside coupling (dipolar modes of individual NPs are aligned side by side). In this point of view, the side by side coupling is quite trivial compared with end to end coupling

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which could cause strong coupling explained by hybridization model 10. However, the side-by-side coupling also has some interesting features to be explored and utilized. For example, J.F. Martin et al.

11

construct Fano resonance utilizing only bright dipolar

modes with nanorods aligned side by side where destructive interference happens. Furthermore, there have been few reports on the optical properties of plasmonic homotrimers in terms of symmetry

12.

However, it remains unknown how plasmon

coupling occurs on plasmonic heterotrimers aligned side by side, where the detuning between individual dipole modes should become important. In addition, most investigations on plasmon coupling only focus on numerical simulation results and some experimental far-field properties correlated

with

far-field

properties,

near-field

properties,

11, 13-14.

However,

especially

those

experimentally proven, are also important as they offer intuitive pictures of electromagnetic field behaviors. Photoemission electron microscopy (PEEM) using femtosecond laser pulses as an excitation source has proven to be a powerful tool to investigate the near-field properties of surface plasmons 15-23. Previously, we employed PEEM to investigate the near-field properties of Au NPs with different shapes in terms of near-field mapping, near-field spectra, and ultrafast dynamics. In particular, the nearfield mapping was directly obtained as the distribution of photoemission (PE) in PEEM images

15.

We also utilized PEEM to investigate coupled dolmen plasmonic system

drawing the conclusion that plasmon hybridized modes dominated in the near-field enhancement instead of Fano resonance 18.

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In this paper, we propose an Au heterotrimer structure with three nanorods aligned side by side and investigate its optical properties in both the far field and near field. We find a unique phenomenon in which the intensity of dipole mode of the middle nanorod is greatly suppressed both in the far field and near field numerically and experimentally. In our subsequent experiments, we enlarge the detuning of eigenfrequencies of adjacent nanorods slightly and the previous mode suppression phenomenon becomes weak. We further adopt a theory to explain the abnormal phenomenon and find that radiative field coupling takes an essential role in this system. Our work provides crucial insights into the mechanism of plasmon coupling and further suggests more possible plasmonic applications, including nanoscale spectroscopy and sensing. Experimental Methods Fabrication of heterotrimer structure. The samples were fabricated through standard electron-beam lithography (EBL, ELS-F125; Elionix, Tokyo, Japan), sputtering (MPS-4000, ULVAC) and lift-off process. The heterotrimer structures were arranged on a two-dimensional square array in a 75 μm  75 μm area with a pitch size of 1 μm to avoid near-field interaction of adjacent units. A 2-nm-thick Ti adhesion layer is deposited between Au and the ITO substrate. The substrate is ITO-coated glass with an ITO thickness of approximately 150 nm. Scanning electron microscopy (SEM) and spectroscopic characterizations. Field-emission scanning electron microscopy (JSM-6700FT; JEOL, Tokyo, Japan) was used to characterize the morphologies of our samples. The far-field extinction spectra were measured by a Fourier transform infrared (FTIR, FT/IR-6000TM-M; JASCO,

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Tokyo, Japan) spectrometer with an infrared microscope. The area for the extinction spectrum measurement in this study was 50 μm × 50 μm. The extinction spectrum of the bare substrate was used as the reference to obtain the extinction spectra of the Au nanostructures. Near-field mapping and spectral properties measured by PEEM. We employed a PEEM system (Elmitec GmbH, Germany) to investigate the near-field properties of the Au nanostructures. A Ti:sapphire femtosecond laser system (Tsunami, SpectraPhysics, USA) was employed as the main excitation source, which was used for the measurements of near-field mapping and spectra. The laser source could deliver 100-fs laser pulses with the central wavelength tunable from 720 nm to 920 nm at a repetition rate of 77 MHz. The laser beam was focused onto the sample surface with a focal spot diameter of approximately 120 μm by a lens with a focal length of 500 m. An additional Hg lamp was employed to characterize the morphologies of the structures via a single-photon photoemission process. Numerical simulations. Numerical simulations of the optical properties of the Au heterotrimers were performed using the FDTD software package Lumerical. The geometry of the Au structures was chosen according to the experimental designed values and had a 24-nm radius of curvatures at the edges and corners. The refractive index of ITO substrate was assumed to be 1.55 in the simulation. The optical properties of gold were obtained using the data from Johnson and Christy 31. A plane wave is used as an excitation source on the sample with normal incidence. The periodic boundary

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condition was used in the perpendicular direction to the incident excitation in correspondence with our periodic structure. Results and Discussion The schematic diagrams of the structures are shown in Figure 1a,b. Each trimer unit consists of three Au nanorods with the same designed width (100 nm) and thickness (30 nm), but different lengths. The lengths of the three nanorods of the first structures, the SEM image of which is shown in Figure 1c, are designed as 170 nm, 150 nm, and 130 nm. The edge-to-edge distance of each adjacent nanorod is designed to be 50 nm. From the SEM image, we can see that the sample is highly homogeneous. A pseudocolor single-photon PEEM image at the field of view (FOV) of 2.5 μm was obtained under mercury lamp excitation as a direct characterization of sample morphologies, as shown in Figure 1d 20.

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Figure 1. Schematics and characterizations of topography of the sample. (a), (b) Schematic diagrams of the structure. The pitch size Λ and width of the nanorod are set 1 μm and 100 nm as invariants. L1, L2, and L3 are primarily designed to be 170 nm, 150 nm, and 130 nm. (c) SEM characterization of the Au trimer array. The scale bar is 500 nm. (d) Pseudocolor picture of PEEM image of Au trimer structure excited by mercury lamp. The brighter color corresponds to a stronger photoemission yield. The scale bar is 500 nm. Spectroscopic investigations of the sample are exhibited in Figure 2a including both the far-field and near-field spectra with the polarization parallel to the long axis of the nanorods. We can clearly see that there are two extinction peaks located at approximately 750 nm and 860 nm. The two counterintuitive peaks will be discussed later in this section. For the near-field spectrum, we perform PEEM measurements

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using a wavelength-tunable laser ranging from 720 nm to 920 nm with a pulse duration of 100 fs and repetition rate of 77 MHz. As reported before 18, the PEEM images of plasmonic structures with femtosecond laser pulse excitation could be regarded as a nonlinear near-field mapping of the structures. To obtain the near-field spectrum, we image and integrate the photoemission intensity over a FOV of 10 μm for the illumination wavelength ranging from 720 nm to 920 nm in 10-nm increments. From the near-field spectrum, we can also observe two peaks located at 760 nm and 860 nm corresponding well to those of the far-field extinction peaks. To better understand the correspondence of the plasmonic modes and spectroscopic peaks, we plot three pseudocolor PEEM images at the three characteristic laser wavelengths labelled in Figure 2a, which are shown as Figures 2c–e. As the structures are excited by the femtosecond laser and UV light simultaneously, we can determine the locations of hotspots as UV excitation can reflect the positions of the trimer while the femtosecond laser will excite the plasmonic hotspots 15. As the UV light from the mercury lamp can’t excite LSPR modes, the near-field mapping (the distribution of the plasmonic hotspots) is not influenced by the UV light. It is also noted that the near-field spectra are obtained based on the PEEM images with femtosecond laser excitation alone. At 760 nm and 860 nm, corresponding to the two peaks in the near-field spectra, the shortest and longest nanorods are excited independently, leaving the other two nanorods unexcited (no hotspots), although with a large intensity difference. At 810 nm, corresponding to the dip in the near-field spectra, however, the mid-nanorod is not independently excited as it was at the other two characteristic wavelengths. On the contrary, at 810 nm, the

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hotspots are, to some degree, randomly distributed at terminals of each three nanorods manifesting a near-field suppression for the mid-nanorod.

Figure 2. Spectroscopic characterizations of the sample and PEEM images. (a) Farfield and near-field spectra with polarization along the long axis of the nanorods. (b) Integrated photoemission intensity at selected regions as indicated in the inset. (c)–(e) Pseudocolor PEEM images excited using laser and mercury lamp simultaneously. The wavelengths of laser are selected at three characteristic wavelengths in the near-field spectrum, indicated in (a), which are 760 nm, 810 nm, and 860 nm. The scale bar in (e) is 200 nm, and it is applied throughout from (c) to (e). The yellow frames indicate the positions of a heterotrimer, which is the single heterotrimer used for obtaining the spectra in (b). To distinguish the near-field intensities of each nanorod instead of as a whole, we investigate the near-field intensities regionally as shown in inset of Figure 2b. We measure the integrated photoemission (PE) intensities of each selected region with the same area size individually from a single heterotrimer as a representation of the nearfield intensity of the corresponding nanorod. The single heterotrimer of the lower right corner in Figures 2c-e was chosen, because its near-field spectrum is most similar to

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The Journal of Physical Chemistry

that in Figure 2a, which is the average spectrum of the hetrotrimers within the FOV of 10 μm. As we can see in Figure 2b, the shortest nanorod has the strongest near-field intensity, followed by the longest. For the mid-nanorod, the near-field intensity is quite trivial, with a tiny peak compared to the other two at about 800 nm, which further proves the strong suppression of the dipolar mode of the mid-nanorod. To better understand why there are two peaks in the far- and near-field spectra, we perform FDTD simulations (the results are shown in Figure 3) with the same design parameters in addition that a rounded corner with a radius of 24 nm is considered. In 4 I Figure 3a, the near-field spectra is calculated as the integral of ( I ) in an 0

interface of 500 nm × 400 nm between gold nanostructures and the substrate (monitor plane) as a result of the assumption of an average four-photon photoemission process, where I and I0 represent the local field intensity on the monitor plane from which electrons are mostly excited

16

and the incident field intensity, respectively.

Above all, we can compare the simulated spectra with the experimental spectra, and we find that they match qualitatively. We can see from the simulated spectra that for both the far-field and near-field spectra, there are three peaks, including a trivial peak at approximately 850 nm. One should be reminded that the simulated peak P3 at approximately 915 nm corresponds to the experimental spectra peak on the red side at 860 nm, which has been proven in our PEEM images of Figures 2c–e compared with the simulated near-field intensity distribution. The electric field intensity |𝐸|2 at these three peak wavelengths is plotted in Figures 3b–d, from which we can conclude that these three peak wavelengths correspond to the dipolar-mode wavelengths of each

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nanorod. One extraordinary phenomenon we can clearly see is that either the near-field intensity or the far-field extinction peak becomes very weak for the middle nanorod, whose wavelength is located at around 850 nm. In addition, we find that the simulated electric field distribution at 850 nm has a lower contrast of intensity between the excited nanorod, which is the mid-nanorod, and the side-nanorods. This is a quite abnormal phenomenon, and we pursue subsequent analyses and experiments to yield a deeper understanding of this phenomenon.

Figure 3. FDTD simulated spectra, field distribution and charge distribution. (a) Simulated far-field extinction spectrum and near-field spectrum with the same design parameters of the sample. (b)–(d) Simulated near-field intensity distribution |E|2 at each near-field peak wavelength, as indicated in (a), in the lower plane of gold nanorods. (e)–(f) Simulated charge distributions corresponding to Fig 3 (b)–(d). The

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refractive index of the ITO substrate is set 1.55 in the simulation. The scale bar in (g) is 100 nm, and it is applied throughout from (b) to (g). To understand the mode suppression in the far field, we plot the real part of out-ofplane electric field in Figures 3e–g which indicate the charge distribution at the monitor plane

11, 18, 24.

It has been reported that the phase of the dipolar resonance will be

reversed if the frequency of the incident light is lower than that of the eigenfrequency of the dipolar resonance 11, 25. Under this theory, it is not difficult for us to understand the phase distribution at each mode wavelength. Given Figure 3e as an example, the incident wavelength is shorter than the eigenwavelengths of the other two, which will make the three modes oscillate in phase according to the theory, whereas for Figure 3f, the incident wavelength lies between the eigenwavelengths of the shortest and longest nanorods, reversing the phase responses of these two dipolar modes. Now, it is clear that at wavelength P1, the three modes are oscillating in phase, resulting in constructive interference, whereas at wavelength P2, the dipolar modes of the shortest and longest nanorods are anti-phase with comparable amplitude, resulting in destructive interference. The charge distribution in the middle nanorod at wavelength P2 exhibits a quadrupole mode, which hardly radiates into the far field, caused by Coulomb interactions. Although at wavelength P3, destructive interference will occur, the interference has a large different amplitude, which is why the extinction peak in P3 is less pronounced than that in P1 but more pronounced than that in P2. As our sample is heterotrimer, it is natural to consider the effect of detuning of eigenfrequencies (detuning in short) of adjacent nanorods takes. For an Au nanorod with a certain width and depth, the eigenfrequency is determined by its length.

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Hereinafter, we use detuning of the length of adjacent nanorods for simplicity. However, when we enlarge the detuning from 20 nm to 30 nm, the phenomenon of mode suppression vanishes. We fabricate samples of the same width and depth as before, but with detuning of 30 nm, the lengths of which are 180 nm, 150 nm, and 120 nm. In the same manner, we measure the near- and far-field spectra, which are shown in Figure 4a. Compared with previous spectra of detuning 20 nm shown in Figure 2a, we can clearly see for the trimer system with detuning of 30 nm that there are three peaks both in the near field and far field corresponding to the dipolar mode of each nanorod.

Figure 4. Experimental results of trimer sample with detuning of 30 nm. (a) Far- and near-field spectra with polarization along the long axis of the nanorods. (b) Integrated photoemission intensity at different regions, as indicated in the inset. (c)–(e) Pseudocolor PEEM images excited using laser and mercury lamp simultaneously. The

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laser wavelengths are selected at three characteristic wavelengths in the near-field spectrum indicated in (a), which are 760 nm, 810 nm, and 870 nm. The scale bar in (e) is 200 nm, and it is applied throughout from (c) to (e). (f)–(h) Simulated electric field distribution at corresponding simulative peak laser wavelengths. The scale bar in (h) is 100 nm, and it is applied throughout from (f) to (h). The yellow frames indicate the positions of a heterotrimer, which is the single heterotrimer used for obtaining the spectra in (b). To identify the intensities of each mode more intuitively, we measure the regional PE as in Figure 2b. We can observe that the PE from three different regions are comparable exhibiting a strong contrast compared with that of detuning of 20 nm. Three pseudocolor PEEM images at characteristic laser wavelengths marked in Figure 4a are also provided in Figures 4c–e. Clearly, we can see at each characteristic wavelength that each corresponding dipolar mode is independently excited even for the midnanorod (Figure 4d) which cannot be excited in Figure 2d. The field distribution can be verified also from FDTD simulations as shown in Figures 4f–h exhibiting the same properties as our experimental results. Thus, we experimentally prove that the midmode suppression is very sensitive to detuning. With a larger detuning, the mid-mode suppression becomes less pronounced. To deeply understand the mode suppression phenomenon especially in the near field, we systematically investigate the coupling behaviors in the trimers. When we consider the problem of mode suppression of a coupled system, the direct coupling in the near field seems intuitive. However, according to the report by Zhang et al., in a plasmonic system consisting of nanoantennas with the same side-by-side orientation positioned in proximity to each other, the coupling can be divided into two parts: direct coupling mediated by the near field and indirect coupling mediated by the radiative field

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Moreover, it has been also reported that changing the separation of adjacent NPs or nanocavities will significantly alter the resonance properties, especially its linewidth 2627.

By taking both coupling channels into consideration for the trimer system, we

propose an analytical model using coupled-mode theory accompanied with FDTD simulations. Take the 170-150-130 trimer as an example, the coupled-mode equations of the system can be written as 28

[

―𝜔 + 𝜔1 ― 𝑖𝛾1 ―𝜅1― 0

― 𝜅1 ―𝜔 + 𝜔2 ― 𝑖𝛾2 ― 𝜅2

][ ] [ ]

0 𝐴1 𝑔1 𝐴2 = 𝑔2 𝐸0, ―𝜅2― 𝑔3 ―𝜔 + 𝜔3 ― 𝑖𝛾3 𝐴3

(1)

where 𝜔1, 𝜔2 and 𝜔3 are the eigen-circular frequencies of each nanorod from the length of 170 nm to 130 nm (denoted as 1, 2, and 3, respectively); 𝛾1, 𝛾2, and 𝛾3 are the damping loss of corresponding nanorod; 𝜅1 and 𝜅1― are two coupling strengths in which both the near-field coupling and radiative field coupling exist between nanorod 1 and 2, and 𝜅2 and 𝜅2― are the same parameters for nanorods 2 and 3. The analytical relation between 𝜅1 (and also 𝜅1― , 𝜅2, and 𝜅2― ) and the two coupling channels can be found in the supporting information. 𝐴1, 𝐴2, and 𝐴3 are the respective complex amplitudes of dipolar mode of each nanorod, 𝑔1, 𝑔2, and 𝑔3 are the excitation coefficients from incident light to each nanorod, and 𝐸0 represents incident light. We use the intensities of the electric field at points close to the nanorods, which are shown in the inset of Figure 5a to fit all the parameters in equation (1). The detailed methods to obtain all the parameters can be found in the supporting information. With all the parameters above independently obtained, the complex amplitudes of each coupled mode at each representative point shown in Figure 5a can be calculated using equation

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(1). Comparing Figure 5a with numerical results shown in Figure 5b we can see they match well, reflecting the validity of our model. Clearly, the intensity of the dipolar mode of the mid-nanorod lies between that of the shortest and longest nanorods with a relatively small difference compared with our experimental results shown in Figure 2b in which the intensity of the mode of mid-nanorod is severely suppressed. To explain this, we emphasize that the PE intensity information obtained in our PEEM experiments is directly proportional to an integrated value of approximately the fourth power of electric field intensity (E2) over a given region, whereas in the analytical model, we only select a probe monitor close to a corresponding nanorod as a representation for the mode of the very nanorod. After renormalization, we can obtain an analytical reference of regional PE intensities corresponding well to the experimental results in Figure 2b, shown in Figure S2a, which further proves the validity of our model. One advantage of our model is that the near-field coupling and radiative field coupling can be distinguished.

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Figure 5. Analytical model compared with FDTD simulation results. (a) Analytical model results of mode intensities of individual nanorod represented by the electric field intensities of M1, M2, and M3 arranged close to the top edge of the nanostructures which are shown in the inset of (a) for 170-150-130 system. The distances from the representative points to the corresponding nanorod edges are 5 nm. (b) FDTD results of electric field intensities at the same points as indicated in (a) probed by point monitors for 170-150-130 system. (c) Control calculations of analytical model results without considering indirect radiative field coupling (wo RFC) for 170-150-130 system. (d)–(f) are corresponding results for 180-150-120 system.

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To verify the role of far-field coupling, we perform control calculations where only near-field coupling is considered. The results shown in Figure 5c are, as expected, absolutely far away from the numerical results, exhibiting no mode-suppression phenomenon. The control calculations prove that radiative field coupling cannot be neglected in this case. For the 180-150-120 trimer system, we perform the same calculations and obtain the corresponding results as shown in Figures 5d–f. Both analytical and simulative results suggest the mode of the mid-nanorod is much less suppressed than that of detuning of 20 nm corresponding well to our previous experimental results. To determine why the mode suppression happens in 170-150-130 trimer system but vanishes in 180-150-120 trimer system, we extract the values of the two coupling channels for these two trimer systems with different detuning, which are 𝜅𝑛𝑓𝑐 170 ― 150 ― 130 = ―0.6 + 0.11i, 𝑛𝑓𝑐 𝑟𝑓𝑐 𝜅𝑟𝑓𝑐 170 ― 150 ― 130 = ―0.08 + 1.03i, 𝜅180 ― 150 ― 120 = ―0.55 + 0.01i, 𝜅180 ― 150 ― 120

= 0.09 + 0.84𝑖, where the superscripts nfc and rfc stand for near-field coupling and radiative field coupling, respectively (the details can be found in the supporting information). We can find that the coupling coefficients via the near field are close to real numbers, whereas those via the radiative field are close to imaginary numbers, which correspond to Hermitian coupling and anti-Hermitian coupling, respectively, as reported in [25]. Comparing the two trimer systems, we find that the near-field coupling of these two trimer systems is close to each other while the radiative field coupling for 180-150-120 trimer is about 25% smaller than that of 170-150-130 trimer. Therefore, we can conclude that both direct near-field coupling and radiative field coupling take

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place in the trimer system and the suppression of the mode of mid-nanorod happens at a smaller detuning is mainly due to larger radiative field coupling. Conclusions In conclusion, we systematically investigate the far-field and near-field properties of Au heterotrimer with small detuning of eigenfrequency. Both experiments and simulations suggest the dipole mode of the middle nanorod is greatly suppressed. We explain that the suppression in the far-field extinction spectrum is caused by the destructive interference from anti-phase dipole modes due to the phase transition effect. Furthermore, the mode suppression vanishes when the detuning is slightly enlarged. We propose an analytical model with coupled mode theory, and the model results match well with the numerical results, proving that both direct coupling mediated by the near field and indirect coupling mediated by the radiative field take effect in the system. Our model also demonstrates that stronger radiative field coupling in a trimer system with smaller detuning leads to the phenomenon of mode suppression. This work helps us to deeply understand the mechanism of plasmon coupling and offers new ideas on designing plasmonic devices for various applications.

Supporting information The detailed methods on how to obtain all the related parameters including coupling strengths through fitting and the renormalizations for mode coefficients. This material is available free of charge via the Internet at http://pubs.acs.org.

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Acknowledgement The authors acknowledge financial support from the National Science Foundation of China (NSFC) (No. 11527901) and Grants-in-Aid for Scientific Research (Grant Nos. JP18H05205, JP17H01041, JP17H05245, and JP17H05459). We acknowledge the support from the Nanotechnology Platform (Hokkaido University) and Dynamic Alliance for Open Innovation Bridging Human, Environment and Materials (Five-Star Alliance) of MEXT. This work was also supported by the Center for Emergent Functional Matter Science of National Chiao Tung University from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan.

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