Selected mode mixing and interference visualized within a single

Subscriber access provided by Kaohsiung Medical University

Article

Selected mode mixing and interference visualized within a single optical nanoantenna Taeko Matsukata, Carl Wadell, Nikolaos Matthaiakakis, Naoki Yamamoto, and Takumi Sannomiya ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01231 • Publication Date (Web): 21 Nov 2018 Downloaded from http://pubs.acs.org on November 21, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

ACS Photonics

Page 1 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Selected mode mixing and interference visualized within a single optical nanoantenna Taeko Matsukata1, Carl Wadell1, Nikolaos Matthaiakakis1, Naoki Yamamoto1, Takumi Sannomiya1,2*

1

Department of Materials Science and Engineering, School of Materials and Chemical

Technologies, Tokyo Institute of Technology, 4259 Nagatsuta, Midoriku, Yokohama, 2268503 Japan.

2

JST, PRESTO, 4259 Nagatsuta, Midoriku, Yokohama, 226-8503 Japan.

Corresponding Author *e-mail: [email protected]

KEYWORDS Cathodoluminescence,

Nanodisk,

Multipole,

Surface

Plasmon,

Scanning

Transmission Electron Microscopy

1 ACS Paragon Plus Environment

ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 29

Abstract Interference-based directional antennas typically consist of multiple dipoles with properly set distances and phases, which cause constructive interferences towards certain directions in radiation or reception. For nano optical antennas, the directionality can be realized by superposition of multiple eigen modes in a single structure. Such mode mixing creates locally strong field enhancement, which should be properly controlled for energyconversion or sensing applications. However, experimental verification of the nano optical field, or especially the hot-spots, created by interference of selected eigen modes is not trivial. We here visualize how optical fields are distributed when multiple modes interfere within a silver disk nano antenna. We use angle- and polarization-resolved cathodoluminescence based on scanning transmission electron microscopy to select specific modes and visualize the field distribution at the nanoscale. The interfered field distribution significantly changes depending on the detection angles even when the detection geometry is symmetric, which can be explained by the phase difference of the excited mode. The cathodoluminescence signals are also modeled as superpositions of


Page 3 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

analytical eigen mode functions consisting of multipoles in space and complex Lorentzians in frequency to reproduce the experimentally obtained photon maps.

TOC Figure


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 29

Strong field confinement and enhancement is the key property in wave cavities. To achieve electromagnetic field confinement in the optical regime, metallic nano-antennas have been proposed and applied to e.g. high efficiency photo-catalysis, biosensing, light energy conversion, and nano-optical circuits.1-3 Optical nano-antennas convert propagating electromagnetic waves to local near fields or excited “hot” electrons.1 It can inversely also work as an efficient emission antenna for light emitting devices.2,

3

Furthermore, multiple nano-antennas can be combined together to work as metamaterials with applications such as phased arrays, hyper lenses, waveguides and color filters.4 When originally separate modes are brought into a single structure, or are located close to each other, one may need to consider hybridized modes of the original modes due to cross coupling between them. Such couplings are classified as Rabi splitting for coupling between two high-Q resonators, and as Fano resonance for coupling between high- and low-Q resonators.3,

5, 6

Such strong couplings between eigen modes exhibit splitting of

resonances and are sometimes described in analogy to molecular systems.7 In metallic nano-antennas, eigen modes tend to have low Q-factors due to the lossy nature of metals,


Page 5 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

which causes overlaps between eigen modes with different eigen frequencies. For weak coupling, such as low-Q mode coupling, the eigen mode mixing becomes a simple sum of the two modes in the energy spectrum. In all cases, the electromagnetic field created from multiple modes reflects their interferences including the phase of each mode since they are coherently excited. It has been predicted that the interference may create highly confined near-field hot spots far below the vacuum wavelength.8 Although interfered fields have been visualized previously,9, 10 direct comparison between directionality, mode phase, and hotspot control has never been performed. To perform experimental verification of such interfered nano-optical fields with directionality, an angle-resolved detection method with nanoscale spatial resolution is necessary. Mapping of optical fields with high spatial resolution can be conventionally realized by electron microscopy based methods, such as electron energy loss spectroscopy (EELS) and cathodoluminescence (CL). By EELS, coupled modes have been visualized and discussed in detail in previous studies.11-14 However with conventional EELS, interferences of degenerate modes cannot be selectively captured and the resultant directionality of the antenna cannot be directly evaluated. To visualize interferences, the CL method is probably more suitable. Indeed, interferences of surface plasmons with transition


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 29

radiation or Smith-Purcell emission has been reported using CL.15, 16 Since polarization filtering is available in CL, degenerate mode selection17 or visualization of “hidden chirality” is possible.17, 18 In this work, we visualize the interfered local fields of degenerate as well as nondegenerate eigen modes that have different relative phases. We use an angle- and polarization- selected cathodoluminescence (CL) measurement to selectively study the interference of eigen modes.19, 20 Silver nanodisks are used as nanoantennas whose eigen modes have different energies with rather wide energy widths (low-Q factor), resulting in the overlap and interference of various modes with different relative phases. Here we demonstrate the direct connection of the resonance phase, nanoscale field distribution and directionality, based on interference of eigen modes. To analyze and confirm the interference of different relative phase modes, we derive an analytical expression of the electric field distribution taking into account the superposition of multipole modes. We note that we here deal with interferences of the existent modes in a fixed structure, and not the coupling creating new modes in a new structure such as hybridization.


Page 7 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

Disks on a free-standing SiO2 membrane For CL measurements based on scanning transmission electron microscopy (STEM), the substrate gives considerable background signal including transition radiation as well as emission from impurities or defects.21 Therefore, we fabricate disks on a free-standing SiO2 membrane to minimize the influence from the substrate. The nanodisk fabrication is based on hole-mask colloidal lithography (HCL) and film transfer using a sacrificial layer.22,23]

(Figure 1) The HCL procedure was applied on a SiO2/Al/glass substrate so

that the film can be delaminated after fabricating the disk on the SiO2 film. The standard HCL process was applied, and then the SiO2 film was transferred to a TEM grid by etching the aluminum sacrificial layer.

Figure 1

Fabrication procedure of nanodisks on a free-standing membrane.


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 29

The dimension of the fabricated disk is shown in Figure 2a. Nanodisks are located on a free-hanging 30 nm thick SiO2 membrane and covered by 20 nm layer of SiO2- Scanning electron microscopy (SEM) images of the fabricated nanodisks are shown in Figure 2b-c. We also confirmed that the background radiation, typically transition radiation of this free-standing membrane structure, was negligibly small.

Figure 2

(a) Dimension and (b-c) SEM images of the fabricated disks.

Theory To understand the interference of the multiple modes in the silver nanodisk, we here derive theoretical expressions. The eigen modes in a single particle can be decomposed using multipoles.24 For a spherical particle, where multipole modes are degenerate and in-phase, angle- and polarization-dependent radiation of the multipole modes have been shown previously.17 In order to describe disks, we expand the previous formula to include


Page 9 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

interference of the modes with different orders, thus different relative phases. In Figure 3a, the coordinate system employed for the calculation is shown. For a given detection position 𝒓 = (𝑟, 𝜃, 𝜙) = (𝑟, Ω) and electron beam position R, the scalar function 𝜓𝐸,𝑖𝑛𝑑(𝒓,𝑹) corresponding to the induced radiation field by a spherical particle can be expressed using multipoles as17 : 𝑙

𝜓𝐸,𝑖𝑛𝑑(𝒓,𝑹) = 𝑡𝐸𝜓𝐸,𝑒𝑥𝑡 = ∑𝑙∑𝑚 = ―𝑙𝑖𝑙ℎ(𝑙 + )(𝑘𝑟)𝑌𝑙,𝑚(𝛺𝑟)𝑡𝐸𝑙,𝑚𝜓𝐸,𝑒𝑥𝑡 𝑙,𝑚 (𝑹) =

―2𝜋𝑖𝑘 𝑐𝛾

1

∑ 𝑙(1 + 1)𝑡𝐸𝑙,𝑚ℎ(𝑙 + )(𝑘𝑟)∑𝑙 𝐵 𝐾 𝑙 𝑚 = ―𝑙 𝑙,𝑚 𝑚

( )𝑌 𝜔𝑏 𝑣𝛾

𝑙,𝑚(𝛺𝑟)𝑒

―𝑖𝑚𝜑0

,

(1)

where the external field coefficient is given in atomic units by 𝜓𝐸,𝑒𝑥𝑡 𝑙,𝑚 (𝑹) =

―2𝜋𝑖1 ― 𝑙𝑘 𝐵𝑙,𝑚 𝑐𝛾

( )𝑒 𝜔𝑏

𝑙(𝑖 + 1)𝐾𝑚 𝑣𝛾

ℎ𝑙( + )(𝑘𝑟), 𝑌𝑙,𝑚(𝛺𝒓) and

―𝑖𝑚𝜑0

.

(2)

𝑡𝐸𝑙,𝑚 are spherical Hankel function (ℎ𝑙( + ) = 𝑖ℎ(1) 𝑙 ), spherical

harmonic function, and the scattering matrix element for electric field, respectively. 𝐵𝑙,𝑚 is the parameter including the excitation phase of each mode. (The details of each function are shown in the Supplementary Information.) 𝐾𝑚 is the modified Bessel function of order m, and 𝛾 = 1 1 ― (𝑣/𝑐) is the Lorentz factor. In this expression, the excitation (+) (𝑘𝑟)𝑌𝑙,𝑚(𝛺𝑟) amplitude of each mode can be considered as 𝑡𝐸𝑙,𝑚𝜓𝐸,𝑒𝑥𝑡 𝑙,𝑚 (𝑹) and the rest ℎ𝑙

as the radiation field. The 𝑧 dependence can be omitted when the electron beam is approximated to interact only with strong near-field for a relatively flat structure like a


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 29

disk. Here we introduce vector spherical harmonics 𝑬𝑙,𝑚(𝜃, 𝜑) =

1

𝑳𝒀𝒍,𝒎(𝜃, 𝜑) × 𝒏 for

𝑙(𝑙 + 1)

the angular component of the radiation electric field.17, 25 (See also the Supplementary Information.) Comparing this radiation part with the previous Equation 1 of the wave function, the radiation intensity of each mode in the far-field approximation can be expressed as: 𝐼𝑙𝑚(𝛀𝒓) ∝ |𝑡𝐸𝑙𝐵𝑙𝑚 𝐾𝑚 𝑬𝑙𝑚(𝜃,𝜑) 𝑒 ―𝑖𝑚𝜑0|

2

(3)

+ = Using the modified basis functions of standing wave forms of 𝑬𝑙,𝑚

― = 𝐸𝑙,𝑚

1

1

(𝑬𝑙,𝑚 + 𝑬𝑙, ― 𝑚) and

2

(𝑬𝑙,𝑚 ― 𝑬𝑙, ― 𝑚) needed for polarimetry, the radiation intensity with interference

2𝑖

can be expressed as

𝐼∝

| [ ∑𝑡

𝐸 𝑙

𝑙

𝐶𝑙0𝑬𝑙0 + 𝑖

𝑙

∑ {𝐶

𝑅𝑒 ― 𝑙𝑚𝑬𝑙𝑚

𝑚=1 𝑚 ∈ 𝑜𝑑𝑑

𝑙

+ +𝐶𝐼𝑚 𝑙𝑚 𝑬𝑙𝑚 } +

∑

― 𝑅𝑒 + { ―𝐶𝐼𝑚 𝑙𝑚 𝑬𝑙𝑚 + 𝐶𝑙𝑚𝑬𝑙𝑚 }

𝑚=2 𝑚 ∈ 𝑒𝑣𝑒𝑛

]|

2

(4) This expression includes interference of non-degenerate multipoles, which has not been considered previously because of energy separation. The coefficient 𝐶𝑙𝑚, corresponding to the excitation amplitude of each eigen mode, is given as :

𝐶𝑙0(𝑹) ∝ 𝐵𝑙,0𝐾0

( ) 𝜔𝑏 𝑣𝛾

𝐶𝑅𝑒 𝑙𝑚(𝑹) ∝ 2𝐵𝑙,𝑚𝐾𝑚

( ) 𝑅𝑒[ 𝑒

―𝑖𝑚𝜑0

( ) 𝐼𝑚[ 𝑒

―𝑖𝑚𝜑0

𝐶𝐼𝑚 𝑙𝑚 (𝑹) ∝ 2𝐵𝑙,𝑚𝐾𝑚

𝜔𝑏 𝑣𝛾

𝜔𝑏 𝑣𝛾

], ],

(5)


Page 11 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

The polarization dependence can be included by separating the  and 𝜑 components of the radiation electric field.17 The angle dependent radiation distribution of each (l,m) mode up to quadrupole order is shown in Figure 3. The so-called “breathing mode” corresponds to m = 0 modes especially for l > 1.26

Figure 3. Angular distribution of multipole radiation modes with different polarizations. (a) Coordinate and polarization definition. (b) Illustration of charge and radiation distribution of each multipole mode with different polarization conditions.

Interference of in-plane modes To perform the mode selective observation, we used angle-resolved CL based on scanning transmission electron microscopy (STEM). With the accelerated electron beam, the


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 29

electromagnetic local density of states can be detected.27, 28 The used STEM setup consists of a parabolic mirror inserted at the sample position to collimate the light radiated from the sample.(Figure 4) The light is transferred to a spectrometer through an optical lens system as schematically illustrated in Figure 4d.20, 29 By placing a pinhole mask in the light path, angle-resolved measurements can be performed. We note that in this configuration p-polarization corresponds to  -polarization in the Theory section and spolarization to 𝜑- polarization, when the pinhole mask position is on the x-z plane, which is the case in the present experiment.20, 30 The coordinate definition in the measurement setup is shown in Figure 4. Further experimental details can be found in the Method section.

Figure 4. Illustration of an angle-resolved cathodoluminescence measurement. sand p-polarizations correspond to 𝜑- and - polarizations in Figure 3 when the detection angle is close to the x -z plane. 12 ACS Paragon Plus Environment

Page 13 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

In this section we discuss the selective observation of in-plane modes. We first show noninterfering conditions where only a single mode is observed. For the observation from top ( = 0˚, 𝜑 = 0˚) with s-polarization, corresponding to 𝜑-polarization in Figure 4, only an inplane dipole mode (l,m)=(1,1) has been observed as shown in Figures 5a-d. The resonance of this mode is found at 2.3 - 2.4 eV in the spectrum in Figure 5c. According to the theory, only (l,m)=(1,1) and (2,1) gives upwards radiation. We could not see the (2,1) mode most probably due to the disk shape in contrast to the spherical one in the previous study. This is further confirmed by boundary element method (BEM) calculations as shown in the Supplementary Information.31 The photon maps show only typical dipole field distribution with hot-spots along the y-axis. When the detection angle  becomes 45° with the same s-polarization, the in-plane quadrupole (l,m)=(2,-2) starts to be included and starts to interfere.(Figures 5e-h) The spectrum shown in Figure 5g shows an in-plane quadrupole peak around 3.5 eV. This type of mode selective observation is in agreement with the previous work. Indeed, the photon maps show an in-plane dipole pattern in the energy range below 2.5 eV and an in-plane quadrupole pattern of four-fold symmetry at around 3.5 eV (Figure 5h). For the energies


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 29

in between, the interference of these two modes creates an asymmetric field pattern as shown in the photon map at 3.0 eV. This is due to field canceling of the dipole and quadrupole charges with opposite signs on the upper sides in the photon map, leaving only the field on the lower side of the disk (Figure 5i).

Figure 5. CL results obtained with s-polarization for in-plane mode detection. The detection angle was set at ( , 𝜑) = (0˚, 0˚) for (a-d), and ( , �) = (45˚, 0˚) for (e-h). (a,e), STEM dark-field images of the observed Ag nanodisk. (b,f) Schematics of the detection configuration. (c,g) Selected area spectra from the boxed area in the STEM dark-field images. (d,h) Photon maps at selected energies. The axis coordinates of the photon maps are also shown in panel d. The polarization 14 ACS Paragon Plus Environment

Page 15 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

direction corresponds to horizontal direction as shown by the green arrow. (i) Illustration of interfering dipole and quadrupole modes.

Interference of in-plane and out-of-plane modes For p-polarization, corresponding to  -polarization in Fig. 2, both in-plane and out-ofplane modes can be detected. According to the theory, observation with this polarization at the angle of  = 45˚ and 𝜑 = 0˚ includes (l,m) = (1,0), (1,-1), (2,0), and (2,+2). Figures 6a-d show the CL measurement results under this condition. The spectra from the selected areas on the disk show multiple peaks, which are not straightforward to understand due to interference. Considering the symmetry of the modes, signals with the beam position at the center of the disk correspond to the axisymmetric mode, (1,0) and (2,0). From the spectrum of the center beam position (yellow plot in Figure 6c), the out-of-plane dipole (1,0) resonance is estimated to be around 3.0 eV. Since no other modes contribute to the signal around this energy, the spectra of +45° and +135° detections are similar, as shown by the yellow line spectra in Figure 6c,g. In contrast, at higher energies, a higher order mode l =2 starts to contribute to the spectrum. This (2,0) mode has symmetric charge distribution with


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 29

respect to the x-y plane, while the (1,0) mode has anti-symmetric charge distribution (see Fig 3). Therefore, the interference between these two modes has asymmetry also in the far-field detection. This can be seen as a constructive interference at 3.65 eV for 45° detection and a destructive one for 135°, as shown in Fig. 6 by the yellow line spectra as well as the hot spots at the center in the photon mapping. This “breathing” quadrupole mode (2,0) starts to go into the non-plasmonic (non-metallic) regime. Therefore, Ferrel mode-like resonance is probably observed, which could also be interpreted as superposition of higher order (l, 0) modes.32 BEM simulation predicts that the energy of (2,0) mode appears around 3.6 eV. (See the Supporting Information) The extracted spectra in Figure 6, together with the previous in-plane measurement, indicate the resonances of (l,m) = (1,1), (1,0), (2,2) and (2,0) modes at around 2.3 - 2.4 eV, 2.9 - 3.0 eV, 3.4 - 3.5 eV, and 3.7 eV, respectively. The photon maps at selected energies give asymmetric field patterns. The in-plane dipole (1,-1), at the lower energies (below 2.5 eV) with hot-spots along the x-axis, is asymmetric having stronger field on the upper side, which is due to the interference with the out-ofplane dipole (1,0) as illustrated in Figure 6i; the resulting tilted dipole generates radiation to the upper side direction toward the parabolic mirror.33 At higher energies, where


Page 17 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

quadrupoles come into play, the field pattern is complicated and cannot be easily decomposed into separate modes. At the detection angle  = 135˚ and 𝜑 = 0˚ (Figure 6f), which is geometrically symmetric to the previous case with the mirroring plane of the x-y plane, the symmetry of the field pattern totally changes. The in-plane dipolar pattern in Figure 6h at 2.0 - 2.5 eV shows stronger intensity on the lower side, which is opposite from the pattern at  = 45˚. This is due to the opposite polarity of the out-of-plane dipole (1,0) with respect to the x-y plane generating the radiation wave with a sign-flipped phase. The resulting tilted dipole generates radiation to the lower side direction towards the mirror. The spectral features from the selected areas of  = 135˚ are also inversed compared to  = 45˚, as seen as the blue and red curves in Figure 6c and g. This characteristic can be understood in terms of point-symmetric radiation. The superposed radiation of in-plane and out-of-plane dipole modes has the point symmetry, which results in the identical response of the top excitation with 45° detection to the bottom excitation with 135° detection. General relation of the point-symmetric radiation is described in the Supporting Information. At higher energies (> 3.0 eV), the contrast of the  = 135˚ detection is not anymore inversed from that of 45°. This is because the influence of the quadrupole mode (2,2) increases and


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 29

the interfered radiation pattern loses its point symmetry. In the intensity spectra, the intensity inversion cannot be detected explicitly.

Figure 6. CL results obtained with p-polarization to include the interference measurement of in-plane and out-of-plane modes. The detection angle was set at ( , 𝜑 ) = (45˚, 0˚) for (a-d), and ( , 𝜑 ) = (135˚, 0˚) for (e-h). (a,e) STEM dark-field images of the observed Ag nanodisk. (b,f) Schematics for the detection configuration. (c,g) Selected area spectra from the boxed area in the STEM darkfield images of panel a and e, where the color of the box corresponds to that of the spectrum plot. (d,h) Photon maps at selected energies. The axis coordinates of the photon maps are also shown in panel d. The polarization direction corresponds to 18 ACS Paragon Plus Environment

Page 19 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

horizontal direction as shown by the green arrow. (i) Illustration of interfering inplane and out-of-plane dipoles resulting in asymmetric radiation.

Superposition of modeled eigen functions with phase Since the overlap of modes results in complicated field patterns, we here try to understand this as a superposition of the individual modes. According to the expression in Eq. (6), the radiation field at a given electron beam position can be calculated when the excitation amplitude 𝑡𝐸𝑙,𝑚𝜓𝐸,𝑒𝑥𝑡 is known. For simplicity we assume that 𝜓𝐸,𝑒𝑥𝑡 has the spatial 𝑙,𝑚 𝑙,𝑚 distribution as shown in Figure 7a and 𝑡𝐸𝑙,𝑚 as a simple Lorentzian function as shown in Figure 7b. The spatial distribution of the excitation amplitude is based on the 2D Bessel functions with rotational multipole symmetry, and the Lorentzian resonance energies were set based on the experimental CL measurement. (for details see the Supporting Information) The widths of the Lorentzian peaks were chosen to best reproduce the experimental results. We note that the phase of the finally radiated light is determined by all the products of excitation, scattering and radiation amplitudes. We omit (2,1) modes since they have not been observed in the experiment. The same intensities of the eigen mode functions were used to reproduce the results.


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 29

Using this model, we plot the calculated photon maps as shown in Figures 7c-e. With spolarization at  = 45°, the initially symmetric dipole pattern with two hot spots shifts downwards as the energy increases and finally shows a quadrupole pattern, which matches nicely with the experimental results shown in Figure 5h. This calculation confirms that the interference of dipole and quadrupole modes can result in such photon maps. For p-polarization at  = 45°, the asymmetric dipole hot spots with higher intensity on the upper side are also reproduced in Figure 7d, as in the measurement in Figure 6d. This hot spot intensity distribution flips when the measurement angle is flipped to  = 135° (Figure 7e), which also nicely matches the CL data of Figure 6h. The other patterns, including higher order modes, qualitatively match the experiment. This simplified model confirms that interference of multiple modes with different relative phases can result in the complex patterns observed in the CL measurements. Such an interference-based measurement allows optical phases to be measured at the nano scale, which has not been possible in the frequency domain. These results also tell that hotspots can be controlled by illumination angle and polarization for far-field optical excitation, considering the reciprocity of light propagation. As additional examples, hot-spot distributions with mixed


Page 21 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

polarization are also shown in the Supporting Information, which are also reproduced by eigen mode superposition.

Figure 7. Model basis functions for Eigen mode superposition. (a) Normalized intensity of the spatial distribution of the excitation amplitude. (b) Normalized Lorentzian functions for scattering amplitude of each mode. (c-e) Reproduced photon maps using the model functions. (c) s-polarization at  = 45°. (d) ppolarization at  = 45°. (e) p-polarization at  = 135°. The axis coordinate in the photon map is shown on the right of panel a.


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 29

Conclusion We have demonstrated nanoscale visualization of low-Q mode interferences by angleand polarization- resolved cathodoluminescence method. The obtained photon maps of silver nanodisks were reproduced by analytical models where the eigen modes with different phases are superimposed. The optical hotspots resulting from the interference of different modes appear in different locations depending on the energy, angle and polarization. Since the hot-spot represents high density electron charges, controlling the interference of the existing mode as well as its phase is beneficial for energy conversions such as photovoltaics or photocatalysis. The performed interference based method gives access to the local optical phases, which may also enable extraction of the mode phase relative to the excitation electron beam when a certain mode is considered as reference.34 This could give new insights into the interaction of electrons and photons mediated through materials.35 .

Method Disk Fabrication


Page 23 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

The fabrication of the nanodisk samples is based on hole-mask colloidal lithography (HCL) with some additional steps in order to produce samples thin enough to be transparent to the electron beam in the STEM-CL system. The fabrication starts by depositing a sacrificial Al layer and a SiO2 support layer on a glass substrate (Fig. S1 a). On this substrate, the normal HCL procedure is used to produce Ag nanodisks, which are subsequently covered by a second protecting SiO2 layer (Figure 1 b-e). Silver, aluminum and SiO2 were deposited by thermal evaporation, DC sputtering and RF sputtering respectively. The support carbon film (< 10 nm) on the bottom side of the sample was deposited by arch evaporation. 150 nm polystyrene colloids (Microparticles, Germany) were used for the HCL process. A PMMA layer is spin-coated on top of the sample (Figure 1 f) and a piece of the desired size is cut from the sample of the desired size. This piece is then let to float on top of a 1M KOH solution to dissolve the sacrificial Al layer and release the sample from the support. The hydrophobicity of the PMMA ensures that the sample does not submerge into the solution. After the sample has been released from the substrate a TEM microgrid is used to pick up the floating film (Figure 1 g-h). A thin carbon film is evaporated onto the bottom side of the sample to enhance its mechanical stability, as well as to avoid charging of the sample under electron beam illumination (Figure 1 i).


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 29

As a last step the covering PMMA layer is removed by placing the sample on an absorbing paper and carefully dripping acetone onto it (Figure 1 j).

CL measurement For the presented CL measurement, a modified JEM-2100F (JEOL, Japan) with a Cscorrector is used at an acceleration voltage of 80 kV. The electron probe current is about 1 nA with about 20 mrad illumination half angle. The solid angle of the light detection by the pinhole mask is approximately 0.25 sr.,(1 mm circular pinhole) which is chosen to achieve reasonable angular resolution while still retaining high enough signal intensity. The photon maps are obtained by collecting the optical spectrum at each electron beam position, synchronized with the electron beam scan. For the photon map representation, signals over ±0.1 eV energy range are averaged. Instrumentation details can also be found elsewhere. 20, 29

ASSOCIATED CONTENT

Supporting Information.


Page 25 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

Expression of used coefficients of multipole radiation, calculation of excitation amplitude, BEM calculation, mode interference with mixed polarization, comparison of directionality with previous research, verification of directionality by detection angle scan, and radiation with point symmetry. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *Email: [email protected]

Author Contributions CW and TS conceived the research. TM and CW carried out the experiment. TM, NM, NY, TS performed the calculation, analysis and modelling. All authors contributed to the manuscript preparation.


ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 29

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT We thank A. Yasuhara (JEOL Ltd.) for the disk shape evaluation, Prof K. Kajikawa for helping us with lithography as well as valuable discussion, and Prof. U. Hohenester for

advising us about BEM calculation. We also appreciate kind support in graphics by A. Makropoulos. This work was supported by JST PRESTO Grant #17940502 and

Japanese Society for the Promotion of Science #15F15744 and #17K19025.

REFERENCES

1.

Clavero,

C.,

Plasmon-induced

hot-electron

generation

at

nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices.

Nat. Photon. 2014, 8 , 95-103. 2.

Lozano, G.; Rodriguez, S.; Verschuuren, M.; Rivas, J., Metallic

nanostructures for efficient LED lighting. Light Sci. Appl. 2016, 5, e16080. 3.

des Francs, G.; Barthes, J.; Bouhelier, A.; Weeber, J.; Dereux, A.; Cuche, 26 ACS Paragon Plus Environment

Page 27 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

A.; Girard, C., Plasmonic Purcell factor and coupling efficiency to surface plasmons. Implications for addressing and controlling optical nanosources. J. Opt. 2016, 18 (9). 4.

Kosako, T.; Kadoya, Y.; Hofmann, H., Directional control of light by a

nano-optical Yagi-Uda antenna. Nat. Photon. 2010, 4 , 312-315. 5.

Liu, N.; Langguth, L.; Weiss, T.; Kastel, J.; Fleischhauer, M.; Pfau, T.;

Giessen, H., Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit. Nat. Mater. 2009, 8, 758-762. 6.

Fox, M., Quantum Optics: An Introduction. Oxford Univ Press: 2006; Vol.

6. 7.

Nordlander, P.; Oubre, C.; Prodan, E.; Li, K.; Stockman, M., Plasmon

hybridizaton in nanoparticle dimers. Nano Lett. 2004, 4, 899-903. 8.

Tanaka, Y.; Sanada, A.; Sasaki, K., Nanoscale interference patterns of

gap-mode multipolar plasmonic fields. Sci. Rep. 2012, 2, 764. 9.

Yurtsever, A.; Baskin, J. S.; Zewail, A. H., Entangled Nanoparticles:

Discovery by Visualization in 4D Electron Microscopy. Nano Lett. 2012, 12, 50275032. 10.

Yang, J. H.; Sun, Q.; Yu, H.; Ueno, K.; Misawa, H.; Gong, Q. H., Spatial

evolution of the near-field distribution on planar gold nanoparticles with the excitation wavelength across dipole and quadrupole modes. Photon. Research 2017, 5, 187-193. 11.

Collins, S. M.; Nicoletti, O.; Rossouw, D.; Ostasevicius, T.; Midgley, P. A.,

Excitation dependent Fano-like interference effects in plasmonic silver nanorods.

Phys. Rev. B 2014, 90, 155419. 12.

Schmidt, F. P.; Ditlbacher, H.; Hofer, F.; Krenn, J. R.; Hohenester, U.,

Morphing a Plasmonic Nanodisk into a Nanotriangle. Nano Lett. 2014, 14, 48104815. 13.

Lourenco-Martins, H.; Das, P.; Tizei, L. H. G.; Weil, R.; Kociak, M., Self-

hybridization within non-Hermitian localized plasmonic systems. Nat. Phys. 2018,

14 , 360-364. 14.

Fujiyoshi, Y.; Kurata, H., Surface plasmon resonances in a branched

silver nanorod. J. Appl. Phys. 2018, 124, 093103. 15.

Kuttge, M.; Vesseur, E. J. R.; Koenderink, A. F.; Lezec, H. J.; Atwater, H.

A.; Garcia de Abajo, F. J.; Polman, A., Local density of states, spectrum, and far27 ACS Paragon Plus Environment

ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 29

field interference of surface plasmon polaritons probed by cathodoluminescence.

Phys. Rev. B 2009, 79, 113405. 16.

Yamamoto, N.; de Abajo, F. J. G.; Myroshnychenko, V., Interference of

surface plasmons and Smith-Purcell emission probed by angle-resolved cathodoluminescence spectroscopy. Phys. Rev. B 2015, 91, 125144. 17.

Thollar, Z.; Wadell, C.; Matsukata, T.; Yamamoto, N.; Sannomiya, T.,

Three-Dimensional Multipole Rotation in Spherical Silver Observed by Cathodoluminescence 18.

Nanoparticles

ACS Photon. 2018, 5, 2555–2560.

Zu, S.; Han, T. Y.; Jiang, M. L.; Lin, F.; Zhu, X.; Fang, Z. Y., Deep-

Subwavelength Resolving and Manipulating of Hidden Chirality in Achiral Nanostructures. ACS Nano 2018, 12, 3908-3916. 19.

Kociak, M.; Zagonel, L. F., Cathodoluminescence in the scanning

transmission electron microscope. Ultramicroscopy 2017, 176, 112–131 20.

Yamamoto, N., Development of high-resolution cathodoluminescence

system for STEM and application to plasmonic nanostructures. Microscopy 2016,

65, 282-295. 21.

de Abajo, F. J. G., Optical excitations in electron microscopy. Rev. Mod.

Phys. 2010, 82, 209-275. 22.

Fredriksson, H.; Alaverdyan, Y.; Dmitriev, A.; Langhammer, C.;

Sutherland, D.; Zaech, M.; Kasemo, B., Hole-mask colloidal lithography. Adv.

Mater. 2007, 19, 4297-4302. 23.

Junesch, J.; Sannomiya, T., Ultrathin Suspended Nanopores with

Surface Plasmon Resonance Fabricated by Combined Colloidal Lithography and Film Transfer. ACS Appl. Mater. Interfaces 2014, 6, 6322-6331. 24.

Hafner, C., Boundary methods for optical nano structures. Phys. Status

Solidi B 2007, 244 , 3435-3447. 25.

de Abajo, F. J. G., Relativistic energy loss and induced photon emission

in the interaction of a dielectric sphere with an external electron beam. Phys. Rev.

B 1999, 59, 3095-3107. 26.

Schmidt, F. P.; Losquin, A.; Hofer, F.; Hohenau, A.; Krenn, J. R.; Kociak,

M., How Dark Are Radial Breathing Modes in Plasmonic Nanodisks? ACS Photon. 2018, 5, 861-866. 27.

de Abajo, F. J. G.; Kociak, M., Probing the photonic local density of states

with electron energy loss spectroscopy. Phys. Rev. Lett. 2008, 100, 106804. 28 ACS Paragon Plus Environment

Page 29 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

28.

Losquin, A.; Kociak, M., Link between Cathodoluminescence and

Electron Energy Loss Spectroscopy and the Radiative and Full Electromagnetic Local Density of States. ACS Photon. 2015, 2, 1619-1627. 29.

Sannomiya, T.; Saito, H.; Junesch, J.; Yamamoto, N., Coupling of

plasmonic nanopore pairs: facing dipoles attract each other. Light Sci. Appl. 2016,

5, e16146. 30.

Coenen, T.; Polman, A., Polarization-sensitive cathodoluminescence

Fourier microscopy. Opt. Expr. 2012, 20, 18679-18691. 31.

Hohenester, U.; Trugler, A., MNPBEM - A Matlab toolbox for the

simulation of plasmonic nanoparticles. Comput. Phys. Commun. 2012, 183, 370381. 32.

Yamamoto, N.; Sugiyama, H.; Toda, A., Cherenkov and transition

radiation from thin plate crystals detected in the transmission electron microscope.

Proc. Royal Soc. A 1996, 452, 2279-2301. 33.

Coenen, T.; Arango, F.; Koenderink, A.; Polman, A., Directional emission

from a single plasmonic scatterer. Nat. Commun. 2014, 5, 3250. 34.

Feist, A.; Echternkamp, K.; Schauss, J.; Yalunin, S.; Schafer, S.; Ropers,

C., Quantum coherent optical phase modulation in an ultrafast transmission electron microscope. Nature 2015, 521, 200-203. 35.

Guzzinati, G.; Beche, A.; Lourenco-Martins, H.; Martin, J.; Kociak, M.;

Verbeeck, J., Probing the symmetry of the potential of localized surface plasmon resonances with phase-shaped electron beams. Nat. Commun. 2017, 8, 14999.


Selected mode mixing and interference visualized within a single

Recommend Documents