Characterization of Nonradiative Bloch Modes in a Plasmonic

Article Cite This: ACS Photonics XXXX, XXX, XXX−XXX

pubs.acs.org/journal/apchd5

Characterization of Nonradiative Bloch Modes in a Plasmonic Triangular Lattice by Electron Energy-Loss Spectroscopy Daichi Yoshimoto,† Hikaru Saito,*,‡ Satoshi Hata,‡ Yoshifumi Fujiyoshi,§ and Hiroki Kurata§ †

Department of Applied Science for Electronics and Materials and ‡Department of Advanced Materials Science and Engineering, Kyushu University, 6-1 Kasugakoen, Kasuga, Fukuoka 816-8580, Japan § Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan

ACS Photonics Downloaded from pubs.acs.org by UNIV OF SUNDERLAND on 10/30/18. For personal use only.

S Supporting Information *

ABSTRACT: Electron beam spectroscopy has recently attracted much attention in the modal analysis of nanophotonic and plasmonic systems. In principle, electron energy-loss spectroscopy (EELS) provides information about the electromagnetic local density of states of all sorts of electromagnetic modes as well as nonradiative modes. However, there have not been many examples related to the EELS analyses for electromagnetic Bloch modes. Herein, EELS measurements are performed for the characterization of nonradiative band-edge modes facing the first bandgap in a plasmonic crystal with a triangular lattice, which is well-known for its full bandgap formation. The obtained spectrum images clearly determine the characteristics of the lower and upper band-edge modes, compared with an analytical model based on group theory and a numerical simulation by the finite-difference time-domain method. The EELS spectra also reveal differences in the plasmonic density of states between the lower and upper band-edges, which provides information about the band deformation near the bandgap. KEYWORDS: plasmonic band structure, plasmonic crystal, electron energy-loss spectroscopy, scanning transmission electron microscopy, triangular lattice ecent advances in fine processing technology have enabled the control of interactions between light and materials by nanoscale surface structures. The light absorption and emission efficiency of a material depend on the electromagnetic local density of states (EMLDOS), which can be effectively deformed from that in a uniform bulk by designing surface fine structures. Therefore, knowledge about the surface-shape dependency of EMLDOS is important to develop high speed and efficient nanophotonic devices.1−6 Electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL), performed by using a nanometer electron probe, are powerful tools to visualize modal shapes. Analyses of the electromagnetic modes by using both electron beam spectroscopies have been mostly applied for localized surface plasmons excited on isolated metal nanostructures. EELS and CL provide complementary information, and their combination enables measurement of radiation efficiency.7 CL has an advantage in polarization analysis, which visualizes multipoles by properly selecting the polarization and emission angle.8 It should be mentioned that local Purcell enhancement has recently been detected by using a Hanbury Brown and Twiss interferometer combined with CL,9 which provides more direct information about the enhanced light−material interaction by nanoscale surface structures. Periodic structures, as well as photonic crystals, are effective for various purposes. Especially for plasmonic resonators, use of Bloch modes is one of the promising solutions to reduce radiative and ohmic losses,2−5,10,11 which improves the quality

R

© XXXX American Chemical Society

factor, leading to surface plasmon lasing.2−5 Periodic structures also provide a control of direction or directivity in luminescence from organic and inorganic materials,12,13 which can be another way to improve the extraction efficiency of light emitting devices. In the same way, periodic structures provide tunability in light receiving characteristics such as wavelength- or polarization-dependent sensitivity.14−17 CL has been applied to a variety of periodic structures, where momentum-resolved analyses18,19 and polarization analyses20,21 have been demonstrated. CL analysis in real and momentum space enabled classification of band-edge modes based on group theory,22 which provided fundamental knowledge to design advanced structures, such as defects23,24 and heterostructures.25 Other important structures like crystal boundaries for edge states26,27 will be fully characterized by advanced CL techniques in the near future. However, CL experiments are unable to directly detect nonradiative modes as a matter of course. Most of the previous studies using CL have targeted the Γ point where light is emitted in the direction of the surface normal.22,23,25 In a plasmonic crystal with a triangular lattice (Tri-PlC), a plasmonic full bandgap opens between the lower band-edge at the K point and the upper band-edge at the M point,28 which can be used to control the surface plasmon polariton (SPP) propagation.24,29,30 The band-edges at the M and K points are located Received: July 10, 2018 Published: October 17, 2018 A

DOI: 10.1021/acsphotonics.8b00936 ACS Photonics XXXX, XXX, XXX−XXX

ACS Photonics

Article

Figure 1. Band dispersion calculated under the empty lattice approximation. (a) Schematic drawing of the Tri-PlC. (b) Reciprocal lattice of the triangular lattice. (c) Plasmonic band structure of an aluminum Tri-PlC with a 600 nm period in a vacuum. The blue dashed curves are dispersion curves calculated under the empty lattice (EL) approximation. The red solid lines are light lines in a vacuum. Band folding at the M and K points is magnified in the side insets.

by reciprocal lattice vectors. Figure 1c shows a band structure of an aluminum Tri-PlC with a 600 nm period in a vacuum, which was calculated under the EL approximation using eq 1. Here the dielectric function of aluminum was assumed to follow the Drude model without damping, ε = 1 − ω2P/ω2, where ωP is the plasma frequency of aluminum, that is, ℏωP = 14.9 eV,31 and ℏ is Planck’s constant divided by 2π. The energy values of the first band folding points at the M and K points were calculated to be 1.19 and 1.36 eV using eq 1, respectively. At the M point in the reciprocal space, two dispersion cones are merged and therefore possess the C2v point group symmetry. The band-edge modes at the M point are approximately expressed as linear combinations of two basis functions, eikMr and e−ikMr, where kM is the wave vector at the M point. The traces of the representations for the four symmetry operations in the C2v point group are {2, 0, 2, 0} based on these two basis functions, which can be decomposed into two irreducible representations, A1M and B1, as their direct sum (Table 1). Therefore, the surface charge

outside the light cone, and thus, direct detection of the bandedge modes at the M and K points is not easy using optical methods as well as CL. Momentum-resolved spectroscopy for photonic and plasmonic band dispersions remains a challenge for EELS, because high energy and momentum resolutions, highly sensitive detection, and total stability of the instrument must be simultaneously achieved, although a high momentum resolution has been achieved in the past.31,32 There have not been many examples related to EELS analyses for electromagnetic Bloch modes.33,34 However, EELS enables access to the SPP plane waves outside the light cone31 and nonradiative modes without dipole moments,7,35,36 which are potential advantages of EELS in the analyses of electromagnetic Bloch modes. Herein, we show the characterization of the nonradiative bandedge modes by EELS in a Tri-PlC, and the correlation between the obtained information and the plasmonic density of states is discussed. In this study, we have not performed momentumresolved spectroscopy but spatially resolved spectroscopy. Nevertheless, modal symmetry for each band-edge was clearly determined, because the band-edge modes at the M and K points can be classified into lattice point modes and interlattice modes, which are divided below and above the full bandgap.

Table 1. Character Table for the C2v Point Group

■

PLASMONIC BAND STRUCTURE UNDER EMPTY LATTICE APPROXIMATION On a flat metal surface, the dispersion relation of SPPs is isotropic, and the wavenumber k is written as ÄÅ É ε ÑÑÑÑ ÅÅÅ ω k = ReÅÅ Ñ ÅÅÇ c ε + 1 ÑÑÑÖ (1) where ω is the angular frequency, c is the speed of light in a vacuum, and ε is the dielectric function of the metal. If there is a periodic surface structure as depicted in Figure 1a, SPPs behave as Bloch waves. The surface charge distribution of SPPs can be expressed using the in-plane position vector r and time t Ψl (r, t ) = e

i(k·r − ωt )

∑

Cgl e ig·r

=e

−iωt

E

C2

σv

σv′

A1 A2 B1 B2 Mred

1 1 1 1 2

1 1 −1 −1 0

1 −1 1 −1 2

1 −1 −1 1 0

σA1M(r) σB1(r) A1⊕B1

distribution of the band-edge modes at the M point can be derived by applying the projection operators of A1M and B1 to one of the basis functions and are expressed as σA1M(r) = cos(kM ·r)

(3)

σB1(r) = sin(kM ·r)

(4)

In the same way, the surface charge distribution of the bandedge modes at the K point can be determined based on the C3v point group symmetry (Table 2) as

σl(r) (2)

g

C2v

Clg

where the index l specifies the eigenmode, and is the coefficient of each plane wave whose wave vector is shifted by a reciprocal lattice vector g owing to Bragg reflection. When the periodic structure forms a triangular lattice, the reciprocal lattice also forms a triangular lattice as shown in Figure 1b. Under the empty lattice (EL) approximation, a plasmonic band structure consists of a set of conical dispersion planes shifted

σA1K(r) = cos(kK1·r) + cos(kK 2·r) + cos(kK 3·r)

(5)

σE(1)K(r) = 2cos(kK1·r) − cos(kK 2·r) − cos(kK 3·r)

(6)

σE(2)K(r) = cos(kK 2·r) − cos(kK 3·r)

(7)

where kK1, kK2, and kK3 are the wave vectors at the K points, which satisfy kK1 + kK2 + kK3 = 0. Here the normalization B


ACS Photonics

Article

each map is proportional to ∑j|Ez,l,j(r)|2 if the height of the structures on the surface is infinitesimal. These patterns suggest that lattice point and interlattice modes can be distinguished by EELS mapping, although it is very difficult to detect any differences between the band-edge modes at the M and K points. Unlike the band structure under the EL approximation, the first bandgap opens at the M and K points in real Tri-PlCs. When the energy gaps are sufficiently wide at the M and K points, a full bandgap is formed in the overlapped region between both energy gaps at the M and K points.28 σl(r) is deformed from those explained as linear combinations of two or three plane waves (eqs 3−7) due to the structured surface as shown in numerical simulations later.

Table 2. Character Table for the C3v Point Group C3v

E

2C3

3σv

A1 A2 E Kred

1 1 2 3

1 1 −1 0

1 −1 0 1

σA1K(r) σE(1)(r),σE(2)(r) A1⊕E

factors are omitted. The E mode is doubly degenerate and expressed as a linear combination of σE(1)K(r) and σE(2)K(r) The same treatment using group theory has been shown in previous reports.14,22,24 As shown in the plots of eqs 3−7 (Figure 2a), the band-edge modes can be categorized into two groups at both M and K points, that is, the A1M and A1K modes are “lattice point modes”, while the B1 and E modes are “interlattice modes”. Unlike the band-edge modes at the M and K points, the triangular lattice itself has a different translation symmetry, which causes arbitrariness in the positional relationship between σl(r) and the triangular lattice. Therefore, there are several nonidentical functions, which can be found in equivalent functions σl(r + ma + nb) produced by translation operations, where a and b are lattice vectors of the triangular lattice, and m and n are integers. Furthermore, the triangular lattice has the C6v point group symmetry, which is different from those of the surface charge distributions of the A1M, B1, and E modes. Therefore, additional nonidentical functions appear by applying the symmetry operations in the C6v point group to σA1M(r), σB1(r), σE(1)K(r), and σE(2)K(r). When σl(r) is related to the excitation probability map produced by EELS imaging, contributions of all nonidentical functions should be considered. The excitation probability of the standing SPP wave by a fast electron going along the z axis is proportional to the z component of EMLDOS (zEMLDOS) Fourier-transformed along the z axis,37 and its spatial dependence is expressed as the electric field strength ∑j|Ez,l,j(r,qz)|2 for a given mode, where qz is the z component of the transfer momentum for the inelastic scattering, and the index j represents a combination of nonidentical but equivalent functions that were discussed above. Under the EL approximation, ∑j|Ez,l,j(r,qz)|2 is proportional to an arbitrary xy cross section ∑j|Ez,l,j(r)|2, because the damping of the electron field in the z direction is constant. Figure 2b shows ∑j|σl,j(r)|2, which is roughly recognized as the expected EELS map for each band-edge mode. The contrast in

■

SPECIMEN FABRICATION

For EELS measurements in a transmission electron microscope, the specimen must be thin enough for incident electrons to penetrate. A Tri-PlC membrane was produced by electron beam lithography, physical deposition techniques, and the replica method as depicted in Figure 3. First, a 200 nm thick positive resist layer (ZEP520A) was formed on an InP substrate by the spin coating method, and disk arrays with three periods P of 500, 600, and 700 nm were patterned by electron beam lithography. Second, a 3 nm thick SiO2 layer and an 87 nm thick aluminum layer were deposited by radio frequency magnetron sputtering and thermal evaporation, respectively. Then, the resist layer was dissolved in acetone to obtain a reversed pattern of the triangular lattice. Next, the triangular lattice pattern was transferred to a replica film. A 7 nm thick nickel layer was then deposited as adhesion layers on the patterned replica film by thermal evaporation. A 130 nm thick aluminum layer was then deposited by thermal evaporation. Finally, the replica film was dissolved in acetone to obtain a Tri-PlC membrane. Both surfaces of the Tri-PlC membrane had different structures to each other; that is, one side had a disk array and the other side had a hole array. However, the 7 nm thick nickel layer behaved as a damper for SPPs on the hole array side.38 Therefore, the structures expected to appear in the EELS spectra, such as peaks and dips, reflect the plasmonic band structure of the disk array side without the nickel layer.

Figure 2. (a) Surface charge distributions of the band-edge modes at the M and K points derived using group theory under the EL approximation. (b) Expected EELS maps of the band-edge modes at the M and K points, where contributions of all nonidentical σl(r) are considered. C


ACS Photonics

Article

Figure 3. Schematic drawing of specimen fabrication for the Tri-PlC membrane.

Figure 4. (a) ADF-STEM image of the Tri-PlC membrane with P = 600 nm and D = 330 nm. (b) EELS spectra averaged over two unit cells in the Tri-PlC membranes with P = 700 nm (blue), P = 600 nm (red), P = 500 nm (green), and with different disk diameters. The black curve is an EELS spectrum taken from a flat Al/Ni membrane with the same layer thicknesses as the Tri-PlC membranes. The ZLP was subtracted from each spectrum by using an EELS spectrum taken with no specimen.

■

EELS MEASUREMENT AND FDTD SIMULATION

their time dependence. The details about calculation parameters are described in Supporting Information A.

A transmission electron microscope FEI Titan Cubed G2, equipped with a Schottky electron source, a monochromator, and a spherical aberration corrector for the probe-forming lens system, was used. A GATAN imaging filter (Quantum filter) was also used for EELS measurements combined with scanning transmission electron microscopy (STEM). The microscope was operated at an accelerating voltage of 300 kV. The energy resolution measured from a full width of half-maximum of the zero loss peak (ZLP) was 120 meV. The convergence semiangle was 1.05 mrad, and the EELS collection semiangle was 1.20 mrad. The probe current was approximately 100 pA. For EELS imaging, a field-of-view of 1.656 × 1.656 μm was chosen, and the pixel size was set to 36 × 36 nm for P = 500 and 600 nm. For P = 700 nm, a field-of-view was set to 2.3 × 2.3 μm, and the pixel size was set to 50 × 50 nm. The acquisition time per pixel was 20 ms. Annular dark-field (ADF) images were also acquired during the EELS measurements. The inner and outer semiangles for the ADF detection were 19 and 92 mrad, respectively. Finite-difference time-domain (FDTD) simulation was performed using the CrystalWave software package (Photon Design). The Tri-PlC membrane was modeled to reproduce the field distributions of the perpendicular electric components Ez,l(r,t) for the band-edge modes at the first bandgap, including

■

RESULTS AND DISCUSSION Figure 4a shows an ADF-STEM image of the Tri-PlC membrane with P = 600 nm and D = 330 nm. A crosssectional observation was also performed to determine the three-dimensional morphology of the fabricated Tri-PlC membrane, which is discussed in Supporting Information B. Figure 4b shows the EELS spectra taken from several specimens with different structural parameters, which are averaged over areas corresponding to two unit cells. These spectra are compared with a spectrum taken from a flat Al/Ni membrane with the same layer thicknesses as those of the TriPlC membranes. The ZLP was subtracted from each spectrum by using an EELS spectrum obtained with no specimen. A peak was observed at about 1.5 eV in the spectra obtained from the flat Al/Ni membrane. This peak was attributed to the interband transition in bulk aluminum.39 Apart from the peak of the interband transition, another peak (identified by arrows in Figure 4b) was observed for each Tri-PlC membrane. The peak position clearly exhibited period dependence while it was less sensitive to the disk diameter, indicating that the observed peak did not originate from localized surface plasmon modes at each aluminum disk but the Bloch modes. Under the EL approximation, the energy levels at the M and K points D


ACS Photonics

Article

Figure 5. (a) EELS spectra obtained near the centers of the disks (lattice points) and outside the disks (interlattice points) for P = 600 nm and D = 330 nm. The ZLP was subtracted from each spectrum by using EELS spectrum taken with no specimen. The sampling locations are marked by the red squares in the volume plasmon maps using the spectral intensity at 14.9 eV (left insets). (b,c) EELS spectrum images averaged from (b) 0.99 to 1.19 eV and (c) 1.37 to 1.57 eV for P = 600 nm and D = 330 nm. (d,e) EELS spectrum images averaged from (d) 0.87 to 1.02 eV and (e) 1.18 to 1.33 eV for P = 700 nm and D = 370 nm. (f,g) EELS spectrum images averaged from (f) 1.13 to 1.43 eV and (g) 1.64 to 1.94 eV for P = 500 nm and D = 290 nm. Spectral intensity after ZLP subtraction is displayed in all of the spectrum images.

Figure 6. FDTD simulation for the band-edge modes. (a) Electric field Ez,l(r) and (b) electric field strength ∑j|Ez,l,j(r)|2 for P = 600 nm and D = 350 nm calculated by FDTD. (c) Line profiles extracted along the lines displayed in Figure 6b.

were similar to those at the M point in Tri-PlCs; that is, their surface charge distributions are expressed as the same equations (eqs 3 and 4), and one is symmetric relative to the center of the terrace of the 1D metallic grating, while the other is antisymmetric. According to the analytical model for 1D metallic gratings given by Barnes et al.,41 the symmetric standing wave mode is located at the lower band-edge as with the lattice point modes in the Tri-PlC. Figure 5b shows the EELS maps using a spectral intensity from 0.99 to 1.19 eV, which exhibited a similar feature to the expected EELS maps for the A1M and A1K modes shown in Figure 2b, that is, the spectral intensity became higher on the disks compared with that outside the disks. From 1.37 to 1.57 eV, the intensity near the center of the disks became the local minimum, as shown in Figure 5c, which indicated that the B1 and E modes were located at the upper band-edges of the M and K points. For P = 700 and 500 nm, in the same way, the

were 1.02 and 1.18 eV for P = 700 nm, 1.19 and 1.37 eV for P = 600 nm, and 1.43 and 1.64 eV for P = 500 nm, respectively. It should be noted that the energy value of the observed peak was lower than that of the M point under the EL approximation for each period, suggesting that the electromagnetic density of states reached the local maximum at the lower band-edge of the first plasmonic bandgap. Figure 5a shows the EELS spectra obtained near the centers of the disks (lattice points) and outside the disks (interlattice points) for P = 600 nm and D = 330 nm. From the comparison between the lattice point spectrum and interlattice point spectrum, it was revealed that the lattice point modes were formed at the lower band-edges, while the interlattice modes were formed at the upper band-edges. The similar energy relationship has been observed at the first bandgap in onedimensional (1D) metallic gratings,40,41 where the bandgap opens at the X point. The two band-edge modes at the X point E


ACS Photonics

Article

Figure 7. (a) P dependence of energy levels of the A1K (red line), E (red dashed line), A1M (blue line), and B1 (blue dashed line) modes for D = 350 nm calculated by FDTD. Experimental peaks of the lattice point modes identified by arrows in Figure 4b are also plotted (white circles). (b) Schematic drawing of the plasmonic band dispersions and density of states (DOS) in the Tri-PlC. (c) D dependence of energy levels of the A1K (red line) and B1 (blue dashed line) modes calculated by FDTD.

intensity in the part of the energy range lower than the M point estimated by the EL approximation became stronger on the disks, while the intensity in the part of the energy range higher than the K point estimated by the EL approximation became weaker at the centers of the disks (Figure 5d−g). As seen in all of the EELS maps, a bright contrast appeared at the edges of the disks unlike in the expected EELS maps (Figure 2b). It seemed to be contributions of higher order components of the Bloch waves, which were not included in the analytical models (eqs 3−7). In the FDTD simulation, the bright contrast at the edge positions was actually reproduced as discussed in the next paragraph. However, as shown in the ADF-STEM image (Figure 4a) and volume plasmon maps (insets of Figure 5a), the specimen was thicker at the lower side of the edges, which could increase the signals of the volume excitation such as intraband transition and bremsstrahlung at the edges of the disks. This thickness effect seemed to be the main reason for the bright contrast at the edges of the disks, since the edge contrast corresponded to the thickness contrast. The above experimental results concerning the band-edge modes were confirmed by FDTD simulation as follows. Figure 6a,b shows the calculated electric field Ez,l(r) and electric field strength ∑j|Ez,l,j(r)|2 for P = 600 nm and D = 350 nm. Although the electric field became much stronger near the edges of the disks, unlike the surface charge distribution predicted by group theory under the EL approximation, the symmetry and periodicity of the patterns agreed with each other (Figures 2b and 6a). As understood from the line profiles in Figure 6c, the difference in ∑j|Ez,l,j(r)|2 between the two lattice point modes (A1M and A1K) is very tiny, suggesting that it should be hard to resolve them by the difference in spatial distribution. The same is applied to the two interlattice modes (B1 and E). The calculated energy values of the band-edge modes and the experimental peaks of the lattice point modes are plotted in Figure 7a. As suggested by the calculated energy levels, the two lattice point modes might be resolved in spectra if the energy resolution was sufficiently high. However, the observed peaks of the lattice point modes were not split into two in the experimental spectra (Figure 4b) probably because the energy difference in the period range of the present experiment was smaller than the energy resolution (120 meV). For the two interlattice modes, the energy difference was calculated to be larger than the energy resolution. However, the upper bandedges were not observed as strong peaks like the lower bandedges (Figure 4b), suggesting a large difference in the plasmonic density of states between the lattice point modes and the interlattice point modes. The calculated energy values of the lattice point modes were much lower than those

estimated by the EL approximation, while those of the interlattice modes were almost the same as those estimated by the EL approximation, suggesting that the disk array structure mainly deformed the band dispersion near the lower band-edges as depicted in Figure 7b. This was consistent with the experimental results, that is, an increase of the plasmonic density of states owing to the disk array structure was observed only around the lower band-edges (Figure 4b). Figure 7c shows the D dependence of the energy levels of the B1 and A1K modes for P = 600 nm. The calculated energy value of the A1K modes exhibited stronger D dependence than that of the B1 mode, although the amount of the change was less than 0.06 eV in the diameter range from 150 to 500 nm. Such a small D dependence was not clearly detected in the present experiment. However, the D dependence becomes important for the full bandgap formation. The calculated energy value of the B1 mode was higher than that of the A1K mode from D = 200 to 450 nm, where the full bandgap was expected to be formed. However, below D = 150 nm and above D = 500 nm, the energy differences between lattice point modes and interlattice modes were not sufficiently large, which resulted in the formation of an imperfect bandgap.

■

CONCLUSION The nonradiative band-edge modes in the Tri-PlC have been experimentally characterized by STEM-EELS in this study. The lattice point modes A1M and A1K are located at the lower band-edges of the M and K points, and the interlattice modes B1 and E are located at the upper band-edges. The FDTD simulation indicates that the energy levels of the lattice point modes (A1M and A1K) are largely lower than those obtained under the EL approximation, while the energy levels of the interlattice modes (B1 and E) are almost the same as those obtained under the EL approximation, which suggests that the disk array structure mainly deforms the band dispersion and increases the plasmonic density of states near the lower bandedges. This is consistent with the experimental results, that is, an increase of the plasmonic density of states owing to the disk array structure is observed only around the lower band-edges. Therefore, information about the plasmonic density of states is reflected in the EELS spectra, and thus, EELS is potentially a powerful tool to probe the band structures of electromagnetic Bloch waves at a high spatial resolution.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.8b00936. F


ACS Photonics

■

Article

(12) Lozano, G.; Louwers, D. J.; Rodríguez, S. R. K.; Murai, S.; Jansen, O. T. A.; Verschuuren, M. A.; Gómez Rivas, J. Plasmonics for Solid-State Lighting: Enhanced Excitation and Directional Emission of Highly Efficient Light Sources. Light: Sci. Appl. 2013, 2, e66. (13) Murai, S.; Verschuuren, M. A.; Lozano, G.; Pirruccio, G.; Rodriguez, S. R. K.; Rivas, J. G. Hybrid plasmonic-photonic modes in diffractive arrays of nanoparticles coupled to light-emitting optical waveguides. Opt. Express 2013, 21, 4250−4262. (14) Rosenberg, J.; Shenoi, R. V.; Krishna, S.; Painter, O. Design of Plasmonic Photonic Crystal Resonant Cavities for Polarization Sensitive Infrared Photodetectors. Opt. Express 2010, 18, 3672−3686. (15) Hao, J.; Wang, J.; Liu, X.; Padilla, W. J.; Zhou, L.; Qiu, M. High performance optical absorber based on a plasmonic metamaterial. Appl. Phys. Lett. 2010, 96, 251104. (16) Li, Q.; Gao, J.; Yang, H.; Liu, H.; Wang, X.; Li, Z.; Guo, X. Tunable Plasmonic Absorber Based on Propagating and Localized Surface Plasmons Using Metal-Dielectric-Metal Structure. Plasmonics 2017, 12, 1037−1043. (17) Ghobadi, A.; Hajian, H.; Gokbayrak, M.; Dereshgi, S. A.; Toprak, A.; Butun, B.; Ozbay, E. Visible light nearly perfect absorber: an optimum unit cell arrangement for near absolute polarization insensitivity. Opt. Express 2017, 25, 27624−27634. (18) Suzuki, T.; Yamamoto, N. Cathodoluminescent Spectroscopic Imaging of Surface Plasmon Polaritons in a 1-Dimensional Plasmonic Crystal. Opt. Express 2009, 17, 23664−23671. (19) Mignuzzi, S.; Mota, M.; Coenen, T.; Li, Yi.; Mihai, A. P.; Petrov, P. K.; Oulton, R. F. M.; Maier, S. A.; Sapienza, R. EnergyMomentum Cathodoluminescence Spectroscopy of Dielectric Nanostructures. ACS Photonics 2018, 5, 1381−1387. (20) Osorio, C. I.; Coenen, T.; Brenny, B. J. M.; Polman, A.; Koenderink, A. F. Angle-Resolved Cathodoluminescence Imaging Polarimetry. ACS Photonics 2016, 3, 147−154. (21) Brenny, B. J. M.; Beggs, D. M.; van der Wel, R. E. C.; Kuipers, L.; Polman, A. Near-Infrared Spectroscopic Cathodoluminescence Imaging Polarimetry on Silicon Photonic Crystal Waveguides. ACS Photonics 2016, 3, 2112−2121. (22) Saito, H.; Yamamoto, N. Size Dependence of Bandgaps in a Two-Dimensional Plasmonic Crystal with a Hexagonal Lattice. Opt. Express 2015, 23, 2524−2540. (23) Saito, H.; Yamamoto, N. Control of Light Emission by a Plasmonic Crystal Cavity. Nano Lett. 2015, 15, 5764−5769. (24) Saito, H.; Yamamoto, N.; Sannomiya, T. Waveguide Bandgap in Crystalline Bandgap Slows Down Surface Plasmon Polariton. ACS Photonics 2017, 4, 1361−1370. (25) Saito, H.; Mizuma, S.; Yamamoto, N. Confinement of Surface Plasmon Polaritons by Heterostructures of Plasmon Crystals. Nano Lett. 2015, 15, 6789−6793. (26) Wu, L. H.; Hu, X. Scheme for Achieving a Topological Photonic Crystal by Using Dielectric Material. Phys. Rev. Lett. 2015, 114, 223901. (27) Gómez, D. E.; Hwang, Y.; Lin, J.; Davis, T. J.; Roberts, A. Plasmonic Edge States: An Electrostatic Eigenmode Description. ACS Photonics 2017, 4, 1607−1614. (28) Kitson, S. C.; Barnes, W. L.; Sambles, J. R. Full Photonic Band Gap for Surface Modes in the Visible. Phys. Rev. Lett. 1996, 77, 2670− 2673. (29) Bozhevolnyi, S. I.; Volkov, V. S.; Søndergaard, T.; Boltasseva, A.; Borel, P. I.; Kristensen, M. Near-Field Imaging of Light Propagation in Photonic Crystal Waveguide: Explicit Role of Bloch Harmonics. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 235204. (30) Marquart, C.; Bozhevolnyi, S. I.; Leosson, K. Near-field imaging of surface plasmon-polariton guiding in band gap structures at telecom wavelengths. Opt. Express 2005, 13, 3303−3309. (31) Pettit, R. B.; Silcox, J.; Vincent, R. Measurement of SurfacePlasmon Dispersion in Oxidized Aluminum Films. Phys. Rev. B 1975, 11, 3116−3123. (32) Midgley, P. A. A Simple New Method to Obtain High Angular Resolution ω−q Patterns. Ultramicroscopy 1999, 76, 91−96.

FDTD simulation; cross-sectional observation of the Tri-PlC membrane (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Phone: 81-92583-7579; Fax: 81-92-583-7580 (H.S.) ORCID

Hikaru Saito: 0000-0001-9578-1433 Yoshifumi Fujiyoshi: 0000-0002-0192-8041 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Tokyo Institute of Technology and Kyoto University in the “Nanotechnology Platform Project” sponsored by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, and the Japan Society for the Promotion of Science Kakenhi No. 17K14118, The Murata Science Foundation, and Kazato Research Foundation. We thank the Edanz Group (www. edanzediting.com/ac) for editing a draft of this manuscript.

■

REFERENCES

(1) Russell, K. J.; Liu, T. L.; Cui, S.; Hu, E. L. Large Spontaneous Emission Enhancement in Plasmonic Nanocavities. Nat. Photonics 2012, 6, 459−462. (2) Zhou, W.; Dridi, M.; Suh, J. Y.; Kim, C. H.; Co, D. T.; Wasielewski, M. R.; Schatz, G. C.; Odom, T. W. Lasing Action in Strongly Coupled Plasmonic Nanocavity Arrays. Nat. Nanotechnol. 2013, 8, 506−511. (3) van Beijnum, F.; Van Veldhoven, P. J.; Geluk, E. J.; De Dood, M. J. A.; ’tHooft, G. W.; Van Exter, M. P. Surface Plasmon Lasing Observed in Metal Hole Arrays. Phys. Rev. Lett. 2013, 110, 206802. (4) Hakala, T. K.; Rekola, H. T.; Väkeväinen, A. I.; Martikainen, J. P.; Nečada, M.; Moilanen, A. J.; Törmä, P. Lasing in dark and bright modes of a finite-sized plasmonic lattice. Nat. Commun. 2017, 8, 13687. (5) Tenner, V. T.; De Dood, M. J. A.; Van Exter, M. P. Two-mode surface plasmon lasing in hexagonal arrays. Opt. Lett. 2018, 43, 166− 169. (6) Chou, Y. H.; Hong, K. B.; Chang, C. T.; Chang, T. C.; Huang, Z. T.; Cheng, P. J.; Yang, J. H.; Lin, M. H.; Lin, T. R.; Chen, K. P.; Gwo, S.; Lu, T. C. Ultracompact Pseudowedge Plasmonic Lasers and Laser Arrays. Nano Lett. 2018, 18, 747−753. (7) Schmidt, F. P.; Losquin, A.; Hofer, F.; Hohenau, A.; Krenn, J. R.; Kociak, M. How Dark Are Radial Breathing Modes in Plasmonic Nanodisks? ACS Photonics 2018, 5, 861−866. (8) Thollar, Z.; Wadell, C.; Matsukata, T.; Yamamoto, N.; Sannomiya, T. Three-Dimensional Multipole Rotation in Spherical Silver Nanoparticles Observed by Cathodoluminescence. ACS Photonics 2018, 5, 2555. (9) Lourenço-Martins, H.; Kociak, M.; Meuret, S.; Treussart, F.; Lee, Y. H.; Ling, X. Y.; Chang, H. C.; Galvão Tizei, L. H. Probing Plasmon-NV0 Coupling at the Nanometer Scale with Photons and Fast Electrons. ACS Photonics 2018, 5, 324−328. (10) Todisco, F.; Esposito, M.; Panaro, S.; De Giorgi, M.; Dominici, L.; Ballarini, D.; Fernández-Domínguez, A. I.; Tasco, V.; Cuscunà, M.; Passaseo, A.; Ciracì, C.; Gigli, G.; Sanvitto, D. Toward Cavity Quantum Electrodynamics with Hybrid Photon Gap-Plasmon States. ACS Nano 2016, 10, 11360−11368. (11) Khlopin, D.; Laux, F.; Wardley, W. P.; Martin, J.; Wurtz, G. A.; Plain, J.; Bonod, N.; Zayats, A. V.; Dickson, W.; Gérard, D. Lattice modes and plasmonic linewidth engineering in gold and aluminum nanoparticle arrays. J. Opt. Soc. Am. B 2017, 34, 691−700. G


ACS Photonics

Article

(33) García de Abajo, F. J.; Pattantyus-Abraham, A. G.; Zabala, N.; Rivacoba, A.; Wolf, M. O.; Echenique, P. M. Cherenkov Effect as a Probe of Photonic Nanostructures. Phys. Rev. Lett. 2003, 91, 143902. (34) Le Thomas, N.; Alexander, D. T. L.; Cantoni, M.; Sigle, W.; Houdré, R.; Hébert, C. Imaging of High-Q Cavity Optical Modes by Electron Energy-Loss Microscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 155314. (35) Koh, A. L.; Bao, K.; Khan, I.; Smith, W. E.; Kothleitner, G.; Nordlander, P.; Maier, S. A.; McComb, D. W. Electron Energy-Loss Spectroscopy (EELS) of Surface Plasmons in Single Silver Nanoparticles and Dimers: Influence of Beam Damage and Mapping of Dark Modes. ACS Nano 2009, 3, 3015−3022. (36) Ö güt, B.; Talebi, N.; Vogelgesang, R.; Sigle, W.; van Aken, P. A. Toroidal Plasmonic Eigenmodes in Oligomer Nanocavities for the Visible. Nano Lett. 2012, 12, 5239−5244. (37) García de Abajo, F. J.; Kociak, M. Probing the Photonic Local Density of States with Electron Energy-Loss Spectroscopy. Phys. Rev. Lett. 2008, 100, 106804. (38) Kuttge, M.; Cai, W.; García de Abajo, F. J.; Polman, A. Dispersion of Metal-Insulator-Metal Plasmon Polaritons Probed by Cathodoluminescence Imaging Spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 033409. (39) Ehrenreich, H.; Philipp, H. R.; Segall, B. Optical Properties of Aluminum. Phys. Rev. 1963, 132, 1918−1928. (40) Kitson, S. C.; Barnes, W. L.; Bradberry, G. W.; Sambles, J. R. Surface Profile Dependence of Surface Plasmon Band Gaps on Metallic Gratings. J. Appl. Phys. 1996, 79, 7383. (41) Barnes, W. L.; Preist, T. W.; Kitson, S. C.; Sambles, J. R. Physical Origin of Photonic Energy Gaps in the Propagation of Surface Plasmons on Gratings. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 6227−6244.

H


Characterization of Nonradiative Bloch Modes in a Plasmonic

Recommend Documents