Confinement of Surface Plasmon Polaritons by Heterostructures of

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Confinement of surface plasmon polaritons by heterostructures of plasmonic crystals Hikaru Saito, Shohei Mizuma, and Naoki Yamamoto Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b02623 • Publication Date (Web): 28 Sep 2015 Downloaded from http://pubs.acs.org on September 28, 2015

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Confinement of surface plasmon polaritons by heterostructures of plasmonic crystals Hikaru Saito*,1,2, Shohei Mizuma3,4, and Naoki Yamamoto*,1,4,5 1

Quantum Nanoelectronics Reserch Center, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan. 2 Center of Advanced Instrumental Analysis, Kyushu University, 6-1 Kasugakoen, Kasuga, Fukuoka 816-8580, Japan 3 Graduate School of Decision Science and Technology, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan. 4 Department of Condensed Matter Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan. 5 Department of Innovative and Engineered Materials, Tokyo Institute of Technology, Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8503, Japan. *corresponding authors: HS : [email protected] NY : [email protected]

ABSTRACT Square lattice plasmonic crystals (SQ-PlCs) composed of silver pillars generate large bandgaps for surface plasmon polaritons (SPPs). SPP confinement is demonstrated using one- and two-dimensional heterostructures of SQ-PlCs comprised of cylindrical pillars with different diameters in a common square lattice. Two kinds of localized modes are observed to appear in the heterostructures by photon map imaging using cathodoluminescence (CL) technique combined with a scanning transmission electron microscopy (STEM). Angle-resolved CL spectroscopy reveals contrasting characteristics of the two localized modes in their emission distributions, indicating that they originate from the band-edge A and E modes of the matrix SQ-PlC.

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KEYWORDS Surface plasmon polariton, Plasmonic crystal, Heterostructure, Cavity, Cathodoluminescence, Scanning transmission electron microscopy

TABLE OF CONTENTS GRAPHIC

Surface plasmon polaritons (SPPs) are collective electron oscillations coupled with an electromagnetic near-field which propagate along the interface between a metal and a dielectric.1 Various SPP applications have been considered to increase light–matter interactions in optoelectronic devices. Surface structures can control the optical properties of SPPs, and one of the most promising is a periodically corrugated metal surface, the so-called plasmonic crystal (PlC).2 Similar to electrons in crystals, the dispersions of SPPs in PlCs are folded back and enter the inside of the dispersion of light, where SPPs and light can be converted into each other. Band-edge modes of the Г point are typically used for SPP–light conversions. Moreover, PlCs can be easily introduced into practical applications because the metal layers also function as electrodes. Previously PlCs have been applied as sensors,3,4 photodetectors,5 solar cells,6 light-emitting diodes (LEDs),7,8 and lasers.9,10


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The bandgap is also useful to manipulate SPPs on a metal surface where PlCs act as mirrors. SPP waveguides using PlCs have been demonstrated,11,12 and can be utilized in nanophotonic devices and circuits.13 Recently, confinement of SPPs in local cavity structures using PlCs have been studied to further enhance light–matter interactions.14-17 Due to the small mode volume, cavity structures should realize a large Purcell enhancement18 However, confinement of SPPs using heterostructures of PlCs which have higher degree of design freedom has yet to be reported. Herein we demonstrate confinement of SPPs using a PlC-based “heterostructure” with a square lattice. Compared to the original PlC (single crystal), only one parameter, the element size (i.e., pillar diameter) in the inner area of the matrix lattice, is modified. This simple and local modification causes confinement of SPPs inside the structure. Previously we revealed the plasmonic band structure around the Г point of the square lattice PlC composed of silver pillars (SQ-PlCs).19 The SQ-PlC contains the three band-edge modes A, B, and E modes at the Г point of the second bandgap. Figure 1a shows the electric field normal to the surface calculated by group theory,19 which is proportional to the surface charge. The A and B modes are dark modes that do not form a surface parallel dipole moment on each pillar. The E mode is a doubly degenerate bright mode with a dipole moment parallel to the pillar terrace. The energies of the A and E modes strongly depend on the pillar diameter (Fig. 1b). This dependences of the A and E band-edge energies are similar to those of the symmetric and antisymmetric band-edge modes on the terrace width in the one-dimensional PlC, 20 as discussed in the previous paper.19 Barnes et al. have given the explanation about the physical origin of the bandgap for a one-dimensional PlC.21 On the other hand, the B mode is insensitive to the pillar diameter because their surface charges are mainly distributed on the flat surface outside of the


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pillars. The strong dependence of A and E modes on the pillar diameter suggests that the local confinement of SPPs can be achieved by a heterostructure composed of two types of pillars with different diameters D1 and D2. As illustrated in Fig. 1c, if a PlC composed of pillars with a small D1 (matrix) surrounds a PlC with a large D2, the energy level of the A-like mode (A’ mode) in the inner PlC should be elevated as indicated in Fig. 1b. The A’ mode can be confined in the inner PlC since the energy level of the A’ mode stands within the energy range of the bandgap of the matrix. Figure 1d shows the electric field distribution E z ( x , y ) calculated by the finite-difference time-domain (FDTD) method, which indicates that the A’ mode is localized inside the inner PlC. This also applies to the E-like mode (E’ mode). That is, the energy level of the E’ mode should lower and stand within the energy range of the bandgap of the matrix. However, it might be difficult to form a localized B mode because the energy of the B mode is insensitive to the pillar diameter. Electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL) performed in electron microscopes are powerful tools to probe photonic and plasmonic nanostructures at high spatial resolution.16,19,20,22-32 Even with respect to periodic structures, a variety of structures including PlCs have been studied by both spectroscopies19,20,22-26 since a pioneer work of García de Abajo et al.25 To detect SPPs confined in the heterostructures, we used CL spectroscopy combined with scanning transmission electron microscopy (STEM). A use of high-energy electron beam has an advantage in the high excitation probability of SPPs.33 The details of the experimental setup are explained elsewhere.16,19,22 Briefly we used a parabolic mirror and pinhole to collect the light emission from the sample and to select the emission angle, as depicted in Fig. 2. The sample is set such that the surface normal direction (the z direction) is slightly tilted from the incident beam direction (the Z direction). Our experimental setup allows the


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plasmonic band structures and standing waves of the band-edge modes to be visualized as the angle-resolved spectral (ARS) patterns and high-resolution spectral images, respectively.19,22,32 Collecting angle-resolved CL spectrum is a key technique to investigate photonic and plasmonic band structures as demonstrated before.19,20,22-24,27 In particular, the symmetry of the local mode charge distribution can be determined directly from the angular distribution of the CL emission.16,32 First, we investigated one-dimensional confinement of SPPs in double heterostructures (DHSs) composed of two SQ-PlCs where diameter D1 of the cylindrical pillars in a matrix and diameter D2 in a sandwiched region are 250 nm and 400 nm, respectively. The two SQ-PlCs have a common lattice with period P of 600 nm and pillar height h of 100 nm. DHSs involve a number of substituted rows N in the sandwiched region where N=1–3. Electron beam lithography was used to fabricate the samples. A positive resist layer of ZEP520A was spin-coated onto an InP substrate on which the cylindrical pillars were patterned. Then a 200-nm thick silver layer was deposited on the patterned substrate by thermal evaporation in a vacuum. Figures 3a and 3b show the ARS patterns of the matrix area and the DHS with three substituted rows using s-polarized light (see the definition of s-polarization in Fig. 2). The electron beam was scanned over an area about 3×3 µm2 during the ARS measurements. These ARS patterns correspond to the dispersion curves in the plasmonic band structure along the Г-X line in the reciprocal space. Figure 3a shows the bandgap at the Г point of the matrix. From the DHS, new peaks at two energy levels are observed in the bandgap (Fig. 3b, arrows). On the lower energy side, the peak is split into two around the surface normal (blue arrows), which is typical for SPP modes with symmetric charge distributions.16 These observations suggest that this low energy mode is the A’ mode with a symmetric charge distribution with respect to the


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center of the DHS. The other peak on the higher energy side (red arrow) indicates an emission with a broad angular distribution around the surface normal. This high energy mode is attributed to the E’ mode with an anti-symmetric charge distribution. To observe the electric field distributions of these new modes, the spectral images (photon maps) of a pillar array across the row (Fig. 3c) were acquired by successively recording the emission spectra with the pinhole fixed to the Г point while scanning the electron beam (Figs. 3d–3f). In our previous paper on the 2D-PlCs, it was reported that the CL spectral image of the eigen mode well reveals the square of the z-component of the electric eigen-field which is proportional to the surface charge distribution of the mode.19,22 The CL intensity can be given by the product of the excitation efficiency of SPP and the SPP to photon conversion efficiency for each mode. Only the former depends on the incident beam position (X, Y), and is directly related to EELS.19,22 It was theoretically confirmed that EELS is closely related to the electromagnetic local density of states Fourier-transformed along the direction of the electron trajectory (the Z direction) (zEMLDOS) for a given mode, and CL as well.34-38 Recently it was shown that once the eigenmode decomposition is defined even in the case of a dissipative material such as PlCs, spatial distribution of EELS and CL are expressed to be proportional to the electric field strength EZ ( X , Y , qZ )

2

Fourier transformed along the Z direction, where q Z is the Z component of transfer

momentum for the inelastic scattering and qZ = ω v , ω is the angular frequency of the excited mode and v is the speed of incident electrons.31,35,38 For planer configuration such as PlCs, EZ ( X ,Y , qZ )

field

2

along

can be approximately expressed as EZ ( X , Y ) the

Z

direction

E Z ( X , Y , Z ) ≈ E Z ( X , Y ) e −kZ Z .

31,38

is

constant

2

because the damping of electric

everywhere

in

the

flat

surface,

i.e.,

Therefore the photon maps in Figs. 3d–3f are considered to


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qualitatively reveal the distribution of the electric field strength of the A’ and E’ modes except for the regions near the terrace edges where additional contrasts appear due to another origin such as edge plasmons.19,22 Figure 3f is a photon map of the new mode appearing on the lower energy side taken using non-polarized light. The new mode should be the A’ mode because the contrast is similar to the field strength distribution of the A mode. Figures 3d and 3e show photon maps of the other new modes, which appear on the higher energy side taken using s-polarized and p-polarized light, respectively. These photon maps indicate that the observed broad peak in Fig. 3b at the higher energy side actually consists of two modes: the E(1)’ and E(2)’ modes. In Figs. 3d and 3e, strong contrasts appear at opposite edges of each pillar in the DHS, suggesting the formation of electric dipoles on the pillar terraces in the E(1)’ and E(2)’ modes. The dipoles are perpendicular to each other between the two modes. The dissociation of modal degeneracy between the E(1)’ and E(2)’ modes is due to the reduced symmetry caused by the insertion of the DHS into the SQ-PlC. Figures 3g–3i show the electric field distribution E z ( x, y )

of the new modes simulated by the FDTD method. The simulated electric field

distributions correspond to the experimental photon maps well enough to identify each mode. Figures 3g and 3h clearly indicate that the E(1)’ and E(2)’ modes have electric dipole moments parallel to the x and y axes, respectively. Accordingly, the E(1)’ mode emits s-polarized light in the surface normal direction, while the E(2)’ mode emits p-polarized light. The energies of the E(1)’ and E(2)’ modes are very close to each other, making it difficult to distinguish these two modes using the non-polarized photon map.


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The DHS involving only one substituted row (N=1) can support the new localized modes (Figs. 4a–4c). Although the monochromatic photon map of the E(2)’ mode (Fig. 4b) was taken using non-polarized light, the dipole-like pattern is clear at the larger pillar due to the increased energy difference between the E(1)’ and E(2)’ modes compared to N=3. Figure 4d shows the dependence of the mode energies on the number of substituted rows N. As N increases, the energy of the A’ mode gradually increases, while those of the E(1)’ and E(2)’ modes gradually decrease. These energies should approach the band-edge energies of the SQ-PlC with a pillar diameter of 400 nm as N increases. The spectral peak of the A’ mode is much sharper than those of the E(1)’ and E(2)’ modes as seen in Fig. 3b. The quality factor of the A’ mode reaches about 100. The quality factor of the A’ mode drastically decreases with N (Fig. 4d). The quality factor of the A’ mode is measured by fitting Lorenz functions to each spectral peak near the Г point. The spectrum is extracted from the ARS pattern taken using s-polarized light to reduce the background around the peak of the A’ mode due to the dissipative E(2)’ mode. Next, we extended the use of the heterostructure to realize two-dimensional confinement of SPPs. Figures 5a–5h show monochromatic photon maps of “nanoislands,” which consist of inner pillars with diameter D2 = 500 nm in 2×2 (Fig. 5a–5d) or 3×3 unit cells (Fig. 5e–5h) surrounded by the matrix with diameter D1 = 250 nm. The panchromatic photon map in Fig. 5i shows the heterostructure geometry of the nanoisland composed of 3×3 substituted pillars. New modes localized on the nanoisland (the A’ and E’ modes) are observed at energies inside the bandgap of the matrix (Figs. 5b, 5c, 5f, and 5g), whereas the intensities of the band-edge modes (the A and E modes) are distributed throughout the nanoisland and the matrix (Fig. 5a, 5e, 5d, and 5h). Unlike in the DHS, the E’ mode is doubly degenerate due to the four-fold symmetry of the structure. Figure 5j shows spectra acquired from a few specific beam positions [i.e., the center of the


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nanoisland (blue), the edge of the central pillar (red), and the boundary between the nanoisland and the matrix (aqua)]. The spectra suggest that the A’ and E’ modes differ significantly in terms of the mode volume and the quality factor. The SPP of the A’ mode is dispersed around the nanoisland, whereas the SPP of the E’ mode is concentrated on the nanoisland. Consequently, the mode volume of the E’ mode is smaller than that of the A’ mode. On the other hand, the A’ mode shows a sharper peak similar to the case of the DHS. In summary, we have demonstrated the confinement of SPPs in the local area inside the SQ-PlC using the concept of a heterostructure. A simple modification of the pillar diameter effectively forms new modes localized around the substituted pillars. This result should pave the way to utilize PlCs as plasmonic circuits because the heterostructures improve the degree of design freedom. The STEM-CL analysis clearly reveals that one mode is A-like (the A’ mode) and the other is E-like (the E’ mode). The A’ mode is superior to the E’ mode in terms of the quality factor, while the E’ mode has a higher locality. Our findings provide important guides to design local resonators using PlCs for multiple purposes.

METHODS Cathodoluminescence Measurements A scanning transmission electron microscope (STEM; JEOL JEM-2000FX and JEOL JEM-2100F) equipped with a light detection system was used for the CL analyses. A parabolic mirror corrected the light emission from the sample and a pinhole selected the emission angle as depicted in Fig. 2. The sample is set such that the surface normal direction (the z direction) is slightly tilted by less than 10° from the incident beam direction (the Z direction) as indicated in Fig. 2. This experimental setup is described elsewhere in detail19,22. The STEM-CL system was


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operated with a beam current of 1 nA at acceleration voltages of 80 kV (JEM2100F) and 200 kV (JEM2000FX) with electron beam diameters of 1 and 10 nm, respectively. The solid angle selected by the pinhole was 0.016π sr from the surface normal direction (the Г point) in the ARS measurements. For photon map imaging, the solid angle subtended by the pinhole was 0.056π sr to detect the emission over a wide angular range. The typical acquisition time for photon map imaging was 1 s per pixel when the electron beam step was about 20 nm while scanning. FDTD Simulations Finite difference time domain (FDTD) simulations were performed using the CrystalWave software package (Photon Design) for the DHS with three substituted rows. Cubic calculation cells measured 5 nm × 5 nm × 5 nm. The calculation space was set to 11400 nm × 600 nm × 900 nm. The periodic boundaries were set at the end planes of the y direction. The perfectly matched layers were set at the end planes in the x and z directions. The dielectric function for silver was derived by fitting the Drude model to the permittivity data given by Palik.39 The three substituted rows with D2 = 400 nm were sandwiched by SQ-PlCs with D1 = 250 nm in the calculation space. Each SQ-PlC had eight rows in the x axis. Period P was 600 nm similar to the experiment but a height of 50 nm was adopted for the simulation because this height better reproduced the actual band-edge energies as reported in the previous study.19 The calculated energies of A and E modes were 1.76 eV and 1.98 eV, respectively. The simulated Ez distributions on a plane 25 nm above the tops of pillars are shown in Fig. 2d and Figs. 3g–3i. The tilted angle between the z and Z axes is small enough that the electric field E z ( x, y) can be approximately equivalent to EZ ( X , Y ) .

AUTHOR INFORMATION


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Corresponding Authors HS : [email protected] NY : [email protected]

ACKNOWLEDGEMENTS This work was supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) Nanotechnology Platform 12025014.

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COMPETING FINANCIAL INTERESTS The authors declare no competing financial interests.


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Figure 1. Band-edge modes of a plasmonic crystal with a square lattice and the concept of heterostructure. (a) Band-edge modes of SQ-PlCs at the Г point (A, B, and E modes) calculated by group theory. Square in the middle of each pattern indicates a unit cell. (upper) Electric field normal to the surface Ez(t). (lower) Time-averaged electric-field strength

Ez

2

. (b) t

Dependence of the band-edge energies on the pillar diameter measured from SQ-PlCs with period P of 600 nm and pillar height h of 100 nm.19 (c) Illustration of the heterostructure composed of two lattices with different pillar diameters. (d) Ez(t) of the A’ mode simulated by the FDTD method.


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Figure 2. Experimental setup for angle-resolved CL spectroscopy. Coordinates of xyz and XYZ are fixed at the sample and the parabolic mirror, respectively.


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Figure 3. STEM-CL analyses of the new modes localized at the three substituted rows of the double heterostructure. Period P is 600 nm and pillar height h is 100 nm. Pillar diameter of matrix D1 and substituted rows D2 are 250 nm and 400 nm, respectively. (a and b) ARS patterns taken from (a) the matrix and (b) the substituted rows using s-polarized light. (c) Panchromatic photon map of one pillar array across the row taken using non-polarized light. Monochromatic photon maps of the (d) E(1)’, (e) E(2)’, and (f) A’ modes taken using (d) s-polarized, (e) p-polarized, and (f) non-polarized light. Ez(t) of the (g) E(1)’, (h) E(2)’, and (i) A’ modes simulated by the FDTD method.


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Nano Letters

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Figure 4. (a–c) Monochromatic photon maps of (a) E(1)’, (b) E(2)’, and (c) A’ mode in the N=1 substituted row taken using non-polarized light at 1.90 eV, 1.86 eV and 1.79 eV, respectively. (d) Dependences of the new mode energies (solid lines) and the quality factor (dashed line) of the A’ mode on the number of substituted rows N where period P is 600 nm and pillar height h is 100 nm. Pillar diameter of matrix D1 and substituted rows D2 are 250 nm and 400 nm, respectively.


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Figure 5. STEM-CL analyses of the new modes localized on a nanoisland. Period P is 600 nm and pillar height h is 100 nm. Pillar diameter of matrix D1 and nanoisland D2 are 250 nm and 500 nm, respectively. Monochromatic photon maps of the (a) E, (b) E’, (c) A’, and (d) A modes of the 2×2 nanoisland acquired using non-polarized light. Monochromatic photon maps of the (e) E, (f) E’, (g) A’, and (h) A modes of the 3×3 nanoisland acquired using non-polarized light. (i) Panchromatic photon map of the 3×3 nanoisland acquired using non-polarized light. (j) Spectra


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Nano Letters

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taken from three typical beam positions: center of the nanoisland (blue), edge of the central pillar (red), and boundary between the nanoisland and the matrix (aqua).


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Confinement of Surface Plasmon Polaritons by Heterostructures of

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