TY - JOUR
AU - Kurata,, Hiroki
AB - Abstract We investigated the degree to which the dispersion relation of surface plasmon-polaritons excited on silver nanoantennas depends on length. To accomplish this, dispersion measurements for individual silver nanoantennas with lengths from 220 nm to 2.5 μm were performed using angle-resolved electron energy-loss spectroscopy (AREELS) and spatially resolved EELS (SREELS). AREELS enabled measurements of the dispersion relation extending into the high-energy region of 2.6 eV for a 2.5-μm-long silver nanoantenna, without the need to excite Fabry–Perot-type resonances. Our experiments showed that the dispersion relation of silver nanoantennas that have the same diameter is independent of their individual lengths. surface plasmon-polariton, electron energy-loss spectroscopy, dispersion relation, silver nanowire, nanoantenna, waveguide Recently, metallic nanostructures have attracted a significant amount of interest because of their potential applications in nanoscale optical technologies, such as optical circuits [1]. Metallic surfaces can confine electromagnetic energy as surface plasmon-polaritons (SPPs) in the nanoscale region. SPP waves are the collective oscillations of free electrons coupled with electromagnetic waves at the surface [2]. A number of geometries for one-dimensional waveguides based on SPPs have been proposed, such as cylindrical metal nanorods [3], linear chains of metal nanoparticles [4], metal nanostripes on or in a dielectric substrate [5, 6], nanogaps between two parallel metallic plates [7], sharp metal wedges [8] and nanogrooves in metal substrates [9]. Hybrid plasmonic waveguides formed by dielectric nanowires coupled to a metal surface have also been investigated [10, 11]. Among these strategies, silver nanowires are considered one of the most practical structures, because they can be reproducibly fabricated with smooth surfaces and uniform diameters [12]. In the past, silver nanowires have been experimentally analyzed to determine their optical SPP wave properties, such as propagation loss [13, 14] and end-face reflectivity [13]. The results of the end-face reflectivity analysis determined that Fabry–Perot-type resonances could be set up in a silver nanowire, which led to the development of tunable nanoantennas capable of enhancing specific electromagnetic waves that satisfy the specific resonance conditions. High spatial resolution electron energy-loss spectroscopy (EELS) is a powerful tool for investigating the characteristics of SPP in a single nanoantenna. Rossouw et al. [15] and Rossouw and Botton [16] clearly visualized the intensity distribution of resonant SPP standing waves set up on individual silver nanoantennas via spatial-resolved EELS (SREELS) using a scanning transmission electron microscopy (STEM) system equipped with a monochromated electron gun. They also extracted the dispersion relations of SPP waves propagating along the silver nanoantennas using the energy-filtered EELS images of a given resonance mode specified by an energy E and wavenumber, k, which was extracted from the distance between the antinodes in the image. Moreover, they also directly determined the decay length of the evanescent field from the intensity distribution along the direction perpendicular to the surface in the EELS image [16]. The analytical dispersion relation for an infinite metal cylinder has already been solved [17]. Those results suggested that the dispersion relation depends on the diameter, the dielectric functions of the cylinder and the surrounding dielectric media. However, since actual silver nanoantennas have finite lengths, we felt that the length dependence of the dispersion relation should be investigated. In previous studies, Rossouw et al. [15] extracted the dispersion relations for approximately 500-nm-long silver nanoantennas and Rossouw and Botton [16] extracted a 2-μm-long silver nanoantenna. Dispersion relations below 2.3 eV were extracted for the short nanoantennas, while the dispersion relation for the long nanoantenna was restricted to below 1.2 eV because SPP waves with high resonance energies do not possess sufficiently large propagation lengths to form resonant peaks. This result suggests that an alternative approach that does not require resonant peaks is needed for such long silver nanoantennas in order to measure the dispersion relation as it extends into the high-energy region. Additionally, it should be pointed out that the dispersion relations of SPPs on metal nanowires approach the light line, which makes it difficult to evaluate the length dependence from the low-energy region alone. Here, we show an alternative approach in which angle-resolved EELS (AREELS) is used for SPP dispersion measurements on long silver nanoantennas with micrometer order lengths. Since AREELS can directly visualize the inelastic scattering probability of incident electrons interacting with a sample as a function of the energy loss, E, and the scattering vector, q, the pattern imaged by AREELS is called an E–q map. The use of AREELS also enables us to measure the dispersion relations of SPPs and other optical modes without using resonant phenomena [18–20]. Since the scattering angle of SPP excitations is quite small, AREELS measurements of SPP sacrifice spatial resolution for improved high angular resolution, which makes the application of the technique to short silver nanoantennas difficult. Therefore, we used AREELS for long nanowire, while applying SREELS to short nanoantennas, as was done in previous studies [15, 16]. The results obtained by both methods were compared to clarify the length dependence of the dispersion relation. In our present work, AREELS and SREELS measurements were performed at room temperature using a 200 kV TEM/STEM (JEM-9980 TKP1) equipped with a spherical aberration corrector for the illuminating lens system, a cold-field emission gun and an omega filter that was used as the spectrometer. The energy resolution measured by the full-width at half-maximum of zero-loss peak was 0.4–0.5 eV. In the AREELS measurement, a high wave vector resolution of 6.2 × 10−3 nm−1 was achieved by lifting up a sample as described in Ref. [21]. In this method, the angular selecting slit was placed on the entrance plane of the spectrometer with the direction of slit set perpendicular to the energy dispersion. The E–q maps were recorded on a charge-coupled device camera. A pixel size of 27 meV was set on the loss energy axis and 5.2 × 10−4 nm−1 was set on the scattering vector axis. The E–q map acquisition time was kept shorter than 10 s to minimize wavenumber resolution degradation that could result from beam drifting. Approximately 10 E–q maps taken under the same conditions were accumulated to increase the signal-to-noise ratio. In the SREELS measurement, an incident probe <0.1 nm in diameter with a convergent semi-angle of 23 mrad was scanned along the long axis of silver nanoantennas. The collection semi-angle in the SREELS measurement was 10 mrad. An aloof scattering condition was applied to enhance the surface excitations [22]. Silver nanoantennas synthesized using a polyol process [12]. After the reduction, a drop of solution was placed on thin carbon film and dried. Silver nanoantennas with the same diameter and supported on the same carbon thin film were carefully chosen for the AREELS and SREELS experiments. This was considered essential in our investigation of the length dependence of the dispersion relation. Figure 1a shows an annular dark-field STEM image of a silver nanoantenna examined using AREELS. Its diameter (d) and length (L) are 47 nm and 2.5 μm, respectively. Figure 1b shows an E–q map obtained by inserting the angular selection slit parallel to the long axis of this silver nanoantenna. The SPP dispersion curve, showing the intensity distribution shifting to the higher energy side with the increasing wave vector, can be observed directly. This is important because SPP dispersion curves of this nature cannot be observed when the angular selecting slit is not parallel to the long axis of silver nanoantenna, which means that the SPP wave propagates along the long axis. The black solid curve in this E–q map shows the dispersion relation of an infinite silver cylinder with a diameter of 47 nm calculated by the analytical formula [17] using the dielectric function of silver measured by an optical method [23]. In this calculation, it was assumed that the lowest order SPP mode would only be excited on an infinite silver cylinder under vacuum conditions. The experimental dispersion curve deviates from the calculated one on the large wave vector side. The reasons for this deviation seem to be related to the surface condition of the nanoantenna and the differences in the surrounding environment. Actually, it is known that the nanoantenna surface is covered with a thin layer of poly vinyl pyrrolidone surfactant [24] and that the nanowire cross-section is pentagonal rather than circular. Therefore, it appears that the use of a surfactant-free infinite silver cylinder in a vacuum is unsuitable for approximating the geometry and environment of the examined silver nanoantenna. This was pointed in the results of an experiment utilizing 500-nm-long silver nanoantennas by Rossouw et al. [15]. Fig. 1. Open in new tabDownload slide (a) HAADF-STEM image of a 2.5-μm-long silver nanoantenna. (b) An E–q map of a silver nanoantenna taken by AREELS. The black solid curve is the calculated dispersion relation for the infinite silver cylinder with d = 47 nm. The black solid line is the dispersion relation of light propagating in a vacuum. Fig. 1. Open in new tabDownload slide (a) HAADF-STEM image of a 2.5-μm-long silver nanoantenna. (b) An E–q map of a silver nanoantenna taken by AREELS. The black solid curve is the calculated dispersion relation for the infinite silver cylinder with d = 47 nm. The black solid line is the dispersion relation of light propagating in a vacuum. Figure 2a shows an SREELS pattern taken from a silver nanoantenna with d = 49 nm and L = 220 nm. The energy resolution was improved to 0.3 eV by deconvolution of the zero-loss peak using the Richardson [25] and Lucy [26] method. The characteristic intensity distribution is found at 1.5 and 2.4 eV in the SREELS pattern. Figure 2c shows the intensity profiles extracted from the SREELS pattern at 1.5 and 2.4 eV. Since the loss probability in SREELS is directly related to the photonic local density of states in arbitrary systems [27], the excitation probability of SPP in a short silver nanoantenna reaches its maximum value when an electron probe is placed on the antinode positions of the SPP standing wave. The intensity profile at 1.5 eV in Fig. 2c shows a peak at each end of the silver nanoantenna. Therefore, this excitation can be attributed to the first resonant SPP mode (m = 1). Furthermore, the intensity profile at 2.4 eV, which shows three peaks (both ends and the center of the silver nanoantenna), is attributed to the second resonant mode (m = 2). It was expected that the intensity distribution from 2.4 to 3.4 eV would involve higher order resonant modes, but their peaks could not be resolved because of the limited energy resolution. Similar results were observed for a longer nanoantenna with d = 47 nm and L = 508 nm in Fig. 2b and d, in which three resonant modes (m = 2, 3, 4) appear. The first resonant mode is hidden under the tail of the zero-loss peak. The local maxima and minima of the intensity profiles correspond to the antinodes and nodes of SPP standing waves, respectively [15, 27]. From these intensity profiles, we could evaluate the SPP wave vector k with specific resonance energy using the following equation: $$k = \displaystyle{{2\pi } \over \lambda } = \displaystyle{\pi \over {d_{{\rm EELS}} }},$$ (1) where the wavelength of SPP λ is equal to twice the node spacing dEELS in the intensity profile. We plotted the dispersion data for short nanoantennas using the resonance energies of SPPs and their wave vectors. Fig. 2. Open in new tabDownload slide Silver nanoantenna patterns obtained via SREELS (a) d = 49 nm and L = 220 nm, (b) d = 47 nm and L = 508 nm. (c, d) The intensity profiles of the first (blue), second (red), third (black) and fourth (green) resonant modes taken from (a) and (b) parallel to the position axis, respectively. Fig. 2. Open in new tabDownload slide Silver nanoantenna patterns obtained via SREELS (a) d = 49 nm and L = 220 nm, (b) d = 47 nm and L = 508 nm. (c, d) The intensity profiles of the first (blue), second (red), third (black) and fourth (green) resonant modes taken from (a) and (b) parallel to the position axis, respectively. Finally, we will discuss the length dependence of the dispersion relation of SPP excited on a silver nanoantenna. Figure 3 shows the dispersion plots taken from the five short silver nanoantennas with d = 47 ± 2 nm and L in the range of 220–508 nm. These are compared with the dispersion curve, which is the ridge curve in the E–q map in Fig. 1b, as measured from the L = 2.5 μm silver nanoantenna. The dispersion data for the short nanoantennas agree well with the dispersion curve for the long one. This result demonstrates that the dispersion relation is independent of the silver nanoantenna length. Furthermore, it should be emphasized that all experimental dispersion data shift uniformly to the large wave vector side when compared with the curve calculated for an infinite silver cylinder with d = 47 nm (solid curve). This suggests that all of the polyol process synthesized silver nanoantennas examined in this study had approximately the same cross-sectional shape and environmental conditions. More specifically, the poly vinyl pyrrolidone surfactant covers them in the same way. In addition, it should be noted that all measurements were carried out for silver nanoantennas supported on the same type of carbon film, which was also important for suppressing unrelated environment effects. Fig. 3. Open in new tabDownload slide The dispersion plots of silver nanoantennas with L = 2.5 μm (black plots), 220 nm (red), 274 nm (purple), 404 nm (blue), 428 nm (green) and 508 nm (yellow). All diameters are 47 ± 2 nm. The black solid curve is the calculated dispersion relation for an infinite silver cylinder with d = 47 nm. The black solid line is the dispersion relation of light propagating in a vacuum. Fig. 3. Open in new tabDownload slide The dispersion plots of silver nanoantennas with L = 2.5 μm (black plots), 220 nm (red), 274 nm (purple), 404 nm (blue), 428 nm (green) and 508 nm (yellow). All diameters are 47 ± 2 nm. The black solid curve is the calculated dispersion relation for an infinite silver cylinder with d = 47 nm. The black solid line is the dispersion relation of light propagating in a vacuum. To summarize, in this study, we attempted to measure the dispersion relation of SPP excited on 220-nm- to 2.5-μm-long silver nanoantennas utilizing two different methods, AREELS and SREELS. As can be seen in our results, we successfully measured the dispersion relation of a long nanoantenna further into the high-energy region than had been achieved in previous EELS studies [16], thus confirming that the SPP dispersion relation does not depend on the length of the silver nanoantenna. All experimental dispersion data uniformly deviated from the calculated curve for a silver cylinder with an infinite length. This uniform shift of experimental data suggests that the cross-sectional shape and surfactant are nearly identical for all polyol process synthesized silver nanoantennas of the same diameter. Although it is difficult to evaluate the effects of these factors quantitatively, it is felt that well-controlled experimental environments are essential for obtaining reproducible results. References 1 Ozbay E . Merging photonics and electronics at nanoscale dimensions , Science , 2006 , vol. 311 (pg. 189 - 193 ) 10.1126/science.1114849 Google Scholar Crossref Search ADS PubMed WorldCat Crossref 2 Ritchie R H . Plasma losses by fast electrons in thin films , Phys. Rev. , 1957 , vol. 106 (pg. 874 - 881 ) 10.1103/PhysRev.106.874 Google Scholar Crossref Search ADS WorldCat Crossref 3 Takahara J , Yamagishi S , Taki H , Morimoto A , Kobayashi T . Guiding of a one-dimensional optical beam with nanometer diameter , Opt. Lett. , 1997 , vol. 22 (pg. 475 - 477 ) 10.1364/OL.22.000475 Google Scholar Crossref Search ADS PubMed WorldCat Crossref 4 Quinten M , Leitner A , Krenn J R , Aussenegg F R . Electromagnetic energy transport via linear chains of silver nanoparticles , Opt. Lett. , 1998 , vol. 23 (pg. 1331 - 1333 ) 10.1364/OL.23.001331 Google Scholar Crossref Search ADS PubMed WorldCat Crossref 5 Berini P . Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of asymmetric structures , Phys. Rev. B , 2001 , vol. 63 pg. 125417 10.1103/PhysRevB.63.125417 Google Scholar Crossref Search ADS WorldCat Crossref 6 Boltasseva A , Nikolajsen T , Leosson K , Kjaer K , Larsen M S , Bozhevolnyi S I . Integrated optical components utilizing long-range surface plasmon polaritons , J. Lightwave Technol. , 2005 , vol. 23 (pg. 413 - 422 ) 10.1109/JLT.2004.835749 Google Scholar Crossref Search ADS WorldCat Crossref 7 Tanaka K , Tanaka M . Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide , Appl. Phys. Lett. , 2003 , vol. 82 (pg. 1158 - 1160 ) 10.1063/1.1557323 Google Scholar Crossref Search ADS WorldCat Crossref 8 Boardman A D , Aers G C , Teshima R . Retarded edge modes of a parabolic wedge , Phys. Rev. B , 1981 , vol. 24 (pg. 5703 - 5712 ) 10.1103/PhysRevB.24.5703 Google Scholar Crossref Search ADS WorldCat Crossref 9 Novikov I V , Maradudin A A . Channel polaritons , Phys. Rev. B , 2002 , vol. 66 pg. 035403 10.1103/PhysRevB.66.035403 Google Scholar Crossref Search ADS WorldCat Crossref 10 Oulton R F , Sorger V J , Genov D A , Pile D F P , Zhang X A . A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation , Nat. Photon. , 2008 , vol. 2 (pg. 496 - 500 ) 10.1038/nphoton.2008.131 Google Scholar Crossref Search ADS WorldCat Crossref 11 Chen L , Zhang T , Li X , Huang W . Novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film , Opt. Express , 2012 , vol. 20 (pg. 20535 - 20544 ) 10.1364/OE.20.020535 Google Scholar Crossref Search ADS PubMed WorldCat Crossref 12 Sun Y G , Xia Y N . Large-scale synthesis of uniform silver nanowires through a soft, self-seeding, polyol process , Adv. Mater. , 2002 , vol. 14 (pg. 833 - 837 ) 10.1002/1521-4095(20020605)14:11<833::AID-ADMA833>3.0.CO;2-K Google Scholar Crossref Search ADS WorldCat Crossref 13 Ditlbacher H , Hohenau A , Wagner D , Krebig U , Rogers M , Hofer F , Aussenegg F R , Krenn J R . Silver nanowires as surface plasmon resonators , Phys. Rev. Lett. , 2005 , vol. 95 pg. 257403 10.1103/PhysRevLett.95.257403 Google Scholar Crossref Search ADS PubMed WorldCat Crossref 14 Ma Y , Li X , Yu H , Tong L , Gu Y , Gong Q . Direct measurement of propagation losses in silver nanowires , Opt. Lett. , 2010 , vol. 35 (pg. 1160 - 1162 ) 10.1364/OL.35.001160 Google Scholar Crossref Search ADS PubMed WorldCat Crossref 15 Rossouw D , Couillard M , Vickery J , Kumacheva E , Botton G A . Multipolar plasmonic resonances in silver nanowire antennas imaged with a subnanometer electron probe , Nano Lett. , 2011 , vol. 11 (pg. 1499 - 1504 ) 10.1021/nl200634w Google Scholar Crossref Search ADS PubMed WorldCat Crossref 16 Rossouw D , Botton G A . Plasmonic response of bent silver nanowires for nanophotonic subwavelength waveguiding , Phys. Rev. Lett. , 2013 , vol. 110 pg. 066801 10.1103/PhysRevLett.110.066801 Google Scholar Crossref Search ADS PubMed WorldCat Crossref 17 Ashley J C , Emerson L C . Dispersion-relations for non-radiative surface plasmons on cylinders , Surf. Sci. , 1974 , vol. 41 (pg. 615 - 618 ) 10.1016/0039-6028(74)90080-6 Google Scholar Crossref Search ADS WorldCat Crossref 18 Pettit R B , Silcox J , Vincent R . Measurement of surface-plasmon dispersion in oxidized aluminum films , Phys. Rev. B , 1975 , vol. 11 (pg. 3116 - 3123 ) 10.1103/PhysRevB.11.3116 Google Scholar Crossref Search ADS WorldCat Crossref 19 Chen C H , Silcox J , Vincent R . Electron-energy losses in silicon: bulk and surface plasmons and Čerenkov radiation , Phys. Rev. B , 1975 , vol. 12 (pg. 64 - 71 ) 10.1103/PhysRevB.12.64 Google Scholar Crossref Search ADS WorldCat Crossref 20 Saito H , Chen C H , Kurata H . Optical guided modes coupled with Čerenkov radiation excited in Si slab using angular-resolved electron energy-loss spectrum , J. Appl. Phys. , 2013 , vol. 113 pg. 113509 10.1063/1.4796140 Google Scholar Crossref Search ADS WorldCat Crossref 21 Midgley P A . A simple new method to obtain high angular resolution ω–q patterns , Ultramicroscopy , 1999 , vol. 76 (pg. 91 - 96 ) 10.1016/S0304-3991(98)00088-6 Google Scholar Crossref Search ADS WorldCat Crossref 22 Huang M R S , Erni R , Lin H Y , Wang R C , Liu C P . Characterization of wurtzite ZnO using valence electron energy loss spectroscopy , Phys. Rev. B , 2011 , vol. 84 pg. 155203 10.1103/PhysRevB.84.155203 Google Scholar Crossref Search ADS WorldCat Crossref 23 Johnson P B , Christy R W . Optical constants of the noble metals , Phys. Rev. B , 1972 , vol. 6 (pg. 4370 - 4379 ) 10.1103/PhysRevB.6.4370 Google Scholar Crossref Search ADS WorldCat Crossref 24 Sun Y , Mayers B , Herricks T , Xia Y . Polyol synthesis of uniform silver nanowires: a plausible growth mechanism and the supporting evidence , Nano Lett. , 2003 , vol. 3 (pg. 955 - 960 ) 10.1021/nl034312m Google Scholar Crossref Search ADS WorldCat Crossref 25 Richardson W H . Bayesian-based iterative method of image restoration , J. Opt. Soc. Am. , 1972 , vol. 62 (pg. 55 - 59 ) 10.1364/JOSA.62.000055 Google Scholar Crossref Search ADS WorldCat Crossref 26 Lucy L B . An iterative technique for the rectification of observed distributions , Astron. J. , 1974 , vol. 74 (pg. 745 - 754 ) 10.1086/111605 Google Scholar Crossref Search ADS WorldCat Crossref 27 Garcia de Abajo F J , Kociak M . Probing the photonic local density of states with electron energy loss spectroscopy , Phys. Rev. Lett. , 2008 , vol. 100 pg. 106804 10.1103/PhysRevLett.100.106804 Google Scholar Crossref Search ADS PubMed WorldCat Crossref © The Author 2013. Published by Oxford University Press on behalf of The Japanese Society of Microscopy. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com
TI - Direct measurement of dispersion relation for surface plasmon-polaritons on silver nanoantennas
JF - Microscopy
DO - 10.1093/jmicro/dft048
DA - 2014-04-01
UR - https://www.deepdyve.com/lp/oxford-university-press/direct-measurement-of-dispersion-relation-for-surface-plasmon-HaLj3c6Odf
SP - 155
EP - 159
VL - 63
IS - 2
DP - DeepDyve
ER -