From Isolated Metaatoms to Photonic Metamaterials: Evolution of the

Letter pubs.acs.org/NanoLett

From Isolated Metaatoms to Photonic Metamaterials: Evolution of the Plasmonic Near-Field Felix von Cube,*,†,‡ Stephan Irsen,‡ Richard Diehl,§ Jens Niegemann,∥ Kurt Busch,⊥ and Stefan Linden†,# †

Physikalisches Institut, Universität Bonn, Nußallee 12, D-53115 Bonn, Germany Electron Microscopy and Analytics (EMA), Center of Advanced European Studies and Research (caesar), Ludwig-Erhard-Allee 2, D-53175 Bonn, Germany § Institut für Theoretische Festkörperphysik, DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Strasse 1, D-76131 Karlsruhe, Germany ∥ Laboratory for Electromagnetic Fields and Microwave Electronics, Swiss Federal Institute of Technology (ETH), Gloriastrasse 35, CH-8009 Zürich, Switzerland ⊥ Humboldt-Universität zu Berlin, Institut für Physik, AG Theoretische Optik & Photonik, Newtonstr. 15, D-12489 Berlin and Max-Born-Institut, Max-Born-Str. 2A, D-12489 Berlin, Germany # Institut für Nanotechnologie, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany ‡

S Supporting Information *

ABSTRACT: Metamaterials are artificial media which can provide optical properties not available from natural materials. These properties often result from the resonant excitation of plasmonic modes in the metallic building blocks (“metaatoms”) of the metamaterial. Electromagnetic interactions between the metaatoms significantly modify the resonances of the individual metaatoms and influence the optical properties of the whole metamaterial. To better understand these interactions, we study in this Letter the evolution of the plasmonic near-field in the course of the transition from an isolated metaatom, in our case a split-ring resonator (SRR), to a photonic metamaterial via electron energy-loss spectroscopy. For small SRR ensembles, we observe the formation of discrete optical bright and dark modes due to coupling of the metaatoms. Large SRR arrays reveal a quasi-continuum of modes in the interior and distinct edge modes at the boundaries of the array. Our experimental results are in excellent agreement with numerical calculations. KEYWORDS: Photonic metamaterials, plasmonic modes, plasmon hybridization, low loss electron energy-loss spectroscopy, near-field mapping, split−ring resonator

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he metamaterial concept1−3 is based on our ability to tailor the effective optical material parameters of an artificial medium by proper design and fabrication of its subwavelength building blocks (“metaatoms”). This approach has led to metamaterials with astonishing optical properties, for example, artificial magnetism at optical frequencies,4−6 a negative index of refraction,7−9 or strong artificial optical activity.10−12 For most metamaterials operating at optical frequencies, the mesoscopic origin of these phenomena is the excitation of plasmonic modes in its metallic metaatoms. Thus, a qualitative first understanding of the features of a given metamaterial can often be obtained by considering the plasmonic resonances of an isolated metaatom. However, a number of recent experimental and theoretical investigations have shown that electromagnetic interactions between the metaatoms can have a significant impact on the properties of the metamaterial. For instance, experiments on two-dimensional arrays of split-ring resonators (SRRs)13,14 and SRR dimers15 have demonstrated that the resonance energy and the © 2013 American Chemical Society

spectral width of the fundamental plasmonic resonance depend on the separation and relative orientation of the SRRs. The interplay of electric and magnetic interactions has been found to play a crucial role for the optical properties of stereometamaterials16 consisting of stacked layers of SRRs. Other examples of coupling effects in metamaterials are the formation of magnetoinductive waves,17 Fano resonances,18 a nontrivial dependence of the second harmonic generation efficiency of metamaterials on the period,19 and the observation of plasmoninduced transparency.20 Furthermore, electromagnetic interaction effects between metallic nanostructures have also been theoretically21 and experimentally22−24 investigated in the context of plasmonic particles. So far, most studies on coupling effects in metamaterials rely on optical far-field methods, for example, linear transmittance Received: November 28, 2012 Revised: January 17, 2013 Published: January 22, 2013 703

dx.doi.org/10.1021/nl3043757 | Nano Lett. 2013, 13, 703−708

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relative phase from the EELS signal strength between the two SRRs. The in-phase oscillation of two neighboring SRRs results in an electric field between the two SRRs which is mainly oriented perpendicular to the electron beam. In contrast, the out-of-phase coupling of two neighboring SRRs results in a strong component of the electric field parallel to the electron beam between the two SRRs. Thus, we anticipate in the case of in-phase coupling a weak EELS signal between two SRRs, while for out-of-phase coupling we expect a strong EELS signal between two SRRs. For our experiments, we have fabricated a series of SRR samples by electron-beam lithography on 30 nm thin Si3N4 membranes in which we start with a single gold SRR (see inset of Figure 2) and successively assemble a metamaterial by

or reflectance spectroscopy. However, a great wealth of information regarding the electromagnetic interaction is encoded in the near-field which is not accessible by these experiments. Furthermore, these methods are only sensitive to modes of a metamaterial that exhibit a nonvanishing electric dipole moment (bright modes). In contrast, modes with a vanishing electric dipole moment (dark modes) are not directly accessible in far-field experiments. However, these dark modes play an important role for the coupling of quantum emitters to metallic nanostructures, for example, in the context of optical antennas25 or the spaser.26 For planar metallic nanostructures, a combination of electron energy-loss spectroscopy (EELS) and scanning transmission electron microscopy (STEM) allows overcoming the aforementioned limitations of the optical far-field methods. In STEM-EELS, a focused electron beam is raster scanned over the sample, and the energy-loss of the electrons due to interaction with the sample is recorded for every position of the beam. In a classical picture, strong EELS signals are expected for a given electron loss energy, if the excited mode of the sample has a large electric field component Ez along the electron trajectory (z-axis).27,28 For planar metallic nanostructures, these positions usually correspond to the antinodes of the charge density oscillation. Recent STEM-EELS experiments on metallic nanoparticles29−32 and single metaatoms33,34 have demonstrated that plasmonic modes can be mapped with nanometer spatial resolution. Since STEM-EELS is sensitive to both optical bright and dark modes,35−37 it allows to access the full-modal spectrum of metallic metaatoms. Here, we use STEM-EELS to study collective near-field phenomena in the course of the transition from an isolated metaatom to a photonic metamaterial. As our model metaatom, we have chosen the SRR, which has served as the paradigm building block of many magnetic metamaterials. For small ensembles containing only a few SRRs, we anticipate that the electromagnetic interaction between the SRRs results in plasmon hybridization;21 that is, the fundamental plasmonic mode of a single SRR evolves into a set of discrete optical bright and dark modes (see Figure 1). Whether a mode of the

Figure 2. EELS spectra of an isolated SRR (blue) and a SRR dimer (red, green). The dashed lines indicate the spectral positions of the resonance peaks. In the insets, the corresponding electron beam locations are marked in the same color as the respective spectra. The scale bars are 200 nm.

adding further SRRs. The thickness of the gold film is 35 nm for all SRRs. The STEM-EELS experiments have been performed with a Zeiss Libra 200 MC Cs-STEM (CRISP) operated at 200 kV. The microscope is equipped with a monochromator, a Cs-corrector for the illumination system, and a second order corrected in-column energy filter, resulting in an energy resolution of 150 meV (fwhm of the zero loss peak). Details on the sample fabrication, the measurement, and the normalization procedure can be found in ref 34. The experimental results are compared with numerical calculations performed with an in-house nodal discontinuous Galerkin time-domain (DGTD) software (ref 39 and references therein). This method allows efficient time-domain calculations in complex systems and is particularly well suited for the accurate simulation of complex plasmonic nanostructures. For the extraction of the electron energy-loss spectra from DGTD calculations, we follow the approach discussed in ref 40 with the exception that we use a pure scattered-field excitation instead of the total-field/scattered-field source originally proposed. This allows us to also calculate electron energy-loss spectra for electron beams penetrating the plasmonic nanostructures. Since the DGTD method is a time-domain approach, we need to employ a suitable material model to describe the dispersive response of gold. For all calculations in this paper, we used a Drude-Lorentz model with the parameters stated in ref 34. All calculations were performed on NVIDIA GeForce GTX 580 cards, and we observe a speed-up factor of up to 50 for our calculations when compared to equivalent calculations on a single core of a traditional CPU (e.g., the ones used in ref 34).

Figure 1. Plasmon hybridization model: The number of plasmonic modes increases linearly with the number of SRRs. In the case of an infinite array of SRRs the coupled modes form a continuum.

ensemble is bright or dark depends on how the electric dipoles of the different SRRs couple and how strong the resulting net dipole moment is. For large SRR arrays with tens of thousands of metaatoms, we expect in analogy to the tight-binding model of solid state physics38 the formation of a quasi-continuum of modes. The relative phase of the plasmon oscillations in neighboring SRRs plays an important role for the character of the corresponding coupled plasmon mode. EELS is not directly sensitive to this phase. However, one can indirectly infer the 704


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Figure 3. Single SRR and SRR dimer (side-by-side configuration). (a) The experimental EELS distribution, (b) the calculated EELS distribution, and (c) a snapshot of the calculated Ez distribution of an isolated SRR are presented in the left column. The corresponding data of the optical bright (d,e,f) and dark mode (g,h,i) of the SRR dimer are depicted in the center and right column, respectively. The white curves indicate the boundaries of the SRRs. The resonance energy is stated in each case. The scale bars are 200 nm.

beam, which causes small EELS signals at the inner arms of the dimer. In contrast, the antiphase coupling of the two individual plasmonic modes results in an optical dark mode with increased resonance energy. It exhibits a strong Ez component (see Figure 3i) and hence a strong EELS signal in the middle of the dimer. Note that the optical dark mode has not been observed in previous optical experiments. For the on-top dimer configuration (see Figure 4), we likewise observe the formation of two new eigenmodes. In contrast to the side-by-side dimer configuration, its low-energy mode is an optical dark mode which results from an antiphase coupling of the two individual plasmonic modes (see Figure 4c). It has strong EELS maxima at the ends of the bottom SRR (see Figure 4a,b). The in-phase coupling (see Figure 4f) produces an optical bright mode whose resonance energy is raised relative to an isolated SRR and which exhibits strong EELS maxima at the ends of the top SRR (see Figure 4d,e). Experimental EELS spectra recorded at one end of the top and bottom SRR, respectively, are presented in the Supporting Information (Figure S1). According to the plasmon hybridization model, we expect that the number of eigenmodes linearly increases with the number of SRRs in the ensemble. As an example, we consider the case of four SRRs arranged in the side-by-side configuration (see Figure 5), where we anticipate the formation of four different eigenmodes. In the calculated EELS signals, we can indeed identify four different modes (see Figure 5d−g) with the corresponding calculated Ez distributions as depicted in Figure 5h−k, respectively. Contrary to the calculations, we can resolve in the experimental EELS data only three modes (see Figure 5a−c). This inconsistency between experiment and theory is a result of the spectral resolution (150 meV) of our experimental setup and the spectral overlap of the eigenmodes. A comparison with the calculated EELS maps suggests that the experimental EELS distribution in Figure 5c results from the superimposition of the EELS signals of the two highest energy modes (Figure 5f,g). Experimental EELS spectra recorded at characteristic

The eigenmodes of an isolated SRR are standing plasmonic waves with antinodes of the charge density oscillation at the ends of the wire. An EELS spectrum recorded at one end of the SRR is shown in Figure 2 (blue). The two maxima at 0.75 and 1.3 eV correspond to the fundamental and the second order plasmonic mode, respectively. In the following, we will only consider the fundamental plasmonic mode. The corresponding experimental EELS map is depicted in Figure 3a. In accordance with previous EELS experiments,33,34 we find pronounced maxima at the ends of the SRR wire. This behavior is also reproduced by the DGTD calculations (see Figure 3b). The slightly smaller value of the calculated resonance energy (ℏωpl = 0.69 eV) can be attributed to deviations of the fabricated SRR from the ideal shape. SRR dimers can serve as a model system for systematic studies of the pairwise interaction of metaatoms. We start our discussion with the side-by-side dimer configuration (see inset of Figure 2), which shows a particular strong interaction between two SRRs.15 Without coupling, the resonance energies of the fundamental modes of both SRRs would be identical. However, the coupling of the two SRRs lifts the energetic degeneracy (see Figure 2) and results in the formation of two new eigenmodes with distinct EELS signal distributions. Both the experimental data (see Figure 3d) and the numerical calculations (see Figure 3e) show that the low-energy mode exhibits strong EELS signals at the outer arms of the dimer. In contrast, we consistently find a maximum of the EELS signal in the middle of the dimer for the high energy mode (see Figure 3g,h). The energetic splitting of the two modes, their optical character, and the positions of the maxima in the corresponding EELS maps can qualitatively be understood in terms of the plasmon hybridization model: The in-phase coupling of the individual plasmonic modes (see Figure 3f) yields an optical bright mode whose resonance energy is lowered compared to an isolated SRR.15 Between the two SRRs, the electric field is mainly oriented perpendicular to the trajectory of the electron 705


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Figure 6. SRR metamaterial. (a) STEM darkfield images of a 100 × 100 SRR array. Center: overview; top: close-up of the upper left corner of the array; bottom: close-up of the interior. The scale bars are 200 nm. (b) EELS signal distribution of the upper left corner. (c) EELS signal distribution of the interior. The two EELS signal distributions are displayed at the same energy and use the same normalization.

Figure 4. SRR dimer (on-top configuration). Top row: (a) Experimental EELS distribution, (b) calculated EELS distribution, and (c) snapshot of the Ez distribution of the optical dark mode. Bottom row (d−f): Corresponding data of the optical bright mode. The scale bars are 200 nm.

results in the formation of a quasi-continuum of modes, where the spectral separation of neighboring modes is much smaller than their spectral widths. In optical far-field experiments, this quasi-continuum of modes gives rise to a single plasmonic resonance whose spectral width depends on the properties of both the individual SRRs and their interaction.13,14 In the

positions of the four SRRs are depicted in Figure S2 of the Supporting Information. For typical two-dimensional metamaterials containing tens of thousands of SRRs (see Figure 6a), we anticipate that coupling

Figure 5. Ensemble of four SRRs. The left, center, and right column depict the experimental EELS distributions, the calculated EELS distributions, and snapshots of the calculated Ez distributions, respectively. The scale bars are 200 nm. Note that the experimental EELS distributions in a and b do not correspond to the respective resonance energies of the modes, but to slightly smaller electron loss energies. Through this shift, we reduce the spectral overlap with the higher energy modes and thus obtain a better visual separation of the modes. The first stated value corresponds to the displayed energy, while the second value in brackets corresponds to the resonance energy obtained from the spectra (see Supporting Information Figure S2). 706


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interior of a periodic array, each SRR “sees” the same environment. Hence, we expect to find for a given electron energy-loss the same EELS signal distribution within each unit cell, which stems from the incoherent superposition of many modes. Figure 6c exemplifies the EELS map recorded in the center of the array at an electron energy-loss corresponding to the peak of the plasmonic resonance (0.55 eV). As expected, we find within our experimental accuracy identical EELS signal distributions for all unit cells: The EELS signal is always concentrated between two neighboring SRRs of a row. However, at the boundary of the SRR array, the different sites are not equivalent, and we anticipate in analogy to electronic surface states38 the formation of photonic edge modes. For example, a SRR at the edge of the array has only three nearest neighbors instead of four as in the interior of the metamaterial. As a consequence, the electromagnetic near-field distribution is different. Figure 6b depicts the EELS signal distribution for a corner of the array at the same electron energy-loss as in the previous case. Here, we find clear evidence for the anticipated photonic edge modes. We observe particularly strong EELS signals at the ends of the SRRs in the top row of the array. In contrast, the EELS intensity is considerably reduced for the SRRs of the outer left column of the array. The corresponding edge mode at the outer left column has a resonance energy, which is red-shifted by 65 meV (not shown). Experimental EELS spectra recorded in the interior and at the boundaries of the array can be found in the Supporting Information (Figure S3). In conclusion, we have investigated the evolution of the plasmonic near-field in the transition from an isolated SRR to a metamaterial by STEM-EELS. The ability to map the full modal spectrum of metal nanostructures with nanometer spatial resolution distinguishes this method as a valuable extension of optical far-field experiments to study coupling effects in metamaterials. For small SRR ensembles, we find that the interaction of the SRRs results in the formation of distinct optical bright and dark eigenmodes. For large SRR arrays, we observe the formation of a quasi-continuum of modes in the interior and edge modes at the boundaries.

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REFERENCES

(1) Zheludev, N. I. Science 2010, 328, 582−583. (2) Soukoulis, C. M.; Wegener, M. Nat. Photonics 2011, 5, 523−530. (3) Liu, Y.; Zhang, X. Chem. Soc. Rev. 2011, 40, 2494−2507. (4) Linden, S.; Enkrich, C.; Wegener, M.; Zhou, J.; Koschny, T.; Soukoulis, C. M. Science 2004, 306, 1351−1353. (5) Zhang, S.; Fan, W.; Minhas, B. K.; Frauenglass, A.; Malloy, K. J.; Brueck, S. R. Phys. Rev. Lett. 2005, 94, 037402. (6) Dolling, G.; Enkrich, C.; Wegener, M.; Zhou, J. F.; Soukoulis, C. M.; Linden, S. Opt. Lett. 2005, 30, 3198−3200. (7) Shalaev, V. M.; Cai, W.; Chettiar, U. K.; Yuan, H.-K.; Sarychev, A. K.; Drachev, V. P.; Kildishev, A. V. Opt. Lett. 2005, 30, 3356−3358. (8) Zhang, S.; Fan, W.; Panoiu, N. C.; Malloy, K. J.; Osgood, R. M.; Brueck, S. R. J. Phys. Rev. Lett. 2005, 95, 137404. (9) Dolling, G.; Enkrich, C.; Wegener, M.; Soukoulis, C. M.; Linden, S. Science 2006, 312, 892−894. (10) Zhang, S.; Park, Y.-S.; Li, J.; Lu, X.; Zhang, W.; Zhang, X. Phys. Rev. Lett. 2009, 102, 023901. (11) Decker, M.; Ruther, M.; Kriegler, C. E.; Zhou, J.; Soukoulis, C. M.; Linden, S.; Wegener, M. Opt. Lett. 2009, 34, 2501−2503. (12) Gansel, J. K.; Thiel, M.; Rill, S.; Decker, M. S.; Bade, M.; Saile, K.; von Freymann, V.; Linden, G.; Wegener, S. Science 2009, 325, 1513−1515. (13) Sersic, I.; Frimmer, M.; Verhagen, E.; Koenderink, A. F. Phys. Rev. Lett. 2009, 103, 213902. (14) Decker, M.; Feth, N.; Soukoulis, C. M.; Linden, S.; Wegener, M. Phys. Rev. B 2011, 84, 085416. (15) Feth, N.; König, M.; Husnik, M.; Stannigel, K.; Niegemann, J.; Busch, K.; Wegener, M.; Linden, S. Opt. Express 2010, 18, 6545−6554. (16) Liu, N.; Liu, H.; Zhu, S.; Giessen, H. Nat. Photonics 2009, 3, 157−162. (17) Decker, M.; Burger, S.; Linden, S.; Wegener, M. Phys. Rev. B 2009, 80, 193102. (18) Luk’yanchuk, B.; Zheludev, N. I.; Maier, S. A.; Halas, N. J.; Nordlander, P.; Giessen, H.; Chong, C. T. Nat. Mater. 2010, 9, 707− 715. (19) Linden, S.; Niesler, F. B. P.; Foerstner, J.; Grynko, Y.; Meier, T.; Wegener, M. Phys. Rev. Lett. 2012, 109, 015502. (20) Zhang, S.; Genov, D. A.; Wang, Y.; Liu, M.; Zhang, X. Phys. Rev. Lett. 2008, 101, 047401. (21) Prodan, E.; Radloff, C.; Halas, N. J.; Nordlander, P. A. Science 2003, 302, 419−422. (22) Rechberger, C.; Hohenau, A.; Leitner, A.; Krenn, J. R.; Lamprecht, B.; Aussenegg, F. R. Opt. Commun. 2003, 220, 137−141. (23) Fan, J. A.; Wu, C.; Bao, J.; Bardhan, R.; Halas, N. J.; Manoharan, V. N.; Nordlander, P.; Shvets, G.; Capasso, F. Science 2010, 328, 1135−1138. (24) Hentschel, M.; Dregely, D.; Vogelgesang, R.; Giessen, H.; Liu, N. ACS Nano 2011, 3, 2042−2050. (25) Bharadwaj, P.; Deutsch, B.; Novotny, L. Adv. Opt. Photonics 2009, 1, 438−483. (26) Bergman, D. J.; Stockman, M. I. Phys. Rev. Lett. 2003, 90, 027402. (27) García de Abajo, F. J.; Kociak, M. Phys. Rev. Lett. 2008, 100, 106804. (28) Hohenester, U.; Ditlbacher, H.; Krenn, J. R. Phys. Rev. Lett. 2009, 103, 106801. (29) Nelayah, J.; Kociak, M.; Stéphan, O.; García de Abajo, F. J.; Tencé, M.; Henrard, L.; Taverna, D.; Pastoriza-Santos, I.; Liz-Marzán, L. M.; Colliex, C. Nat. Phys. 2007, 3, 348 −353. (30) Bosman, M.; Keast, V. J.; Watanabe, M.; Maaroof, A. I.; Cortie, M. B. Nanotechnology 2007, 18, 165505. (31) Ö güt, B.; Talebi, N.; Vogelgesang, R.; Sigle, W.; van Aken, P. A. Nano Lett. 2012, 12, 5239−5244. (32) Koh, A. L.; Fernández-Domínguez, A. I.; McComb, A. W.; Maier, S. A.; Yang, J. K. W. Nano Lett. 2011, 11, 1323−1330. (33) Boudarham, G.; Feth, N.; Myroshnychenko, V.; Linden, S.; García de Abajo, J.; Wegener, M.; Kociak, M. Phys. Rev. Lett. 2010, 105, 255501.

ASSOCIATED CONTENT

S Supporting Information *

Selected EELS spectra of the structures shown in Figures 4−6. This material is available free of charge via the Internet at http://pubs.acs.org.

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Letter

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; phone: 0049 228 9656299; fax: 0049 22896569299. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.I. and S.L. acknowledge the financial support of the DFGProject LI 1641/2-1. Author contributions are as follows: F.v.C. performed the EELS experiments and analyzed the data. S.I. supervised the EELS experiments. R.D. and J.N. performed the numerical calculations. K.B. supervised the numerical calculations. S.L. fabricated the samples and supervised the project. All authors contributed to writing the Letter. 707


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(34) von Cube, F.; Irsen, S.; Niegemann, J.; Matyssek, C.; Hergert, W.; Busch, K.; Linden, S. Opt. Mater. Express 2011, 1, 1009−1018. (35) Chu, M. W.; Myroshnychenko, V.; Chen, C. H.; Deng, J. P.; Mou, C. Y.; García de Abajo, F. J. Nano Lett. 2009, 9, 399−404. (36) Koh, A. L.; Bao, K.; Khan, I.; Smith, W. E.; Kothleitner, G.; Nordlander, P.; Maier, S. A.; McComb, D. W. ACS Nano 2009, 3, 3015−22. (37) Alber, I.; Sigle, W.; Mueller, S.; Neumann, R.; Picht, O.; Rauber, M.; van Aken, P. A.; Toimil-Molares, M. E. ACS Nano 2011, 5, 9845− 9853. (38) Kittel, C. Introduction to Solid State Physics, 8th ed.; Wiley: New York, 2005. (39) Busch, K.; König, M.; Niegemann, J. Laser Photonics Rev. 2011, 5, 773. (40) Matyssek, C.; Niegemann, J.; Hergert, W.; Busch, K. Photonics Nanotechnol. Fund. Appl. 2011, 9, 367.

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From Isolated Metaatoms to Photonic Metamaterials: Evolution of the

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