Scanning transmission electron microscopy in combination with electron energy-loss spectroscopy is a powerful tool for the spatial and spectral characterization of the plasmonic modes of lithographically defined photonic meta-atoms. As an example, we present a size dependence study of the resonance energies of the plasmonic modes of a series of isolated split-ring resonators. Furthermore, we show that the comparison of the plasmonic maps of a split-ring resonator and the corresponding complementary split-ring resonator allows a direct visualization of Babinet’s principle. Our experiments are in good agreement with numerical calculations based on a discontinuous Galerkin time-domain approach.

© 2011 OSA

1. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
2. S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett.94(3), 037402 (2005). [CrossRef] [PubMed]
3. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005). [CrossRef] [PubMed]
4. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007). [CrossRef]
5. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007). [CrossRef] [PubMed]
6. A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure,” Phys. Rev. Lett.97(17), 177401 (2006). [CrossRef] [PubMed]
7. S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett.102(2), 023901 (2009). [CrossRef] [PubMed]
8. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325(5947), 1513–1515 (2009). [CrossRef] [PubMed]
9. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999). [CrossRef]
10. J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007). [CrossRef]
11. M. Bosman, V. J. Keast, M. Watanabe, A. I. Maaroof, and M. B. Cortie, “Mapping surface plasmons at the nanometre scale with an electron beam,” Nanotechnology18(16), 165505 (2007). [CrossRef]
12. M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett.9(1), 399–404 (2009). [CrossRef] [PubMed]
13. B. Schaffer, U. Hohenester, A. Trügler, and F. Hofer, “High-resolution surface plasmon imaging of gold nanoparticles by energy-filtered transmission electron microscopy,” Phys. Rev. B79(4), 041401 (2009). [CrossRef]
14. M. N’Gom, S. Li, G. Schatz, R. Erni, A. Agarwal, N. Kotov, and T. Norris, “Electron-beam mapping of plasmon resonances in electromagnetically interacting gold nanorods,” Phys. Rev. B80(11), 113411 (2009). [CrossRef]
15. F. Song, T. Wang, X. Wang, C. Xu, L. He, J. Wan, C. Van Haesendonck, S. P. Ringer, M. Han, Z. Liu, and G. Wang, “Visualizing plasmon coupling in closely spaced chains of Ag nanoparticles by electron energy-loss spectroscopy,” Small6(3), 446–451 (2010). [CrossRef] [PubMed]
16. W. Sigle, J. Nelayah, C. T. Koch, and P. A. van Aken, “Electron energy losses in Ag nanoholes--from localized surface plasmon resonances to rings of fire,” Opt. Lett.34(14), 2150–2152 (2009). [CrossRef] [PubMed]
17. G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett.105(25), 255501 (2010). [CrossRef] [PubMed]
18. A. L. Koh, A. I. Fernández-Domínguez, D. W. McComb, S. A. Maier, and J. K. W. Yang, “High-resolution mapping of electron-beam-excited plasmon modes in lithographically defined gold nanostructures,” Nano Lett.11(3), 1323–1330 (2011). [CrossRef] [PubMed]
19. F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett.100(10), 106804 (2008). [CrossRef] [PubMed]
20. U. Hohenester, H. Ditlbacher, and J. R. Krenn, “Electron-energy-loss spectra of plasmonic nanoparticles,” Phys. Rev. Lett.103(10), 106801 (2009). [CrossRef] [PubMed]
21. T. Walther, E. Quandt, H. Stegmann, A. Thesen, and G. Benner, “First experimental test of a new monochromated and aberration-corrected 200 kV field-emission scanning transmission electron microscope,” Ultramicroscopy106(11-12), 963–969 (2006). [CrossRef] [PubMed]
22. J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods (Springer, 2008).
23. J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photonics Nanostruct. Fundam. Appl.7(1), 2–11 (2009). [CrossRef]
24. K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express17(17), 14934–14947 (2009). [CrossRef] [PubMed]
25. K. Busch, M. König, and J. Niegemann, “Discontinuous Galerkin methods in nanophotonics,” Laser Photon. Rev. (to be published), doi:. [CrossRef]
26. C. Matyssek, J. Niegemann, W. Hergert, and K. Busch, “Computing electron energy loss spectra with the Discontinuous Galerkin Time-Domain method,” Photonics Nanostruct. Fundam. Appl. (to be published), doi:. [CrossRef]
27. P.-B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
28. C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express14(19), 8827–8836 (2006). [CrossRef] [PubMed]
29. M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett.31(9), 1259–1261 (2006). [CrossRef] [PubMed]
30. F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett.93(19), 197401 (2004). [CrossRef] [PubMed]
31. T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B76(3), 033407 (2007). [CrossRef]
32. A. Bitzer, A. Ortner, H. Merbold, T. Feurer, and M. Walther, “Terahertz near-field microscopy of complementary planar metamaterials: Babinet’s principle,” Opt. Express19(3), 2537–2545 (2011). [CrossRef] [PubMed]

IEEE Trans. Microw. Theory Tech.

• J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999). [CrossRef]

Laser Photon. Rev.

• K. Busch, M. König, and J. Niegemann, “Discontinuous Galerkin methods in nanophotonics,” Laser Photon. Rev. (to be published), doi:. [CrossRef]

Nano Lett.

• A. L. Koh, A. I. Fernández-Domínguez, D. W. McComb, S. A. Maier, and J. K. W. Yang, “High-resolution mapping of electron-beam-excited plasmon modes in lithographically defined gold nanostructures,” Nano Lett.11(3), 1323–1330 (2011). [CrossRef] [PubMed]
• M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett.9(1), 399–404 (2009). [CrossRef] [PubMed]

Nanotechnology

• M. Bosman, V. J. Keast, M. Watanabe, A. I. Maaroof, and M. B. Cortie, “Mapping surface plasmons at the nanometre scale with an electron beam,” Nanotechnology18(16), 165505 (2007). [CrossRef]

Nat. Photonics

• V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007). [CrossRef]

Nat. Phys.

• J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys.3(5), 348–353 (2007). [CrossRef]

Opt. Express

• K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express17(17), 14934–14947 (2009). [CrossRef] [PubMed]
• C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express14(19), 8827–8836 (2006). [CrossRef] [PubMed]
• A. Bitzer, A. Ortner, H. Merbold, T. Feurer, and M. Walther, “Terahertz near-field microscopy of complementary planar metamaterials: Babinet’s principle,” Opt. Express19(3), 2537–2545 (2011). [CrossRef] [PubMed]

Opt. Lett.

• M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett.31(9), 1259–1261 (2006). [CrossRef] [PubMed]
• W. Sigle, J. Nelayah, C. T. Koch, and P. A. van Aken, “Electron energy losses in Ag nanoholes--from localized surface plasmon resonances to rings of fire,” Opt. Lett.34(14), 2150–2152 (2009). [CrossRef] [PubMed]

Photonics Nanostruct. Fundam. Appl.

• J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photonics Nanostruct. Fundam. Appl.7(1), 2–11 (2009). [CrossRef]
• C. Matyssek, J. Niegemann, W. Hergert, and K. Busch, “Computing electron energy loss spectra with the Discontinuous Galerkin Time-Domain method,” Photonics Nanostruct. Fundam. Appl. (to be published), doi:. [CrossRef]

Phys. Rev. B

• P.-B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
• T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B76(3), 033407 (2007). [CrossRef]
• B. Schaffer, U. Hohenester, A. Trügler, and F. Hofer, “High-resolution surface plasmon imaging of gold nanoparticles by energy-filtered transmission electron microscopy,” Phys. Rev. B79(4), 041401 (2009). [CrossRef]
• M. N’Gom, S. Li, G. Schatz, R. Erni, A. Agarwal, N. Kotov, and T. Norris, “Electron-beam mapping of plasmon resonances in electromagnetically interacting gold nanorods,” Phys. Rev. B80(11), 113411 (2009). [CrossRef]

Phys. Rev. Lett.

• G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. García de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett.105(25), 255501 (2010). [CrossRef] [PubMed]
• A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure,” Phys. Rev. Lett.97(17), 177401 (2006). [CrossRef] [PubMed]
• S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett.102(2), 023901 (2009). [CrossRef] [PubMed]
• S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett.94(3), 037402 (2005). [CrossRef] [PubMed]
• C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005). [CrossRef] [PubMed]
• F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett.93(19), 197401 (2004). [CrossRef] [PubMed]
• F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett.100(10), 106804 (2008). [CrossRef] [PubMed]
• U. Hohenester, H. Ditlbacher, and J. R. Krenn, “Electron-energy-loss spectra of plasmonic nanoparticles,” Phys. Rev. Lett.103(10), 106801 (2009). [CrossRef] [PubMed]

Science

• C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007). [CrossRef] [PubMed]
• J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325(5947), 1513–1515 (2009). [CrossRef] [PubMed]
• S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

Small

• F. Song, T. Wang, X. Wang, C. Xu, L. He, J. Wan, C. Van Haesendonck, S. P. Ringer, M. Han, Z. Liu, and G. Wang, “Visualizing plasmon coupling in closely spaced chains of Ag nanoparticles by electron energy-loss spectroscopy,” Small6(3), 446–451 (2010). [CrossRef] [PubMed]

Ultramicroscopy

• T. Walther, E. Quandt, H. Stegmann, A. Thesen, and G. Benner, “First experimental test of a new monochromated and aberration-corrected 200 kV field-emission scanning transmission electron microscope,” Ultramicroscopy106(11-12), 963–969 (2006). [CrossRef] [PubMed]

Other

• J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods (Springer, 2008).

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