Abstract

We present a comprehensive theoretical and experimental investigation of the plasmon hybridization of coupled split-ring resonators by means of the electron energy-loss spectroscopy. Split-ring resonator is a key element in design of negative refractive index metamaterials, and has been therefore intensively studied in the literature. Here, our aim is the study of hybridization effects for higher-order non-dipolar modes, which have been not investigated beforehand. We provide a complete scheme of the multimodal distribution of the coupled and single-element split-ring resonators, with a precise attention to the hybridization of those modes according to the induced moments. Our study suggests a clear dominance of electric and magnetic dipole moments over higher-order modes in the far-field radiation spectrum.

© 2015 Optical Society of America

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References

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and miu,” Sov. Phys. Usp. 10(4), 509–514 (1968).
    [Crossref]
  2. H. J. Lee and J. G. Yook, “Biosensing using split-ring resonators at microwave regime,” Appl. Phys. Lett. 92(25), 254103 (2008).
    [Crossref]
  3. K. B. Alici, A. E. Serebryannikov, and E. Ozbay, “Radiation properties and coupling analysis of a metamaterial based, dual polarization, dual band, multiple split ring resonator antenna,” J. Electromagn. Waves Appl. 24(8-9), 1183–1193 (2010).
    [Crossref]
  4. Y. Z. Cheng, H. L. Yang, Z. Z. Cheng, and N. Wu, “Perfect metamaterial absorber based on a split-ring-cross resonator,” Appl. Phys. Mater. Sci. 102, 99–103 (2011).
  5. Y. D. Dong, T. Yang, and T. Itoh, “Substrate integrated waveguide loaded by complementary split-ring resonators and its applications to miniaturized waveguide filters,” IEEE Trans. Microw. Theory Tech. 57(9), 2211–2223 (2009).
    [Crossref]
  6. N. Talebi, B. Ogut, W. Sigle, R. Vogelgesang, and P. A. van Aken, “On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities,” Appl. Phys. Mater. Sci. 116, 947–954 (2014).
  7. B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
    [Crossref] [PubMed]
  8. N. Talebi, A. Mahjoubfar, and M. Shahabadi, “Plasmonic ring resonator,” J. Opt. Soc. Am. B 25(12), 2116–2122 (2008).
    [Crossref]
  9. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
    [Crossref] [PubMed]
  10. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
    [Crossref]
  11. T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
    [Crossref] [PubMed]
  12. H. Guo, N. Liu, L. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
    [Crossref] [PubMed]
  13. F. von Cube, S. Irsen, and S. Linden, “From isolated metaatoms to photonic metamaterials: mapping of collective near-field phenomena with EELS,” 2012 Conference on Lasers and Electro-Optics (CLEO) San Jose, USA (2012).
    [Crossref]
  14. N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010).
    [Crossref] [PubMed]
  15. K. Aydin, I. M. Pryce, and H. A. Atwater, “Symmetry breaking and strong coupling in planar optical metamaterials,” Opt. Express 18(13), 13407–13417 (2010).
    [Crossref] [PubMed]
  16. M. Decker, N. Feth, C. M. Soukoulis, S. Linden, and M. Wegener, “Retarded long-range interaction in split-ring-resonator square arrays,” Phys. Rev. B 84(8), 085416 (2011).
    [Crossref]
  17. P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
    [Crossref]
  18. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
    [Crossref] [PubMed]
  19. J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
    [Crossref]
  20. D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadrupole resonance in optical metamaterials,” Phys. Rev. B 78(12), 121101 (2008).
    [Crossref]
  21. N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
    [Crossref] [PubMed]
  22. 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]
  23. L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
    [Crossref]
  24. F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
    [Crossref] [PubMed]
  25. A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
    [Crossref] [PubMed]
  26. F. J. G. de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. 82(1), 209–275 (2010).
    [Crossref]
  27. M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
    [Crossref] [PubMed]
  28. E. C. Le Ru and P. G. Etchegoin, “Sub-wavelength localization of hot-spots in SERS,” Chem. Phys. Lett. 396(4-6), 393–397 (2004).
    [Crossref]
  29. G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
    [Crossref] [PubMed]
  30. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  31. C. O. M. S. O. L. Multiphysics, https://www.comsol.de/
  32. N. Geuquet and L. Henrard, “EELS and optical response of a noble metal nanoparticle in the frame of a discrete dipole approximation,” Ultramicroscopy 110(8), 1075–1080 (2010).
    [Crossref]
  33. N. Talebi, “A directional, ultrafast and integrated few-photon source utilizing the interaction of electron beams and plasmonic nanoantennas,” New J. Phys. 16(5), 053021 (2014).
    [Crossref]
  34. C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
    [Crossref] [PubMed]
  35. F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-type resonant energy transfer influenced by metal nanoparticles,” Nano Lett. 8(12), 4128–4133 (2008).
    [Crossref] [PubMed]
  36. N. Talebi and M. Shahabdi, “Analysis of the propagation of light along an array of nanorods using the generalized multipole techniques,” J. Comput. Theor. Nanosci. 5(4), 711–716 (2008).
    [Crossref]
  37. R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106(6), 1693–1698 (2009).
    [Crossref] [PubMed]
  38. Y. W. Huang, W. T. Chen, P. C. Wu, V. Fedotov, V. Savinov, Y. Z. Ho, Y. F. Chau, N. I. Zheludev, and D. P. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012).
    [Crossref] [PubMed]

2015 (1)

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

2014 (2)

N. Talebi, “A directional, ultrafast and integrated few-photon source utilizing the interaction of electron beams and plasmonic nanoantennas,” New J. Phys. 16(5), 053021 (2014).
[Crossref]

N. Talebi, B. Ogut, W. Sigle, R. Vogelgesang, and P. A. van Aken, “On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities,” Appl. Phys. Mater. Sci. 116, 947–954 (2014).

2012 (4)

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
[Crossref] [PubMed]

F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
[Crossref] [PubMed]

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

Y. W. Huang, W. T. Chen, P. C. Wu, V. Fedotov, V. Savinov, Y. Z. Ho, Y. F. Chau, N. I. Zheludev, and D. P. Tsai, “Design of plasmonic toroidal metamaterials at optical frequencies,” Opt. Express 20(2), 1760–1768 (2012).
[Crossref] [PubMed]

2011 (4)

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
[Crossref] [PubMed]

Y. Z. Cheng, H. L. Yang, Z. Z. Cheng, and N. Wu, “Perfect metamaterial absorber based on a split-ring-cross resonator,” Appl. Phys. Mater. Sci. 102, 99–103 (2011).

M. Decker, N. Feth, C. M. Soukoulis, S. Linden, and M. Wegener, “Retarded long-range interaction in split-ring-resonator square arrays,” Phys. Rev. B 84(8), 085416 (2011).
[Crossref]

2010 (7)

N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010).
[Crossref] [PubMed]

K. Aydin, I. M. Pryce, and H. A. Atwater, “Symmetry breaking and strong coupling in planar optical metamaterials,” Opt. Express 18(13), 13407–13417 (2010).
[Crossref] [PubMed]

K. B. Alici, A. E. Serebryannikov, and E. Ozbay, “Radiation properties and coupling analysis of a metamaterial based, dual polarization, dual band, multiple split ring resonator antenna,” J. Electromagn. Waves Appl. 24(8-9), 1183–1193 (2010).
[Crossref]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[Crossref] [PubMed]

F. J. G. de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. 82(1), 209–275 (2010).
[Crossref]

N. Geuquet and L. Henrard, “EELS and optical response of a noble metal nanoparticle in the frame of a discrete dipole approximation,” Ultramicroscopy 110(8), 1075–1080 (2010).
[Crossref]

2009 (4)

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106(6), 1693–1698 (2009).
[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]

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
[Crossref]

Y. D. Dong, T. Yang, and T. Itoh, “Substrate integrated waveguide loaded by complementary split-ring resonators and its applications to miniaturized waveguide filters,” IEEE Trans. Microw. Theory Tech. 57(9), 2211–2223 (2009).
[Crossref]

2008 (6)

H. J. Lee and J. G. Yook, “Biosensing using split-ring resonators at microwave regime,” Appl. Phys. Lett. 92(25), 254103 (2008).
[Crossref]

N. Talebi, A. Mahjoubfar, and M. Shahabadi, “Plasmonic ring resonator,” J. Opt. Soc. Am. B 25(12), 2116–2122 (2008).
[Crossref]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadrupole resonance in optical metamaterials,” Phys. Rev. B 78(12), 121101 (2008).
[Crossref]

F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-type resonant energy transfer influenced by metal nanoparticles,” Nano Lett. 8(12), 4128–4133 (2008).
[Crossref] [PubMed]

N. Talebi and M. Shahabdi, “Analysis of the propagation of light along an array of nanorods using the generalized multipole techniques,” J. Comput. Theor. Nanosci. 5(4), 711–716 (2008).
[Crossref]

2007 (1)

2006 (1)

C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
[Crossref] [PubMed]

2004 (2)

E. C. Le Ru and P. G. Etchegoin, “Sub-wavelength localization of hot-spots in SERS,” Chem. Phys. Lett. 396(4-6), 393–397 (2004).
[Crossref]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[Crossref]

2003 (2)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and miu,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

Alici, K. B.

K. B. Alici, A. E. Serebryannikov, and E. Ozbay, “Radiation properties and coupling analysis of a metamaterial based, dual polarization, dual band, multiple split ring resonator antenna,” J. Electromagn. Waves Appl. 24(8-9), 1183–1193 (2010).
[Crossref]

Atwater, H. A.

Aydin, K.

Benner, G.

C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
[Crossref] [PubMed]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

Bharadwaj, P.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
[Crossref]

Boudarham, G.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[Crossref] [PubMed]

Chau, Y. F.

Chen, C. H.

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]

Chen, W. T.

Cheng, Y. Z.

Y. Z. Cheng, H. L. Yang, Z. Z. Cheng, and N. Wu, “Perfect metamaterial absorber based on a split-ring-cross resonator,” Appl. Phys. Mater. Sci. 102, 99–103 (2011).

Cheng, Z. Z.

Y. Z. Cheng, H. L. Yang, Z. Z. Cheng, and N. Wu, “Perfect metamaterial absorber based on a split-ring-cross resonator,” Appl. Phys. Mater. Sci. 102, 99–103 (2011).

Chipouline, A.

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

Cho, D. J.

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadrupole resonance in optical metamaterials,” Phys. Rev. B 78(12), 121101 (2008).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Chu, M. W.

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]

Davis, T. J.

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

de Abajo, F. J. G.

F. J. G. de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. 82(1), 209–275 (2010).
[Crossref]

de Abajo, J. G.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[Crossref] [PubMed]

Decker, M.

M. Decker, N. Feth, C. M. Soukoulis, S. Linden, and M. Wegener, “Retarded long-range interaction in split-ring-resonator square arrays,” Phys. Rev. B 84(8), 085416 (2011).
[Crossref]

Deng, J. P.

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]

Deutsch, B.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
[Crossref]

Ditlbacher, H.

F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
[Crossref] [PubMed]

Dong, Y. D.

Y. D. Dong, T. Yang, and T. Itoh, “Substrate integrated waveguide loaded by complementary split-ring resonators and its applications to miniaturized waveguide filters,” IEEE Trans. Microw. Theory Tech. 57(9), 2211–2223 (2009).
[Crossref]

Essers, E.

C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
[Crossref] [PubMed]

Etchegoin, P. G.

E. C. Le Ru and P. G. Etchegoin, “Sub-wavelength localization of hot-spots in SERS,” Chem. Phys. Lett. 396(4-6), 393–397 (2004).
[Crossref]

Fedotov, V.

Fernández-López, C.

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

Feth, N.

M. Decker, N. Feth, C. M. Soukoulis, S. Linden, and M. Wegener, “Retarded long-range interaction in split-ring-resonator square arrays,” Phys. Rev. B 84(8), 085416 (2011).
[Crossref]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[Crossref] [PubMed]

Förstner, J.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

Fu, L.

García de Abajo, F. J.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[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]

Geuquet, N.

N. Geuquet and L. Henrard, “EELS and optical response of a noble metal nanoparticle in the frame of a discrete dipole approximation,” Ultramicroscopy 110(8), 1075–1080 (2010).
[Crossref]

Giessen, H.

Gómez, D. E.

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

Gu, L.

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

Guo, H.

Halas, N. J.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

Henrard, L.

N. Geuquet and L. Henrard, “EELS and optical response of a noble metal nanoparticle in the frame of a discrete dipole approximation,” Ultramicroscopy 110(8), 1075–1080 (2010).
[Crossref]

Ho, Y. Z.

Hofer, F.

F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
[Crossref] [PubMed]

Hohenau, A.

F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
[Crossref] [PubMed]

Hohenester, U.

F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
[Crossref] [PubMed]

F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-type resonant energy transfer influenced by metal nanoparticles,” Nano Lett. 8(12), 4128–4133 (2008).
[Crossref] [PubMed]

Höschen, R.

C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
[Crossref] [PubMed]

Huang, Y. W.

Itoh, T.

Y. D. Dong, T. Yang, and T. Itoh, “Substrate integrated waveguide loaded by complementary split-ring resonators and its applications to miniaturized waveguide filters,” IEEE Trans. Microw. Theory Tech. 57(9), 2211–2223 (2009).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Koch, C. T.

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
[Crossref] [PubMed]

Kociak, M.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[Crossref] [PubMed]

Krenn, J. R.

F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
[Crossref] [PubMed]

F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-type resonant energy transfer influenced by metal nanoparticles,” Nano Lett. 8(12), 4128–4133 (2008).
[Crossref] [PubMed]

Le Ru, E. C.

E. C. Le Ru and P. G. Etchegoin, “Sub-wavelength localization of hot-spots in SERS,” Chem. Phys. Lett. 396(4-6), 393–397 (2004).
[Crossref]

Lederer, F.

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

Lee, H. J.

H. J. Lee and J. G. Yook, “Biosensing using split-ring resonators at microwave regime,” Appl. Phys. Lett. 92(25), 254103 (2008).
[Crossref]

Leitner, A.

F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-type resonant energy transfer influenced by metal nanoparticles,” Nano Lett. 8(12), 4128–4133 (2008).
[Crossref] [PubMed]

Li, K.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[Crossref]

Li, Z.-Y.

M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
[Crossref] [PubMed]

Linden, S.

M. Decker, N. Feth, C. M. Soukoulis, S. Linden, and M. Wegener, “Retarded long-range interaction in split-ring-resonator square arrays,” Phys. Rev. B 84(8), 085416 (2011).
[Crossref]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[Crossref] [PubMed]

Liu, N.

Liz-Marzán, L. M.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

Losquin, A.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

Mahjoubfar, A.

Mao, J.

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

Matijevic, M.

C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
[Crossref] [PubMed]

Menzel, C.

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

Merlin, R.

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106(6), 1693–1698 (2009).
[Crossref] [PubMed]

Meyrath, T. P.

Moran, C. H.

M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
[Crossref] [PubMed]

Mou, C. Y.

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]

Mu, J. L.

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

Myroshnychenko, V.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[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]

Nordlander, P.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[Crossref]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

Novotny, L.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
[Crossref]

Ogut, B.

N. Talebi, B. Ogut, W. Sigle, R. Vogelgesang, and P. A. van Aken, “On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities,” Appl. Phys. Mater. Sci. 116, 947–954 (2014).

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

Ögüt, B.

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
[Crossref] [PubMed]

Oubre, C.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[Crossref]

Ozbay, E.

K. B. Alici, A. E. Serebryannikov, and E. Ozbay, “Radiation properties and coupling analysis of a metamaterial based, dual polarization, dual band, multiple split ring resonator antenna,” J. Electromagn. Waves Appl. 24(8-9), 1183–1193 (2010).
[Crossref]

Pertsch, T.

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

Petschulat, J.

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

Prodan, E.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[Crossref]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

Pryce, I. M.

Qin, D.

M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
[Crossref] [PubMed]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

Reil, F.

F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-type resonant energy transfer influenced by metal nanoparticles,” Nano Lett. 8(12), 4128–4133 (2008).
[Crossref] [PubMed]

Rockstuhl, C.

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

Rodríguez-González, B.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

Rohm, M.

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

Rühle, M.

C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
[Crossref] [PubMed]

Rycenga, M.

M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
[Crossref] [PubMed]

Savinov, V.

Scarabelli, L.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

Schmidt, F. P.

F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
[Crossref] [PubMed]

Schweizer, H.

Serebryannikov, A. E.

K. B. Alici, A. E. Serebryannikov, and E. Ozbay, “Radiation properties and coupling analysis of a metamaterial based, dual polarization, dual band, multiple split ring resonator antenna,” J. Electromagn. Waves Appl. 24(8-9), 1183–1193 (2010).
[Crossref]

Shahabadi, M.

Shahabdi, M.

N. Talebi and M. Shahabdi, “Analysis of the propagation of light along an array of nanorods using the generalized multipole techniques,” J. Comput. Theor. Nanosci. 5(4), 711–716 (2008).
[Crossref]

Shen, Y. R.

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadrupole resonance in optical metamaterials,” Phys. Rev. B 78(12), 121101 (2008).
[Crossref]

Sigle, W.

N. Talebi, B. Ogut, W. Sigle, R. Vogelgesang, and P. A. van Aken, “On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities,” Appl. Phys. Mater. Sci. 116, 947–954 (2014).

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
[Crossref] [PubMed]

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
[Crossref] [PubMed]

Soukoulis, C. M.

M. Decker, N. Feth, C. M. Soukoulis, S. Linden, and M. Wegener, “Retarded long-range interaction in split-ring-resonator square arrays,” Phys. Rev. B 84(8), 085416 (2011).
[Crossref]

Stéphan, O.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

Stockman, M. I.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[Crossref]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

Talebi, N.

N. Talebi, B. Ogut, W. Sigle, R. Vogelgesang, and P. A. van Aken, “On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities,” Appl. Phys. Mater. Sci. 116, 947–954 (2014).

N. Talebi, “A directional, ultrafast and integrated few-photon source utilizing the interaction of electron beams and plasmonic nanoantennas,” New J. Phys. 16(5), 053021 (2014).
[Crossref]

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
[Crossref] [PubMed]

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

N. Talebi, A. Mahjoubfar, and M. Shahabadi, “Plasmonic ring resonator,” J. Opt. Soc. Am. B 25(12), 2116–2122 (2008).
[Crossref]

N. Talebi and M. Shahabdi, “Analysis of the propagation of light along an array of nanorods using the generalized multipole techniques,” J. Comput. Theor. Nanosci. 5(4), 711–716 (2008).
[Crossref]

Tencé, M.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

Tsai, D. P.

Tunnermann, A.

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

van Aken, P. A.

N. Talebi, B. Ogut, W. Sigle, R. Vogelgesang, and P. A. van Aken, “On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities,” Appl. Phys. Mater. Sci. 116, 947–954 (2014).

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
[Crossref] [PubMed]

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

Vernon, K. C.

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and miu,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

Vogelgesang, R.

N. Talebi, B. Ogut, W. Sigle, R. Vogelgesang, and P. A. van Aken, “On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities,” Appl. Phys. Mater. Sci. 116, 947–954 (2014).

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
[Crossref] [PubMed]

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

Wang, F.

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadrupole resonance in optical metamaterials,” Phys. Rev. B 78(12), 121101 (2008).
[Crossref]

Wegener, M.

M. Decker, N. Feth, C. M. Soukoulis, S. Linden, and M. Wegener, “Retarded long-range interaction in split-ring-resonator square arrays,” Phys. Rev. B 84(8), 085416 (2011).
[Crossref]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[Crossref] [PubMed]

Wen, X. G.

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

Wu, N.

Y. Z. Cheng, H. L. Yang, Z. Z. Cheng, and N. Wu, “Perfect metamaterial absorber based on a split-ring-cross resonator,” Appl. Phys. Mater. Sci. 102, 99–103 (2011).

Wu, P. C.

Xia, X.

M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
[Crossref] [PubMed]

Xia, Y.

M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
[Crossref] [PubMed]

Yang, H. L.

Y. Z. Cheng, H. L. Yang, Z. Z. Cheng, and N. Wu, “Perfect metamaterial absorber based on a split-ring-cross resonator,” Appl. Phys. Mater. Sci. 102, 99–103 (2011).

Yang, T.

Y. D. Dong, T. Yang, and T. Itoh, “Substrate integrated waveguide loaded by complementary split-ring resonators and its applications to miniaturized waveguide filters,” IEEE Trans. Microw. Theory Tech. 57(9), 2211–2223 (2009).
[Crossref]

Yook, J. G.

H. J. Lee and J. G. Yook, “Biosensing using split-ring resonators at microwave regime,” Appl. Phys. Lett. 92(25), 254103 (2008).
[Crossref]

Zagonel, L. F.

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

Zentgraf, T.

Zhang, X.

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadrupole resonance in optical metamaterials,” Phys. Rev. B 78(12), 121101 (2008).
[Crossref]

Zheludev, N. I.

Zhou, F.

M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photonics 1(3), 438–483 (2009).
[Crossref]

Angew. Chem. Int. Ed. Engl. (2)

N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010).
[Crossref] [PubMed]

M. Rycenga, X. Xia, C. H. Moran, F. Zhou, D. Qin, Z.-Y. Li, and Y. Xia, “Generation of hot spots with silver nanocubes for single-molecule detection by surface-enhanced raman scattering,” Angew. Chem. Int. Ed. Engl. 50(24), 5473–5477 (2011).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

H. J. Lee and J. G. Yook, “Biosensing using split-ring resonators at microwave regime,” Appl. Phys. Lett. 92(25), 254103 (2008).
[Crossref]

Appl. Phys. Mater. Sci. (2)

Y. Z. Cheng, H. L. Yang, Z. Z. Cheng, and N. Wu, “Perfect metamaterial absorber based on a split-ring-cross resonator,” Appl. Phys. Mater. Sci. 102, 99–103 (2011).

N. Talebi, B. Ogut, W. Sigle, R. Vogelgesang, and P. A. van Aken, “On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities,” Appl. Phys. Mater. Sci. 116, 947–954 (2014).

Chem. Phys. Lett. (1)

E. C. Le Ru and P. G. Etchegoin, “Sub-wavelength localization of hot-spots in SERS,” Chem. Phys. Lett. 396(4-6), 393–397 (2004).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

Y. D. Dong, T. Yang, and T. Itoh, “Substrate integrated waveguide loaded by complementary split-ring resonators and its applications to miniaturized waveguide filters,” IEEE Trans. Microw. Theory Tech. 57(9), 2211–2223 (2009).
[Crossref]

J. Comput. Theor. Nanosci. (1)

N. Talebi and M. Shahabdi, “Analysis of the propagation of light along an array of nanorods using the generalized multipole techniques,” J. Comput. Theor. Nanosci. 5(4), 711–716 (2008).
[Crossref]

J. Electromagn. Waves Appl. (1)

K. B. Alici, A. E. Serebryannikov, and E. Ozbay, “Radiation properties and coupling analysis of a metamaterial based, dual polarization, dual band, multiple split ring resonator antenna,” J. Electromagn. Waves Appl. 24(8-9), 1183–1193 (2010).
[Crossref]

J. Opt. Soc. Am. B (1)

Langmuir (1)

N. Talebi, W. Sigle, R. Vogelgesang, C. T. Koch, C. Fernández-López, L. M. Liz-Marzán, B. Ögüt, M. Rohm, and P. A. van Aken, “Breaking the mode degeneracy of surface plasmon resonances in a triangular system,” Langmuir 28(24), 8867–8873 (2012).
[Crossref] [PubMed]

Microsc. Microanal. (1)

C. T. Koch, W. Sigle, R. Höschen, M. Rühle, E. Essers, G. Benner, and M. Matijevic, “SESAM: exploring the frontiers of electron microscopy,” Microsc. Microanal. 12(06), 506–514 (2006).
[Crossref] [PubMed]

Nano Lett. (7)

F. Reil, U. Hohenester, J. R. Krenn, and A. Leitner, “Förster-type resonant energy transfer influenced by metal nanoparticles,” Nano Lett. 8(12), 4128–4133 (2008).
[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]

F. P. Schmidt, H. Ditlbacher, U. Hohenester, A. Hohenau, F. Hofer, and J. R. Krenn, “Dark plasmonic breathing modes in silver nanodisks,” Nano Lett. 12(11), 5780–5783 (2012).
[Crossref] [PubMed]

A. Losquin, L. F. Zagonel, V. Myroshnychenko, B. Rodríguez-González, M. Tencé, L. Scarabelli, J. Förstner, L. M. Liz-Marzán, F. J. García de Abajo, O. Stéphan, and M. Kociak, “Unveiling nanometer scale extinction and scattering phenomena through combined electron energy loss spectroscopy and cathodoluminescence measurements,” Nano Lett. 15(2), 1229–1237 (2015).
[Crossref] [PubMed]

B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, and P. A. van Aken, “Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible,” Nano Lett. 12(10), 5239–5244 (2012).
[Crossref] [PubMed]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[Crossref]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

New J. Phys. (1)

N. Talebi, “A directional, ultrafast and integrated few-photon source utilizing the interaction of electron beams and plasmonic nanoantennas,” New J. Phys. 16(5), 053021 (2014).
[Crossref]

Opt. Express (3)

Phys. Rev. A (1)

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78(4), 043811 (2008).
[Crossref]

Phys. Rev. B (4)

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadrupole resonance in optical metamaterials,” Phys. Rev. B 78(12), 121101 (2008).
[Crossref]

L. Gu, W. Sigle, C. T. Koch, B. Ogut, P. A. van Aken, N. Talebi, R. Vogelgesang, J. L. Mu, X. G. Wen, and J. Mao, “Resonant wedge-plasmon modes in single-crystalline gold nanoplatelets,” Phys. Rev. B 83(19), 195433 (2011).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

M. Decker, N. Feth, C. M. Soukoulis, S. Linden, and M. Wegener, “Retarded long-range interaction in split-ring-resonator square arrays,” Phys. Rev. B 84(8), 085416 (2011).
[Crossref]

Phys. Rev. Lett. (2)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[Crossref] [PubMed]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106(6), 1693–1698 (2009).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

F. J. G. de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. 82(1), 209–275 (2010).
[Crossref]

Science (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[Crossref] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and miu,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

Ultramicroscopy (1)

N. Geuquet and L. Henrard, “EELS and optical response of a noble metal nanoparticle in the frame of a discrete dipole approximation,” Ultramicroscopy 110(8), 1075–1080 (2010).
[Crossref]

Other (2)

C. O. M. S. O. L. Multiphysics, https://www.comsol.de/

F. von Cube, S. Irsen, and S. Linden, “From isolated metaatoms to photonic metamaterials: mapping of collective near-field phenomena with EELS,” 2012 Conference on Lasers and Electro-Optics (CLEO) San Jose, USA (2012).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Calculated spectra of (a) an isolated SRR structure S, (b) a 0°-rotated coupled SRRs structure A, (c) a 180°-rotated coupled SRRs structure B, and (d) a 90°-rotated coupled SRRs structure C. The parameters of the SRRs in the simulations are: thickness H = 30 nm, length L = 120 nm, width W = 30 nm and gap distance between the left and right SRRs G = 20 nm. The inserts depict the schemes of the SRR structures used in the simulations. The excitation positions of the electron beam are indicated by the “1”, “2”, and “3”. Three maxima at energies of 0.98 eV, 1.68 eV, and 1.98 eV are visible in the calculated EELS spectra of the isolated SRR, corresponding to the fundamental (I), second (II)-, and third (III)-order plasmonic modes. The fundamental, second-, and third-order plasmonic modes split into two new modes in the structures A and B. However, only the third-order plasmonic mode splits into two new modes in structure C.
Fig. 2
Fig. 2 (a) The calculated EELS maps, (b) the experimental EFTEM images, and (c) the calculated charge-density maps and magnetic moment distributions of the isolated SRR structure S and the 0°-rotated coupled SRRs structure A at resonance energies of the fundamental, second- and third-order plasmonic modes. Charges are marked by “+” and “-”, magnetic moments are marked by “⊗” and “☉”. The scale bars of the EFTEM images are 100 nm and the color codes for the intensities in (a)−(c) are presented accordingly.
Fig. 3
Fig. 3 (a) The calculated EELS maps, (b) the experimental EFTEM images, and (c) the calculated charge-density maps and magnetic moment distributions of the isolated SRR structure S and the 180°-rotated coupled SRRs structure B at resonance energies of the fundamental, second- and third-order plasmonic modes. Charges are marked by “+” and “-”, magnetic moments are marked by “⊗” and “☉”. The scale bars of the EFTEM images are 100 nm and the color codes for the intensities in (a)−(c) are presented accordingly.
Fig. 4
Fig. 4 (a) The calculated EELS maps, (b) the experimental EFTEM images, and (c) the calculated charge-density maps and magnetic moment distributions of the 90°-rotated SRRs structure C at resonance energies of the fundamental, second- and third-order plasmonic modes. Charges are marked by “+” and “-”, magnetic moments are marked by “⊗” and “☉”. The scale bars of the EFTEM images are 100 nm and the color codes for the intensities in (a)−(c) are presented accordingly.
Fig. 5
Fig. 5 Plasmon hybridization schemes of the SRR structure S and the coupled SRRs A, B and C with different relative orientations. Charges are marked by “+” and “-”, strong electric dipoles are marked by solid arrows “↑” and “↓”, magnetic dipole moments are marked by “⊗” and “☉”. The dashed arrows represent weak electric dipoles.
Fig. 6
Fig. 6 Radiated power spectra of the x-component of the electric dipole moment P x , the y-component of the electric dipole moment P y , the z-component of the magnetic dipole moment M Z and the total radiated power for (a) the isolated SRR structure S, (b) the coupled SRRs structure A, (c) the coupled SRRs structure B, and (d) the coupled SRRs structure C. The locations of the electron beam excitation and the origins of the coordinates are at the same positions which is marked in the insets schemes.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

J ( r ,ω)=e z ^ δ( R R 0 ) e iωz/ V el
Γ EELS (ω)= 1 πω v dv E ind ( r ,ω) J * ( r ,ω)
Γ EELS (ω)= e πω + dz E z ind ( R 0 ,z,ω ) e iωz/ V el
ρ( r ,ω)= 1 ε 0 ε r E ( r ,ω)

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