Coupling strength of complex plasmonic structures in the multiple dipole approximation

doi:10.1364/OE.19.022156

Coupling strength of complex plasmonic structures in the multiple dipole approximation

Lutz Langguth and Harald Giessen »View Author Affiliations

Optics Express, Vol. 19, Issue 22, pp. 22156-22166 (2011)
http://dx.doi.org/10.1364/OE.19.022156

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Abstract

We present a simple model to calculate the spatial dependence of the interaction strength between two plasmonic objects. Our approach is based on a multiple dipole approximation and utilizes the current distributions at the resonances in single objects. To obtain the interaction strength, we compute the potential energy of discrete weighted dipoles associated with the current distributions of the plasmonic modes in the scattered fields of their mutual partners. We investigate in detail coupled stacked plasmonic wires, stereometamaterials and plasmon-induced transparency materials. Our calculation scheme includes retardation and can be carried out in seconds on a standard PC.

OCIS Codes
(160.3918) Materials : Metamaterials
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Plasmonics

History
Original Manuscript: June 7, 2011
Revised Manuscript: July 9, 2011
Manuscript Accepted: July 11, 2011
Published: October 24, 2011

Virtual Issues
Collective Phenomena (2011) Optics Express

Citation
Lutz Langguth and Harald Giessen, "Coupling strength of complex plasmonic structures in the multiple dipole approximation," Opt. Express 19, 22156-22166 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-22156

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References

C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7, 318–322 (2007). [CrossRef] [PubMed]
N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19, 3628–3632 (2007). [CrossRef]
B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000). [CrossRef] [PubMed]
S.-C. Yang, H. Kobori, C.-L. He, M.-H. Lin, H.-Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010). [CrossRef] [PubMed]
S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004). [CrossRef] [PubMed]
N. Liu and H. Giessen “Coupling effects in optical metamaterials,” Angew. Chem., Int. Ed. 49, 9838–9852 (2010). [CrossRef]
M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A 7, S12–S22 (2005).
V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007). [CrossRef]
N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7, 31–37 (2008). [CrossRef]
N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3, 157–162 (2009). [CrossRef]
D. A. Powell, K. Hannam, I. V. Shadrivov, and Y. S. Kivshar, “Near-field interaction of twisted split-ring resonators,” Phys. Rev. B 83, 235420 (2011). [CrossRef]
N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009). [CrossRef] [PubMed]
S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008). [CrossRef] [PubMed]
N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009). [CrossRef] [PubMed]
M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10, 2721–2726 (2010). [CrossRef] [PubMed]
J. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010). [CrossRef] [PubMed]
J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10, 3184–3189 (2010). [CrossRef] [PubMed]
H. Liu, J. X. Cao, and S. N. Zhu, “Lagrange model for the chiral optical properties of stereometamaterials,” Phys. Rev. B 81, 241403 (2010). [CrossRef]
B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010). [CrossRef]
N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010). [CrossRef] [PubMed]
E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120, 5444–5454 (2004). [CrossRef] [PubMed]
E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003). [CrossRef] [PubMed]
P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004). [CrossRef]
T. J. Davis, D. E. Gomez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10, 2618–2625 (2010). [CrossRef] [PubMed]
I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magneto-electric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83, 245102 (2011). [CrossRef]
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. Express 14, 8827–8836 (2006). [CrossRef] [PubMed]
J. Dorfmüller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010). [CrossRef] [PubMed]
J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009). [CrossRef] [PubMed]
T. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007). [CrossRef]
CST. CST Microwave Studio (2009).
C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70, 37 (2002). [CrossRef]
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,” Science 325, 1513–1515 (2009). [CrossRef] [PubMed]
N. Liu, M. Hentschel, Th. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science 332, 1407–1410 (2011). [CrossRef] [PubMed]

Alivisatos, A. P.
Aussenegg, F. R.
Bade, K.
Bao, J.
Bao, K.
Bardhan, R.
Cao, J. X.
Capasso, F.
Chen, H.-Y.
Chong, C. T.
Dahmen, C.
Davis, T. J.
Decker, M.
Ditlbacher, H.
Dorfmüller, J.
Economou, E. N.
Enkrich, C.
Etrich, C.
Fan, J.
Fan, J. A.
Fleischhauer, M.
Fu, L.
Gansel, J. K.
Garrido Alzar, C. L.
Genov, D. A.
Giessen, H.
Gomez, D. E.
Gundogdu, T. F.
Guo, H.
Gwo, S.
Halas, N. J.
Hannam, K.
Hao, F.
He, C.-L.
Hentschel, M.
Kafesaki, M.
Kaiser, S.
Kampfrath, T.
Kanehara, M.
Kästel, J.
Kern, K.
Khunsin, W.
Kivshar, Y. S.
Kobori, H.
Koenderink, A. F.
Koschny, T.
Krenn, J. R.
Kuhl, J.
Kundu, J.
Lamprecht, B.
Langguth, L.
Lassiter, J. B.
Lechner, R. T.
Lederer, F.
Leitner, A.
Li, C.
Li, K.
Lin, M.-H.
Linden, S.
Liu, H.
Liu, M.
Liu, N.
Luk’yanchuk, B.
Maier, S. A.
Manoharan, V. N.
Martinez, M. A. G.
Mesch, M.
Meyrath, T.
Moshchalkov, V. V.
Nordlander, P.
Nussenzveig, P.
Oubre, C.
Penciu, R. S.
Pertsch, T.
Pfau, T.
Powell, D. A.
Prodan, E.
Radloff, C.
Rill, M. S.
Rockstuhl, C.
Saile, V.
Saliba, M.
Schider, G.
Schmidt, B.
Schweizer, H.
Sersic, I.
Shadrivov, I. V.
Shalaev, V. M.
Shvets, G.
Sobhani, H.
Sonnefraud, Y.
Soukoulis, C. M.
Stockman, M. I.
Teranishi, T.
Thiel, M.
Tuambilangana, C.
Van Dorpe, P.
Verellen, N.
Vernon, K. C.
Vogelgesang, R.
von Freymann, G.
von Plessen, G.
Wang, Y.
Wegener, M.
Weiss, T.
Weiss, Th.
Weitz, R. T.
Wu, C.
Yang, S.-C.
Zentgraf, T.
Zhang, S.
Zhang, X.
Zheludev, N. I.
Zhou, J.
Zhu, S.
Zhu, S. N.

Adv. Mater.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19, 3628–3632 (2007). [CrossRef]

Am. J. Phys.

C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70, 37 (2002). [CrossRef]

Angew. Chem., Int. Ed.

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

J. Chem. Phys.

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120, 5444–5454 (2004). [CrossRef] [PubMed]

J. Opt. A

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A 7, S12–S22 (2005).

Nano Lett.

S.-C. Yang, H. Kobori, C.-L. He, M.-H. Lin, H.-Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010). [CrossRef] [PubMed]
N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, “Fano resonances in individual coherent plasmonic nanocavities,” Nano Lett. 9, 1663–1667 (2009). [CrossRef] [PubMed]
M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10, 2721–2726 (2010). [CrossRef] [PubMed]
J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10, 3184–3189 (2010). [CrossRef] [PubMed]
C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7, 318–322 (2007). [CrossRef] [PubMed]
P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004). [CrossRef]
T. J. Davis, D. E. Gomez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10, 2618–2625 (2010). [CrossRef] [PubMed]
J. Dorfmüller, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010). [CrossRef] [PubMed]
J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009). [CrossRef] [PubMed]
N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010). [CrossRef] [PubMed]

Nat. Mater.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010). [CrossRef]
N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009). [CrossRef] [PubMed]
N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7, 31–37 (2008). [CrossRef]

Nat. Photonics

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3, 157–162 (2009). [CrossRef]
V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007). [CrossRef]

Opt. Express

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. Express 14, 8827–8836 (2006). [CrossRef] [PubMed]

Phys. Rev. B

T. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007). [CrossRef]
I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magneto-electric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83, 245102 (2011). [CrossRef]
D. A. Powell, K. Hannam, I. V. Shadrivov, and Y. S. Kivshar, “Near-field interaction of twisted split-ring resonators,” Phys. Rev. B 83, 235420 (2011). [CrossRef]
H. Liu, J. X. Cao, and S. N. Zhu, “Lagrange model for the chiral optical properties of stereometamaterials,” Phys. Rev. B 81, 241403 (2010). [CrossRef]

Phys. Rev. Lett.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008). [CrossRef] [PubMed]
B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000). [CrossRef] [PubMed]

Science

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004). [CrossRef] [PubMed]
J. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010). [CrossRef] [PubMed]
E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003). [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,” Science 325, 1513–1515 (2009). [CrossRef] [PubMed]
N. Liu, M. Hentschel, Th. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science 332, 1407–1410 (2011). [CrossRef] [PubMed]

Other

CST. CST Microwave Studio (2009).

2011, Powell, Phys. Rev. B
2011, Sersic, Phys. Rev. B
2011, Liu, Science
2010, Dorfmüller, Nano Lett.
2010, Davis, Nano Lett.
2010, Yang, Nano Lett.
2010, Liu, Angew. Chem., Int. Ed.
2010, Hentschel, Nano Lett.
2010, Fan, Science
2010, Lassiter, Nano Lett.
2010, Liu, Phys. Rev. B
2010, Luk’yanchuk, Nat. Mater.
2010, Liu, Nano Lett.
2009, Liu, Nat. Mater.
2009, Liu, Nat. Photonics
2009, Verellen, Nano Lett.
2009, Dorfmüller, Nano Lett.
2009, Gansel, Science
2008, Zhang, Phys. Rev. Lett.
2008, Liu, Nat. Mater.
2007, Shalaev, Nat. Photonics
2007, Dahmen, Nano Lett.
2007, Liu, Adv. Mater.
2007, Meyrath, Phys. Rev. B
2006, Rockstuhl, Opt. Express
2005, Kafesaki, J. Opt. A
2004, Linden, Science
2004, Prodan, J. Chem. Phys.
2004, Nordlander, Nano Lett.
2003, Prodan, Science
2002, Garrido Alzar, Am. J. Phys.
2000, Lamprecht, Phys. Rev. Lett.

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