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Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation
Nils Feth, Michael König, Martin Husnik, Kai Stannigel, Jens Niegemann, Kurt Busch, Martin Wegener, and Stefan Linden »View Author Affiliations
1Institut für Nanotechnologie, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
2Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology (KIT), D-76128 Karlsruhe, Germany
3Institut für Angewandte Physik and DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), D-76128 Karlsruhe, Germany
*Corresponding author: nils.feth@kit.edu
Optics Express, Vol. 18, Issue 7, pp. 6545-6554 (2010)
http://dx.doi.org/10.1364/OE.18.006545
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Abstract
Extinction cross-section spectra of split-ring-resonator dimers have been measured at near-infrared frequencies with a sensitive spatial modulation technique. The resonance frequency of the dimer's coupled mode as well as its extinction cross-section and its quality factor depend on the relative orientation and separation of the two split-ring resonators. The findings can be interpreted in terms of electric and magnetic dipole-dipole interaction. Numerical calculations based on a Discontinuous Galerkin Time-Domain approach are in good agreement with the experiments and support our physical interpretation.
© 2010 OSA
OCIS Codes
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials
ToC Category:
Metamaterials
History
Original Manuscript: January 15, 2010
Revised Manuscript: February 23, 2010
Manuscript Accepted: February 24, 2010
Published: March 15, 2010
Citation
Nils Feth, Michael König, Martin Husnik, Kai Stannigel, Jens Niegemann, Kurt Busch, Martin Wegener, and Stefan Linden, "Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation," Opt. Express 18, 6545-6554 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-6545
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References
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- A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004). [CrossRef] [PubMed]
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- M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009). [CrossRef]
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- 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), 203901–1 (2005). [CrossRef] [PubMed]
- J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009). [CrossRef]
- K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 . [CrossRef] [PubMed]
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- A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004). [CrossRef] [PubMed]
- C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007). [CrossRef] [PubMed]
- A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009). [CrossRef] [PubMed]
- M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009). [CrossRef]
- M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009). [CrossRef] [PubMed]
- M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). [CrossRef] [PubMed]
- O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006). [CrossRef]
- A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004). [CrossRef] [PubMed]
- G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006). [CrossRef]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008). [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), 203901–1 (2005). [CrossRef] [PubMed]
- S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [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), 037402–1 (2005). [CrossRef] [PubMed]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- 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), 177401–1 (2006). [CrossRef] [PubMed]
- M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008). [CrossRef]
- 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), 037402–1 (2005). [CrossRef] [PubMed]
- I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]
- N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]
- A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009). [CrossRef] [PubMed]
- N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]
- N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008). [CrossRef]
- N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]
- N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- J. S. Hesthaven and T. Warburton, “Nodal high-order methods on unstructured grids - I. Time-domain solution of Maxwell's equations,” J. Comput. Phys. 181(1), 186–221 (2002). [CrossRef]
- W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003). [CrossRef]
- 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]
- O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006). [CrossRef]
- A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004). [CrossRef] [PubMed]
- M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008). [CrossRef]
- N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]
- N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008). [CrossRef]
- M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008). [CrossRef]
- M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). [CrossRef] [PubMed]
- I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]
- K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 . [CrossRef] [PubMed]
- J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009). [CrossRef]
- M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008). [CrossRef]
- 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), 203901–1 (2005). [CrossRef] [PubMed]
- S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
- W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003). [CrossRef]
- W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003). [CrossRef]
- W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003). [CrossRef]
- U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (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), 023901–1 (2009). [CrossRef] [PubMed]
- M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009). [CrossRef] [PubMed]
- M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009). [CrossRef]
- M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008). [CrossRef]
- M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). [CrossRef] [PubMed]
- C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative Refractive Index at Optical Wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]
- G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006). [CrossRef]
- 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), 203901–1 (2005). [CrossRef] [PubMed]
- S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
- N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]
- N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]
- N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]
- N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008). [CrossRef]
- 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), 023901–1 (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), 037402–1 (2005). [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), 037402–1 (2005). [CrossRef] [PubMed]
- K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]
- A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009). [CrossRef] [PubMed]
- O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006). [CrossRef]
- J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009). [CrossRef]
- K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 . [CrossRef] [PubMed]
- M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008). [CrossRef]
- A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009). [CrossRef] [PubMed]
- P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008). [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), 023901–1 (2009). [CrossRef] [PubMed]
- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
- 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]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003). [CrossRef]
- P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008). [CrossRef] [PubMed]
- 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]
- 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), 177401–1 (2006). [CrossRef] [PubMed]
- G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006). [CrossRef]
- C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007). [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), 203901–1 (2005). [CrossRef] [PubMed]
- K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]
- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [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), 177401–1 (2006). [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(1), 31–37 (2008). [CrossRef]
- I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]
- V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005). [CrossRef]
- M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003). [CrossRef]
- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
- K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]
- O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005). [CrossRef]
- M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003). [CrossRef]
- C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative Refractive Index at Optical Wavelengths,” Science 315(5808), 47–49 (2007). [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), 203901–1 (2005). [CrossRef] [PubMed]
- S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
- J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009). [CrossRef]
- K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 . [CrossRef] [PubMed]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- 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]
- K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]
- O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005). [CrossRef]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006). [CrossRef]
- A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004). [CrossRef] [PubMed]
- I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]
- C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007). [CrossRef] [PubMed]
- J. S. Hesthaven and T. Warburton, “Nodal high-order methods on unstructured grids - I. Time-domain solution of Maxwell's equations,” J. Comput. Phys. 181(1), 186–221 (2002). [CrossRef]
- M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009). [CrossRef]
- M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009). [CrossRef] [PubMed]
- M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008). [CrossRef]
- C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative Refractive Index at Optical Wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]
- M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). [CrossRef] [PubMed]
- G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006). [CrossRef]
- 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), 203901–1 (2005). [CrossRef] [PubMed]
- S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
- P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008). [CrossRef] [PubMed]
- K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]
- M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003). [CrossRef]
- M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003). [CrossRef]
- 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), 023901–1 (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), 037402–1 (2005). [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), 023901–1 (2009). [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), 023901–1 (2009). [CrossRef] [PubMed]
- K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]
- 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), 177401–1 (2006). [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), 203901–1 (2005). [CrossRef] [PubMed]
- S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
- N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
- O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005). [CrossRef]
- 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), 203901–1 (2005). [CrossRef] [PubMed]
Adv. Mater.
- N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008). [CrossRef]
Appl. Phys. Lett.
- O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005). [CrossRef]
- G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006). [CrossRef]
- O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006). [CrossRef]
Electron. Lett.
- M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003). [CrossRef]
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]
J. Comput. Phys.
- J. S. Hesthaven and T. Warburton, “Nodal high-order methods on unstructured grids - I. Time-domain solution of Maxwell's equations,” J. Comput. Phys. 181(1), 186–221 (2002). [CrossRef]
Nano Lett.
- K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]
- A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009). [CrossRef] [PubMed]
- C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007). [CrossRef] [PubMed]
- P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008). [CrossRef] [PubMed]
Nat. Mater.
- N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]
Nat. Photonics
- N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]
- V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]
- M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008). [CrossRef]
Opt. Commun.
- W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003). [CrossRef]
Opt. Express
- K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 . [CrossRef] [PubMed]
Opt. Lett.
- M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). [CrossRef] [PubMed]
- M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009). [CrossRef] [PubMed]
Photon. Nanostruct. - Fundamentals Appl.
- J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009). [CrossRef]
Phys. Rev. B
- M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009). [CrossRef]
Phys. Rev. Lett.
- I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]
- 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), 023901–1 (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), 037402–1 (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), 203901–1 (2005). [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), 177401–1 (2006). [CrossRef] [PubMed]
- A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004). [CrossRef] [PubMed]
Phys. Status Solidi
- F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007). [CrossRef]
Science
- S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
- C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative Refractive Index at Optical Wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]
- U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
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