Abstract

Electromagnetic resonance as the most important characteristic of metamaterials enables lots of exotic phenomena, such as invisible, negative refraction, man-made magnetism, etc. Conventional LC-resonance circuit model as the most authoritative and classic model is good at explaining and predicting the fundamental resonance wavelength of a metamaterial, while feels hard for high-order resonances, especially for resonance intensity (strength of resonance, determining on the performance and efficiency of metamaterial-based devices). In present work, via an easy-to-understand mass-spring model, we present a different and comprehensive insight for the resonance mechanism of metamaterials, through which both the resonance wavelengths (including the fundamental and high-order resonance wavelengths) and resonance intensities of metamaterials can be better understood. This developed theory has been well verified by different-material and different-structure resonators. This perspective will provide a broader space for exploring novel optical devices based on metamaterials (or metasurfaces).

© 2015 Optical Society of America

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2015 (5)

2014 (6)

2013 (8)

T. Roy, E. T. Rogers, and N. I. Zheludev, “Sub-wavelength focusing meta-lens,” Opt. Express 21(6), 7577–7582 (2013).
[Crossref] [PubMed]

C. Koechlin, P. Bouchon, F. Pardo, J.-L. Pelouard, and R. Haïdar, “Analytical description of subwavelength plasmonic MIM resonators and of their combination,” Opt. Express 21(6), 7025–7032 (2013).
[Crossref] [PubMed]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

C. J. Zapata-Rodríguez, J. J. Miret, S. Vuković, and M. R. Belić, “Engineered surface waves in hyperbolic metamaterials,” Opt. Express 21(16), 19113–19127 (2013).
[Crossref] [PubMed]

H. Qin and Y. Chen, “Polarization-independent terahertz metamaterial with dual-band double-negative character,” Eur. Phys. J. D 67(11), 1–7 (2013).
[Crossref]

Z. Bai, C. Hang, and G. Huang, “Subluminal and superluminal terahertz radiation in metamaterials with electromagnetically induced transparency,” Opt. Express 21(15), 17736–17744 (2013).
[Crossref] [PubMed]

J. Choi, H. Jung, H. Lee, and H. Choi, “Electromagnetic dipole coupling mechanism in layered terahertz metamaterials,” Opt. Express 21(14), 16975–16979 (2013).
[Crossref] [PubMed]

2012 (3)

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. USA 109(31), 12364–12368 (2012).
[Crossref]

B. Edwards and N. Engheta, “Experimental verification of displacement-current conduits in metamaterials-inspired optical circuitry,” Phys. Rev. Lett. 108(19), 193902 (2012).
[Crossref] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

2011 (8)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

N. Engheta, “Antenna-guided light,” Science 334(6054), 317–318 (2011).
[Crossref] [PubMed]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. Brueck, “Ultrafast nonlinear optical spectroscopy of a dual-band negative index metamaterial all-optical switching device,” Opt. Express 19(5), 3973–3983 (2011).
[Crossref] [PubMed]

C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Chiral metamaterial composed of three-dimensional plasmonic nanostructures,” Nano Lett. 11(10), 4400–4404 (2011).
[Crossref] [PubMed]

M. A. Kats, N. Yu, P. Genevet, Z. Gaburro, and F. Capasso, “Effect of radiation damping on the spectral response of plasmonic components,” Opt. Express 19(22), 21748–21753 (2011).
[Crossref] [PubMed]

J. Zuloaga and P. Nordlander, “On the energy shift between near-field and far-field peak intensities in localized plasmon systems,” Nano Lett. 11(3), 1280–1283 (2011).
[Crossref] [PubMed]

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

C. Jeppesen, S. Xiao, N. A. Mortensen, and A. Kristensen, “Extended verification of scaling behavior in split-ring resonators,” Opt. Commun. 284(3), 799–801 (2011).
[Crossref]

2010 (1)

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

2009 (5)

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
[Crossref]

C.-Y. Chen, I.-W. Un, N.-H. Tai, and T.-J. Yen, “Asymmetric coupling between subradiant and superradiant plasmonic resonances and its enhanced sensing performance,” Opt. Express 17(17), 15372–15380 (2009).
[Crossref] [PubMed]

R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19227–19232 (2009).
[Crossref] [PubMed]

D. J. Cho, W. Wu, E. Ponizovskaya, P. Chaturvedi, A. M. Bratkovsky, S.-Y. Wang, X. Zhang, F. Wang, and Y. R. Shen, “Ultrafast modulation of optical metamaterials,” Opt. Express 17(20), 17652–17657 (2009).
[Crossref] [PubMed]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

2008 (4)

2007 (5)

2006 (7)

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[Crossref] [PubMed]

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14(19), 8827–8836 (2006).
[Crossref] [PubMed]

V. Fedotov, A. Rogacheva, N. Zheludev, P. Mladyonov, and S. Prosvirnin, “Mirror that does not change the phase of reflected waves,” Appl. Phys. Lett. 88(9), 091119 (2006).
[Crossref]

X. Zhou, Q. H. Fu, J. Zhao, Y. Yang, and X. P. Zhao, “Negative permeability and subwavelength focusing of quasi-periodic dendritic cell metamaterials,” Opt. Express 14(16), 7188–7197 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31(9), 1259–1261 (2006).
[Crossref] [PubMed]

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE, J. Sel. Top. Quantum Electron. 12(6), 1097–1105 (2006).
[Crossref]

2005 (3)

T. Koschny, P. Markoš, E. N. Economou, D. Smith, D. Vier, and C. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71(24), 245105 (2005).
[Crossref]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

2004 (2)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

P. Nordlander and E. Prodan, “Plasmon hybridization in nanoparticles near metallic surfaces,” Nano Lett. 4(11), 2209–2213 (2004).
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2002 (1)

D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1985 (1)

1972 (1)

P. B. Johnson and R.-W. Christy, “Optical constants of the 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 permittivity and permeability,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

1967 (1)

A. Karlsson and O. Beckman, “Optical extinction in the colloid system NaCl: Na,” Solid State Commun. 5(10), 795–798 (1967).
[Crossref]

Adato, R.

R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19227–19232 (2009).
[Crossref] [PubMed]

Aieta, F.

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. USA 109(31), 12364–12368 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Alexander, R. W.

Altug, H.

R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19227–19232 (2009).
[Crossref] [PubMed]

Amsden, J. J.

R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19227–19232 (2009).
[Crossref] [PubMed]

Antoniou, N.

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

Aoust, G.

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. USA 109(31), 12364–12368 (2012).
[Crossref]

Ayas, S.

Bai, Y.

Bai, Z.

Bakan, G.

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Basilio, L. I.

W. A. Johnson, M. B. Sinclair, L. K. Warne, W. L. Langston, and L. I. Basilio, “An effective media toolset for use in metamaterial design,” in 2010 International Conference on Electromagnetics in Advanced Applications (2010), pp. 577–580.

Beckman, O.

A. Karlsson and O. Beckman, “Optical extinction in the colloid system NaCl: Na,” Solid State Commun. 5(10), 795–798 (1967).
[Crossref]

Belic, M. R.

Bell, R. J.

Bhattacharyya, S.

S. Ghosh, S. Bhattacharyya, Y. Kaiprath, and K. V. Srivastava, “Bandwidth-enhanced polarization-insensitive microwave metamaterial absorber and its equivalent circuit model,” J. Appl. Phys. 115(10), 104503 (2014).
[Crossref]

Blanchard, R.

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. USA 109(31), 12364–12368 (2012).
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Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
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X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Bouchon, P.

Bour, D.

Bratkovsky, A. M.

Brueck, S. R.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. Brueck, “Ultrafast nonlinear optical spectroscopy of a dual-band negative index metamaterial all-optical switching device,” Opt. Express 19(5), 3973–3983 (2011).
[Crossref] [PubMed]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

Burger, S.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE, J. Sel. Top. Quantum Electron. 12(6), 1097–1105 (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 (2005).
[Crossref] [PubMed]

Byren, R.

Cai, W.

Capasso, F.

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
[Crossref] [PubMed]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. USA 109(31), 12364–12368 (2012).
[Crossref]

M. A. Kats, N. Yu, P. Genevet, Z. Gaburro, and F. Capasso, “Effect of radiation damping on the spectral response of plasmonic components,” Opt. Express 19(22), 21748–21753 (2011).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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N. Yu, E. Cubukcu, L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, K. B. Crozier, and F. Capasso, “Bowtie plasmonic quantum cascade laser antenna,” Opt. Express 15(20), 13272–13281 (2007).
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Castanié, A.

Chaturvedi, P.

Chen, C.-Y.

Chen, Y.

H. Qin and Y. Chen, “Polarization-independent terahertz metamaterial with dual-band double-negative character,” Eur. Phys. J. D 67(11), 1–7 (2013).
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Chettiar, U. K.

Cho, D. J.

Choi, H.

Choi, J.

Christy, R.-W.

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

Corrigan, T. D.

Corzine, S.

Crozier, K. B.

Cubukcu, E.

Dana, A.

Dani, K. M.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. Brueck, “Ultrafast nonlinear optical spectroscopy of a dual-band negative index metamaterial all-optical switching device,” Opt. Express 19(5), 3973–3983 (2011).
[Crossref] [PubMed]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

de Groot, C.

S. A. Gregory, Y. Wang, C. de Groot, and O. L. Muskens, “Extremely subwavelength metal oxide direct and complementary metamaterials,” ACS Photonics 2(5), 606–614 (2015).
[Crossref]

Diehl, L.

Ding, P.

Dodds, R. K.

Dolling, G.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE, J. Sel. Top. Quantum Electron. 12(6), 1097–1105 (2006).
[Crossref]

Drachev, V. P.

Drew, H. D.

Economou, E. N.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

T. Koschny, P. Markoš, E. N. Economou, D. Smith, D. Vier, and C. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71(24), 245105 (2005).
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Edwards, B.

B. Edwards and N. Engheta, “Experimental verification of displacement-current conduits in metamaterials-inspired optical circuitry,” Phys. Rev. Lett. 108(19), 193902 (2012).
[Crossref] [PubMed]

Elson, J. M.

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427 (2012).
[Crossref] [PubMed]

Engheta, N.

B. Edwards and N. Engheta, “Experimental verification of displacement-current conduits in metamaterials-inspired optical circuitry,” Phys. Rev. Lett. 108(19), 193902 (2012).
[Crossref] [PubMed]

N. Engheta, “Antenna-guided light,” Science 334(6054), 317–318 (2011).
[Crossref] [PubMed]

Enkrich, C.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE, J. Sel. Top. Quantum Electron. 12(6), 1097–1105 (2006).
[Crossref]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31(9), 1259–1261 (2006).
[Crossref] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (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 (2005).
[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(5700), 1351–1353 (2004).
[Crossref] [PubMed]

Erramilli, S.

R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19227–19232 (2009).
[Crossref] [PubMed]

Etrich, C.

Falkner, M.

C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Chiral metamaterial composed of three-dimensional plasmonic nanostructures,” Nano Lett. 11(10), 4400–4404 (2011).
[Crossref] [PubMed]

Fan, C.

Fedotov, V.

V. Fedotov, A. Rogacheva, N. Zheludev, P. Mladyonov, and S. Prosvirnin, “Mirror that does not change the phase of reflected waves,” Appl. Phys. Lett. 88(9), 091119 (2006).
[Crossref]

Félix, S.

Feth, N.

Fu, Q. H.

Gaburro, Z.

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. USA 109(31), 12364–12368 (2012).
[Crossref]

M. A. Kats, N. Yu, P. Genevet, Z. Gaburro, and F. Capasso, “Effect of radiation damping on the spectral response of plasmonic components,” Opt. Express 19(22), 21748–21753 (2011).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Genevet, P.

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. USA 109(31), 12364–12368 (2012).
[Crossref]

M. A. Kats, N. Yu, P. Genevet, Z. Gaburro, and F. Capasso, “Effect of radiation damping on the spectral response of plasmonic components,” Opt. Express 19(22), 21748–21753 (2011).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Ghosh, S.

S. Ghosh, S. Bhattacharyya, Y. Kaiprath, and K. V. Srivastava, “Bandwidth-enhanced polarization-insensitive microwave metamaterial absorber and its equivalent circuit model,” J. Appl. Phys. 115(10), 104503 (2014).
[Crossref]

Giessen, H.

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

T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
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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(19), 8827–8836 (2006).
[Crossref] [PubMed]

Gregory, S. A.

S. A. Gregory, Y. Wang, C. de Groot, and O. L. Muskens, “Extremely subwavelength metal oxide direct and complementary metamaterials,” ACS Photonics 2(5), 606–614 (2015).
[Crossref]

Haïdar, R.

Halas, N. J.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Halterman, K.

Han, J.

Hang, C.

He, J.

Helgert, C.

C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Chiral metamaterial composed of three-dimensional plasmonic nanostructures,” Nano Lett. 11(10), 4400–4404 (2011).
[Crossref] [PubMed]

Höfler, G.

Hong, M. K.

R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19227–19232 (2009).
[Crossref] [PubMed]

Hoyer, W.

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
[Crossref]

Huang, G.

Huang, L.

L. Min, L. Huang, R. Sun, and Z. Li, “Incidence ways of electromagnetic wave and their influences on the absorption and resonant wavelength of split-ring resonators,” Plasmonics 10(1), 183–189 (2015).
[Crossref]

Jeppesen, C.

C. Jeppesen, S. Xiao, N. A. Mortensen, and A. Kristensen, “Extended verification of scaling behavior in split-ring resonators,” Opt. Commun. 284(3), 799–801 (2011).
[Crossref]

Jiang, Y.

Johnson, P. B.

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

Johnson, W. A.

W. A. Johnson, M. B. Sinclair, L. K. Warne, W. L. Langston, and L. I. Basilio, “An effective media toolset for use in metamaterial design,” in 2010 International Conference on Electromagnetics in Advanced Applications (2010), pp. 577–580.

Ju, D.

Jung, H.

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

Kaiprath, Y.

S. Ghosh, S. Bhattacharyya, Y. Kaiprath, and K. V. Srivastava, “Bandwidth-enhanced polarization-insensitive microwave metamaterial absorber and its equivalent circuit model,” J. Appl. Phys. 115(10), 104503 (2014).
[Crossref]

Kaiser, S.

T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[Crossref]

Kaplan, D. L.

R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19227–19232 (2009).
[Crossref] [PubMed]

Karlsson, A.

A. Karlsson and O. Beckman, “Optical extinction in the colloid system NaCl: Na,” Solid State Commun. 5(10), 795–798 (1967).
[Crossref]

Kats, M. A.

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. USA 109(31), 12364–12368 (2012).
[Crossref]

M. A. Kats, N. Yu, P. Genevet, Z. Gaburro, and F. Capasso, “Effect of radiation damping on the spectral response of plasmonic components,” Opt. Express 19(22), 21748–21753 (2011).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Kildishev, A. V.

Klein, M. W.

M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
[Crossref] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[Crossref] [PubMed]

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE, J. Sel. Top. Quantum Electron. 12(6), 1097–1105 (2006).
[Crossref]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31(9), 1259–1261 (2006).
[Crossref] [PubMed]

Kley, E.-B.

C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Chiral metamaterial composed of three-dimensional plasmonic nanostructures,” Nano Lett. 11(10), 4400–4404 (2011).
[Crossref] [PubMed]

Knight, M. W.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
[Crossref] [PubMed]

Koch, S. W.

Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
[Crossref]

Koechlin, C.

Kolb, P. W.

Koschny, T.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE, J. Sel. Top. Quantum Electron. 12(6), 1097–1105 (2006).
[Crossref]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

T. Koschny, P. Markoš, E. N. Economou, D. Smith, D. Vier, and C. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71(24), 245105 (2005).
[Crossref]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

Kristensen, A.

C. Jeppesen, S. Xiao, N. A. Mortensen, and A. Kristensen, “Extended verification of scaling behavior in split-ring resonators,” Opt. Commun. 284(3), 799–801 (2011).
[Crossref]

Ku, Z.

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. Brueck, “Ultrafast nonlinear optical spectroscopy of a dual-band negative index metamaterial all-optical switching device,” Opt. Express 19(5), 3973–3983 (2011).
[Crossref] [PubMed]

K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
[Crossref] [PubMed]

Kuhl, J.

Lakhtakia, A.

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
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W. A. Johnson, M. B. Sinclair, L. K. Warne, W. L. Langston, and L. I. Basilio, “An effective media toolset for use in metamaterial design,” in 2010 International Conference on Electromagnetics in Advanced Applications (2010), pp. 577–580.

Lederer, F.

C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Chiral metamaterial composed of three-dimensional plasmonic nanostructures,” Nano Lett. 11(10), 4400–4404 (2011).
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T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
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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(19), 8827–8836 (2006).
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Lee, H.

Lemoult, F.

M. Rupin, F. Lemoult, G. Lerosey, and P. Roux, “Experimental demonstration of ordered and disordered multiresonant metamaterials for lamb waves,” Phys. Rev. Lett. 112(23), 234301 (2014).
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M. Rupin, F. Lemoult, G. Lerosey, and P. Roux, “Experimental demonstration of ordered and disordered multiresonant metamaterials for lamb waves,” Phys. Rev. Lett. 112(23), 234301 (2014).
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L. Min, L. Huang, R. Sun, and Z. Li, “Incidence ways of electromagnetic wave and their influences on the absorption and resonant wavelength of split-ring resonators,” Plasmonics 10(1), 183–189 (2015).
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Lin, J.

J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
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M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
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M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
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M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31(9), 1259–1261 (2006).
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S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE, J. Sel. Top. Quantum Electron. 12(6), 1097–1105 (2006).
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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 (2005).
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S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
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Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
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Liu, M.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
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Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
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D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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Menzel, C.

C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Chiral metamaterial composed of three-dimensional plasmonic nanostructures,” Nano Lett. 11(10), 4400–4404 (2011).
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Meyrath, T.

T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
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Mladyonov, P.

V. Fedotov, A. Rogacheva, N. Zheludev, P. Mladyonov, and S. Prosvirnin, “Mirror that does not change the phase of reflected waves,” Appl. Phys. Lett. 88(9), 091119 (2006).
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N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
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Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. V. Moloney, “Classical theory for second-harmonic generation from metallic nanoparticles,” Phys. Rev. B 79(23), 235109 (2009).
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J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
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S. A. Gregory, Y. Wang, C. de Groot, and O. L. Muskens, “Extremely subwavelength metal oxide direct and complementary metamaterials,” ACS Photonics 2(5), 606–614 (2015).
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R. Adato, A. A. Yanik, J. J. Amsden, D. L. Kaplan, F. G. Omenetto, M. K. Hong, S. Erramilli, and H. Altug, “Ultra-sensitive vibrational spectroscopy of protein monolayers with plasmonic nanoantenna arrays,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19227–19232 (2009).
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Ordal, M. A.

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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Ponizovskaya, E.

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K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. Brueck, “Ultrafast nonlinear optical spectroscopy of a dual-band negative index metamaterial all-optical switching device,” Opt. Express 19(5), 3973–3983 (2011).
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P. Nordlander and E. Prodan, “Plasmon hybridization in nanoparticles near metallic surfaces,” Nano Lett. 4(11), 2209–2213 (2004).
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V. Fedotov, A. Rogacheva, N. Zheludev, P. Mladyonov, and S. Prosvirnin, “Mirror that does not change the phase of reflected waves,” Appl. Phys. Lett. 88(9), 091119 (2006).
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M. Rupin, F. Lemoult, G. Lerosey, and P. Roux, “Experimental demonstration of ordered and disordered multiresonant metamaterials for lamb waves,” Phys. Rev. Lett. 112(23), 234301 (2014).
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Rupin, M.

M. Rupin, F. Lemoult, G. Lerosey, and P. Roux, “Experimental demonstration of ordered and disordered multiresonant metamaterials for lamb waves,” Phys. Rev. Lett. 112(23), 234301 (2014).
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N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
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Schmidt, F.

S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE, J. Sel. Top. Quantum Electron. 12(6), 1097–1105 (2006).
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D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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T. Zentgraf, T. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
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Smith, D.

T. Koschny, P. Markoš, E. N. Economou, D. Smith, D. Vier, and C. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71(24), 245105 (2005).
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D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
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Soukoulis, C.

T. Koschny, P. Markoš, E. N. Economou, D. Smith, D. Vier, and C. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71(24), 245105 (2005).
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D. Smith, S. Schultz, P. Markoš, and C. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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S. Linden, C. Enkrich, G. Dolling, M. W. Klein, J. Zhou, T. Koschny, C. M. Soukoulis, S. Burger, F. Schmidt, and M. Wegener, “Photonic metamaterials: magnetism at optical frequencies,” IEEE, J. Sel. Top. Quantum Electron. 12(6), 1097–1105 (2006).
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M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31(9), 1259–1261 (2006).
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S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
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L. Min, L. Huang, R. Sun, and Z. Li, “Incidence ways of electromagnetic wave and their influences on the absorption and resonant wavelength of split-ring resonators,” Plasmonics 10(1), 183–189 (2015).
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K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, A. J. Taylor, and S. R. Brueck, “Ultrafast nonlinear optical spectroscopy of a dual-band negative index metamaterial all-optical switching device,” Opt. Express 19(5), 3973–3983 (2011).
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K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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C. Helgert, E. Pshenay-Severin, M. Falkner, C. Menzel, C. Rockstuhl, E.-B. Kley, A. Tünnermann, F. Lederer, and T. Pertsch, “Chiral metamaterial composed of three-dimensional plasmonic nanostructures,” Nano Lett. 11(10), 4400–4404 (2011).
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K. M. Dani, Z. Ku, P. C. Upadhya, R. P. Prasankumar, S. R. Brueck, and A. J. Taylor, “Subpicosecond optical switching with a negative index metamaterial,” Nano Lett. 9(10), 3565–3569 (2009).
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J. Lin, J. P. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
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S. A. Gregory, Y. Wang, C. de Groot, and O. L. Muskens, “Extremely subwavelength metal oxide direct and complementary metamaterials,” ACS Photonics 2(5), 606–614 (2015).
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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
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W. A. Johnson, M. B. Sinclair, L. K. Warne, W. L. Langston, and L. I. Basilio, “An effective media toolset for use in metamaterial design,” in 2010 International Conference on Electromagnetics in Advanced Applications (2010), pp. 577–580.

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M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of electric potential difference ∆U in a linear antenna of length l, in which a normally incident wave (along z axis) with a harmonic electric field E impinges on the antenna, θ is the polarization angle between polarization direction and antenna axis in x-y plane, and Ec denotes the coupling electric field in the antenna. (b) Representation of an optical antenna in oscillator form, where q is the charge, m is the inertial mass, x(t) is the displacement from the equilibrium position, and the electric force acting on the resonator is qEc, the deviation angle (from x axis of) of which is θ. (c) Description of the electron’s motion, the equilibrium position of the resonator is at the origin of x axis; its resonance amplitude, effective path length (EPL) and velocity are |x0 (ω)|, s and vF, respectively.
Fig. 2
Fig. 2 (a) Schematic of a gold antenna, in which the antenna’s width w = 25 nm and thickness t = 20 nm; the thickness of SiO2 substance is 40 nm. Ec is the coupling electric field induced by the electric potential difference ∆U, θ is the polarization angle between polarization direction and the antenna axis. When θ = 0, (b) transmittance spectra for these antennas of different lengths l (400 nm, 500 nm, 700 nm, 900 nm and 1000 nm); dash curves indicate the positions of resonance dips. (c) Resonance wavelengths (λ0) vary with the length l of the antenna, and the blue, red and green circulars (dash lines) denote the simulated resonance wavelengths (calculated resonance wavelengths) for the 1st-, 2nd- and 3rd- order resonances, respectively. (d) In the dash boxes d1, d2 and d3, current distributions in the 400nm-length antenna at the 1st-, 2nd- and 3rd- order resonance wavelengths, respectively. Black arrows denote electrons’ flow directions. s1i (i = 1), s2i (i = 1, 2) and s3i (i = 1, 2 and 3) denote the corresponding electrons’ EPLs for 1st-, 2nd- and 3rd- order resonances, respectively. (e) Transmittance spectra for the 400nm-length antenna under different polarization angles θ (15°, 45°, 75° and 90°); the red dash line indicates the position of the first-order resonance wavelength in transmittance spectra. (f) At 1.9 μm, current distributions in 375nm-length antenna under polarization angles θ (15°, 45°, 75° and 90°).
Fig. 3
Fig. 3 (a) Schematic of five types of variation gold antennas (A)~(E); all the antennas A~E have the same line lengths (l = 420nm), width (w = 25 nm), thicknesses (t = 20 nm) and lattice constants 450 nm, and the split angles (α) of the four A~D are 45°, 90°, 120° and 180°, respectively; their thicknesses of SiO2 substance are 40 nm; the incident wave polarized in y-axis direction normally impinges on these antennas. (b) Transmittance spectra for the five types of antenna A~E; the dash line indicates the position of their 1st-order resonance wavelengths. (c) Current distributions for the five antennas A~E at 1st-order resonance wavelength of 2.1 μm; the effective lengths along polarization direction (i.e., y-axis direction) of the five antennas are denoted by leff; black arrows denote the directions of current flow.
Fig. 4
Fig. 4 (a) Schematic of a C-shaped GaAs metamaterial unit cell, in which the length, width (w), thickness (t) and split angle (α) of the unit cell are 10 μm, 0.5 μm, 0.2 μm and 60°, respectively; the thickness of SiO2 substrate is 0.4 μm and the lattice constant is p = 4 μm. The normally incident wave (along z axis) is polarized along y axis. For different doped densities ne (1 × 1018cm−3, 1.6 × 1018cm−3, 2.5 × 1018cm−3, 4.0 × 1018cm−3, 6.3 × 1018cm−3 and 1 × 1019cm−3), (b) transmittance spectra and (c) effective permittivity (real part of εeff) spectra of the C-shaped GaAs metamaterial, in which the dash lines denote the position of the resonance wavelength of 24 μm.
Fig. 5
Fig. 5 Effective permittivity variations Δε for semiconductor (GaAs) metamaterials (red solid line) and for metallic (Ag, Al, Au, Co, Cu, Fe, Ni, Pd, Pt, Ti and W) metamaterials (circles) around the resonance wavelength of 24 μm; insets (a) and (b) denote the schematics of the unit cell of semiconductor metamaterials and metallic metamaterials, respectively; both of the two types of metamaterial unit cell have the same geometrical sizes, as shown in the caption of Fig. 4(a).

Equations (8)

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

ΔU= E c lcos(θ)
m 2 x(ω,t) 2 t +mγ x(ω,t) t +kx(ω,t)= qΔU e iωt l
x(ω,t)= qΔU ml( ω 0 2 ω 2 )+imωγl e iωt = x 0 (ω) e iωt
f 0 = c λ 0 = v F 2s
λ 0 s
λ 0 l
1 s i = 1 s + a l
D( ω )= ε 0 E 0 + q 2 n e ΔU ml( ω 0 2 ω 2 +iγω)

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