Abstract

We experimentally and theoretically study the interplay between capacitive electric and inductive magnetic couplings in infrared metamaterials consisting of densely-packed three-dimensional (3D) meta-atoms. The meta-atom is made of metal-stress-driven assembled 3D split-ring resonators to exhibit strong bi-anisotropy, where electric and magnetic resonances occur simultaneously. By varying the spatial arrangement of the arrayed meta-atoms, the mutual coupling between meta-atoms dramatically modifies their mode profiles and resultant spectral responses. The corresponding numerical simulations evidently retrieved current densities and magnetic field strengths, as well as the transmittance, to reveal the important resonant behavior in the coupled meta-atom systems. We conclude that the mutual electric coupling between the neighboring meta-atoms plays a crucial role to the scattering behaviors of the bi-anisotropic metamaterials.

© 2017 Optical Society of America

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    [Crossref]
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    [Crossref]

2016 (2)

L. Cong, Y. K. Srivastava, and R. Singh, “Near-Field Inductive Coupling Induced Polarization Control in Metasurfaces,” Adv. Opt. Mater. 4(6), 848–852 (2016).
[Crossref]

N. Xu, R. Singh, and W. Zhang, “High-Q lattice mode matched structural resonances in terahertz metasurfaces,” Appl. Phys. Lett. 109(2), 021108 (2016).
[Crossref]

2015 (5)

C.-C. Chen, A. Ishikawa, Y.-H. Tang, M.-H. Shiao, D. P. Tsai, and T. Tanaka, “Uniaxial-isotropic Metamaterials by Three-Dimensional Split-Ring Resonators,” Adv. Opt. Mater. 3(1), 44–48 (2015).
[Crossref]

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications,” Phys. Rev. B 91(11), 115119 (2015).
[Crossref]

W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
[Crossref]

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient Nonlinear Pancharatnam-Berry Metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
[Crossref] [PubMed]

2014 (2)

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[Crossref]

2012 (3)

C. C. Chen, C. T. Hsiao, S. Sun, K.-Y. Yang, P. C. Wu, W. T. Chen, Y. H. Tang, Y.-F. Chau, E. Plum, G.-Y. Guo, N. I. Zheludev, and D. P. Tsai, “Fabrication of three dimensional split ring resonators by stress-driven assembly method,” Opt. Express 20(9), 9415–9420 (2012).
[Crossref] [PubMed]

P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
[Crossref]

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
[Crossref]

2011 (1)

2010 (2)

D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, J. C. Ginn, A. R. Ellis, I. Brener, and M. B. Sinclair, “Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers,” Adv. Mater. 22(44), 5053–5057 (2010).
[Crossref] [PubMed]

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic Photonic Metamaterials,” IEEE J. Sel. Top. Quantum Electron. 16(2), 367–375 (2010).
[Crossref]

2009 (2)

2008 (2)

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] [PubMed]

2007 (5)

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi., A Appl. Mater. Sci. 204(11), 3886–3900 (2007).
[Crossref]

O. Merchiers, F. Moreno, F. González, and J. M. Saiz, “Light scattering by an ensemble of interacting dipolar particles with both electric and magnetic polarizabilities,” Phys. Rev. A 76(4), 043834 (2007).
[Crossref]

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[Crossref]

I. V. Shadrivov, D. A. Powell, S. K. Morrison, Y. S. Kivshar, and G. N. Milford, “Scattering of electromagnetic waves in metamaterial superlattices,” Appl. Phys. Lett. 90(20), 201919 (2007).
[Crossref]

I. V. Shadrivov, A. N. Reznik, and Y. S. Kivshar, “Magnetoinductive waves in arrays of split-ring resonators,” Physica B 394(2), 180–183 (2007).
[Crossref]

2006 (2)

T. Tanaka, A. Ishikawa, and S. Kawata, “Two-photon-induced reduction of metal ions for fabricating three-dimensional electrically conductive metallic microstructure,” Appl. Phys. Lett. 88(8), 081107 (2006).
[Crossref]

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]

2004 (1)

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[Crossref] [PubMed]

1999 (1)

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]

1998 (1)

1980 (1)

H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980).
[Crossref]

Alaee, R.

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications,” Phys. Rev. B 91(11), 115119 (2015).
[Crossref]

Albooyeh, M.

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications,” Phys. Rev. B 91(11), 115119 (2015).
[Crossref]

Alù, A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient Nonlinear Pancharatnam-Berry Metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
[Crossref] [PubMed]

Averitt, R. D.

Belkin, M. A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient Nonlinear Pancharatnam-Berry Metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
[Crossref] [PubMed]

Brener, I.

D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, J. C. Ginn, A. R. Ellis, I. Brener, and M. B. Sinclair, “Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers,” Adv. Mater. 22(44), 5053–5057 (2010).
[Crossref] [PubMed]

Burckel, D. B.

D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, J. C. Ginn, A. R. Ellis, I. Brener, and M. B. Sinclair, “Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers,” Adv. Mater. 22(44), 5053–5057 (2010).
[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]

Chau, Y.-F.

Chen, C. C.

Chen, C.-C.

C.-C. Chen, A. Ishikawa, Y.-H. Tang, M.-H. Shiao, D. P. Tsai, and T. Tanaka, “Uniaxial-isotropic Metamaterials by Three-Dimensional Split-Ring Resonators,” Adv. Opt. Mater. 3(1), 44–48 (2015).
[Crossref]

Chen, J.-W.

W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

Chen, T.-Y.

W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

Chen, W. T.

W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

C. C. Chen, C. T. Hsiao, S. Sun, K.-Y. Yang, P. C. Wu, W. T. Chen, Y. H. Tang, Y.-F. Chau, E. Plum, G.-Y. Guo, N. I. Zheludev, and D. P. Tsai, “Fabrication of three dimensional split ring resonators by stress-driven assembly method,” Opt. Express 20(9), 9415–9420 (2012).
[Crossref] [PubMed]

P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
[Crossref]

Chen, Y.-H.

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

Cheng, B. H.

W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

Chiang, H. P.

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

Ciracì, C.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
[Crossref]

Cong, L.

L. Cong, Y. K. Srivastava, and R. Singh, “Near-Field Inductive Coupling Induced Polarization Control in Metasurfaces,” Adv. Opt. Mater. 4(6), 848–852 (2016).
[Crossref]

Djurišic, A. B.

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]

Economou, E. N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004).
[Crossref]

Elazar, J. M.

Ellenbogen, T.

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
[Crossref]

Ellis, A. R.

D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, J. C. Ginn, A. R. Ellis, I. Brener, and M. B. Sinclair, “Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers,” Adv. Mater. 22(44), 5053–5057 (2010).
[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]

Fan, K.

Fedotov, V. A.

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[Crossref]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009).
[Crossref] [PubMed]

Fu, L.

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] [PubMed]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi., A Appl. Mater. Sci. 204(11), 3886–3900 (2007).
[Crossref]

García de Abajo, F. J.

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[Crossref]

Giessen, H.

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] [PubMed]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[Crossref]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi., A Appl. Mater. Sci. 204(11), 3886–3900 (2007).
[Crossref]

Ginn, J. C.

D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, J. C. Ginn, A. R. Ellis, I. Brener, and M. B. Sinclair, “Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers,” Adv. Mater. 22(44), 5053–5057 (2010).
[Crossref] [PubMed]

Gomez-Diaz, J. S.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient Nonlinear Pancharatnam-Berry Metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
[Crossref] [PubMed]

González, F.

O. Merchiers, F. Moreno, F. González, and J. M. Saiz, “Light scattering by an ensemble of interacting dipolar particles with both electric and magnetic polarizabilities,” Phys. Rev. A 76(4), 043834 (2007).
[Crossref]

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H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi., A Appl. Mater. Sci. 204(11), 3886–3900 (2007).
[Crossref]

Guo, G.-Y.

Guo, H.

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] [PubMed]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi., A Appl. Mater. Sci. 204(11), 3886–3900 (2007).
[Crossref]

Hendler, N.

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
[Crossref]

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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]

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P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
[Crossref]

C. C. Chen, C. T. Hsiao, S. Sun, K.-Y. Yang, P. C. Wu, W. T. Chen, Y. H. Tang, Y.-F. Chau, E. Plum, G.-Y. Guo, N. I. Zheludev, and D. P. Tsai, “Fabrication of three dimensional split ring resonators by stress-driven assembly method,” Opt. Express 20(9), 9415–9420 (2012).
[Crossref] [PubMed]

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W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

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P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

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W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
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C.-C. Chen, A. Ishikawa, Y.-H. Tang, M.-H. Shiao, D. P. Tsai, and T. Tanaka, “Uniaxial-isotropic Metamaterials by Three-Dimensional Split-Ring Resonators,” Adv. Opt. Mater. 3(1), 44–48 (2015).
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T. Tanaka, A. Ishikawa, and S. Kawata, “Two-photon-induced reduction of metal ions for fabricating three-dimensional electrically conductive metallic microstructure,” Appl. Phys. Lett. 88(8), 081107 (2006).
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N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004).
[Crossref]

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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] [PubMed]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[Crossref]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi., A Appl. Mater. Sci. 204(11), 3886–3900 (2007).
[Crossref]

Katsarakis, N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004).
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T. Tanaka, A. Ishikawa, and S. Kawata, “Two-photon-induced reduction of metal ions for fabricating three-dimensional electrically conductive metallic microstructure,” Appl. Phys. Lett. 88(8), 081107 (2006).
[Crossref]

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N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
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I. V. Shadrivov, A. N. Reznik, and Y. S. Kivshar, “Magnetoinductive waves in arrays of split-ring resonators,” Physica B 394(2), 180–183 (2007).
[Crossref]

I. V. Shadrivov, D. A. Powell, S. K. Morrison, Y. S. Kivshar, and G. N. Milford, “Scattering of electromagnetic waves in metamaterial superlattices,” Appl. Phys. Lett. 90(20), 201919 (2007).
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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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R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications,” Phys. Rev. B 91(11), 115119 (2015).
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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).
[Crossref]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004).
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C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic Photonic Metamaterials,” IEEE J. Sel. Top. Quantum Electron. 16(2), 367–375 (2010).
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Lederer, F.

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications,” Phys. Rev. B 91(11), 115119 (2015).
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M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient Nonlinear Pancharatnam-Berry Metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
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W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
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C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic Photonic Metamaterials,” IEEE J. Sel. Top. Quantum Electron. 16(2), 367–375 (2010).
[Crossref]

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]

Liu, A. Q.

P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
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N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
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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] [PubMed]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[Crossref]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi., A Appl. Mater. Sci. 204(11), 3886–3900 (2007).
[Crossref]

Majewski, M. L.

Merchiers, O.

O. Merchiers, F. Moreno, F. González, and J. M. Saiz, “Light scattering by an ensemble of interacting dipolar particles with both electric and magnetic polarizabilities,” Phys. Rev. A 76(4), 043834 (2007).
[Crossref]

Milford, G. N.

I. V. Shadrivov, D. A. Powell, S. K. Morrison, Y. S. Kivshar, and G. N. Milford, “Scattering of electromagnetic waves in metamaterial superlattices,” Appl. Phys. Lett. 90(20), 201919 (2007).
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O. Merchiers, F. Moreno, F. González, and J. M. Saiz, “Light scattering by an ensemble of interacting dipolar particles with both electric and magnetic polarizabilities,” Phys. Rev. A 76(4), 043834 (2007).
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Morrison, S. K.

I. V. Shadrivov, D. A. Powell, S. K. Morrison, Y. S. Kivshar, and G. N. Milford, “Scattering of electromagnetic waves in metamaterial superlattices,” Appl. Phys. Lett. 90(20), 201919 (2007).
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D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
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M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient Nonlinear Pancharatnam-Berry Metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
[Crossref] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
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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).
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Plum, E.

Poutrina, E.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
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Powell, D. A.

I. V. Shadrivov, D. A. Powell, S. K. Morrison, Y. S. Kivshar, and G. N. Milford, “Scattering of electromagnetic waves in metamaterial superlattices,” Appl. Phys. Lett. 90(20), 201919 (2007).
[Crossref]

Rakic, A. D.

Reznik, A. N.

I. V. Shadrivov, A. N. Reznik, and Y. S. Kivshar, “Magnetoinductive waves in arrays of split-ring resonators,” Physica B 394(2), 180–183 (2007).
[Crossref]

Rill, M. S.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic Photonic Metamaterials,” IEEE J. Sel. Top. Quantum Electron. 16(2), 367–375 (2010).
[Crossref]

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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]

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R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications,” Phys. Rev. B 91(11), 115119 (2015).
[Crossref]

Saiz, J. M.

O. Merchiers, F. Moreno, F. González, and J. M. Saiz, “Light scattering by an ensemble of interacting dipolar particles with both electric and magnetic polarizabilities,” Phys. Rev. A 76(4), 043834 (2007).
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V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
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C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
[Crossref]

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).
[Crossref]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[Crossref] [PubMed]

Schweizer, H.

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] [PubMed]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi., A Appl. Mater. Sci. 204(11), 3886–3900 (2007).
[Crossref]

Segal, N.

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
[Crossref]

Shadrivov, I. V.

I. V. Shadrivov, A. N. Reznik, and Y. S. Kivshar, “Magnetoinductive waves in arrays of split-ring resonators,” Physica B 394(2), 180–183 (2007).
[Crossref]

I. V. Shadrivov, D. A. Powell, S. K. Morrison, Y. S. Kivshar, and G. N. Milford, “Scattering of electromagnetic waves in metamaterial superlattices,” Appl. Phys. Lett. 90(20), 201919 (2007).
[Crossref]

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R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Shiao, M.-H.

C.-C. Chen, A. Ishikawa, Y.-H. Tang, M.-H. Shiao, D. P. Tsai, and T. Tanaka, “Uniaxial-isotropic Metamaterials by Three-Dimensional Split-Ring Resonators,” Adv. Opt. Mater. 3(1), 44–48 (2015).
[Crossref]

Simovski, C.

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications,” Phys. Rev. B 91(11), 115119 (2015).
[Crossref]

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D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, J. C. Ginn, A. R. Ellis, I. Brener, and M. B. Sinclair, “Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers,” Adv. Mater. 22(44), 5053–5057 (2010).
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N. Xu, R. Singh, and W. Zhang, “High-Q lattice mode matched structural resonances in terahertz metasurfaces,” Appl. Phys. Lett. 109(2), 021108 (2016).
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L. Cong, Y. K. Srivastava, and R. Singh, “Near-Field Inductive Coupling Induced Polarization Control in Metasurfaces,” Adv. Opt. Mater. 4(6), 848–852 (2016).
[Crossref]

Smith, D. R.

C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[Crossref] [PubMed]

Soukoulis, C. M.

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]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004).
[Crossref]

Srivastava, Y. K.

L. Cong, Y. K. Srivastava, and R. Singh, “Near-Field Inductive Coupling Induced Polarization Control in Metasurfaces,” Adv. Opt. Mater. 4(6), 848–852 (2016).
[Crossref]

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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]

Strikwerda, A. C.

Sun, G.

W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
[Crossref]

Sun, S.

Tanaka, T.

C.-C. Chen, A. Ishikawa, Y.-H. Tang, M.-H. Shiao, D. P. Tsai, and T. Tanaka, “Uniaxial-isotropic Metamaterials by Three-Dimensional Split-Ring Resonators,” Adv. Opt. Mater. 3(1), 44–48 (2015).
[Crossref]

T. Tanaka, A. Ishikawa, and S. Kawata, “Two-photon-induced reduction of metal ions for fabricating three-dimensional electrically conductive metallic microstructure,” Appl. Phys. Lett. 88(8), 081107 (2006).
[Crossref]

Tang, Y. H.

Tang, Y.-H.

C.-C. Chen, A. Ishikawa, Y.-H. Tang, M.-H. Shiao, D. P. Tsai, and T. Tanaka, “Uniaxial-isotropic Metamaterials by Three-Dimensional Split-Ring Resonators,” Adv. Opt. Mater. 3(1), 44–48 (2015).
[Crossref]

Tao, H.

Ten Eyck, G. A.

D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, J. C. Ginn, A. R. Ellis, I. Brener, and M. B. Sinclair, “Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers,” Adv. Mater. 22(44), 5053–5057 (2010).
[Crossref] [PubMed]

Tsai, D. P.

W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

C.-C. Chen, A. Ishikawa, Y.-H. Tang, M.-H. Shiao, D. P. Tsai, and T. Tanaka, “Uniaxial-isotropic Metamaterials by Three-Dimensional Split-Ring Resonators,” Adv. Opt. Mater. 3(1), 44–48 (2015).
[Crossref]

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

C. C. Chen, C. T. Hsiao, S. Sun, K.-Y. Yang, P. C. Wu, W. T. Chen, Y. H. Tang, Y.-F. Chau, E. Plum, G.-Y. Guo, N. I. Zheludev, and D. P. Tsai, “Fabrication of three dimensional split ring resonators by stress-driven assembly method,” Opt. Express 20(9), 9415–9420 (2012).
[Crossref] [PubMed]

P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
[Crossref]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009).
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Tymchenko, M.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient Nonlinear Pancharatnam-Berry Metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
[Crossref] [PubMed]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
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Wegener, M.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic Photonic Metamaterials,” IEEE J. Sel. Top. Quantum Electron. 16(2), 367–375 (2010).
[Crossref]

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]

Wendt, J. R.

D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, J. C. Ginn, A. R. Ellis, I. Brener, and M. B. Sinclair, “Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers,” Adv. Mater. 22(44), 5053–5057 (2010).
[Crossref] [PubMed]

Wu, P. C.

W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
[Crossref] [PubMed]

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
[Crossref]

C. C. Chen, C. T. Hsiao, S. Sun, K.-Y. Yang, P. C. Wu, W. T. Chen, Y. H. Tang, Y.-F. Chau, E. Plum, G.-Y. Guo, N. I. Zheludev, and D. P. Tsai, “Fabrication of three dimensional split ring resonators by stress-driven assembly method,” Opt. Express 20(9), 9415–9420 (2012).
[Crossref] [PubMed]

Xu, N.

N. Xu, R. Singh, and W. Zhang, “High-Q lattice mode matched structural resonances in terahertz metasurfaces,” Appl. Phys. Lett. 109(2), 021108 (2016).
[Crossref]

Yang, K.-Y.

P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

C. C. Chen, C. T. Hsiao, S. Sun, K.-Y. Yang, P. C. Wu, W. T. Chen, Y. H. Tang, Y.-F. Chau, E. Plum, G.-Y. Guo, N. I. Zheludev, and D. P. Tsai, “Fabrication of three dimensional split ring resonators by stress-driven assembly method,” Opt. Express 20(9), 9415–9420 (2012).
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P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
[Crossref]

Yazdi, M.

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications,” Phys. Rev. B 91(11), 115119 (2015).
[Crossref]

Zhang, W.

N. Xu, R. Singh, and W. Zhang, “High-Q lattice mode matched structural resonances in terahertz metasurfaces,” Appl. Phys. Lett. 109(2), 021108 (2016).
[Crossref]

Zhang, X.

Zheludev, N. I.

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[Crossref]

P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
[Crossref]

C. C. Chen, C. T. Hsiao, S. Sun, K.-Y. Yang, P. C. Wu, W. T. Chen, Y. H. Tang, Y.-F. Chau, E. Plum, G.-Y. Guo, N. I. Zheludev, and D. P. Tsai, “Fabrication of three dimensional split ring resonators by stress-driven assembly method,” Opt. Express 20(9), 9415–9420 (2012).
[Crossref] [PubMed]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009).
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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).
[Crossref]

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N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
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Adv. Mater. (2)

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
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D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, J. C. Ginn, A. R. Ellis, I. Brener, and M. B. Sinclair, “Micrometer-Scale Cubic Unit Cell 3D Metamaterial Layers,” Adv. Mater. 22(44), 5053–5057 (2010).
[Crossref] [PubMed]

Adv. Opt. Mater. (2)

C.-C. Chen, A. Ishikawa, Y.-H. Tang, M.-H. Shiao, D. P. Tsai, and T. Tanaka, “Uniaxial-isotropic Metamaterials by Three-Dimensional Split-Ring Resonators,” Adv. Opt. Mater. 3(1), 44–48 (2015).
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L. Cong, Y. K. Srivastava, and R. Singh, “Near-Field Inductive Coupling Induced Polarization Control in Metasurfaces,” Adv. Opt. Mater. 4(6), 848–852 (2016).
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Appl. Opt. (1)

Appl. Phys. Lett. (5)

N. Xu, R. Singh, and W. Zhang, “High-Q lattice mode matched structural resonances in terahertz metasurfaces,” Appl. Phys. Lett. 109(2), 021108 (2016).
[Crossref]

I. V. Shadrivov, D. A. Powell, S. K. Morrison, Y. S. Kivshar, and G. N. Milford, “Scattering of electromagnetic waves in metamaterial superlattices,” Appl. Phys. Lett. 90(20), 201919 (2007).
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N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84(15), 2943–2945 (2004).
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T. Tanaka, A. Ishikawa, and S. Kawata, “Two-photon-induced reduction of metal ions for fabricating three-dimensional electrically conductive metallic microstructure,” Appl. Phys. Lett. 88(8), 081107 (2006).
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P. C. Wu, G. Sun, W. T. Chen, K.-Y. Yang, Y.-W. Huang, Y.-H. Chen, H. L. Huang, W.-L. Hsu, H. P. Chiang, and D. P. Tsai, “Vertical split-ring resonator based nanoplasmonic sensor,” Appl. Phys. Lett. 105(3), 033105 (2014).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic Photonic Metamaterials,” IEEE J. Sel. Top. Quantum Electron. 16(2), 367–375 (2010).
[Crossref]

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]

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Nanophotonics (1)

P. C. Wu, W. T. Chen, K.-Y. Yang, C. T. Hsiao, G. Sun, A. Q. Liu, N. I. Zheludev, and D. P. Tsai, “Magnetic plasmon induced transparency in three-dimensional metamolecules,” Nanophotonics 1(2), 131–138 (2012).
[Crossref]

Nat. Mater. (1)

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] [PubMed]

Nat. Photonics (2)

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[Crossref]

N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, “Controlling light with metamaterial-based nonlinear photonic crystals,” Nat. Photonics 9(3), 180–184 (2015).
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Opt. Express (3)

Phys. Rev. A (1)

O. Merchiers, F. Moreno, F. González, and J. M. Saiz, “Light scattering by an ensemble of interacting dipolar particles with both electric and magnetic polarizabilities,” Phys. Rev. A 76(4), 043834 (2007).
[Crossref]

Phys. Rev. B (3)

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[Crossref]

R. Alaee, M. Albooyeh, M. Yazdi, N. Komjani, C. Simovski, F. Lederer, and C. Rockstuhl, “Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications,” Phys. Rev. B 91(11), 115119 (2015).
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C. Ciracì, E. Poutrina, M. Scalora, and D. R. Smith, “Origin of second-harmonic generation enhancement in optical split-ring resonators,” Phys. Rev. B 85(20), 201403 (2012).
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M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient Nonlinear Pancharatnam-Berry Metasurfaces,” Phys. Rev. Lett. 115(20), 207403 (2015).
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D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[Crossref] [PubMed]

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H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, “Negative permeability around 630 nm in nanofabricated vertical meander metamaterials,” Phys. Status Solidi., A Appl. Mater. Sci. 204(11), 3886–3900 (2007).
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Physica B (1)

I. V. Shadrivov, A. N. Reznik, and Y. S. Kivshar, “Magnetoinductive waves in arrays of split-ring resonators,” Physica B 394(2), 180–183 (2007).
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F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
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W.-L. Hsu, P. C. Wu, J.-W. Chen, T.-Y. Chen, B. H. Cheng, W. T. Chen, Y.-W. Huang, C. Y. Liao, G. Sun, and D. P. Tsai, “Vertical split-ring resonator based anomalous beam steering with high extinction ratio,” Sci. Rep. 5, 11226 (2015).
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Science (1)

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[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Schematics of designed planar SRR-arrays and a unit 3D-SRR with fixed geometric parameters of P x =5.8μm , l arm =2.5μm , w arm =125nm , l pad =300nm , w pad =250nm : (a) rectangular arrays with P y of 0.8,1.3,2.3,3.3μm . (b) interlacing-rectangular arrays by shifting the neighboring rows by half P x of rectangular arrays with P y =0.8,1.3μm . (c) 3D geometric parameters with G=1.3μm , D=2μm , and H=1.9μm .

Fig. 2
Fig. 2

(a) The red dot and dashed boxes represent respectively the unit cells and boundaries of a rectangular array for numerical calculations. (b) The blue dot and boxes represent respectively the unit cells and boundaries of an interlacing-rectangular array for numerical calculations. (c) Three periodic boundary conditions for an interlacing-rectangular array with A-A, B-B, and C-C.

Fig. 3
Fig. 3

(a–f) Oblique-viewed SEM images of 3D SRRs. The rectangular arrays with P y of (a) 0.8, (b) 1.3, (c) 2.3, and (d) 3.3μm . The interlacing-rectangular arrays by shifting the neighboring rows by half P x with P y of (e) 0.8, (f) 1.3μm .

Fig. 4
Fig. 4

Transmission spectra of rectangular arrays with P y =0.8,1.3,2.3,3.3μm and interlacing–rectangular arrays with P y =0.8,1.3μm . (a) Experimental characterizations by FTIR. (b) Numerical simulations by COMSOL Multiphysics.

Fig. 5
Fig. 5

(a) The current density, J x , of 3D-SRR arrays. The inset shows the J x distribution inside a 3D SRR under the resonance. (b) The magnetic field norm around 3D-SRR arrays. The inset shows the H distribution around a 3D SRR under the resonance. (c) The maximum current densities/magnetic field strengths versus inter-distances between SRRs.

Fig. 6
Fig. 6

Schematic diagram of the mutual electric and magnetic couplings for (a) a rectangular array. (b) an interlacing-rectangular array.

Fig. 7
Fig. 7

Scattering power of multipole moments in both rectangular and interlacing-rectangular arrays with P y =0.8μm where P stands for electric dipole and M for magnetic dipole.

Equations (1)

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ϖ LC = 1 LC .

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