Abstract

This paper investigates three-dimensional cut wire pair (CWP) behavior in vertically oriented meta-atoms. We first analyze CWP metamaterial inclusions using full-wave electromagnetic simulations. The scattering behavior of the vertical CWP differs substantially from that of the planar version of the same structure. In particular, we show that the vertical CWP supports a magnetic resonance that is solely excited by the incident magnetic field. This is in stark contrast to the bianisotropic resonant excitation of in-plane CWPs. We further show that this CWP behavior can occur in other vertical metamaterial resonators, such as back-to-back linear dipoles and back-to-back split ring resonators (SRRs), due to the strong coupling between the closely spaced metallic elements in the back-to-back configuration. In the case of SRRs, the vertical CWP mode (unexplored in previous literature) can be excited with a magnetic field that is parallel to both SRR loops, and exists in addition to the familiar fundamental resonances of the individual SRRs. In order to fully describe the scattering behavior from such dense arrays of three-dimensional structures, coupling effects between the close-packed inclusions must be included. The new flexibility afforded by using vertical resonators allows us to controllably create purely electric inclusions, purely magnetic inclusions, as well as bianisotropic inclusions, and vastly increases the degrees of freedom for the design of metafilms.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  7. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2017 (2)

D. B. Burckel, S. Campione, P. S. Davids, and M. B. Sinclair, “Three dimensional metafilms with dual channel unit cells,” Appl. Phys. Lett. 110(14), 143107 (2017).
[Crossref]

Y. Ra’di, D. L. Sounas, and A. Alù, “Metagratings: Beyond the limits of graded metasurfaces for wave front control,” Phys. Rev. Lett. 119(6), 067404 (2017).
[Crossref] [PubMed]

2015 (2)

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

D. B. Burckel, P. J. Resnick, P. S. Finnegan, M. B. Sinclair, and P. S. Davids, “Micrometer-scale Fabrication of complex three-dimensional lattice+basis structures in silicon,” Opt. Mater. Express 5(10), 2231–2239 (2015).
[Crossref]

2014 (1)

F. Monticone and A. Alu, “The quest for optical magnetism: from split-ring resonators to plasmonic nanoparticles and nanoclusters,” J. Mater. Chem. C Mater. Opt. Electron. Devices 2(43), 9059–9072 (2014).
[Crossref]

2011 (1)

2010 (5)

N. Feth, M. König, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010).
[Crossref] [PubMed]

R. S. Penciu, M. Kafesaki, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Magnetic response of nanoscale left-handed metamaterials,” Phys. Rev. B 81(23), 235111 (2010).
[Crossref]

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]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[Crossref] [PubMed]

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81(7), 075116 (2010).
[Crossref]

2006 (1)

2005 (5)

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]

2003 (1)

R. Marques, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design – theory and experiments,” IEEE Trans. Antenn. Propag. 51(10), 2572–2581 (2003).
[Crossref]

2002 (1)

R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

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]

Alu, A.

F. Monticone and A. Alu, “The quest for optical magnetism: from split-ring resonators to plasmonic nanoparticles and nanoclusters,” J. Mater. Chem. C Mater. Opt. Electron. Devices 2(43), 9059–9072 (2014).
[Crossref]

Alù, A.

Y. Ra’di, D. L. Sounas, and A. Alù, “Metagratings: Beyond the limits of graded metasurfaces for wave front control,” Phys. Rev. Lett. 119(6), 067404 (2017).
[Crossref] [PubMed]

Averitt, R. D.

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]

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Burckel, D. B.

D. B. Burckel, S. Campione, P. S. Davids, and M. B. Sinclair, “Three dimensional metafilms with dual channel unit cells,” Appl. Phys. Lett. 110(14), 143107 (2017).
[Crossref]

D. B. Burckel, P. J. Resnick, P. S. Finnegan, M. B. Sinclair, and P. S. Davids, “Micrometer-scale Fabrication of complex three-dimensional lattice+basis structures in silicon,” Opt. Mater. Express 5(10), 2231–2239 (2015).
[Crossref]

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]

Busch, K.

Cai, W.

Campione, S.

D. B. Burckel, S. Campione, P. S. Davids, and M. B. Sinclair, “Three dimensional metafilms with dual channel unit cells,” Appl. Phys. Lett. 110(14), 143107 (2017).
[Crossref]

Chen, W. T.

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[Crossref] [PubMed]

Davids, P. S.

D. B. Burckel, S. Campione, P. S. Davids, and M. B. Sinclair, “Three dimensional metafilms with dual channel unit cells,” Appl. Phys. Lett. 110(14), 143107 (2017).
[Crossref]

D. B. Burckel, P. J. Resnick, P. S. Finnegan, M. B. Sinclair, and P. S. Davids, “Micrometer-scale Fabrication of complex three-dimensional lattice+basis structures in silicon,” Opt. Mater. Express 5(10), 2231–2239 (2015).
[Crossref]

Dineen, C.

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81(7), 075116 (2010).
[Crossref]

Dolling, G.

Drachev, V. P.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[Crossref] [PubMed]

Economou, E. N.

R. S. Penciu, M. Kafesaki, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Magnetic response of nanoscale left-handed metamaterials,” Phys. Rev. B 81(23), 235111 (2010).
[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]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the far-infrared frequency regime,” Opt. Lett. 30(11), 1348–1350 (2005).
[Crossref] [PubMed]

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]

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.

Etrich, C.

Fan, K.

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Feth, N.

Finnegan, P. S.

Giessen, H.

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]

Gundogdu, T. F.

Holden, A. J.

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]

Hsu, W.-L.

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

Huang, Y.-W.

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

Husnik, M.

Kafesaki, M.

R. S. Penciu, M. Kafesaki, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Magnetic response of nanoscale left-handed metamaterials,” Phys. Rev. B 81(23), 235111 (2010).
[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]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the far-infrared frequency regime,” Opt. Lett. 30(11), 1348–1350 (2005).
[Crossref] [PubMed]

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]

Katsarakis, N.

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the far-infrared frequency regime,” Opt. Lett. 30(11), 1348–1350 (2005).
[Crossref] [PubMed]

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]

Kildishev, A. V.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[Crossref] [PubMed]

König, M.

Konstantinidis, G.

Koschny, T.

R. S. Penciu, M. Kafesaki, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Magnetic response of nanoscale left-handed metamaterials,” Phys. Rev. B 81(23), 235111 (2010).
[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]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the far-infrared frequency regime,” Opt. Lett. 30(11), 1348–1350 (2005).
[Crossref] [PubMed]

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]

Kostopoulos, A.

Kuhl, J.

Lederer, F.

Liao, C. Y.

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

Linden, S.

Liu, A. Q.

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Marques, R.

R. Marques, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design – theory and experiments,” IEEE Trans. Antenn. Propag. 51(10), 2572–2581 (2003).
[Crossref]

R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

Martel, J.

R. Marques, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design – theory and experiments,” IEEE Trans. Antenn. Propag. 51(10), 2572–2581 (2003).
[Crossref]

Medina, F.

R. Marques, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design – theory and experiments,” IEEE Trans. Antenn. Propag. 51(10), 2572–2581 (2003).
[Crossref]

R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

Mesa, F.

R. Marques, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design – theory and experiments,” IEEE Trans. Antenn. Propag. 51(10), 2572–2581 (2003).
[Crossref]

Moloney, J. V.

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81(7), 075116 (2010).
[Crossref]

Monticone, F.

F. Monticone and A. Alu, “The quest for optical magnetism: from split-ring resonators to plasmonic nanoparticles and nanoclusters,” J. Mater. Chem. C Mater. Opt. Electron. Devices 2(43), 9059–9072 (2014).
[Crossref]

Ni, X.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[Crossref] [PubMed]

Niegemann, J.

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
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Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Penciu, R. S.

Pendry, J. B.

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]

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]

Ra’di, Y.

Y. Ra’di, D. L. Sounas, and A. Alù, “Metagratings: Beyond the limits of graded metasurfaces for wave front control,” Phys. Rev. Lett. 119(6), 067404 (2017).
[Crossref] [PubMed]

Rafii-El-Idrissi, R.

R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

Resnick, P. J.

Robbins, D. J.

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]

Rockstuhl, C.

Sarychev, A. K.

Shalaev, V. M.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[Crossref] [PubMed]

Sinclair, M. B.

D. B. Burckel, S. Campione, P. S. Davids, and M. B. Sinclair, “Three dimensional metafilms with dual channel unit cells,” Appl. Phys. Lett. 110(14), 143107 (2017).
[Crossref]

D. B. Burckel, P. J. Resnick, P. S. Finnegan, M. B. Sinclair, and P. S. Davids, “Micrometer-scale Fabrication of complex three-dimensional lattice+basis structures in silicon,” Opt. Mater. Express 5(10), 2231–2239 (2015).
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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]

Soukoulis, C. M.

R. S. Penciu, M. Kafesaki, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Magnetic response of nanoscale left-handed metamaterials,” Phys. Rev. B 81(23), 235111 (2010).
[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).
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[Crossref] [PubMed]

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]

Sounas, D. L.

Y. Ra’di, D. L. Sounas, and A. Alù, “Metagratings: Beyond the limits of graded metasurfaces for wave front control,” Phys. Rev. Lett. 119(6), 067404 (2017).
[Crossref] [PubMed]

Stannigel, K.

Stewart, W. J.

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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Sun, G.

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

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.

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

Wegener, M.

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.

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[Crossref] [PubMed]

Yuan, H.-K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[Crossref] [PubMed]

Zeng, Y.

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81(7), 075116 (2010).
[Crossref]

Zentgraf, T.

Zhang, S.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Zhang, X.

Zheludev, N. I.

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

Zhou, J.

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]

Zhou, J. F.

Adv. Mater. (1)

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]

Appl. Phys. Lett. (2)

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]

D. B. Burckel, S. Campione, P. S. Davids, and M. B. Sinclair, “Three dimensional metafilms with dual channel unit cells,” Appl. Phys. Lett. 110(14), 143107 (2017).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

R. Marques, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design – theory and experiments,” IEEE Trans. Antenn. Propag. 51(10), 2572–2581 (2003).
[Crossref]

IEEE Trans. Microw. Theory Tech. (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]

J. Mater. Chem. C Mater. Opt. Electron. Devices (1)

F. Monticone and A. Alu, “The quest for optical magnetism: from split-ring resonators to plasmonic nanoparticles and nanoclusters,” J. Mater. Chem. C Mater. Opt. Electron. Devices 2(43), 9059–9072 (2014).
[Crossref]

Nature (1)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

Opt. Mater. Express (1)

Phys. Rev. B (3)

R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

R. S. Penciu, M. Kafesaki, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Magnetic response of nanoscale left-handed metamaterials,” Phys. Rev. B 81(23), 235111 (2010).
[Crossref]

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81(7), 075116 (2010).
[Crossref]

Phys. Rev. Lett. (3)

Y. Ra’di, D. L. Sounas, and A. Alù, “Metagratings: Beyond the limits of graded metasurfaces for wave front control,” Phys. Rev. Lett. 119(6), 067404 (2017).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

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]

Sci. Rep. (1)

P. C. Wu, W.-L. Hsu, W. T. Chen, Y.-W. Huang, C. Y. Liao, A. Q. Liu, N. I. Zheludev, G. Sun, and D.-P. Tsai, “Plasmon coupling in vertical split-ring resonator metamolecules,” Sci. Rep. 5(1), 9726 (2015).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 Schematic diagrams showing the excitation of a) planar CWP; b) vertical CWP in the transparent polarization; and c) vertical CWP in the 3D CWP polarization. d) Plot of absorption for both transparent and 3D CWP polarizations of the vertical CWP. Note the rise of a pronounced absorption peak for the 3D CWP mode. Physical dimensions of the CWP: l = 2.12 μm, w = 0.3 μm, and t = 0.16 μm.
Fig. 2
Fig. 2 a) Single SRR in the resonant polarization. b) Single SRR in the transparent polarization. c) Back-to-back SRRs in the resonant polarization. d) Back-to-back SRRs in the 3D CWP polarization.
Fig. 3
Fig. 3 a) Two-by-two unit cell section of the dense periodic meta-film with 2.14 µm unit cells on a 2.3 µm period. Each unit cell has SRRs on opposite interior faces, so that the SRRs are arranged back-to-back through the unit cell wall with the next-nearest-neighbor unit cell. b) Physical dimensions of the SRRs used in modeling; metal thickness is 50 nm. c) Graph of modeled absorption for single (blue) and back-to-back (red) SRR meta-atoms.
Fig. 4
Fig. 4 Vector plots of the current flowing in the back-to-back SRRs for both the a) resonant and b) the 3D CWP modes (at the absorption peaks shown in Fig. 3(c)).

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