Abstract

Magnetic localized surface plasmon modes are supported on metallic spiral structures. Coupling mechanisms for these metamaterial resonators, which are the joint action of magnetic and electric coupling, are studied. Based on the strong coupling, spoof magnetic plasmon modes propagating in the backward direction are proposed along a chain of subwavelength resonators. The theoretical analysis, numerical simulations, and experiments are in good agreement. The proposed novel route for achieving negative-index waveguiding has potential applications in integrated devices and circuits.

© 2019 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]

2018 (1)

2017 (4)

Y. J. Zhou, C. Zhang, L. Yang, and Q. X. Xiao, “Electronically switchable and tunable bandpass filters based on spoof localized surface plasmons,” J. Opt. Soc. Am. B 34, D9–D12 (2017).
[Crossref]

Y. J. Zhou, C. Zhang, L. Yang, and Q. X. Xiao, “Electronically controllable spoof localized surface plasmons,” J. Phys. D 50, 425102 (2017).
[Crossref]

Z. Gao, F. Gao, Y. Zhang, H. Xu, Y. Luo, and B. Zhang, “Forward/backward switching of plasmonic wave propagation using sign-reversal coupling,” Adv. Mater. 29, 1700018 (2017).
[Crossref]

J. Zhang, Z. Liao, Y. Luo, X. Shen, S. A. Maier, and T. J. Cui, “Spoof plasmon hybridization,” Laser Photon. Rev. 11, 1600191 (2017).
[Crossref]

2016 (3)

Z. Gao, F. Gao, Y. Zhang, and B. Zhang, “Deep-subwavelength magnetic-coupling-dominant interaction among magnetic localized surface plasmons,” Phys. Rev. B 93, 195410 (2016).
[Crossref]

F. Gao, Z. Gao, Y. Luo, and B. Zhang, “Invisibility dips of near-field energy transport in a spoof plasmonic metadimer,” Adv. Funct. Mater. 26, 8307–8312 (2016).
[Crossref]

X. Y. Liu, Y. J. Feng, B. Zhu, J. M. Zhao, and T. Jiang, “Backward spoof surface wave in plasmonic metamaterial of ultrathin metallic structure,” Sci. Rep. 6, 20448 (2016).
[Crossref]

2015 (2)

F. Gao, Z. Gao, Y. Zhang, X. Shi, Z. Yang, and B. Zhang, “Vertical transport of subwavelength localized surface electromagnetic modes,” Laser Photon. Rev. 9, 571–576 (2015).
[Crossref]

S. Lan, L. Kang, D. Schoen, S. Podrigues, Y. Cui, M. Brongersma, and W. Cai, “Backward phase-matching for nonlinear optical generation in negative-index materials,” Nat. Mater. 14, 807–811 (2015).
[Crossref]

2014 (3)

R. Quesada, D. Martín-Cano, F. J. García-Vidal, and J. Bravo-Abad, “Deep-subwavelength negative-index waveguiding enabled by coupled conformal surface plasmons,” Opt. Lett. 39, 2990–2993 (2014).
[Crossref]

X. Shen and T. J. Cui, “Ultrathin plasmonic metamaterial for spoof localized surface plasmons,” Laser Photon. Rev. 8, 137–145 (2014).
[Crossref]

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

2012 (1)

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108, 223905 (2012).
[Crossref]

2010 (1)

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[Crossref]

2008 (1)

Y. Weitsch and T. F. Eibert, “Analysis and design of a composite left-/right-handed leaky wave antenna based on the H10 rectangular waveguide mode,” Adv. Radio Sci. 6, 49–54 (2008).
[Crossref]

2007 (3)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[Crossref]

2006 (3)

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96, 073907 (2006).
[Crossref]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6, 827–832 (2006).
[Crossref]

2005 (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref]

2004 (2)

C. Caloz and T. Itoh, “Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line,” IEEE Trans. Anntenas Propag. 52, 1159–1166 (2004).
[Crossref]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

2003 (2)

G. V. Eleftheriades, O. Siddiqui, and A. K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wireless Compon. Lett. 13, 51–53 (2003).
[Crossref]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref]

2002 (1)

L. Liu, C. Caloz, C. Chang, and T. Itoh, “Forward coupling phenomena between artificial left-handed transmission lines,” J. Appl. Phys. 92, 5560–5565 (2002).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

2000 (1)

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

1999 (1)

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Atwater, H. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[Crossref]

Brandl, D. W.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6, 827–832 (2006).
[Crossref]

Bravo-Abad, J.

Brongersma, M.

S. Lan, L. Kang, D. Schoen, S. Podrigues, Y. Cui, M. Brongersma, and W. Cai, “Backward phase-matching for nonlinear optical generation in negative-index materials,” Nat. Mater. 14, 807–811 (2015).
[Crossref]

Cai, J.

Cai, W.

S. Lan, L. Kang, D. Schoen, S. Podrigues, Y. Cui, M. Brongersma, and W. Cai, “Backward phase-matching for nonlinear optical generation in negative-index materials,” Nat. Mater. 14, 807–811 (2015).
[Crossref]

Caloz, C.

C. Caloz and T. Itoh, “Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line,” IEEE Trans. Anntenas Propag. 52, 1159–1166 (2004).
[Crossref]

L. Liu, C. Caloz, C. Chang, and T. Itoh, “Forward coupling phenomena between artificial left-handed transmission lines,” J. Appl. Phys. 92, 5560–5565 (2002).
[Crossref]

C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (Wiley, 2005).

Chang, C.

L. Liu, C. Caloz, C. Chang, and T. Itoh, “Forward coupling phenomena between artificial left-handed transmission lines,” J. Appl. Phys. 92, 5560–5565 (2002).
[Crossref]

Cuerda, J.

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

Cui, T. J.

J. Zhang, Z. Liao, Y. Luo, X. Shen, S. A. Maier, and T. J. Cui, “Spoof plasmon hybridization,” Laser Photon. Rev. 11, 1600191 (2017).
[Crossref]

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

X. Shen and T. J. Cui, “Ultrathin plasmonic metamaterial for spoof localized surface plasmons,” Laser Photon. Rev. 8, 137–145 (2014).
[Crossref]

Cui, Y.

S. Lan, L. Kang, D. Schoen, S. Podrigues, Y. Cui, M. Brongersma, and W. Cai, “Backward phase-matching for nonlinear optical generation in negative-index materials,” Nat. Mater. 14, 807–811 (2015).
[Crossref]

Davis, C. C.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref]

de Waele, R.

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[Crossref]

Dionne, J. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[Crossref]

Eibert, T. F.

Y. Weitsch and T. F. Eibert, “Analysis and design of a composite left-/right-handed leaky wave antenna based on the H10 rectangular waveguide mode,” Adv. Radio Sci. 6, 49–54 (2008).
[Crossref]

Eleftheriades, G. V.

G. V. Eleftheriades, O. Siddiqui, and A. K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wireless Compon. Lett. 13, 51–53 (2003).
[Crossref]

Fan, S.

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96, 073907 (2006).
[Crossref]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref]

Feng, Y. J.

X. Y. Liu, Y. J. Feng, B. Zhu, J. M. Zhao, and T. Jiang, “Backward spoof surface wave in plasmonic metamaterial of ultrathin metallic structure,” Sci. Rep. 6, 20448 (2016).
[Crossref]

Gao, F.

Z. Gao, F. Gao, Y. Zhang, H. Xu, Y. Luo, and B. Zhang, “Forward/backward switching of plasmonic wave propagation using sign-reversal coupling,” Adv. Mater. 29, 1700018 (2017).
[Crossref]

Z. Gao, F. Gao, Y. Zhang, and B. Zhang, “Deep-subwavelength magnetic-coupling-dominant interaction among magnetic localized surface plasmons,” Phys. Rev. B 93, 195410 (2016).
[Crossref]

F. Gao, Z. Gao, Y. Luo, and B. Zhang, “Invisibility dips of near-field energy transport in a spoof plasmonic metadimer,” Adv. Funct. Mater. 26, 8307–8312 (2016).
[Crossref]

F. Gao, Z. Gao, Y. Zhang, X. Shi, Z. Yang, and B. Zhang, “Vertical transport of subwavelength localized surface electromagnetic modes,” Laser Photon. Rev. 9, 571–576 (2015).
[Crossref]

Gao, Z.

Z. Gao, F. Gao, Y. Zhang, H. Xu, Y. Luo, and B. Zhang, “Forward/backward switching of plasmonic wave propagation using sign-reversal coupling,” Adv. Mater. 29, 1700018 (2017).
[Crossref]

F. Gao, Z. Gao, Y. Luo, and B. Zhang, “Invisibility dips of near-field energy transport in a spoof plasmonic metadimer,” Adv. Funct. Mater. 26, 8307–8312 (2016).
[Crossref]

Z. Gao, F. Gao, Y. Zhang, and B. Zhang, “Deep-subwavelength magnetic-coupling-dominant interaction among magnetic localized surface plasmons,” Phys. Rev. B 93, 195410 (2016).
[Crossref]

F. Gao, Z. Gao, Y. Zhang, X. Shi, Z. Yang, and B. Zhang, “Vertical transport of subwavelength localized surface electromagnetic modes,” Laser Photon. Rev. 9, 571–576 (2015).
[Crossref]

Garcia-Vidal, F. J.

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108, 223905 (2012).
[Crossref]

García-Vidal, F. J.

Genov, D. A.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

Halas, N. J.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6, 827–832 (2006).
[Crossref]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref]

Huidobro, P. A.

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

Hung, Y.-J.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref]

Itoh, T.

C. Caloz and T. Itoh, “Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line,” IEEE Trans. Anntenas Propag. 52, 1159–1166 (2004).
[Crossref]

L. Liu, C. Caloz, C. Chang, and T. Itoh, “Forward coupling phenomena between artificial left-handed transmission lines,” J. Appl. Phys. 92, 5560–5565 (2002).
[Crossref]

C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (Wiley, 2005).

Iyer, A. K.

G. V. Eleftheriades, O. Siddiqui, and A. K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wireless Compon. Lett. 13, 51–53 (2003).
[Crossref]

Jiang, T.

X. Y. Liu, Y. J. Feng, B. Zhu, J. M. Zhao, and T. Jiang, “Backward spoof surface wave in plasmonic metamaterial of ultrathin metallic structure,” Sci. Rep. 6, 20448 (2016).
[Crossref]

Kang, L.

S. Lan, L. Kang, D. Schoen, S. Podrigues, Y. Cui, M. Brongersma, and W. Cai, “Backward phase-matching for nonlinear optical generation in negative-index materials,” Nat. Mater. 14, 807–811 (2015).
[Crossref]

Kuipers, L.

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[Crossref]

Lan, S.

S. Lan, L. Kang, D. Schoen, S. Podrigues, Y. Cui, M. Brongersma, and W. Cai, “Backward phase-matching for nonlinear optical generation in negative-index materials,” Nat. Mater. 14, 807–811 (2015).
[Crossref]

Le, F.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6, 827–832 (2006).
[Crossref]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref]

Lee, R. K.

Lezec, H. J.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[Crossref]

Li, K.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Li, Q. Y.

Liao, Z.

J. Zhang, Z. Liao, Y. Luo, X. Shen, S. A. Maier, and T. J. Cui, “Spoof plasmon hybridization,” Laser Photon. Rev. 11, 1600191 (2017).
[Crossref]

Liu, H.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

Liu, L.

L. Liu, C. Caloz, C. Chang, and T. Itoh, “Forward coupling phenomena between artificial left-handed transmission lines,” J. Appl. Phys. 92, 5560–5565 (2002).
[Crossref]

Liu, X. Y.

X. Y. Liu, Y. J. Feng, B. Zhu, J. M. Zhao, and T. Jiang, “Backward spoof surface wave in plasmonic metamaterial of ultrathin metallic structure,” Sci. Rep. 6, 20448 (2016).
[Crossref]

Liu, Y. M.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

Luo, Y.

J. Zhang, Z. Liao, Y. Luo, X. Shen, S. A. Maier, and T. J. Cui, “Spoof plasmon hybridization,” Laser Photon. Rev. 11, 1600191 (2017).
[Crossref]

Z. Gao, F. Gao, Y. Zhang, H. Xu, Y. Luo, and B. Zhang, “Forward/backward switching of plasmonic wave propagation using sign-reversal coupling,” Adv. Mater. 29, 1700018 (2017).
[Crossref]

F. Gao, Z. Gao, Y. Luo, and B. Zhang, “Invisibility dips of near-field energy transport in a spoof plasmonic metadimer,” Adv. Funct. Mater. 26, 8307–8312 (2016).
[Crossref]

Maier, S. A.

J. Zhang, Z. Liao, Y. Luo, X. Shen, S. A. Maier, and T. J. Cui, “Spoof plasmon hybridization,” Laser Photon. Rev. 11, 1600191 (2017).
[Crossref]

Marqués, R.

R. Marqués, F. Martín, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications (Wiley, 2011).

Martín, F.

R. Marqués, F. Martín, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications (Wiley, 2011).

Martín-Cano, D.

Martin-Moreno, L.

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108, 223905 (2012).
[Crossref]

Moreno, E.

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108, 223905 (2012).
[Crossref]

Nordlander, P.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6, 827–832 (2006).
[Crossref]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref]

Oubre, C.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Pendry, J. B.

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108, 223905 (2012).
[Crossref]

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

Podrigues, S.

S. Lan, L. Kang, D. Schoen, S. Podrigues, Y. Cui, M. Brongersma, and W. Cai, “Backward phase-matching for nonlinear optical generation in negative-index materials,” Nat. Mater. 14, 807–811 (2015).
[Crossref]

Polman, A.

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[Crossref]

Pors, A.

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108, 223905 (2012).
[Crossref]

Prodan, E.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref]

Quesada, R.

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref]

Ramo, S.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 2008).

Scherer, A.

Schoen, D.

S. Lan, L. Kang, D. Schoen, S. Podrigues, Y. Cui, M. Brongersma, and W. Cai, “Backward phase-matching for nonlinear optical generation in negative-index materials,” Nat. Mater. 14, 807–811 (2015).
[Crossref]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

Shamonina, E.

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford University, 2009).

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

Shen, X.

J. Zhang, Z. Liao, Y. Luo, X. Shen, S. A. Maier, and T. J. Cui, “Spoof plasmon hybridization,” Laser Photon. Rev. 11, 1600191 (2017).
[Crossref]

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

X. Shen and T. J. Cui, “Ultrathin plasmonic metamaterial for spoof localized surface plasmons,” Laser Photon. Rev. 8, 137–145 (2014).
[Crossref]

Shi, X.

F. Gao, Z. Gao, Y. Zhang, X. Shi, Z. Yang, and B. Zhang, “Vertical transport of subwavelength localized surface electromagnetic modes,” Laser Photon. Rev. 9, 571–576 (2015).
[Crossref]

Shin, H.

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96, 073907 (2006).
[Crossref]

Siddiqui, O.

G. V. Eleftheriades, O. Siddiqui, and A. K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wireless Compon. Lett. 13, 51–53 (2003).
[Crossref]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

Smolyaninov, I. I.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref]

Solymar, L.

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford University, 2009).

Sorolla, M.

R. Marqués, F. Martín, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications (Wiley, 2011).

Steele, J. M.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

Stockman, M. I.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref]

Van Duzer, T.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 2008).

Verhagen, E.

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[Crossref]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Wang, H.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6, 827–832 (2006).
[Crossref]

Weitsch, Y.

Y. Weitsch and T. F. Eibert, “Analysis and design of a composite left-/right-handed leaky wave antenna based on the H10 rectangular waveguide mode,” Adv. Radio Sci. 6, 49–54 (2008).
[Crossref]

Whinnery, J. R.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 2008).

Wu, D. M.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

Xiao, Q. X.

Y. J. Zhou, C. Zhang, L. Yang, and Q. X. Xiao, “Electronically controllable spoof localized surface plasmons,” J. Phys. D 50, 425102 (2017).
[Crossref]

Y. J. Zhou, C. Zhang, L. Yang, and Q. X. Xiao, “Electronically switchable and tunable bandpass filters based on spoof localized surface plasmons,” J. Opt. Soc. Am. B 34, D9–D12 (2017).
[Crossref]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

Xu, H.

Z. Gao, F. Gao, Y. Zhang, H. Xu, Y. Luo, and B. Zhang, “Forward/backward switching of plasmonic wave propagation using sign-reversal coupling,” Adv. Mater. 29, 1700018 (2017).
[Crossref]

Xu, Y.

Yang, L.

Y. J. Zhou, C. Zhang, L. Yang, and Q. X. Xiao, “Electronically controllable spoof localized surface plasmons,” J. Phys. D 50, 425102 (2017).
[Crossref]

Y. J. Zhou, C. Zhang, L. Yang, and Q. X. Xiao, “Electronically switchable and tunable bandpass filters based on spoof localized surface plasmons,” J. Opt. Soc. Am. B 34, D9–D12 (2017).
[Crossref]

Yang, Z.

F. Gao, Z. Gao, Y. Zhang, X. Shi, Z. Yang, and B. Zhang, “Vertical transport of subwavelength localized surface electromagnetic modes,” Laser Photon. Rev. 9, 571–576 (2015).
[Crossref]

Yariv, A.

Zhang, B.

Z. Gao, F. Gao, Y. Zhang, H. Xu, Y. Luo, and B. Zhang, “Forward/backward switching of plasmonic wave propagation using sign-reversal coupling,” Adv. Mater. 29, 1700018 (2017).
[Crossref]

F. Gao, Z. Gao, Y. Luo, and B. Zhang, “Invisibility dips of near-field energy transport in a spoof plasmonic metadimer,” Adv. Funct. Mater. 26, 8307–8312 (2016).
[Crossref]

Z. Gao, F. Gao, Y. Zhang, and B. Zhang, “Deep-subwavelength magnetic-coupling-dominant interaction among magnetic localized surface plasmons,” Phys. Rev. B 93, 195410 (2016).
[Crossref]

F. Gao, Z. Gao, Y. Zhang, X. Shi, Z. Yang, and B. Zhang, “Vertical transport of subwavelength localized surface electromagnetic modes,” Laser Photon. Rev. 9, 571–576 (2015).
[Crossref]

Zhang, C.

Y. J. Zhou, C. Zhang, L. Yang, and Q. X. Xiao, “Electronically controllable spoof localized surface plasmons,” J. Phys. D 50, 425102 (2017).
[Crossref]

Y. J. Zhou, C. Zhang, L. Yang, and Q. X. Xiao, “Electronically switchable and tunable bandpass filters based on spoof localized surface plasmons,” J. Opt. Soc. Am. B 34, D9–D12 (2017).
[Crossref]

Zhang, J.

J. Zhang, Z. Liao, Y. Luo, X. Shen, S. A. Maier, and T. J. Cui, “Spoof plasmon hybridization,” Laser Photon. Rev. 11, 1600191 (2017).
[Crossref]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref]

Zhang, Y.

J. Cai, Y. J. Zhou, Y. Zhang, and Q. Y. Li, “Gain-assisted ultra-high-Q spoof plasmonic resonator for the sensing of polar liquids,” Opt. Express 26, 25460–25470 (2018).
[Crossref]

Z. Gao, F. Gao, Y. Zhang, H. Xu, Y. Luo, and B. Zhang, “Forward/backward switching of plasmonic wave propagation using sign-reversal coupling,” Adv. Mater. 29, 1700018 (2017).
[Crossref]

Z. Gao, F. Gao, Y. Zhang, and B. Zhang, “Deep-subwavelength magnetic-coupling-dominant interaction among magnetic localized surface plasmons,” Phys. Rev. B 93, 195410 (2016).
[Crossref]

F. Gao, Z. Gao, Y. Zhang, X. Shi, Z. Yang, and B. Zhang, “Vertical transport of subwavelength localized surface electromagnetic modes,” Laser Photon. Rev. 9, 571–576 (2015).
[Crossref]

Zhao, J. M.

X. Y. Liu, Y. J. Feng, B. Zhu, J. M. Zhao, and T. Jiang, “Backward spoof surface wave in plasmonic metamaterial of ultrathin metallic structure,” Sci. Rep. 6, 20448 (2016).
[Crossref]

Zhou, Y. J.

Zhu, B.

X. Y. Liu, Y. J. Feng, B. Zhu, J. M. Zhao, and T. Jiang, “Backward spoof surface wave in plasmonic metamaterial of ultrathin metallic structure,” Sci. Rep. 6, 20448 (2016).
[Crossref]

Zhu, S. N.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

Adv. Funct. Mater. (1)

F. Gao, Z. Gao, Y. Luo, and B. Zhang, “Invisibility dips of near-field energy transport in a spoof plasmonic metadimer,” Adv. Funct. Mater. 26, 8307–8312 (2016).
[Crossref]

Adv. Mater. (1)

Z. Gao, F. Gao, Y. Zhang, H. Xu, Y. Luo, and B. Zhang, “Forward/backward switching of plasmonic wave propagation using sign-reversal coupling,” Adv. Mater. 29, 1700018 (2017).
[Crossref]

Adv. Radio Sci. (1)

Y. Weitsch and T. F. Eibert, “Analysis and design of a composite left-/right-handed leaky wave antenna based on the H10 rectangular waveguide mode,” Adv. Radio Sci. 6, 49–54 (2008).
[Crossref]

IEEE Microw. Wireless Compon. Lett. (1)

G. V. Eleftheriades, O. Siddiqui, and A. K. Iyer, “Transmission line models for negative refractive index media and associated implementations without excess resonators,” IEEE Microw. Wireless Compon. Lett. 13, 51–53 (2003).
[Crossref]

IEEE Trans. Anntenas Propag. (1)

C. Caloz and T. Itoh, “Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line,” IEEE Trans. Anntenas Propag. 52, 1159–1166 (2004).
[Crossref]

J. Appl. Phys. (1)

L. Liu, C. Caloz, C. Chang, and T. Itoh, “Forward coupling phenomena between artificial left-handed transmission lines,” J. Appl. Phys. 92, 5560–5565 (2002).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. D (1)

Y. J. Zhou, C. Zhang, L. Yang, and Q. X. Xiao, “Electronically controllable spoof localized surface plasmons,” J. Phys. D 50, 425102 (2017).
[Crossref]

Laser Photon. Rev. (3)

X. Shen and T. J. Cui, “Ultrathin plasmonic metamaterial for spoof localized surface plasmons,” Laser Photon. Rev. 8, 137–145 (2014).
[Crossref]

F. Gao, Z. Gao, Y. Zhang, X. Shi, Z. Yang, and B. Zhang, “Vertical transport of subwavelength localized surface electromagnetic modes,” Laser Photon. Rev. 9, 571–576 (2015).
[Crossref]

J. Zhang, Z. Liao, Y. Luo, X. Shen, S. A. Maier, and T. J. Cui, “Spoof plasmon hybridization,” Laser Photon. Rev. 11, 1600191 (2017).
[Crossref]

Nano Lett. (2)

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6, 827–832 (2006).
[Crossref]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[Crossref]

Nat. Mater. (1)

S. Lan, L. Kang, D. Schoen, S. Podrigues, Y. Cui, M. Brongersma, and W. Cai, “Backward phase-matching for nonlinear optical generation in negative-index materials,” Nat. Mater. 14, 807–811 (2015).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (1)

Z. Gao, F. Gao, Y. Zhang, and B. Zhang, “Deep-subwavelength magnetic-coupling-dominant interaction among magnetic localized surface plasmons,” Phys. Rev. B 93, 195410 (2016).
[Crossref]

Phys. Rev. Lett. (5)

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96, 073907 (2006).
[Crossref]

E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett. 105, 223901 (2010).
[Crossref]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, “Localized spoof plasmons arise while texturing closed surfaces,” Phys. Rev. Lett. 108, 223905 (2012).
[Crossref]

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

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97, 243902 (2006).
[Crossref]

Phys. Rev. X (1)

P. A. Huidobro, X. Shen, J. Cuerda, E. Moreno, L. Martin-Moreno, F. J. Garcia-Vidal, T. J. Cui, and J. B. Pendry, “Magnetic localized surface plasmons,” Phys. Rev. X 4, 021003 (2014).
[Crossref]

Sci. Rep. (1)

X. Y. Liu, Y. J. Feng, B. Zhu, J. M. Zhao, and T. Jiang, “Backward spoof surface wave in plasmonic metamaterial of ultrathin metallic structure,” Sci. Rep. 6, 20448 (2016).
[Crossref]

Science (6)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[Crossref]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Other (4)

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 2008).

R. Marqués, F. Martín, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications (Wiley, 2011).

L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford University, 2009).

C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (Wiley, 2005).

Supplementary Material (1)

NameDescription
» Visualization 1       The instantaneous magnetic field distribution movie at 1.86GHz.

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Figures (9)

Fig. 1.
Fig. 1. (a) Magnetic field amplitude intensity detected at the center of the resonators; the inset is a schematic illustration of the metallic spiral structure. (b) Current distribution at z=0, (c) magnetic field at x=0, (d) electric field at x=0.
Fig. 2.
Fig. 2. Simulation and measurement setups of the MSS dimers are shown in (a) and (b), respectively. The near-field response spectra for a single MSS (black line) and MSS dimer (red line) in (c) simulations and (d) measurements. The insets correspond to the electric field maps for the split higher and lower modes, respectively.
Fig. 3.
Fig. 3. Dispersion diagrams of infinite chains of metallic spiral structures based on Lagrangian analytical mode (black line), coupled mode theory (red symbols), and numerical simulation (square symbols). The blue dash line is the dispersion of the light in free space.
Fig. 4.
Fig. 4. (a) Geometry of MSS chain. The red dash line indicates the observed cross section. The blue line indicates the observation line. The magnetic fields in the z=1  mm plane and y=0 plane are presented in (b) and (c), respectively.
Fig. 5.
Fig. 5. (a) Magnetic field distributions along the z axis; (b) magnetic field distributions on the cross sections of the MSS chain at 1.84 and 1.88 GHz.
Fig. 6.
Fig. 6. Magnetic field distributions along the MSS chain at different frequencies.
Fig. 7.
Fig. 7. (a) Simulation and experimental setup, (b) simulated and measured transmission spectra for the metamaterial resonator waveguides that consist of 10 MSSs, (c) simulated and (d) experimental amplitude of electric field Ez above the waveguide.
Fig. 8.
Fig. 8. (a) Simulation of transmission spectra for adjacent MSSs with varying gap size from 10 to 0.5 mm. (b) Resonance frequency of two modes as a function of gap size. (c) Dispersion relation with different gap sizes. (d) Transmissions of MSS chains with different gap sizes.
Fig. 9.
Fig. 9. Simulated vertical magnetic-field distributions of the waves on the MSS chain.

Equations (8)

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

Γ=12L(Q˙12+Q˙22)12Lω02(Q12+Q22)+MmQ˙1Q˙2+Meω02Q1Q2,
ddt(ΓQ˙m)ΓQm=0(m=1,2).
LQ¨1+Lω02Q1+MmQ¨2Meω02Q2=0.
{ω=ω01+κe1κmQ1=Q2,ω+=ω01κe1+κmQ1=Q2,
Γ=m(12LQ˙m212Lω02Qm2+MmQ˙mQ˙m+1+Meω02QmQm+1).
LQ¨m+MmQ¨m+1+MmQ¨m1Meω02Qm+1+Lω02QmMeω02Qm1=0.
ω=ω012κecos(kd)1+2κmcos(kd),
{da1dt=iω0a1+iκω0a2,da2dt=iω0a2+iκω0a1,

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