Abstract

Recently, conformal surface plasmon (CSP) structure has been successfully proposed that could support spoof surface plasmon polaritons (SPPs) on corrugated metallic strip with ultrathin thickness [Proc. Natl. Acad. Sci. U.S.A. 110, 40–45 (2013)]. Such concept provides a flexible, conformal, and ultrathin wave-guiding element, very promising for application of plasmonic devices, and circuits in the frequency ranging from microwave to mid-infrared. In this work, we investigated the dispersions and field patterns of high-order modes of spoof SPPs along CSP structure of thin metal film with corrugated edge of periodic array of grooves, and carried out direct measurement on the transmission spectrum of multi-band of surface wave propagation at microwave frequency. It is found that the mode number and mode bands are mainly determined by the depth of the grooves, providing a way to control the multi-band transmission spectrum. We have also experimentally verified the high-order mode spoof SPPs propagation on curved CSP structure with acceptable bending loss. The multi-band propagation of spoof surface wave is believed to be applicable for further design of novel planar devices such as filters, resonators, and couplers, and the concept can be extended to terahertz frequency range.

© 2013 Optical Society of America

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2013

X. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A.110(1), 40–45 (2013).
[CrossRef] [PubMed]

X. Gao, J. H. Shi, X. P. Shen, H. F. Ma, W. X. Jiang, L. M. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett.102(21), 211909 (2013).
[CrossRef]

2011

Y. G. Ma, L. Lan, S. M. Zhong, and C. K. Ong, “Experimental demonstration of subwavelength domino plasmon devices for compact high-frequency circuit,” Opt. Express19(22), 21189–21198 (2011).
[CrossRef] [PubMed]

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett.99(11), 111904 (2011).
[CrossRef]

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Multidirectional surface-wave splitters,” Appl. Phys. Lett.98(22), 221901 (2011).
[CrossRef]

E. M. G. Brock, E. Hendry, and A. P. Hibbins, “Subwavelength lateral confinement of microwave surface waves,” Appl. Phys. Lett.99(5), 051108 (2011).
[CrossRef]

2010

2009

T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface Plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagnetics Res.8, 91–102 (2009).
[CrossRef]

X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys.105(1), 013704 (2009).
[CrossRef]

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and J. F. Garcia-Vidal, “Guiding terahertz waves along subwavelength channels,” Phys. Rev. B79(23), 233104 (2009).
[CrossRef]

2008

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B78(23), 235426 (2008).
[CrossRef]

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics2(3), 175–179 (2008).
[CrossRef]

L. F. Shen, X. D. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express16(5), 3326–3333 (2008).
[CrossRef] [PubMed]

W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express16(9), 6216–6226 (2008).
[CrossRef] [PubMed]

A. P. Hibbins, E. Hendry, M. J. Lockyear, and J. R. Sambles, “Prism coupling to ‘designer’ surface plasmons,” Opt. Express16(25), 20441–20447 (2008).
[CrossRef] [PubMed]

2006

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

2005

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
[CrossRef]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005).
[CrossRef] [PubMed]

F. García de Abajo and J. J. Sáenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett.95(23), 233901 (2005).
[CrossRef] [PubMed]

W. H. Tsai, Y. C. Tsao, H. Y. Lin, and B. C. Sheu, “Cross-point analysis for a multimode fiber sensor based on surface plasmon resonance,” Opt. Lett.30(17), 2209–2211 (2005).
[CrossRef] [PubMed]

2004

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

1960

A. F. Harvey, “Periodic and guiding structures at microwave frequencies,” IRE Trans. Microwave Theor. Tech.8(1), 30–61 (1960).
[CrossRef]

1954

R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans. Antennas Propag.2, 71–81 (1954).

Agrawal, A.

Andrews, S. R.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics2(3), 175–179 (2008).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Brock, E. M. G.

E. M. G. Brock, E. Hendry, and A. P. Hibbins, “Subwavelength lateral confinement of microwave surface waves,” Appl. Phys. Lett.99(5), 051108 (2011).
[CrossRef]

Chen, X. D.

Cui, T. J.

X. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A.110(1), 40–45 (2013).
[CrossRef] [PubMed]

X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett.102(21), 211909 (2013).
[CrossRef]

X. Gao, J. H. Shi, X. P. Shen, H. F. Ma, W. X. Jiang, L. M. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett.99(11), 111904 (2011).
[CrossRef]

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Multidirectional surface-wave splitters,” Appl. Phys. Lett.98(22), 221901 (2011).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Eldaiki, O. M.

Elliott, R. S.

R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans. Antennas Propag.2, 71–81 (1954).

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Fernandez-Dominguez, A. I.

D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express18(2), 754–764 (2010).
[CrossRef] [PubMed]

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics2(3), 175–179 (2008).
[CrossRef]

Fernández-Domínguez, A. I.

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and J. F. Garcia-Vidal, “Guiding terahertz waves along subwavelength channels,” Phys. Rev. B79(23), 233104 (2009).
[CrossRef]

Gao, X.

X. Gao, J. H. Shi, X. P. Shen, H. F. Ma, W. X. Jiang, L. M. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

García de Abajo, F.

F. García de Abajo and J. J. Sáenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett.95(23), 233901 (2005).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

X. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A.110(1), 40–45 (2013).
[CrossRef] [PubMed]

D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express18(2), 754–764 (2010).
[CrossRef] [PubMed]

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics2(3), 175–179 (2008).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Garcia-Vidal, J. F.

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and J. F. Garcia-Vidal, “Guiding terahertz waves along subwavelength channels,” Phys. Rev. B79(23), 233104 (2009).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010).
[CrossRef]

Harvey, A. F.

A. F. Harvey, “Periodic and guiding structures at microwave frequencies,” IRE Trans. Microwave Theor. Tech.8(1), 30–61 (1960).
[CrossRef]

Hendry, E.

E. M. G. Brock, E. Hendry, and A. P. Hibbins, “Subwavelength lateral confinement of microwave surface waves,” Appl. Phys. Lett.99(5), 051108 (2011).
[CrossRef]

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B78(23), 235426 (2008).
[CrossRef]

A. P. Hibbins, E. Hendry, M. J. Lockyear, and J. R. Sambles, “Prism coupling to ‘designer’ surface plasmons,” Opt. Express16(25), 20441–20447 (2008).
[CrossRef] [PubMed]

Hibbins, A. P.

E. M. G. Brock, E. Hendry, and A. P. Hibbins, “Subwavelength lateral confinement of microwave surface waves,” Appl. Phys. Lett.99(5), 051108 (2011).
[CrossRef]

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B78(23), 235426 (2008).
[CrossRef]

A. P. Hibbins, E. Hendry, M. J. Lockyear, and J. R. Sambles, “Prism coupling to ‘designer’ surface plasmons,” Opt. Express16(25), 20441–20447 (2008).
[CrossRef] [PubMed]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Jiang, Q.

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Multidirectional surface-wave splitters,” Appl. Phys. Lett.98(22), 221901 (2011).
[CrossRef]

Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett.99(11), 111904 (2011).
[CrossRef]

Jiang, T.

T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface Plasmon polaritons on periodically corrugated metal surfaces,” Prog. Electromagnetics Res.8, 91–102 (2009).
[CrossRef]

Jiang, W. X.

X. Gao, J. H. Shi, X. P. Shen, H. F. Ma, W. X. Jiang, L. M. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Lan, L.

Li, L. M.

X. Gao, J. H. Shi, X. P. Shen, H. F. Ma, W. X. Jiang, L. M. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Lin, H. Y.

Lockyear, M. J.

Lu, Z. L.

Ma, H. F.

X. Gao, J. H. Shi, X. P. Shen, H. F. Ma, W. X. Jiang, L. M. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett.102(15), 151912 (2013).
[CrossRef]

Ma, Y. G.

Maier, S. A.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics2(3), 175–179 (2008).
[CrossRef]

Martin-Cano, D.

X. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A.110(1), 40–45 (2013).
[CrossRef] [PubMed]

D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express18(2), 754–764 (2010).
[CrossRef] [PubMed]

Martin-Moreno, L.

D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express18(2), 754–764 (2010).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and J. F. Garcia-Vidal, “Guiding terahertz waves along subwavelength channels,” Phys. Rev. B79(23), 233104 (2009).
[CrossRef]

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics2(3), 175–179 (2008).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
[CrossRef]

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Moreno, E.

D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express18(2), 754–764 (2010).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and J. F. Garcia-Vidal, “Guiding terahertz waves along subwavelength channels,” Phys. Rev. B79(23), 233104 (2009).
[CrossRef]

Nahata, A.

Nesterov, M. L.

Ong, C. K.

Ozbay, E.

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Pendry, J. B.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Ran, L.

X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys.105(1), 013704 (2009).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Dispersion curves for both the fundamental and high-order modes of the CSP structure with different thickness of the metallic strip.

Fig. 2
Fig. 2

Transmission spectrum of a long CSP structure as a function of the groove depth.

Fig. 3
Fig. 3

Dispersion curves (a), and the transmission spectrum (b) calculated from a 170 mm long thin metallic corrugated strip on a PCB substrate with h, d, a, w fixed as 15 mm, 8 mm, 3 mm, and 4.5 mm, respectively. The open circles indicate the calculated time-averaged power density ratio of two cross-sections near the input and output edges.

Fig. 4
Fig. 4

The simulated electric field distributions for (a) the fundamental mode, (b) the first high-order mode, and (c) the second high-order mode, at 2.4 GHz, 7.7 GHz and 13.3 GHz, respectively. The left, middle, and right columns indicate the z component of the electric field evaluated at the top of strip in the x-y plane, the electric field amplitude at the y-z plane that cuts the metal strip symmetrically, and in the cross-section perpendicular to the strip, respectively.

Fig. 5
Fig. 5

The simulated magnetic field distributions for (a) the fundamental mode, (b) the first high-order mode, and (c) the second high-order mode, at 2.4 GHz, 7.7 GHz and 13.3 GHz, respectively. The upper or lower row indicates the magnetic field distribution in the cross-sections perpendicular to the strip in y-z, or z-x plane, respectively.

Fig. 6
Fig. 6

(a) The schematics of the proposed CSP structure with input and output CPW sections, and (b) the photograph of the fabricated sample with SMA connectors.

Fig. 7
Fig. 7

(a) Calculated dispersion curves, and (b) the calculated and measured transmission spectrum from a 170 mm long thin metallic corrugated strip on a PCB substrate with h, d, a, w fixed as 22 mm, 8 mm, 3 mm, and 4.5 mm, respectively, supporting three modes of spoof SPP wave propagation.

Fig. 8
Fig. 8

Simulated (solid lines) and measured (dashed lines) transmission spectrum for the CSP structures with different groove periodicity or width. (h = 22 mm, and w = 4.5 mm)

Fig. 9
Fig. 9

The schematics (a) and the photograph of a fabricated sample (b) of a 90 degree bend of the CSP structure. (c) and (d) illustrate the simulated electric field component perpendicular to the surface distributed along the bended metal strip at frequency of 2.5 GHz (the fundamental mode), and 7.8 GHz (the first high-order mode), respectively. (with a = 3 mm, h = 22 mm, d = 8 mm, and w = 4.5 mm)

Fig. 10
Fig. 10

Comparison of the simulated and measured transmission through the 90° bend (with a radius of 70 mm) and straight CSP structures with same length. (a = 5 mm,h = 22 mm,d = 8 mm,w = 4.5 mm)

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