Abstract

The designer surface plasmons (DSPs) are studied by the use of a kind of metamaterial with a structure of double sets of circular holes: subwavelength apertures, and indentations. The diameter and spacing of the indentations are smaller at least one order of magnitude than those of the apertures. A theoretical model is built to analyze the DSPs sustained by the indentations by using effective dipoles method. The influence of the DSPs on the transmission property is revealed for electromagnetic waves passing through the apertures. In order to verify the theoretical predication, a set of the metamaterial samples is made and the transmission spectra are measured in microwave regime. Our results provide a new proof for the existence of DSPs and are promising for proposing some techniques for optoelectronic devices in terahertz and microwave regime.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008).
    [CrossRef]
  7. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

N. Talebi and M. Shahabadi, “Spoof surface plasmons propagating along a periodically corrugated coaxial waveguide,” J. Phys. D Appl. Phys. 43(13), 135302 (2010).
[CrossRef]

2009

2008

L. F. Shen, X. D. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16(5), 3326–3333 (2008).
[CrossRef] [PubMed]

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008).
[CrossRef]

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008).
[CrossRef]

2007

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

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

2006

S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88(25), 251120 (2006).
[CrossRef]

Y. C. Lan and R. L. Chern, “Surface plasmon-like modes on structured perfectly conducting surfaces,” Opt. Express 14(23), 11339–11347 (2006).
[CrossRef] [PubMed]

2005

M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano, “Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays,” Opt. Lett. 30(10), 1210–1212 (2005).
[CrossRef] [PubMed]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[CrossRef] [PubMed]

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]

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

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[CrossRef] [PubMed]

2004

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

1944

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944).
[CrossRef]

Akazawa, M.

Andrews, S. R.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008).
[CrossRef]

S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88(25), 251120 (2006).
[CrossRef]

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944).
[CrossRef]

Capasso, F.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Catrysse, P. B.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[CrossRef] [PubMed]

Chen, X. D.

Chern, R. L.

Davies, A. G.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Ding, L.

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Fan, J. A.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Fan, S.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[CrossRef] [PubMed]

Fernández-Domínguez, A. I.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008).
[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]

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

Garcia-Vidal, F. J.

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,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

García-Vidal, F. J.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008).
[CrossRef]

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Ghaemi, H. F.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Grupp, D. E.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

Hangyo, M.

Hendry, E.

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008).
[CrossRef]

Hibbins, A. P.

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008).
[CrossRef]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Huang, T. J.

Jensen, L.

Juluri, B. K.

Kats, M. A.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Khanna, S. P.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Lan, Y. C.

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

Li, L. H.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Lin, S.-C. S.

Linfield, E. H.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Liu, J. S.

Maier, S. A.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008).
[CrossRef]

S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88(25), 251120 (2006).
[CrossRef]

Martin-Moreno, L.

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.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Miyamaru, F.

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,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Sáenz, J. J.

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

Sambles, J. R.

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008).
[CrossRef]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Sano, E.

Shahabadi, M.

N. Talebi and M. Shahabadi, “Spoof surface plasmons propagating along a periodically corrugated coaxial waveguide,” J. Phys. D Appl. Phys. 43(13), 135302 (2010).
[CrossRef]

Shen, J. T.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[CrossRef] [PubMed]

Shen, L. F.

Talebi, N.

N. Talebi and M. Shahabadi, “Spoof surface plasmons propagating along a periodically corrugated coaxial waveguide,” J. Phys. D Appl. Phys. 43(13), 135302 (2010).
[CrossRef]

Tanaka, M.

Tanaka, T.

Thio, T.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Walker, T. R.

Wang, K. J.

Wang, Q. J.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Williams, C. R.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Yang, T. J.

Yao, J. Q.

Yu, N. F.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett.

S. A. Maier and S. R. Andrews, “Terahertz pulse propagation using plasmon-polariton-like surface modes on structured conductive surfaces,” Appl. Phys. Lett. 88(25), 251120 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

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. Phys. D Appl. Phys.

N. Talebi and M. Shahabadi, “Spoof surface plasmons propagating along a periodically corrugated coaxial waveguide,” J. Phys. D Appl. Phys. 43(13), 135302 (2010).
[CrossRef]

Nat. Mater.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. H. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Nat. Photonics

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2(3), 175–179 (2008).
[CrossRef]

Nature

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944).
[CrossRef]

Phys. Rev. B

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008).
[CrossRef]

Phys. Rev. Lett.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[CrossRef] [PubMed]

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

Rev. Mod. Phys.

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

Science

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Other

S. A. Maier, Plasmonics-Fundamentals and Applications (Springer, New York, 2007)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

(a) A set of circular through holes with diameter 2a arranged on a d × d lattice is pierced into a PCS with infinite depth ( h ). (b) Schematic structure of the designed plasmonic metamaterial with double sets of circular holes. A set of additional subwavelength circular apertures with larger diameter ρ arranged on D × D lattices are structured on the hole-array surface shown in Fig. 1(a). Note that a and d are smaller than ρ and D, respectively, at least one order of magnitude.

Fig. 2
Fig. 2

One of the fabricated samples used in the experiment. The left one is the photograph and the right one used to mark symbols.

Fig. 3
Fig. 3

The measured (a) and simulated (b) transmission spectra for one pair of samples. S0: ρ = 11 mm, and D = 18 mm; S1: a = 1 mm, d = 3 mm, ρ = 11 mm, and D = 18 mm. The simulated ones are related to the metal-plastic interface.

Equations (4)

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k | | 2 = k 2 + P A 3 k 4 d 4 ,
P = 4 π 2 A 3 ( 1 Re { α E 1 } + 1 Re { α M 1 } ) 2 .
k | | = k t ( rad ) + j G x + l G y ,
λ j l = λ j l 0 1 + P 4 π 2 n in 2 A 3 d 4 λ j l 2 ,

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