Abstract

Surface plasmon-like (SPL) modes are the electromagnetic surface eigenmodes supported by the structured perfectly conducting surfaces. The standard eigenvalue-solving method is adopted to solve these SPL modes. The field patterns of the SPL modes in the square holes for inplane wavevectors kx=2π/2d and kx=2π/d are TE10-like and TE11, respectively. However, the field patterns can no longer be identified as any particular waveguide mode for other in-plane wavevectors. The dispersion relations of the SPL modes are obtained numerically. The change in mode character with wavevector prevents the dispersion relation from being derived by assuming only the fundamental mode in the holes. On a thin perfect conductor perforated with structures, the SPL mode splits into a high-frequency anti-symmetric mode and a low-frequency symmetric mode, which is caused by the mutual interaction of the electromagnetic evanescent fields on both sides.

© 2006 Optical Society of America

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References

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  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988).
  2. D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
    [CrossRef]
  3. W. L. Barnes, A. Dereuux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  4. E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  5. A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Grating-coupled surface plasmons at microwave frequencies," J. Appl. Phys. 86, 1791-1795 (1999).
    [CrossRef]
  6. F. Miyamaru and M. Hangyo, "Strong enhancement of terahertz transmission for a three-layer heterostructure of metal hole arrays," Phys. Rev. B 72, 035429 (2005).
    [CrossRef]
  7. J. G. Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201306 (2003).
    [CrossRef]
  8. H. Cao and A. Nahata, "Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures," Opt. Express 12, 1004-1010 (2004).
    [CrossRef] [PubMed]
  9. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  10. 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, S97-S101 (2005).
    [CrossRef]
  11. W. Barnes and R. Sambles, "Only skin deep," Science 305, 785-786 (2004).
    [CrossRef] [PubMed]
  12. A. P. Hibbins, B. R. Evans, and J. R. Sambles, "Experimental verification of designer surface plasmons," Science 308, 670-672 (2005).
    [CrossRef] [PubMed]
  13. A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cutoff," Phys. Rev. Lett. 96, 073904 (2006).
    [CrossRef] [PubMed]
  14. F. J. García de Abajo and J. J. Sáenz, "Electromagnetic surface modes in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233901 (2005).
    [CrossRef] [PubMed]
  15. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge University Press, New York, 1992).
  16. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method 2nd Ed. (Artech House, Norwood, 2000).
  17. Y. C. Lan, "Optical tunneling effect of localized surface plasmon: a simulation study using particle-in-cell method," Appl. Phys. Lett. 88, 071109 (2006).
    [CrossRef]
  18. C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (Institute of Physics Publishing, London, 1991).
    [CrossRef]
  19. C. S. Lee, S. W. Lee, and S. L. Chuang, "Plot of modal field distribution in rectangular and circular waveguides," IEEE Trans. Microwave Theory Tech. 33, 271-274 (1985).
    [CrossRef]
  20. K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001).
  21. F. J. García de Abajo, J. J. Sáenz, I. Campillo, and J. S. Dolado, "Site and lattice resonances in metallic hole arrays," Opt. Express 14, 7-18 (2006).
    [CrossRef]
  22. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
    [CrossRef] [PubMed]

2006 (4)

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cutoff," Phys. Rev. Lett. 96, 073904 (2006).
[CrossRef] [PubMed]

Y. C. Lan, "Optical tunneling effect of localized surface plasmon: a simulation study using particle-in-cell method," Appl. Phys. Lett. 88, 071109 (2006).
[CrossRef]

F. J. García de Abajo, J. J. Sáenz, I. Campillo, and J. S. Dolado, "Site and lattice resonances in metallic hole arrays," Opt. Express 14, 7-18 (2006).
[CrossRef]

2005 (4)

F. J. García de Abajo and J. J. Sáenz, "Electromagnetic surface modes in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233901 (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, S97-S101 (2005).
[CrossRef]

F. Miyamaru and M. Hangyo, "Strong enhancement of terahertz transmission for a three-layer heterostructure of metal hole arrays," Phys. Rev. B 72, 035429 (2005).
[CrossRef]

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

2004 (3)

H. Cao and A. Nahata, "Resonantly enhanced transmission of terahertz radiation through a periodic array of subwavelength apertures," Opt. Express 12, 1004-1010 (2004).
[CrossRef] [PubMed]

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

W. Barnes and R. Sambles, "Only skin deep," Science 305, 785-786 (2004).
[CrossRef] [PubMed]

2003 (2)

J. G. Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201306 (2003).
[CrossRef]

W. L. Barnes, A. Dereuux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2001 (1)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
[CrossRef] [PubMed]

1999 (1)

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Grating-coupled surface plasmons at microwave frequencies," J. Appl. Phys. 86, 1791-1795 (1999).
[CrossRef]

1985 (1)

C. S. Lee, S. W. Lee, and S. L. Chuang, "Plot of modal field distribution in rectangular and circular waveguides," IEEE Trans. Microwave Theory Tech. 33, 271-274 (1985).
[CrossRef]

1981 (1)

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Barnes, W.

W. Barnes and R. Sambles, "Only skin deep," Science 305, 785-786 (2004).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereuux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Bolivar, P. H.

J. G. Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201306 (2003).
[CrossRef]

Campillo, I.

Cao, H.

Chuang, S. L.

C. S. Lee, S. W. Lee, and S. L. Chuang, "Plot of modal field distribution in rectangular and circular waveguides," IEEE Trans. Microwave Theory Tech. 33, 271-274 (1985).
[CrossRef]

Dereuux, A.

W. L. Barnes, A. Dereuux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Dolado, J. S.

Ebbesen, T. W.

W. L. Barnes, A. Dereuux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Evans, B. R.

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

García de Abajo, F. J.

F. J. García de Abajo, J. J. Sáenz, I. Campillo, and J. S. Dolado, "Site and lattice resonances in metallic hole arrays," Opt. Express 14, 7-18 (2006).
[CrossRef]

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

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, S97-S101 (2005).
[CrossRef]

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

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Hangyo, M.

F. Miyamaru and M. Hangyo, "Strong enhancement of terahertz transmission for a three-layer heterostructure of metal hole arrays," Phys. Rev. B 72, 035429 (2005).
[CrossRef]

Hibbins, A. P.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cutoff," Phys. Rev. Lett. 96, 073904 (2006).
[CrossRef] [PubMed]

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

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Grating-coupled surface plasmons at microwave frequencies," J. Appl. Phys. 86, 1791-1795 (1999).
[CrossRef]

Hooper, I. R.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cutoff," Phys. Rev. Lett. 96, 073904 (2006).
[CrossRef] [PubMed]

Kurz, H.

J. G. Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201306 (2003).
[CrossRef]

Lan, Y. C.

Y. C. Lan, "Optical tunneling effect of localized surface plasmon: a simulation study using particle-in-cell method," Appl. Phys. Lett. 88, 071109 (2006).
[CrossRef]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Grating-coupled surface plasmons at microwave frequencies," J. Appl. Phys. 86, 1791-1795 (1999).
[CrossRef]

Lee, C. S.

C. S. Lee, S. W. Lee, and S. L. Chuang, "Plot of modal field distribution in rectangular and circular waveguides," IEEE Trans. Microwave Theory Tech. 33, 271-274 (1985).
[CrossRef]

Lee, S. W.

C. S. Lee, S. W. Lee, and S. L. Chuang, "Plot of modal field distribution in rectangular and circular waveguides," IEEE Trans. Microwave Theory Tech. 33, 271-274 (1985).
[CrossRef]

Lezec, H. J.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Lockyear, M. J.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cutoff," Phys. Rev. Lett. 96, 073904 (2006).
[CrossRef] [PubMed]

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, S97-S101 (2005).
[CrossRef]

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

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Miyamaru, F.

F. Miyamaru and M. Hangyo, "Strong enhancement of terahertz transmission for a three-layer heterostructure of metal hole arrays," Phys. Rev. B 72, 035429 (2005).
[CrossRef]

Nahata, A.

Ozbay, E.

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Pellerin, K. M.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
[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, S97-S101 (2005).
[CrossRef]

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

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Rivas, J. G.

J. G. Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201306 (2003).
[CrossRef]

Sáenz, J. J.

F. J. García de Abajo, J. J. Sáenz, I. Campillo, and J. S. Dolado, "Site and lattice resonances in metallic hole arrays," Opt. Express 14, 7-18 (2006).
[CrossRef]

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

Sambles, J. R.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cutoff," Phys. Rev. Lett. 96, 073904 (2006).
[CrossRef] [PubMed]

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

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Grating-coupled surface plasmons at microwave frequencies," J. Appl. Phys. 86, 1791-1795 (1999).
[CrossRef]

Sambles, R.

W. Barnes and R. Sambles, "Only skin deep," Science 305, 785-786 (2004).
[CrossRef] [PubMed]

Sarid, D.

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Schotsch, C.

J. G. Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201306 (2003).
[CrossRef]

Thio, T.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Y. C. Lan, "Optical tunneling effect of localized surface plasmon: a simulation study using particle-in-cell method," Appl. Phys. Lett. 88, 071109 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

C. S. Lee, S. W. Lee, and S. L. Chuang, "Plot of modal field distribution in rectangular and circular waveguides," IEEE Trans. Microwave Theory Tech. 33, 271-274 (1985).
[CrossRef]

J. Appl. Phys. (1)

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Grating-coupled surface plasmons at microwave frequencies," J. Appl. Phys. 86, 1791-1795 (1999).
[CrossRef]

J. Opt. A: Pure Appl. Opt (1)

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, S97-S101 (2005).
[CrossRef]

Nature (1)

W. L. Barnes, A. Dereuux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. B (2)

F. Miyamaru and M. Hangyo, "Strong enhancement of terahertz transmission for a three-layer heterostructure of metal hole arrays," Phys. Rev. B 72, 035429 (2005).
[CrossRef]

J. G. Rivas, C. Schotsch, P. H. Bolivar, and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201306 (2003).
[CrossRef]

Phys. Rev. Lett (1)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett 86, 1114-1117 (2001).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, "Waveguide arrays as plasmonic metamaterials: transmission below cutoff," Phys. Rev. Lett. 96, 073904 (2006).
[CrossRef] [PubMed]

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

Science (4)

W. Barnes and R. Sambles, "Only skin deep," Science 305, 785-786 (2004).
[CrossRef] [PubMed]

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

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

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

Other (5)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988).

C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (Institute of Physics Publishing, London, 1991).
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge University Press, New York, 1992).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method 2nd Ed. (Artech House, Norwood, 2000).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic simulated structure. The period of the repeated units d and the depth of the square holes t are 10 mm and 30 mm, respectively. The width of the holes w is changed from 1 mm to 9 mm.

Fig. 2.
Fig. 2.

Electric field vectors of SPL modes on holey perfect-conductor surfaces and variations of equivalent charges Q with x-position: (a) kx =2π/2d and (b) kx =2π/d, for the holes of width 7 mm and depth 30 mm.

Fig. 3.
Fig. 3.

Amplitudes of Ex field against z position for SPL modes with the holes of width 7 mm, a depth of 30 mm and in-plane wavevectors of kx =2π/2d and kx =2π/d. The decays of the field on both sides of the peak are fitted to the exponential functions.

Fig. 4.
Fig. 4.

Dispersion relations of SPL modes on holey perfect-conductor surfaces with holes of three widths - 5 mm, 7 mm and 9 mm. The light line is also presented for comparison.

Fig. 5.
Fig. 5.

First branch of dispersion relations of SPL modes in Fig. 4. The analytical dispersion relations derived in Ref. [9] are also presented by dashed lines for comparison.

Fig. 6.
Fig. 6.

Schematic simulated structure for SPL modes on a thin structured perfect conductor. The period of the repeated units, the width of the hole and the thickness of the conductor are 10 mm, 7 mm and 4 mm, respectively.

Fig. 7.
Fig. 7.

Amplitudes of Ex field as a function of z position for SPL modes on a 4 mmthick, holey perfect conductor with holes of width 7 mm and in-plane wavevector kx =2π/2d. The origin of the z-axis is located at the mid depth in the hole.

Fig. 8.
Fig. 8.

Dispersion relations of SPL modes on a thin perfect conductor perforated with square holes. The structure and dimensions are given in Fig. 6. The light line and the dispersion relation of the SPL modes on holey perfect-conductor surfaces with the holes of width 7 mm and depth 30 mm shown in Fig. 4 are also presented for comparison.

Fig. 9.
Fig. 9.

Simulation structure and snapshot of electron sheet for the numerical experiment of SPL modes excited by the electron sheet. The dimensions of the structure are given in Fig. 6.

Fig. 10.
Fig. 10.

Spectrum of the Ex field measured at the center of the hole near the lower interface for the SPL modes excited by the electron sheet. The simulation structure and dimensions are given in Fig. 9.

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