Abstract

We demonstrate that surface waves in structured perfect electric conductor surfaces can be self-collimated using the finite-difference time-domain method. The self-collimation frequency is obtained from the equi-frequency contours of a perfect electric conductor patterned with an array of square holes. The field patterns of the self-collimated surface wave, obtained using the periodic boundary conditions, show that the surface waves propagate with almost no spreading. We also show that self-collimation phenomena can be observed for the hybrid surface plasmon waves in structured metal surfaces using the finite-difference time-domain method with the Drude model. It is shown that for a structured silver surface the self-collimation can be achieved at the frequencies in the infrared region.

© 2007 Optical Society of America

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  1. T. W. Ebbesen, H. J. Lezec, J. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667 (1998).
    [CrossRef]
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824 (2003).
    [CrossRef]
  3. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature (London) 440, 508 (2006).
    [CrossRef]
  4. S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990 (2004).
    [CrossRef]
  5. D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
    [CrossRef]
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2006 (3)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature (London) 440, 508 (2006).
[CrossRef]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Z. Ruan and M. Qiu, "Negative refraction and sub-wavelength imaging through surface waves on structured perfect conductor surfaces," Opt. Express 14, 6172 (2006).
[CrossRef] [PubMed]

2005 (4)

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surfaces with holes in them: new plasmonic metamaterials," J. Opt. A: Pure Appl. Opt. 7, S97 (2005).

F. J. G. de Abajo and J. J. Sáenz, "Electromagnetic surface modes in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233,901 (2005).

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

M. Qiu, "Photonic band structures for surface waves on structured metal surfaces," Opt. Express 13, 7583 (2005).
[CrossRef] [PubMed]

2004 (2)

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with structured surfaces," Science 305, 847 (2004).
[CrossRef] [PubMed]

2003 (2)

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824 (2003).
[CrossRef]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

1998 (1)

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

Ahn, Y. H.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Barclay, P. E.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824 (2003).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature (London) 440, 508 (2006).
[CrossRef]

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

de Abajo, F. J. G.

F. J. G. de Abajo and J. J. Sáenz, "Electromagnetic surface modes in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233,901 (2005).

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824 (2003).
[CrossRef]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature (London) 440, 508 (2006).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature (London) 440, 508 (2006).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature (London) 424, 824 (2003).
[CrossRef]

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

Evans, B. R.

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

Friedman, M. D.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surfaces with holes in them: new plasmonic metamaterials," J. Opt. A: Pure Appl. Opt. 7, S97 (2005).

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with structured surfaces," Science 305, 847 (2004).
[CrossRef] [PubMed]

Ghaemi, J. F.

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

Hibbins, A. P.

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

Hohng, S. C.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Ibanescu, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Joannopoulos, J. D.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Johnson, T. J.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Kim, D. S.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Kim, J.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Kolodziejski, L. A.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Laluet, J.-Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature (London) 440, 508 (2006).
[CrossRef]

Lezec, H. J.

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

Lienau, C.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Maier, S. A.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Malyarchuk, V.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Martín-Moreno, L.

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surfaces with holes in them: new plasmonic metamaterials," J. Opt. A: Pure Appl. Opt. 7, S97 (2005).

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with structured surfaces," Science 305, 847 (2004).
[CrossRef] [PubMed]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Painter, O.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Park, J.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Park, Q. H.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Pendry, J. B.

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surfaces with holes in them: new plasmonic metamaterials," J. Opt. A: Pure Appl. Opt. 7, S97 (2005).

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, "Mimicking Surface Plasmons with structured surfaces," Science 305, 847 (2004).
[CrossRef] [PubMed]

Petrich, G. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Qiu, M.

Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Ruan, Z.

Sáenz, J. J.

F. J. G. de Abajo and J. J. Sáenz, "Electromagnetic surface modes in structured perfect-conductor surfaces," Phys. Rev. Lett. 95, 233,901 (2005).

Sambles, J. R.

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

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Soljacic, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Tandon, S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Thio, T.

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

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature (London) 440, 508 (2006).
[CrossRef]

Wolff, P. A.

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

Yee, K. J.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Yoon, Y. C.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of Surface-Plasmon Radiation in Plasmonic Band-Gap Nanostructures," Phys. Rev. Lett. 91, 143,901 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, "Low-loss fiber accessible plasmon waveguide for planar energy guiding and sensing," Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212 (1999).
[CrossRef]

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

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, "Surfaces with holes in them: new plasmonic metamaterials," J. Opt. A: Pure Appl. Opt. 7, S97 (2005).

Nat. Mater. (1)

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nat. Mater. 5, 93 (2006).
[CrossRef] [PubMed]

Nature (London) (3)

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Figures (6)

Fig. 1.
Fig. 1.

(a). A 3D structure of a PEC or a metal surface with a square array of square holes on its surface. The period is a, the hole size d, and the hole depth h. (b). A unit cell which is used in the calculation of band structure. Periodic boundary conditions are used in the x- and y- directions and PMLs are placed at the boundaries in the z-direction. (c). A unit cell of the size 8√2a×√2a×8a which is used to calculate a mode propagating in the ΓM direction. A Gaussian beam of width 5a is launched along the ΓM direction.

Fig. 2.
Fig. 2.

(a) A band structure and (b) the EFCs for the structured PEC surface with a hole size d = 0.875a and a hole depth h = a. Notice that there are flat contours in the vicinity of f = 0.52c/a.

Fig. 3.
Fig. 3.

The field cross sections of the self-collimated surface wave for the PEC structure shown in Fig. 1; (a) Ez in the x-z plane, (b) Ez in the y-z plane, and (c) Ez at the PEC/air interface in the x-y plane at t = 1048a when a 5a-wide CW source is launched. (d) Ez at the PEC/air interface in the x-y plane at t = 1036a. (e) Ez at the PEC/air interface in the x-y plane at the M point. (f) Time evolution of Ez .

Fig. 4.
Fig. 4.

(a) A band structure and (b) the EFCs for a structured metal surface with the plasma frequency ωp =1, the damping constant γ=0, the hole size d = 0.6a and the hole depth h= a; The equifrequency contours are flat for the frequencies in the vicinity of f = 0.364c/a.

Fig. 5.
Fig. 5.

The field cross sections of the self-collimated surface wave for a structured metal surface with ωp = 1, γ = 0, d = 0.6a and h = a; (a) Ez in the x-z plane, (b) Ez in the y-z plane, and (c) Ez at the metal/air interface in the x-y plane at t = 470a (d) Ez at the metal/air interface in the x-y plane at t = 494a when the 5a-wide CW source is launched. (e) Time evolution of Ez .

Fig. 6.
Fig. 6.

The field cross sections of the self-collimated surface wave for a structured silver surface with ωp = 6.37, γ = 0.042441, d = 0.8a and h = a; (a) Ez through the hole centers in the x-z plane, (b) Ez through the maximum point in the y-z plane, and (c) Ez at the silver/air interface in the x-y plane at t = 54a (d) Ez at the silver/air interface in the x-y plane at t = 120a. (e) Time evolution of Ez .

Equations (2)

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ε m = 1 ω p 2 ω ( ω + i γ ) ,
k SP = k 0 ε m ε d ε m + ε d ,

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