Abstract

Photonic band properties are presented for a two-dimensional rectangular-groove grating of metal into air. The properties of the surface modes are shown and discussed with a perfect electric conductor, and compared to those of surface plasmons with real metal. The same structure is also studied with real metal in the near infrared. The results are obtained with a 3-D finite element numerical code.

© 2006 Optical Society of America

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  1. E. Ozbay“Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311, pages 189–193 (2006).
    [Crossref] [PubMed]
  2. S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
    [Crossref] [PubMed]
  3. J. Zhang, Y.-H. Ye, X. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005).
    [Crossref]
  4. M. Carras and A. De Rossi, “Field concentration by exciting surface defect modes,” Opt. Lett. 31, pages 47–49 (2006).
    [Crossref] [PubMed]
  5. W.L. Barnes, A. Dereux, and T.W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [Crossref] [PubMed]
  6. J. B. Pendry, L. Martin-Moreno, and F.J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004)
    [Crossref] [PubMed]
  7. 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 (2004)
    [Crossref]
  8. F.J. Garcia de Abajo and J.J. Saenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95, 233901-1-4 (2005).
    [Crossref]
  9. Min Qiu, “Photonic band structures for surface waves on structured metal surfaces,” Opt. Express 13, 7583–7588 (2005).
    [Crossref] [PubMed]
  10. A.P. Hibbins, B.R. Evans, and J.R. Sambles, “Experimental Verification of Designer Surface Plasmons,” Science 308, 670–672 (2005).
    [Crossref] [PubMed]
  11. W. Barnes and R. Sambles, “Only Skin Deep,” Science 305, 785–786 (2004).
    [Crossref] [PubMed]
  12. W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N.P.K. Cotter, and D.J. Nash “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B 51, 11 164–11 168 (1995).
    [Crossref]
  13. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
    [Crossref]
  14. A. Giannattasio and W. L. Barnes, “Direct observation of surface plasmon-polariton dispersion,” Opt. Express 13, 428–434 (2005).
    [Crossref] [PubMed]
  15. M. Kretschmann “Phase diagrams of surface plasmon polaritonic crystals” Phys. Rev. B 68, 125419 (2003).
    [Crossref]

2006 (2)

E. Ozbay“Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311, pages 189–193 (2006).
[Crossref] [PubMed]

M. Carras and A. De Rossi, “Field concentration by exciting surface defect modes,” Opt. Lett. 31, pages 47–49 (2006).
[Crossref] [PubMed]

2005 (5)

F.J. Garcia de Abajo and J.J. Saenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95, 233901-1-4 (2005).
[Crossref]

Min Qiu, “Photonic band structures for surface waves on structured metal surfaces,” Opt. Express 13, 7583–7588 (2005).
[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]

J. Zhang, Y.-H. Ye, X. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005).
[Crossref]

A. Giannattasio and W. L. Barnes, “Direct observation of surface plasmon-polariton dispersion,” Opt. Express 13, 428–434 (2005).
[Crossref] [PubMed]

2004 (3)

J. B. Pendry, L. Martin-Moreno, and F.J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004)
[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 (2004)
[Crossref]

W. Barnes and R. Sambles, “Only Skin Deep,” Science 305, 785–786 (2004).
[Crossref] [PubMed]

2003 (2)

W.L. Barnes, A. Dereux, and T.W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

M. Kretschmann “Phase diagrams of surface plasmon polaritonic crystals” Phys. Rev. B 68, 125419 (2003).
[Crossref]

1996 (2)

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

1995 (1)

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N.P.K. Cotter, and D.J. Nash “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B 51, 11 164–11 168 (1995).
[Crossref]

Barnes, W.

W. Barnes and R. Sambles, “Only Skin Deep,” Science 305, 785–786 (2004).
[Crossref] [PubMed]

Barnes, W. L.

A. Giannattasio and W. L. Barnes, “Direct observation of surface plasmon-polariton dispersion,” Opt. Express 13, 428–434 (2005).
[Crossref] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N.P.K. Cotter, and D.J. Nash “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B 51, 11 164–11 168 (1995).
[Crossref]

Barnes, W.L.

W.L. Barnes, A. Dereux, and T.W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Carras, M.

Cotter, N.P.K.

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N.P.K. Cotter, and D.J. Nash “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B 51, 11 164–11 168 (1995).
[Crossref]

De Rossi, A.

Dereux, A.

W.L. Barnes, A. Dereux, and T.W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Ebbesen, T.W.

W.L. Barnes, A. Dereux, and T.W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[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]

Garcia de Abajo, F.J.

F.J. Garcia de Abajo and J.J. Saenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95, 233901-1-4 (2005).
[Crossref]

Garcia-Vidal, F.J.

J. B. Pendry, L. Martin-Moreno, and F.J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004)
[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 (2004)
[Crossref]

Giannattasio, A.

Hibbins, A.P.

A.P. Hibbins, B.R. Evans, and J.R. Sambles, “Experimental Verification of Designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Kitson, S. C.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N.P.K. Cotter, and D.J. Nash “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B 51, 11 164–11 168 (1995).
[Crossref]

Kretschmann, M.

M. Kretschmann “Phase diagrams of surface plasmon polaritonic crystals” Phys. Rev. B 68, 125419 (2003).
[Crossref]

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F.J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004)
[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 (2004)
[Crossref]

Nash, D.J.

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N.P.K. Cotter, and D.J. Nash “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B 51, 11 164–11 168 (1995).
[Crossref]

Ozbay, E.

E. Ozbay“Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311, pages 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, S97–S101 (2004)
[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]

Preist, T. W.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N.P.K. Cotter, and D.J. Nash “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B 51, 11 164–11 168 (1995).
[Crossref]

Qiu, Min

Rochon, P.

J. Zhang, Y.-H. Ye, X. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005).
[Crossref]

Saenz, J.J.

F.J. Garcia de Abajo and J.J. Saenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95, 233901-1-4 (2005).
[Crossref]

Sambles, J. R.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N.P.K. Cotter, and D.J. Nash “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B 51, 11 164–11 168 (1995).
[Crossref]

Sambles, J.R.

A.P. Hibbins, B.R. Evans, and J.R. Sambles, “Experimental Verification of Designer Surface Plasmons,” Science 308, 670–672 (2005).
[Crossref] [PubMed]

Sambles, R.

W. Barnes and R. Sambles, “Only Skin Deep,” Science 305, 785–786 (2004).
[Crossref] [PubMed]

Wang, X.

J. Zhang, Y.-H. Ye, X. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005).
[Crossref]

Xiao, M.

J. Zhang, Y.-H. Ye, X. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005).
[Crossref]

Ye, Y.-H.

J. Zhang, Y.-H. Ye, X. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005).
[Crossref]

Zhang, J.

J. Zhang, Y.-H. Ye, X. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005).
[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 (2004)
[Crossref]

Nature (1)

W.L. Barnes, A. Dereux, and T.W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (4)

J. Zhang, Y.-H. Ye, X. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots and two-dimensional surface plasmons,” Phys. Rev. B 72, 201306 (2005).
[Crossref]

M. Kretschmann “Phase diagrams of surface plasmon polaritonic crystals” Phys. Rev. B 68, 125419 (2003).
[Crossref]

W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N.P.K. Cotter, and D.J. Nash “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B 51, 11 164–11 168 (1995).
[Crossref]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227–6244 (1996).
[Crossref]

Phys. Rev. Lett. (2)

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

F.J. Garcia de Abajo and J.J. Saenz, “Electromagnetic surface modes in structured perfect-conductor surfaces,” Phys. Rev. Lett. 95, 233901-1-4 (2005).
[Crossref]

Science (4)

J. B. Pendry, L. Martin-Moreno, and F.J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004)
[Crossref] [PubMed]

E. Ozbay“Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311, pages 189–193 (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]

W. Barnes and R. Sambles, “Only Skin Deep,” Science 305, 785–786 (2004).
[Crossref] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Structure of the metal coated two-dimensional array of squared bumps

Fig. 2.
Fig. 2.

Photonic bands of surface modes of structure in figure 1 with depth h=0.2×Λ (left) and h=0.4×Λ (right). The thick dark lines correspond to α=Λ/√2 while the thick grey lines correspond to αΛ/2. The solid dots are obtained for metal with finite permittivity ε′=-50, for α=Λ/√2, whereas PEC is simulated in the other cases.

Fig. 3.
Fig. 3.

Magnitude of the Ez field, at an interface PEC/air, on the x-y, z-y and z-x planes corresponding to (a) XX point k = ( π Λ , 0 ) ) and low frequency band, (b) M point, low frequency band, (c) and (d) doubly degenerated M modes of the high frequency band. The depth of the grooves is h=0.2.Λ and α=Λ/√2. The (x,y) cross-section, represented by a dashed-dotted line on the top figures, is situated at 0.3Λ from the metallic plane. The (y,z) and (x,z) planes are also represented by dashed-dotted lines on the bottom figures, where the dotted square shows the position of the bumps.

Fig. 4.
Fig. 4.

Magnitude of the Ez field, at an interface metal(ε=-50)/air, on the x-y plane corresponding to (a) XX point and low frequency band, (b) M point, low frequency band, (c) and (d) doubly degenerated M modes of the high frequency band. The depth of the grooves is h=0.2.Λ and α=Λ/√2. The (x,y) cross-section is situated at 0.3Λ from the metallic plane.

Fig. 5.
Fig. 5.

Field cross sections at the interface metal (ε=-50)/air corresponding to X point and high frequency band : Ex (a), Ey (b) and Ez (c). h=0.4Λ and α=Λ/√2. The (x,y) cross-section is situated at 0.3Λ from the metallic plane.

Fig. 6.
Fig. 6.

Position of the modes at the X and M points for several values of h Λ with PEC, for α=Λ/√2. The corresponding Ez cross-sections in a (x,y) plane are presented near to each set of points. The position of the light line for the X and M points are represented by two grey lines. Index 0 is for the low frequency modes.

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