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, 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, 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, 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. M. 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

E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

M. Carras and A. De Rossi, "Field concentration by exciting surface defect modes," Opt. Lett. 31, 47-49 (2006).
[CrossRef] [PubMed]

2005

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

M. Qiu, "Photonic band structures for surface waves on structured metal surfaces," Opt. Express 13, 7583-7588 (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. P. Hibbins, B. R. Evans, and J. R. Sambles,"Experimental verification of designer surface Plasmons," Science 308, 670-672 (2005).
[CrossRef] [PubMed]

2004

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

J. B. Pendry, L. Martin-Moreno, 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]

2003

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

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]

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, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[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]

Carras, M.

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-Vidal, F. J.

J. B. Pendry, L. Martin-Moreno, 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.

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]

Kretschmann, M.

M. Kretschmann "Phase diagrams of surface plasmon polaritonic crystals" Phys. Rev. B 68, 125419 (2003).
[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, S97-S101 (2004)
[CrossRef]

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

Ozbay, E.

E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 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, 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]

Qiu, M.

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]

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]

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]

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.

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

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

Opt. Express

Opt. Lett.

Phys. Rev. B

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 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.

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]

Science

E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

J. B. Pendry, L. Martin-Moreno, F. J. Garcia-Vidal, "Mimicking surface Plasmons with structured surfaces," Science 305, 847-848 (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]

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

Other

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]

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]

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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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