Abstract

Surface plasmon excitation by normally incident light on surface-relief metallic diffraction gratings is studied numerically. Predominantly unidirectional excitation is achieved with a grating of either a slanted lamellar or an inclined sinusoidal groove profile, both having shallow depths. Maps of Poynting vector illustrate that the energy flow turns from normal incidence in the far-field region to a pattern almost parallel to the grating surface in the required direction of excitation of a single SPP wave.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phylos. Mag. 4, 396-402 (1902).
  2. U. Fano, "The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld’s waves)," J. Opt. Soc. Am. 31, 213-222 (1941).
    [CrossRef]
  3. A. Hessel and A. A. Oliner, "A new theory of Wood’s anomalies on optical gratings," Appl. Opt. 4, 1275-1297 (1965).
    [CrossRef]
  4. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  5. D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
    [CrossRef]
  6. 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, 667 - 669 (1998)
    [CrossRef]
  7. S. Enoch, E. Popov, M. Nevière, and R. Reinisch, "Enhanced light transmission by hole arrays," J. Opt. A: Pure Appl. Opt. 4, S83-S87 (2002).
    [CrossRef]
  8. E. Popov, N. Bonod, M. Neviere, H. Rigneault, P.-F. Lenne, and P. Chaumet, "Surface plasmon excitation on a single subwavelength hole in a metallic sheet," Appl. Opt. 44, 2332-2337 (2005).
    [CrossRef] [PubMed]
  9. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  10. E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  11. E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, "Launching and decoupling surface plasmon via micro-gratings," Appl. Phys. Lett. 83, 4936-4938 (2003).
    [CrossRef]
  12. D. Egorov, B. S. Dennis, G. Blumberg, and M. I. Haftel, "Two-dimensional control of surface plasmons and directional beaming from arrays of sub-wavelength apertures," Phys. Rev. B 70, 033404 (2004).
    [CrossRef]
  13. J.-Y. Laluet, E. Devaux, C. Genet, J.-C. Weeber, and A. Dereux, "Optimization of surface plasmons launching from subwavelength hole arrays: modelling and experiments," Opt. Express 15, 3488-3495 (2007).
    [CrossRef] [PubMed]
  14. F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, A. Dereux, "Efficient unidirectional nanoslit couplers for surface plasmons," Nature Phys. 3, 324-328 (2007).
    [CrossRef]
  15. M. Neviere, "The homogeneous problem," in Electromagnetic theory of gratings, R. Petit ed., (Springer-Verlag, 1980), Chap. 5.
  16. B. Wang, J. Jiang, and G. P. Nordin, "Compact slanted grating couplers," Opt. Express 12, 3313-3326 (2004).
    [CrossRef] [PubMed]
  17. M. Nevière and E. Popov, Light Propagation in Periodic Media: Diffraction Theory and Design (Marcel Dekker, New York, 2003).
  18. T. W. Preist, J. B. Harris, N. P. Wanstall, and J. R. Sambles, "Optical response of blazed and overhanging gratings using oblique Chandezon transformations," J. Mod. Opt. 44, 1073-1080 (1997).
  19. L. Li, "Oblique-coordinate-system-based Chandezon method for modeling one-dimensionally periodic, multilayer, inhomogeneous, anisotropic gratings," J. Opt. Soc. Am. A 16, 2521-2531 (1999).
    [CrossRef]
  20. E. Popov, L. Tsonev, and D. Maystre, "Gratings-general properties of the Littrow mounting and energy flow distribution," J. Mod. Opt. 37, 367-377 (1990).
    [CrossRef]

2007

J.-Y. Laluet, E. Devaux, C. Genet, J.-C. Weeber, and A. Dereux, "Optimization of surface plasmons launching from subwavelength hole arrays: modelling and experiments," Opt. Express 15, 3488-3495 (2007).
[CrossRef] [PubMed]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, A. Dereux, "Efficient unidirectional nanoslit couplers for surface plasmons," Nature Phys. 3, 324-328 (2007).
[CrossRef]

2006

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

2005

2004

B. Wang, J. Jiang, and G. P. Nordin, "Compact slanted grating couplers," Opt. Express 12, 3313-3326 (2004).
[CrossRef] [PubMed]

D. Egorov, B. S. Dennis, G. Blumberg, and M. I. Haftel, "Two-dimensional control of surface plasmons and directional beaming from arrays of sub-wavelength apertures," Phys. Rev. B 70, 033404 (2004).
[CrossRef]

2003

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, "Launching and decoupling surface plasmon via micro-gratings," Appl. Phys. Lett. 83, 4936-4938 (2003).
[CrossRef]

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

2002

S. Enoch, E. Popov, M. Nevière, and R. Reinisch, "Enhanced light transmission by hole arrays," J. Opt. A: Pure Appl. Opt. 4, S83-S87 (2002).
[CrossRef]

1999

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, 667 - 669 (1998)
[CrossRef]

1997

T. W. Preist, J. B. Harris, N. P. Wanstall, and J. R. Sambles, "Optical response of blazed and overhanging gratings using oblique Chandezon transformations," J. Mod. Opt. 44, 1073-1080 (1997).

1990

E. Popov, L. Tsonev, and D. Maystre, "Gratings-general properties of the Littrow mounting and energy flow distribution," J. Mod. Opt. 37, 367-377 (1990).
[CrossRef]

1980

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
[CrossRef]

1965

1941

1902

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phylos. Mag. 4, 396-402 (1902).

Appl. Opt.

Appl. Phys. Lett.

E. Devaux, T. W. Ebbesen, J.-C. Weeber, and A. Dereux, "Launching and decoupling surface plasmon via micro-gratings," Appl. Phys. Lett. 83, 4936-4938 (2003).
[CrossRef]

J. Mod. Opt.

T. W. Preist, J. B. Harris, N. P. Wanstall, and J. R. Sambles, "Optical response of blazed and overhanging gratings using oblique Chandezon transformations," J. Mod. Opt. 44, 1073-1080 (1997).

E. Popov, L. Tsonev, and D. Maystre, "Gratings-general properties of the Littrow mounting and energy flow distribution," J. Mod. Opt. 37, 367-377 (1990).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

S. Enoch, E. Popov, M. Nevière, and R. Reinisch, "Enhanced light transmission by hole arrays," J. Opt. A: Pure Appl. Opt. 4, S83-S87 (2002).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[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, 667 - 669 (1998)
[CrossRef]

Nature Phys.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, A. Dereux, "Efficient unidirectional nanoslit couplers for surface plasmons," Nature Phys. 3, 324-328 (2007).
[CrossRef]

Opt. Express

Phylos. Mag.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phylos. Mag. 4, 396-402 (1902).

Phys. Rev. B

D. Egorov, B. S. Dennis, G. Blumberg, and M. I. Haftel, "Two-dimensional control of surface plasmons and directional beaming from arrays of sub-wavelength apertures," Phys. Rev. B 70, 033404 (2004).
[CrossRef]

Phys. Rev. Lett.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
[CrossRef]

Science

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

Other

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

M. Nevière and E. Popov, Light Propagation in Periodic Media: Diffraction Theory and Design (Marcel Dekker, New York, 2003).

M. Neviere, "The homogeneous problem," in Electromagnetic theory of gratings, R. Petit ed., (Springer-Verlag, 1980), Chap. 5.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Slanted gratings of period d made of aluminium with refractive index n=1.378+i 7.616, illuminated in normal incidence in TM polarization with a wavelength λ=632.8 nm. a. Lamellar grating : groove width c, groove height h, inclination angle α; b. Sinusoidal grating: groove height h, inclination angle α.

Fig. 2.
Fig. 2.

Amplitude ratio of the −1st to the +1st order as a function of the groove height h and the inclination angle α. (a) lamellar geometry, d=600 nm. (b) sinusoidal geometry, d=627 nm.

Figs. 3.
Figs. 3.

Lamellar grating with d=0.6 µm, c=0.4d, λ=632.8 nm. Left vertical axis: normalized H + z,1/H - z,0, H + z,0/H - z,0 and H + z,-1/H - z,0 amplitudes of the −1st, 0th and +1st reflected orders, respectively, as a function (a) of the groove height h (with α=20°) and (b) the inclination angle α (with h=65 nm). Right vertical axis: reflected efficiency.

Fig. 4.
Fig. 4.

Sinusoidal grating. The 0th-order amplitude as a function of h (in µm) and the inclination angle α (in degrees).

Fig. 5.
Fig. 5.

Colour map: Norm of the Poynting vector, black lines: Lines of energy flow. Five periods are represented, and one line is plotted per period for the same grating as in Fig. 3 (with h=65 nm, d=0.6 µm, c=0.4d, λ=632.8 nm).

Fig. 6.
Fig. 6.

Poynting vectors plotted in the near field area above a sinusoidal grating illuminated in normal incidence. d=626.67 nm, α=27.5 ° and h=59.94 nm.

Metrics