Abstract

Effects of nano-scale surface geometry on surface plasmon are studied by the coordinate-transformation differential method to numerically calculate surface plasmon modes on a weakly disordered metallic surface. An air-silver surface profile with a subwavelength period and a nano-scale height at wavelength of 650 nm are chosen and it is found that the Bloch wave numbers and the surface plasmon modes are highly sensitive with distortions of only a few nanometers for periods much less than wavelength. On the contrary, distortions of long periods which are comparable to wavelength have little impact. Three typical surface profiles exhibit surface plasmon modes of wide variations.

© 2005 Optical Society of America

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References

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Appl. Opt.

J. Mod. Opt.

D. J. Nash and J. R. Sambles, “Surface plasmon-polariton study of the optical dielectric function of copper,” J. Mod. Opt. 42, 1639–1647 (1995).
[CrossRef]

D. J. Nash and J. R. Sambles, “Surface plasmon-polariton study of the optical dielectric function of silver,” J. Mod. Opt. 43, 81–91 (1996).

D. J. Nash and J. R. Sambles, “Surface plasmon-polariton study of the optical dielectric function of zinc,” J. Mod. Opt. 45, 2585–2596 (1998).
[CrossRef]

E. Popov, L. Tsonev, and D. Maystre, “Losses of plasmon surface waves on metallic grating,” J. Mod. Opt. 37, 379–387 (1990).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. (Paris)

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Phys. (Paris) 11, 235–241 (1980).

Nature

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]

Opt. Commun.

M. C. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

Opt. Express

Phys. Rev. B

I. Hooper and J. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 165,432 (2002).
[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]

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15,419–15,421 (1998).
[CrossRef]

W.-C. Liu and D. P. Tsai, “Optical tunneling effect of surface plasmon polaritons and localized surface plasmon resonance,” Phys. Rev. B 65, 155,423 (2002).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces,” Phys. Rev. B 70, 045,421 (2004).
[CrossRef]

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: An analytical study,” Phys. Rev. B 67, 35424 (2003).
[CrossRef]

A. M. Dykhne, A. K. Sarychev, and V. M. Shalaev, “Resonant transmittance through metal films with fabricated and light-induced modulation,” Phys. Rev. B 67, 195402 (2003).
[CrossRef]

Phys. Rev. Lett.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
[CrossRef]

L. Martín-Moreno, F. J. García-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]

T. Lopez-Rios, D. Mendoza, F. J. Garcia-Vidal, J. Sanchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. 81, 665–668 (1998).
[CrossRef]

Supplementary Material (9)

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Figures (7)

Fig. 1.
Fig. 1.

Three silver-air surface profiles. (a) sinusoidal profile, f(x) = h cos(2πx/d); (b)groove-like profile, f(x) = h(cos(2πx/d)+cos(3∙2πx/d)/9+cos(5∙2πx/d)/25); (c) square-well-like profile, f(x) = h (cos(2πx/d)-0.2cos(3∙2πx/d)+0.04cos(5∙2πx/d)).

Fig. 2.
Fig. 2.

Complex map of Bloch wave numbers of three air-silver surface profiles at different heights. The number near each symbol is the height of the profile in nanometer. Grating period d is 500 nm and wavelength is 650 nm. The Bloch wave number is normalized to the grating wave number Kd = 2π/d.

Fig. 3.
Fig. 3.

Movies of surface plasmon modes at different heights. (a) sinusoidal profile; (b) groove-like profile;(c) square-well-like profile. Grating period is 500 nm. The length unit is nanometer. [Media 1] [Media 2] [Media 3]

Fig. 4.
Fig. 4.

Complex map of Bloch wave numbers of three silver-air surface profiles at different heights as in Fig. 2. Grating period d is 100 nm.

Fig. 5.
Fig. 5.

Movies of surface plasmon modes at different heights. (a) sinusoidal profile; (b) groove-like profile;(c) square-well-like profile. Grating period is 100 nm. The length unit is nanometer. [Media 4] [Media 5] [Media 6]

Fig. 6.
Fig. 6.

Complex map of Bloch wave numbers of three silver-air surface profiles at different heights as in Fig. 2. Grating period d is 20 nm.

Fig. 7.
Fig. 7.

Movies of surface plasmon modes at different heights. (a) sinusoidal profile; (b) groove-like profile;(c) square-well-like profile. Grating period is 20 nm. The length unit is nanometer. [Media 7] [Media 8] [Media 9]

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