Abstract

We describe a method to observe the directional emission of electromagnetic radiation produced by the radiative decay of surface plasmon-polaritons (SPPs) that allows the dispersion of the modes in k-space to be directly visualized. The method presented here opens up the possibility of characterizing the effect of a wide range of surface morphologies on SPP dispersion. As an example we show the formation of a stop-band for SPPs when the metal surface is modulated in the form of a diffraction grating.

© 2005 Optical Society of America

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References

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  13. S. Wedge, I. R. Hooper, I. Sage, W. L. Barnes, �??Light emission through a corrugated metal film: The role of cross-coupled surface plasmon polaritons,�?? Phys. Rev. B. 69, 245418 (2004).
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Anal. Biochem.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, �??Radiative decay engineering 4. Experimental studies of surface plasmon-coupled directional emission,�?? Anal. Biochem. 324, 170-182 (2004).
[CrossRef]

Appl. Phys. Lett.

Z. Liu, N. Fang, T. J. Yen, X. Zhang, �??Rapid growth of evanescent wave by a silver superlens,�?? Appl. Phys. Lett. 83, 5184-5186 (2003).
[CrossRef]

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

Applied Optics

P. R. Auvil, J. B. Ketterson, Y. Kim, and A. Kryukov, �??Simple model for the observed plasmon conical radiation interference patterns in a Kretschmann configuration,�?? Applied Optics 37, 8448-8452 (1998).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Optics Communications

H. J. Simon and J. K. Guha, �??Directional surface plasmon scattering from silver films,�?? Optics Communications 18, 391-394 (1976).
[CrossRef]

Phys. Rev. B

J. Moreland, A. Adams, and P. K. Hansma, �??Efficiency of light-emission from surface-plasmons,�?? Phys. Rev. B 25, 2297-2300 (1982).
[CrossRef]

W. A. Murray, S. Astilean, and W. L. Barnes, �??Transition from localized surface plasmon resonance to extended surface plasmon-polariton as metallic nanoparticles merge to form a periodic hole array,�?? Phys. Rev. B 69, 165047 (2004).
[CrossRef]

Phys. Rev. B.

S. Wedge, I. R. Hooper, I. Sage, W. L. Barnes, �??Light emission through a corrugated metal film: The role of cross-coupled surface plasmon polaritons,�?? Phys. Rev. B. 69, 245418 (2004).
[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

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, �??Mimicking surface plasmons with structured surfaces,�?? Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Other

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

D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination (Chelsea, New York, 1999).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of the geometry used for the experiment. a) Planar silver surface: a single cone of light is emitted into the silica substrate. b) Corrugated silver surface: the central cone (zero order scattering) is now intersected by the other cones of light due to SPPs scattered by the grating with Bragg vector G .

Fig. 2.
Fig. 2.

Representation of the stop-bands in k-space. The stop-bands form at kx =G/2 where the circles intersect each other.

Fig. 3.
Fig. 3.

Direct image of the conical radiation in k-space as recorded by the CCD. a) Planar control sample. b) The presence of a grating introduces new scattering events. As a result, a stop-band opens up at the intersection of the two circles, one generated by non-scattered SPPs (much brighter) and the other resulting from scattering processes (faint). The extra line that is noted crossing the circle, at the top-left, is due to SPPs excited at the silver/silica interface, but these do not produce a visible stop-band.

Fig. 4.
Fig. 4.

The conical radiation due to the different SPP scattering processes is projected into a flat screen (CCD) and thus the resulting image in k-space is distorted, as shown in this schematic illustration. The image on the screen would have been similar to that drawn in Fig. 1b if the radiation had been projected onto a hemispherical screen.

Fig. 5.
Fig. 5.

Geometry and angles chosen to define the wavevector of the scattered light, n k 0 , in k-space.

Fig. 6.
Fig. 6.

SPP band gaps forming in 50 nm thin metallic films deposited on a grating. Picture (a) shows again the case where the grating is not present. The other pictures refer to gratings with amplitude of approximately (b) 5 nm, (c) 10nm, (d) 20 nm, (e) 30 nm and (f) 40 nm.

Equations (7)

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n k 0 sin θ = k spp
k 1 k 2 = G
k x = ± m G 2 = ± m π a
x 2 = y 2 ( tan 2 θ sin 2 γ cos 2 γ ) + 2 y L ( tan 2 θ + 1 ) sin γ cos γ + L 2 ( tan 2 θ cos 2 γ sin 2 γ )
α = arctan y x ; β = arctan x 2 + y 2 L
k x = n k 0 sin β cos α ± mG
k y = n k 0 sin β sin α

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