Abstract

A directional coupling effect of surface plasmon waves (SPW) in subwavelength metallic slits is studied. The p-polarized wave generates two SPW modes in the subwavelength slit. As the angle of incidence is changed, coupling arises between both SPW modes. The coupling length increases exponentially with the width of the slit but is independent of the angle of incidence. At a coupling length and an incident angle of ~30°, light is emitted from one side of the slit. The single side emission light has a width smaller than 50nm and double peak intensity than at normal incidence. The SPW coupling effect reveals a simple way for producing a nanometer light source of high transmission intensity.

© 2005 Optical Society of America

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References

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App. Phys. Lett.

L. Xiangang, T. Ishihara,, "Surface plasmon resonant interference nanolithography technique," App. Phys. Lett. 84, 4780-4782 (2004)
[CrossRef]

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998)
[CrossRef]

Opt. Express

Phys. Rev.

H. A Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Rev. Phys. Lett.

Jonas O. Tegenfeldt, Olgica Bakajin, Chia-Fu Chou, Shirley S. Chan, Robert Austin, Wunshain Fann, Lim Liou, Eugene Chan, Thomas Duke, and Edward C. Cox, "Near-Field Scanner for Moving Molecules," Rev. Phys. Lett. 86, 1378-1381 (2001).
[CrossRef]

Science

H. J. Lezec, A. Degiron,1 E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T.W. Ebbesen1, "Beaming Light from a Subwavelength Aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

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

Other

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 2nd ed. (Artech House, Boston 2000).

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991), chap. 1

R. G. Hunsperger, Integrated Optics: Theory and Technology, 5th ed (Springer; 5 ed,. 2002), chap. 8

S. Kawata, Near-field optics and surface plasmon polaritons, 1st ed. (Springer, 2001)

Supplementary Material (1)

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Figures (8)

Fig. 1.
Fig. 1.

(a) The directional coupling effect in a conventional dual waveguides. The red line is the fundamental symmetrical mode and the blue line is the first-order asymmetrical mode. (b) The metallic walls in a subwavelength slit are modeled as dual waveguides for SPWs. Normal incidence only excites symmetrical mode. Off-angle incidence can excite both symmetrical and asymmetrical modes and cause coupling effect in the slit.

Fig. 2.
Fig. 2.

2D FDTD simulation domain for a h-thick aluminum film and w-wide slit. A plane wave with 532nm wavelength is incident through the slit at an angle, θ. The mode definitions for p- and s-polarized modes are shown in the box.

Fig. 3.
Fig. 3.

FDTD simulation results for light in various slit widths: (a) w=100nm, (b) w=300nm and (c) w=600nm. The incident wavelength was 532nm with 30° angle of incidence. The polarization is p-polarized. (d) The movie file for 30° angle incident, p-polarized wave in a 300nm-wide slit. [Media 1]

Fig. 4.
Fig. 4.

(a) The model for a directional SPW coupler. The subwavelength slit is regarded as a waveguide system that has two guiding modes, symmetric (SPW(0)) and asymmetric (SPW(1)). (b) The calculated coupling lengths at various slit widths. The coupling length can be fitted by an exponential function.

Fig. 5.
Fig. 5.

The optical power distribution in the slit for various angles of incidence, (a) θ=10°, (b) θ=20° and (c) θ=40°. The slit width is 300nm. The incident wavelength is 532nm and p-polarized. (d) The optical power distribution for s-polarized wave. The incident angle is 30°. (e) The relative optical densities at various angles of incidence. The relative optical intensity is defined as the peak optical density on the right wall over the peak density on the left wall.

Fig. 6.
Fig. 6.

The optical power distribution for light in different metallic slits and surrounding mediums. The slit width is 300nm and incident angle is 30°. The incident wavelength is 532nm. (a) Ag slit in air, (b) Al slit in air, (c) Au slit in air and (d) Al slit in water.

Fig. 7.
Fig. 7.

The optical intensity distributions at 10nm way from the slit surface. The slit width is 300nm and the incident wavelength is 532nm. Top: Light emission from an Al slit with normal incidence (purple line) and 30° incident angle (blue line). Middle: Light emission from an Al slit with a photoresist overlay. Bottom: Light emission form an Al slit in water environment.

Fig. 8.
Fig. 8.

(a) The peak optical intensity as a function of height. (b) The FWHM as a function of height. The slit width is 300nm. The incident wavelength is 532nm with 30° incident angle. The surrounding mediums are air (red line) and water (blue line).

Tables (1)

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Table 1. the calculated propagation constants and lengths of SPWs at 532nm wavelength

Equations (2)

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ε ( ω ¯ ) = 1 + ω ¯ p 2 2 i ω ¯ v c ω ¯ 2
I ( x , y ) = [ SPW ( 0 ) ] 2 + [ SPW ( 1 ) ] 2 + 2 [ SPW ( 0 ) ] [ SPW ( 1 ) ] cos ( Δβz ) exp ( αz )

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