Abstract

Transmission properties of light waves through a horn-opened subwavelength-size single slit in finite-width homogeneous or inhomogeneous metallic films are studied by using the boundary integral method. We calculate transmission spectra in the visible wavelength regime, display the optical field intensity distributions, and demonstrate the directions of the energy flow. The results show that the transmission spectrum crucially depends on the physical and geometrical parameters of samples, for instance, the split angle in the horn-opened region of the slit, the width and depth of the slit, and the metallic materials surrounding the slit, etc. Two peaks in the transmission spectrum are observed for the nanoslit with a horn opening in the homogeneous metallic film, which originate from the metallic film and air slit, respectively. However, there are three peaks for the nanoslit in the hybrid metallic films consisting of two metallic films on either side of the slit, stitched together. Two peaks correspond to two different metallic materials, and the other one corresponds to the air slit, for the slit surrounded by two metallic materials. An equivalent structure is proposed to give an approximate description of the transmitted behavior.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2006 (2)

W. L. Barnes, "Surface plasmon-polariton length scales: a route to sub-wavelength optics," Pure Appl. Opt. 8, s87-s93 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Approximate model for surface-plasmon generation at slit apertures," J. Opt. Soc. Am. A 23, 1608-1615 (2006).
[CrossRef]

2005 (4)

I. I. Smolyaninov, Q. Balzano, and C. C. Davis, "Plasmon-polaritons on the surface of a pseudosphere," Phys. Rev. B 72, 165412 (2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

D. C. Skigin and R. A. Depine, "Transmission resonances of metallic compound gratings with subwavelength slits," Phys. Rev. Lett. 95, 217402 (2005).
[CrossRef] [PubMed]

K. G. Lee and Q-Han. Park, "Coupling of surface plasmon polaritons and light in metallic nanoslits," Phys. Rev. Lett. 95, 103902 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (2)

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

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

2002 (3)

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

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
[CrossRef]

2001 (2)

L. Martin-Moreno, F. J. Garcia-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. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, "Enhanced light transmission through a single subwavelength aperture," Opt. Lett. 26, 1972-1974 (2001).
[CrossRef]

1999 (1)

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]

1998 (1)

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

1974 (1)

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

Nature (2)

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. Ghaeml, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (2)

M. M. J. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105 (2002).
[CrossRef]

I. I. Smolyaninov, Q. Balzano, and C. C. Davis, "Plasmon-polaritons on the surface of a pseudosphere," Phys. Rev. B 72, 165412 (2005).
[CrossRef]

Phys. Rev. Lett. (7)

L. Martin-Moreno, F. J. Garcia-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]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

K. G. Lee and Q-Han. Park, "Coupling of surface plasmon polaritons and light in metallic nanoslits," Phys. Rev. Lett. 95, 103902 (2005).
[CrossRef] [PubMed]

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

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]

D. C. Skigin and R. A. Depine, "Transmission resonances of metallic compound gratings with subwavelength slits," Phys. Rev. Lett. 95, 217402 (2005).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Pure Appl. Opt. (1)

W. L. Barnes, "Surface plasmon-polariton length scales: a route to sub-wavelength optics," Pure Appl. Opt. 8, s87-s93 (2006).
[CrossRef]

Science (1)

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

Other (3)

N. Morita, N. Kumagai, and J. R. Mautz, Integral Equation Methods for Electromagnetics (Artech House, 1990).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

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Figures (12)

Fig. 1
Fig. 1

Schematic of a horn-opened nanoslit opening in metallic films. A p-polarized (transverse magnetic) plane wave is normally incident on the nanoslit.

Fig. 2
Fig. 2

Transmission spectrum for a horn-opened nanoslit opening in the pure silver films when a normally incident, p-polarized plane wave impinges upon the sample. The parameters are chosen as: fixed a = b and varying the values of a: (a) a = b = 0 , 20, 40, 60 nm , (b) a = b = 60 , 80, 90 nm , and (c) a = b = 90 , 100, 110, 120 nm .

Fig. 3
Fig. 3

Variations of peak transmission as a function of the parameter a in the same sample as in Fig. 2. The solid curve corresponds to peak 1 (the short-wavelength peak at 530 nm ), dashed curve to peak 2 (the long-wavelength peaks at 650 nm ).

Fig. 4
Fig. 4

Transmission spectrum for a nanoslit with horn-opened entry shape, opening in the metallic films of silver or gold, when a p-polarized plane wave is normally incident upon the sample. The geometrical parameters are chosen as: a = b = 0 nm and d = 40 nm . The solid curve corresponds to the transmission spectrum in the nanoslit opening in the silver film, the dotted curve to that in the nanoslit opening in the gold film.

Fig. 5
Fig. 5

Transmission spectrum for a horn-opened nanoslit opening in the silver film with the geometric parameters as: fixed a = 40 nm and varying value of b: (a) b = 20 , 50, 80 nm (b) b = 80 , 110, 140 nm . The p-polarized plane wave normally impinges upon the sample.

Fig. 6
Fig. 6

Variations of the peak transmission with the increase of the parameter b, fixed a = 40 nm . The sample is the same as in Fig. 5. The solid curve corresponds to peak 1 (the short-wavelength peak, at 530 nm ), the dashed curve to peak 2, the long-wavelength peak, at 650 nm ).

Fig. 7
Fig. 7

Schematic of a nanoslit opening in the metallic film and its equivalent averaged step-shaped slit.

Fig. 8
Fig. 8

Comparison of the transmission spectrum of the exact horn-opened nanoslit (solid curve) when a = b = 40 nm to that of the equivalent averaged stepped slit (dotted curve) when w = 20 nm and b = 40 nm .

Fig. 9
Fig. 9

Intensity distributions of total magnetic field plotted in a 256 gray-level representation for peak 2 at 656 nm : (a) for the exact horn-opened nanoslit with a = b = 40 nm , and (b) for its equivalent averaged structure of the stepped nanoslit with w = 20 nm and b = 40 nm . Bright regions correspond to the areas of high field intensity, and dark regions to the areas of low field intensity. The white arrows denote the direction of time-averaged Poynting vector. The contours of the structures are indicated by the solid line.

Fig. 10
Fig. 10

Intensity distributions of total magnetic field plotted in a 128 gray-level representation for peak 2: (a) for 648 nm when a = b = 60 nm , (b) for 635 nm when a = b = 90 nm , and (c) for 634 nm when a = b = 120 nm . Bright regions indicate the areas of high field intensity, and dark regions correspond to the areas of low field intensity. The solid lines indicate the contours of the structures.

Fig. 11
Fig. 11

Transmission spectrum for a horn-opened nanoslit opening in the hybrid metallic films, i.e., the slit surrounded by the silver and gold films on either side of it. The parameters are as follows: fixed a = b , and varying parameter a: (a) a = b = 0 , 20, 40, 60 nm and (b) a = b = 60 , 80, 100, 120 nm . A p-polarized plane wave normally impinges upon the sample.

Fig. 12
Fig. 12

Same as Fig. 11 except for different parameters as a = 40 nm and varying parameter b: (a) for b = 20 , 50, 80 nm (b) for b = 80 , 110, 140 nm .

Equations (12)

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2 φ 1 tot ( r ) + k 1 2 φ 1 tot ( r ) = 0 , r V 1 ,
2 φ 2 tot ( r ) + k 2 2 φ 2 tot ( r ) = 0 , r V 2 ,
2 φ 3 tot ( r ) + k 3 2 φ 3 tot ( r ) = f ( r ) , r V 3 ,
φ tot ( r 1 ) = C 1 [ G 1 ( r 1 , r Γ ) φ tot ( r Γ ) n φ tot ( r Γ ) G 1 ( r 1 , r Γ ) n ] d l ,
r 1 V 1 ,
φ tot ( r 2 ) = C 2 [ G 2 ( r 2 , r Γ ) φ tot ( r Γ ) n φ tot ( r Γ ) G 2 ( r 2 , r Γ ) n ] d l ,
r 2 V 2 ,
φ tot ( r 3 ) = C 1 + C 2 [ G 3 ( r 3 , r Γ ) φ tot ( r Γ ) n φ tot ( r Γ ) G 3 ( r 3 , r Γ ) n ] d l + φ inc ( r 3 ) , r 3 V 3 ,
( 1 θ 2 π ) φ tot ( r s ) + C 1 [ φ tot ( r Γ ) G 1 ( r s , r Γ ) n G 1 ( r s , r Γ ) φ tot ( r Γ ) n ] d l = 0 ,
( 1 θ 2 π ) φ tot ( r s ) + C 2 [ φ tot ( r Γ ) G 2 ( r s , r Γ ) n G 2 ( r s , r Γ ) φ tot ( r Γ ) n ] d l = 0 ,
θ 2 π φ tot ( r s ) + C 1 + C 2 [ G 3 ( r s , r Γ ) φ tot ( r Γ ) n φ tot ( r Γ ) G 3 ( r s , r Γ ) n ] d l = φ inc ( r s ) ,
T ( l + d ) 2 ( l + d ) 2 S n tot d x d 2 d 2 S n inc d x ,

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