Theory of transmission of light by sub-wavelength cylindrical holes in metallic films

doi:10.1364/OE.14.010028

Theory of transmission of light by sub-wavelength cylindrical holes in metallic films

N. García and Ming Bai »View Author Affiliations

Optics Express, Vol. 14, Issue 21, pp. 10028-10042 (2006)
http://dx.doi.org/10.1364/OE.14.010028

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Abstract

This paper presents theory and finite-difference time-domain (FDTD) calculations for a single and arrays of sub-wavelength cylindrical holes in metallic films presenting large transmission. These calculations are in excellent agreement with experimental measurements. This effect has to be understood in terms of the properties exhibited by the dielectric constant of metals which cannot be treated as ideal metals for the purpose of transmission and diffraction of light. We discuss the cases of well-differentiated metals silver and tungsten. It is found that the effect of surface plasmons or other surface wave excitations due to a periodical set of holes or other roughness at the surface is marginal. The effect can enhance but also can depress the transmission of the arrays as shown by theory and experiments. The peak structure observed in experiments is a consequence of the interference of the wavefronts transmitted by each hole and is determined by the surface array period independently of the material. Without large transmission through a single hole there is no large transmission through the array. We found that in the case of Ag which at the discussed frequencies is a metal there are cylindrical plasmons at the wall of the hole, as reported by Economu et al 30 years ago, that enhanced the transmission. But it turns out, as will be explained, that for the case of W which behaves as a dielectric, there is also a large transmission when compared with that of an ideal metal waveguide at large wavelengths. To deal with this problem one has to use the measured dielectric function of the metals. We discuss thoroughly all these cases and compare with the data. We notice that to discuss these data, for a single hole’s transmission, in terms of the Bethe approximation of ideal metals is misleading. Therefore, the extraordinary enhancement of the transmission for the holes arrays versus the single hole does not exist.

OCIS Codes
(260.3910) Physical optics : Metal optics
(310.2790) Thin films : Guided waves

ToC Category:
Physical Optics

History
Original Manuscript: August 8, 2006
Revised Manuscript: September 22, 2006
Manuscript Accepted: September 24, 2006
Published: October 16, 2006

Citation
N. García and Ming Bai, "Theory of transmission of light by sub-wavelength cylindrical holes in metallic films," Opt. Express 14, 10028-10042 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-21-10028

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References

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667-669 (1998). [CrossRef]
H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through sub-wavelength hole arrays," Opt. Express 12, 3629-3651 (2004). [CrossRef] [PubMed]
J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, "How Light emerges from an illuminated array of sub-wavelength holes," Nat. Phys., 2, 120-123 (2006). [CrossRef]
H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944). [CrossRef]
H. Shin, P. B. Catrysse, and S. Fan, "Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes," Phys. Rev. B 72, 085436 (2005). [CrossRef]
C. A. Pfeiffer, E. N. Economou and K. L. Ngai, "Surface polaritons in a circularly cylindrical interface: Surface plasmons," Phys. Rev. B 10, 3038-3051 (1974). [CrossRef]
S. S. Martinos and E. N. Economou, "Excitation of surface plasmons in cylinders by electrons," Phys, Rev. B, 24, 6908-6914 (1981). [CrossRef]
P. B. Johnson and R. W. Christy, "Optical constant of the noble metals," Phys. Rev. B 6, 4370 (1972). [CrossRef]
J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, "Optical properties of metals, Physik Daten/Physics Data" No. 18-1 (Fach-Informations-Zentrum, Energie Physick Mathematik GmbH, Karlsruhe, 1981).
A. Taflove, Advances in Computational Electrodynamics, The Finite-Difference Time-Domain Method, (Artech House 1998).
H. Raether, Springer Tracts in Modern Physics, Vol. 111: Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Spinger-Verlag Berlin Heidelberg, 1988).
N. García, "Exact calculations of p-polarized electromagnetic fields incident on grating surfaces: Surface polariton resonances," Opt. Commun. 45, 307(1983). [CrossRef]
N. García, G. Diaz, J. H. Saenz, and C. Ocal, "Intensities and field enhancement of light scattered from periodic gratings: study of Ag, Au and Cu surface," Surf. Sci. 143, 342 (1984). [CrossRef]
John David Jackson, Classical Electrodynamics 3rd edition, (Wiley, 1999).
M. Bai, C. Guerrero, S. Ioanid, E. Paz, M. Sanz and N. García, "Measuring the speed of a surface plasmons," Phys. Rev. B 69, 115416-115421 (2004) [CrossRef]

Bai, M.
Bethe, H. A.
Bravo-Abad, J.
Catrysse, P. B.
Christy, R. W.
Degiron, A.
Diaz, G.
Ebbesen, T. W.
Economou, E. N.
Fan, S.
García, N.
García-Vidal, F. J.
Genet, C.
Ghaemi, H. F.
Guerrero, C.
Ioanid, S.
Johnson, P. B.
Lezec, H. J.
Martín-Moreno, L.
Martinos, S. S.
Ngai, K. L.
Ocal, C.
Paz, E.
Pfeiffer, C. A.
Przybilla, F.
Saenz, J. H.
Sanz, M.
Shin, H.
Thio, T.
Wolff, P. A.

Nat. Phys.

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, "How Light emerges from an illuminated array of sub-wavelength holes," Nat. Phys., 2, 120-123 (2006). [CrossRef]

Nature (London)

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

Opt. Commun.

N. García, "Exact calculations of p-polarized electromagnetic fields incident on grating surfaces: Surface polariton resonances," Opt. Commun. 45, 307(1983). [CrossRef]

Opt. Express

H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through sub-wavelength hole arrays," Opt. Express 12, 3629-3651 (2004). [CrossRef] [PubMed]

Phys, Rev. B

S. S. Martinos and E. N. Economou, "Excitation of surface plasmons in cylinders by electrons," Phys, Rev. B, 24, 6908-6914 (1981). [CrossRef]

Phys. Rev.

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

Phys. Rev. B

H. Shin, P. B. Catrysse, and S. Fan, "Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes," Phys. Rev. B 72, 085436 (2005). [CrossRef]
C. A. Pfeiffer, E. N. Economou and K. L. Ngai, "Surface polaritons in a circularly cylindrical interface: Surface plasmons," Phys. Rev. B 10, 3038-3051 (1974). [CrossRef]
P. B. Johnson and R. W. Christy, "Optical constant of the noble metals," Phys. Rev. B 6, 4370 (1972). [CrossRef]
M. Bai, C. Guerrero, S. Ioanid, E. Paz, M. Sanz and N. García, "Measuring the speed of a surface plasmons," Phys. Rev. B 69, 115416-115421 (2004) [CrossRef]

Surf. Sci.

N. García, G. Diaz, J. H. Saenz, and C. Ocal, "Intensities and field enhancement of light scattered from periodic gratings: study of Ag, Au and Cu surface," Surf. Sci. 143, 342 (1984). [CrossRef]

Other

John David Jackson, Classical Electrodynamics 3rd edition, (Wiley, 1999).
J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, "Optical properties of metals, Physik Daten/Physics Data" No. 18-1 (Fach-Informations-Zentrum, Energie Physick Mathematik GmbH, Karlsruhe, 1981).
A. Taflove, Advances in Computational Electrodynamics, The Finite-Difference Time-Domain Method, (Artech House 1998).
H. Raether, Springer Tracts in Modern Physics, Vol. 111: Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Spinger-Verlag Berlin Heidelberg, 1988).

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