Abstract

Electromagnetic resonances on metallic slit gratings induced by TM polarized incident light have been investigated and physically interpreted. We have developed an electromagnetic model imposing surface impedance boundary conditions on the metallic grating surface from which we derive simple formulas explaining all physical properties of these resonances. It is demonstrated that Fabry–Perot (or cavity) resonances are generated by the zeroth slit mode yielding extraordinary transmission. For very narrow slits, the resonant H-field is squeezed to the slit walls and causes enhanced power losses. The excitation of surface plasmon polaritons (SPPs), however, is generated by two mode coupling. SPPs are linked to sharp absorption peaks and dips in transmittance. It is shown that these phenomena are primarily caused by the interaction of the electromagnetic fields with the finite conducting slit walls. These findings have been confirmed by measured transmittance data of gold gratings with periods of 0.5 μm, 1 μm, and 2 μm.

© 2012 Optical Society of America

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  7. S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
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  20. F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).
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  27. Z.-B. Li, Y.-H. Yang, X. Kong, W. Zhou, and J. Tian, “Fabry Perot resonance in slit and grooves to enhance the transmission through a single subwavelength slit,” J. Opt. A 11, 105002 (2009).
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  32. R. A. Depine, “Perfectly conducting diffraction grating formalisms extended to good conductors via the surface impedance boundary condition,” Appl. Opt. 26, 2348–2354 (1987).
    [CrossRef]
  33. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
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  36. H. Lochbihler, P. Predehl, and B. Tesche, “Reconstruction of the profile of gold wire gratings: A comparison of different methods,” Optik 98, 21–25 (1994).

2011 (2)

M. Guillaumee, L. A. Dunbar, and R. P. Stanley, “Description of the modes governing the optical transmission through metal gratings,” Opt. Express 19, 4740–4755 (2011).
[CrossRef]

R. Yang, R. Rodriguez-Berral, F. Medina, and Y. Hao, “Analytical model for the transmission of electromagnetic waves through arrays of slits in perfect conductors and lossy metal screens,” J. Appl. Phys. 109, 103107 (2011).

2009 (3)

Z.-B. Li, Y.-H. Yang, X. Kong, W. Zhou, and J. Tian, “Fabry Perot resonance in slit and grooves to enhance the transmission through a single subwavelength slit,” J. Opt. A 11, 105002 (2009).

V. E. Babicheva and Y. E. Lozovik, “Role of propagating slit mode in enhanced transmission through slit arrays in a metallic films,” Opt. Quantum Electron. 41, 299–313(2009).
[CrossRef]

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72, 064401 (2009).
[CrossRef]

2008 (2)

D. Wang, W. Liu, Q. Xiao, and J. Shi, “Embedded metal-wire nanograting and its application in an optical polarization beam splitter/combiner,” Appl. Opt. 47, 312–316 (2008).
[CrossRef]

V. Auzelyte, H. H. Solak, Y. Ekinci, R. MacKenzie, J. Vörös, S. Olliges, and R. Spolenak, “Large area arrays of metal nanowires,” Microelectron. Eng. 85, 1131–1134 (2008).

2007 (1)

Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[CrossRef]

2006 (1)

D. C. Skigin and R. A. Depine, “Narrow gaps for transmission through metallic structured gratings with subwavelength slits,” Phys. Rev. E 74, 046606 (2006).
[CrossRef]

2005 (1)

K. G. Lee and Q.-Han Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005).

2003 (1)

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: optical properties,” Phys. Rev. B 68, 205103 (2003).

2002 (5)

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. Pure Appl. Opt. 4, S154–S160 (2002).
[CrossRef]

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).

Q. Cao and Ph. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403–161406 (2002).

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

2000 (3)

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Ph. Lalanne, J.P. Hugonin, S. Astilean, M. Palamaru, and K. D. Mo¨ller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

1999 (1)

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

1998 (1)

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).

1996 (1)

H. Lochbihler, “Surface polaritons on metallic wire gratings studied via power losses,” Phys. Rev. B 53, 10289–10295 (1996).

1994 (3)

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B 50, 4795–4801 (1994).

H. Lochbihler, “Field enhancement on metallic wire gratings,” Opt. Commun. 111, 417–422 (1994).
[CrossRef]

H. Lochbihler, P. Predehl, and B. Tesche, “Reconstruction of the profile of gold wire gratings: A comparison of different methods,” Optik 98, 21–25 (1994).

1993 (3)

1992 (1)

1987 (1)

1985 (1)

J. Y. Suratteau and R. Petit, “Numerical study of perfectly conducting wire gratings in the resonance domain,” Int. J. lnfrared Millim. Waves 6, 831–865 (1985).
[CrossRef]

1982 (1)

A. A. Volkov, B. P. Gorshunov, A. A. Irisov, G. V. Kozlov, and S. P. Lebedev, “Electrodynamic properties of plane wire grids,” Int. J. lnfrared Millim. Waves 3, 19–43 (1982).
[CrossRef]

1981 (1)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Adams, J. L.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Aguirre, C. M.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: optical properties,” Phys. Rev. B 68, 205103 (2003).

Andrewartha, J. R.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Astilean, S.

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Ph. Lalanne, J.P. Hugonin, S. Astilean, M. Palamaru, and K. D. Mo¨ller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Auzelyte, V.

V. Auzelyte, H. H. Solak, Y. Ekinci, R. MacKenzie, J. Vörös, S. Olliges, and R. Spolenak, “Large area arrays of metal nanowires,” Microelectron. Eng. 85, 1131–1134 (2008).

Babicheva, V. E.

V. E. Babicheva and Y. E. Lozovik, “Role of propagating slit mode in enhanced transmission through slit arrays in a metallic films,” Opt. Quantum Electron. 41, 299–313(2009).
[CrossRef]

Barbara, A.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403–161406 (2002).

Botten, L. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Bustarret, E.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403–161406 (2002).

Cao, Q.

Q. Cao and Ph. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).

Collin, S.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. Pure Appl. Opt. 4, S154–S160 (2002).
[CrossRef]

Craig, M. S.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Depine, R. A.

D. C. Skigin and R. A. Depine, “Narrow gaps for transmission through metallic structured gratings with subwavelength slits,” Phys. Rev. E 74, 046606 (2006).
[CrossRef]

H. Lochbihler and R. A. Depine, “Highly conducting wire gratings in the resonance region,” Appl. Opt. 32, 3459–3465 (1993).
[CrossRef]

H. Lochbihler and R. A. Depine, “Characterization of highly conducting wire gratings using an electro-magnetic theory of diffraction,” Opt. Commun. 100, 231–239(1993).
[CrossRef]

R. A. Depine, “Perfectly conducting diffraction grating formalisms extended to good conductors via the surface impedance boundary condition,” Appl. Opt. 26, 2348–2354 (1987).
[CrossRef]

Dunbar, L. A.

Ebbesen, T. W.

Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[CrossRef]

Ekinci, Y.

V. Auzelyte, H. H. Solak, Y. Ekinci, R. MacKenzie, J. Vörös, S. Olliges, and R. Spolenak, “Large area arrays of metal nanowires,” Microelectron. Eng. 85, 1131–1134 (2008).

Enoch, S.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

Garcia-Vidal, F. J.

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).

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

Genet, C.

Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[CrossRef]

Gorshunov, B. P.

A. A. Volkov, B. P. Gorshunov, A. A. Irisov, G. V. Kozlov, and S. P. Lebedev, “Electrodynamic properties of plane wire grids,” Int. J. lnfrared Millim. Waves 3, 19–43 (1982).
[CrossRef]

Guillaumee, M.

Halas, N. J.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: optical properties,” Phys. Rev. B 68, 205103 (2003).

Hao, Y.

R. Yang, R. Rodriguez-Berral, F. Medina, and Y. Hao, “Analytical model for the transmission of electromagnetic waves through arrays of slits in perfect conductors and lossy metal screens,” J. Appl. Phys. 109, 103107 (2011).

Heitmann, D.

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).

Hugonin, J.P.

Ph. Lalanne, J.P. Hugonin, S. Astilean, M. Palamaru, and K. D. Mo¨ller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Irisov, A. A.

A. A. Volkov, B. P. Gorshunov, A. A. Irisov, G. V. Kozlov, and S. P. Lebedev, “Electrodynamic properties of plane wire grids,” Int. J. lnfrared Millim. Waves 3, 19–43 (1982).
[CrossRef]

Kong, X.

Z.-B. Li, Y.-H. Yang, X. Kong, W. Zhou, and J. Tian, “Fabry Perot resonance in slit and grooves to enhance the transmission through a single subwavelength slit,” J. Opt. A 11, 105002 (2009).

Kozlov, G. V.

A. A. Volkov, B. P. Gorshunov, A. A. Irisov, G. V. Kozlov, and S. P. Lebedev, “Electrodynamic properties of plane wire grids,” Int. J. lnfrared Millim. Waves 3, 19–43 (1982).
[CrossRef]

Lalanne, Ph.

Q. Cao and Ph. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).

Ph. Lalanne, J.P. Hugonin, S. Astilean, M. Palamaru, and K. D. Mo¨ller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Lebedev, S. P.

A. A. Volkov, B. P. Gorshunov, A. A. Irisov, G. V. Kozlov, and S. P. Lebedev, “Electrodynamic properties of plane wire grids,” Int. J. lnfrared Millim. Waves 3, 19–43 (1982).
[CrossRef]

Lee, A.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: optical properties,” Phys. Rev. B 68, 205103 (2003).

Lee, K. G.

K. G. Lee and Q.-Han Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005).

Li, L.

Li, Z.-B.

Z.-B. Li, Y.-H. Yang, X. Kong, W. Zhou, and J. Tian, “Fabry Perot resonance in slit and grooves to enhance the transmission through a single subwavelength slit,” J. Opt. A 11, 105002 (2009).

Liu, W.

Lochbihler, H.

H. Lochbihler, “Surface polaritons on metallic wire gratings studied via power losses,” Phys. Rev. B 53, 10289–10295 (1996).

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B 50, 4795–4801 (1994).

H. Lochbihler, “Field enhancement on metallic wire gratings,” Opt. Commun. 111, 417–422 (1994).
[CrossRef]

H. Lochbihler, P. Predehl, and B. Tesche, “Reconstruction of the profile of gold wire gratings: A comparison of different methods,” Optik 98, 21–25 (1994).

H. Lochbihler and R. A. Depine, “Highly conducting wire gratings in the resonance region,” Appl. Opt. 32, 3459–3465 (1993).
[CrossRef]

H. Lochbihler and R. A. Depine, “Characterization of highly conducting wire gratings using an electro-magnetic theory of diffraction,” Opt. Commun. 100, 231–239(1993).
[CrossRef]

H. Lochbihler and P. Predehl, “Characterization of x-ray transmission gratings,” Appl. Opt. 31, 964–971 (1992).
[CrossRef]

Lopez-Rios, T.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403–161406 (2002).

Lozovik, Y. E.

V. E. Babicheva and Y. E. Lozovik, “Role of propagating slit mode in enhanced transmission through slit arrays in a metallic films,” Opt. Quantum Electron. 41, 299–313(2009).
[CrossRef]

MacKenzie, R.

V. Auzelyte, H. H. Solak, Y. Ekinci, R. MacKenzie, J. Vörös, S. Olliges, and R. Spolenak, “Large area arrays of metal nanowires,” Microelectron. Eng. 85, 1131–1134 (2008).

Martin-Moreno, L.

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).

McPhedran, R. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Medina, F.

R. Yang, R. Rodriguez-Berral, F. Medina, and Y. Hao, “Analytical model for the transmission of electromagnetic waves through arrays of slits in perfect conductors and lossy metal screens,” J. Appl. Phys. 109, 103107 (2011).

Mo¨ller, K. D.

Ph. Lalanne, J.P. Hugonin, S. Astilean, M. Palamaru, and K. D. Mo¨ller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Moran, C. E.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: optical properties,” Phys. Rev. B 68, 205103 (2003).

Neviere, M.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

Olliges, S.

V. Auzelyte, H. H. Solak, Y. Ekinci, R. MacKenzie, J. Vörös, S. Olliges, and R. Spolenak, “Large area arrays of metal nanowires,” Microelectron. Eng. 85, 1131–1134 (2008).

Palamaru, M.

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

Ph. Lalanne, J.P. Hugonin, S. Astilean, M. Palamaru, and K. D. Mo¨ller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

Pang, Y.

Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[CrossRef]

Pardo, F.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. Pure Appl. Opt. 4, S154–S160 (2002).
[CrossRef]

Park, Q.-Han

K. G. Lee and Q.-Han Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005).

Pelouard, J.-L.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. Pure Appl. Opt. 4, S154–S160 (2002).
[CrossRef]

Pendry, J. B.

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

Petit, R.

J. Y. Suratteau and R. Petit, “Numerical study of perfectly conducting wire gratings in the resonance domain,” Int. J. lnfrared Millim. Waves 6, 831–865 (1985).
[CrossRef]

Popov, E.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

Porto, J. A.

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

Predehl, P.

H. Lochbihler, P. Predehl, and B. Tesche, “Reconstruction of the profile of gold wire gratings: A comparison of different methods,” Optik 98, 21–25 (1994).

H. Lochbihler and P. Predehl, “Characterization of x-ray transmission gratings,” Appl. Opt. 31, 964–971 (1992).
[CrossRef]

Quemerais, P.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403–161406 (2002).

Räther, H.

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

Reinisch, R.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

Rodriguez-Berral, R.

R. Yang, R. Rodriguez-Berral, F. Medina, and Y. Hao, “Analytical model for the transmission of electromagnetic waves through arrays of slits in perfect conductors and lossy metal screens,” J. Appl. Phys. 109, 103107 (2011).

Schröter, U.

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).

Shi, J.

Skigin, D. C.

D. C. Skigin and R. A. Depine, “Narrow gaps for transmission through metallic structured gratings with subwavelength slits,” Phys. Rev. E 74, 046606 (2006).
[CrossRef]

Solak, H. H.

V. Auzelyte, H. H. Solak, Y. Ekinci, R. MacKenzie, J. Vörös, S. Olliges, and R. Spolenak, “Large area arrays of metal nanowires,” Microelectron. Eng. 85, 1131–1134 (2008).

Spolenak, R.

V. Auzelyte, H. H. Solak, Y. Ekinci, R. MacKenzie, J. Vörös, S. Olliges, and R. Spolenak, “Large area arrays of metal nanowires,” Microelectron. Eng. 85, 1131–1134 (2008).

Stanley, R. P.

Steele, J. M.

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: optical properties,” Phys. Rev. B 68, 205103 (2003).

Suratteau, J. Y.

J. Y. Suratteau and R. Petit, “Numerical study of perfectly conducting wire gratings in the resonance domain,” Int. J. lnfrared Millim. Waves 6, 831–865 (1985).
[CrossRef]

Teissier, R.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. Pure Appl. Opt. 4, S154–S160 (2002).
[CrossRef]

Tesche, B.

H. Lochbihler, P. Predehl, and B. Tesche, “Reconstruction of the profile of gold wire gratings: A comparison of different methods,” Optik 98, 21–25 (1994).

Tian, J.

Z.-B. Li, Y.-H. Yang, X. Kong, W. Zhou, and J. Tian, “Fabry Perot resonance in slit and grooves to enhance the transmission through a single subwavelength slit,” J. Opt. A 11, 105002 (2009).

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

Volkov, A. A.

A. A. Volkov, B. P. Gorshunov, A. A. Irisov, G. V. Kozlov, and S. P. Lebedev, “Electrodynamic properties of plane wire grids,” Int. J. lnfrared Millim. Waves 3, 19–43 (1982).
[CrossRef]

Vörös, J.

V. Auzelyte, H. H. Solak, Y. Ekinci, R. MacKenzie, J. Vörös, S. Olliges, and R. Spolenak, “Large area arrays of metal nanowires,” Microelectron. Eng. 85, 1131–1134 (2008).

Wang, D.

Weiner, J.

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72, 064401 (2009).
[CrossRef]

Xiao, Q.

Yang, R.

R. Yang, R. Rodriguez-Berral, F. Medina, and Y. Hao, “Analytical model for the transmission of electromagnetic waves through arrays of slits in perfect conductors and lossy metal screens,” J. Appl. Phys. 109, 103107 (2011).

Yang, Y.-H.

Z.-B. Li, Y.-H. Yang, X. Kong, W. Zhou, and J. Tian, “Fabry Perot resonance in slit and grooves to enhance the transmission through a single subwavelength slit,” J. Opt. A 11, 105002 (2009).

Zhou, W.

Z.-B. Li, Y.-H. Yang, X. Kong, W. Zhou, and J. Tian, “Fabry Perot resonance in slit and grooves to enhance the transmission through a single subwavelength slit,” J. Opt. A 11, 105002 (2009).

Appl. Opt. (4)

Int. J. lnfrared Millim. Waves (2)

A. A. Volkov, B. P. Gorshunov, A. A. Irisov, G. V. Kozlov, and S. P. Lebedev, “Electrodynamic properties of plane wire grids,” Int. J. lnfrared Millim. Waves 3, 19–43 (1982).
[CrossRef]

J. Y. Suratteau and R. Petit, “Numerical study of perfectly conducting wire gratings in the resonance domain,” Int. J. lnfrared Millim. Waves 6, 831–865 (1985).
[CrossRef]

J. Appl. Phys. (1)

R. Yang, R. Rodriguez-Berral, F. Medina, and Y. Hao, “Analytical model for the transmission of electromagnetic waves through arrays of slits in perfect conductors and lossy metal screens,” J. Appl. Phys. 109, 103107 (2011).

J. Opt. A (1)

Z.-B. Li, Y.-H. Yang, X. Kong, W. Zhou, and J. Tian, “Fabry Perot resonance in slit and grooves to enhance the transmission through a single subwavelength slit,” J. Opt. A 11, 105002 (2009).

J. Opt. Pure Appl. Opt. (2)

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. Pure Appl. Opt. 4, S154–S160 (2002).
[CrossRef]

Ph. Lalanne, J.P. Hugonin, S. Astilean, M. Palamaru, and K. D. Mo¨ller, “One-mode model and Airy-like formulae for one-dimensional metallic gratings,” J. Opt. Pure Appl. Opt. 2, 48–51 (2000).
[CrossRef]

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

Microelectron. Eng. (1)

V. Auzelyte, H. H. Solak, Y. Ekinci, R. MacKenzie, J. Vörös, S. Olliges, and R. Spolenak, “Large area arrays of metal nanowires,” Microelectron. Eng. 85, 1131–1134 (2008).

Opt. Acta (1)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

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Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[CrossRef]

H. Lochbihler, “Field enhancement on metallic wire gratings,” Opt. Commun. 111, 417–422 (1994).
[CrossRef]

S. Astilean, Ph. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
[CrossRef]

H. Lochbihler and R. A. Depine, “Characterization of highly conducting wire gratings using an electro-magnetic theory of diffraction,” Opt. Commun. 100, 231–239(1993).
[CrossRef]

Opt. Express (1)

Opt. Quantum Electron. (1)

V. E. Babicheva and Y. E. Lozovik, “Role of propagating slit mode in enhanced transmission through slit arrays in a metallic films,” Opt. Quantum Electron. 41, 299–313(2009).
[CrossRef]

Optik (1)

H. Lochbihler, P. Predehl, and B. Tesche, “Reconstruction of the profile of gold wire gratings: A comparison of different methods,” Optik 98, 21–25 (1994).

Phys. Rev. B (8)

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).

H. Lochbihler, “Surface polaritons on gold-wire gratings,” Phys. Rev. B 50, 4795–4801 (1994).

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

H. Lochbihler, “Surface polaritons on metallic wire gratings studied via power losses,” Phys. Rev. B 53, 10289–10295 (1996).

U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, “Optical transmission through subwavelength metallic gratings,” Phys. Rev. B 66, 161403–161406 (2002).

J. M. Steele, C. E. Moran, A. Lee, C. M. Aguirre, and N. J. Halas, “Metallodielectric gratings with subwavelength slots: optical properties,” Phys. Rev. B 68, 205103 (2003).

Phys. Rev. E (1)

D. C. Skigin and R. A. Depine, “Narrow gaps for transmission through metallic structured gratings with subwavelength slits,” Phys. Rev. E 74, 046606 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

K. G. Lee and Q.-Han Park, “Coupling of surface plasmon polaritons and light in metallic nanoslits,” Phys. Rev. Lett. 95, 103902 (2005).

Q. Cao and Ph. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 057403 (2002).

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

Rep. Prog. Phys. (1)

J. Weiner, “The physics of light transmission through subwavelength apertures and aperture arrays,” Rep. Prog. Phys. 72, 064401 (2009).
[CrossRef]

Other (3)

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

http://www.nasa.gov/mission_pages/chandra/main/index.html .

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

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Figures (10)

Fig. 1.
Fig. 1.

Transmittance (a) and power losses (b) of a slit grating (gold, d=1μm, h=0.5μm, c=0.05μm) at normal incidence calculated with different methods. The inset illustrates the geometry of a slit grating.

Fig. 2.
Fig. 2.

Detailed analysis of power losses of a slit grating with parameters from Fig. 1.

Fig. 3.
Fig. 3.

Transmittance (a) and power losses (b) of slit gratings (gold, d=1μm, h=0.5μm) at normal incidence for different slit widths c and for M=20 compared with the results of the single-mode approximation M=0.

Fig. 4.
Fig. 4.

H-field in the vicinity of slit gratings with parameters from Fig. 3 in the transmission resonance maximum at normal incidence having different slit widths: c=0.80μm (a), 0.5 μm (b), and 0.1 μm (c).

Fig. 5.
Fig. 5.

Transmittance (a) and power losses (b) of a slit grating (gold, d=1μm, h=0.5μm, c=0.1μm) at normal incidence calculated using a single-mode approximation M=0 for different maximum numbers of Rayleigh coefficients N.

Fig. 6.
Fig. 6.

Fabry–Perot resonances in transmittance of a slit grating (gold, d=1μm, h=1.8μm, c=0.5μm) compared with the estimated using Eq. (33) (dotted line). The dashed line denotes results from the Fabry–Perot term in Eq. (35). The arrows mark the positions of the resonance maxima estimated by Eq. (36).

Fig. 7.
Fig. 7.

SPP excitation on a slit grating (gold, d=1μm, h=0.4μm, c=0.6μm) at Θ0=0.7°. Transmittance (a) and power losses (b) calculated for different parameters M and N.

Fig. 8.
Fig. 8.

Detailed analysis of power losses of slit grating from Fig. 7 at Θ0=0.7°. The contribution of the walls is compared with the estimated losses from Eq. (41) and the total losses. The arrow marks the resonance maximum evaluated by Eq. (44).

Fig. 9.
Fig. 9.

Poynting vector and energy density (a) in the vicinity of a slit grating with parameters from Fig. 3 at the maximum of the Fabry–Perot resonance (λ=1.55μm, Θ0=0°) and (b) in the vicinity of a grating with parameters from Fig. 7 for the maximum of the SPP excitation (λ=1.078μm, Θ0=0.7°). The length of the arrows represents the energy density in logarithmic scale.

Fig. 10.
Fig. 10.

Measured transmittance at normal incidence for gold grating with periods d=0.5μm (a), 0.9913 μm (b), and 2 μm (c) compared with best fit using the parameters h=0.168μm, b=0.165μm for grating (a), h=0.59μm, b=0.497μm for grating (b), and h=0.85μm, b=1.268μm for grating (c). The inset shows the measured and calculated SPP resonance for Θ0=1°. The wavelengths of the resonance maxima are marked by arrows.

Equations (45)

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f(x,y)=n=(Rneiχn(yh/2)+δn,0eiχ0(yh/2))eiαnx,foryh/2
f(x,y)=n=Tneiαnxiχn(y+h/2)foryh/2.
f(x,y)=m=0um(x)(sin(κmy)sin(κmh/2)am+cos(κmy)cos(κmh/2)bm),
E=Zn^×H,
fn^=Zk0if=ηf
um(x)=ηβmsinβmx+cosβmx,
tan(βmc)=2ηβmβm2η2,
aj+bj=n=Kj,n(Rn+δn,0),
aj+bj=n=Kj,nTn,
iχq(Rqδq,0)=m=0Jq,mκm[cot(κmh/2)amtan(κmh/2)bm]+ηn=Qq,n(Rn+δn,0),
iχqTq=m=0Jq,mκm[cot(κmh/2)am+tan(κmh/2)bm]+ηn=Qq,nTn.
Kj,n=1Ijeiαnc/2βj2αn2[(ηiαn)eiαnc+(η+iαn)βj2+η2βj2η2cos(βjc)],
Jq,m=1Imdeiαqc/2βm2αq2×[(η+iαq)eiαqc+(ηiαq)βm2+η2βm2η2cos(βmc)],
Im=[1+(ηβm)2]c2+ηβm2,
Qq,n={b/dforq=n,sin[(nq)πc/d](nq)πforqn.
Rn=[Qp,n]1Qp,0++Un,m[cot(κmh/2)amtan(κmh/2)bm],
Tn=Un,m[cot(κmh/2)am+tan(κmh/2)bm],
am=[δj,mKj,nUn,mcot(κmh/2)]1Fj,
bm=[δj,m+Kj,nUn,mtan(κmh/2)]1Fj,
Fj=12Kj,p([Qq,p]1Qq,0++δp,0).
Un,m=[Qp,n]1Jp,mκm,
Qq,p±=iχqδq,p±ηQq,p.
Pabs=k0(Z)dχ0S|Hz|2ds.
Pabs=Ptop+Pbot+Pwalls,
Ptop=k0(Z)χ0m,nQm,n(Rm*+δm,0)(Rn+δn,0),
Pbot=k0(Z)χ0m,nQm,nTm*Tn,
Pwalls=2k0(Z)χ0m,n1+(1)m+nκm*2κn2[(κncot(κnh2)κm*cot(κm*h2))am*an(κntan(κnh2)κm*tan(κm*h2))bm*bn].
λR=d/n(1±sinΘ0),
I0T=|T0|2|U0,0(cot(κ0h2)a0+tan(κ0h2)b0)|2,
a0(1K0,nUn,0cot(κ0h2))1F0,
b0(1+K0,nUn,0tan(κ0h2))1F0,
F0iχ0iχ0ηb/dK0,0.
I0T|U0,0F0cot(κ0h/2)+tan(κ0h/2)[tan(κ0h/2)ζ0][cot(κ0h/2)+ζ0]|2,
ζ0=K0,nUn,0.
I0T|4κ0χ0J0,0K0,0(iχ0ηb/d)2[1ζ022ζ0cot(κ0h)]·exp(iκ0h)1exp(2iκ0h)|2.
λmFP2hm/[1+12mπ(ln1+2iζ0ζ0212iζ0ζ02)]2+(hmπ(β0))2,
λmFP2hm.
Ptopb/d(Z)cosΘ0n=NN|Rn+δn,0|2,
Pbotb/d(Z)cosΘ0n=NN|Tn|2.
Pwalls4(Z)cosΘ0m=0M1(βm2)[(κmcot(κmh/2))|am|2+(κmtan(κmh/2))|bm|2].
PwallsSP(2(Z)cosΘ0)|b1|2.
b1=V1,0F0+(1+V0,0)F1(1+V0,0)(1+V1,1)V0,1V1,0,
Vj,m=Kj,n[Qp,n]1Jp,mκmtan(κmh/2).
2κ1K1,12([Q]1,11[Q]1,11)cot(κ1h/2),
S=[E×H*].

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