Abstract

Diffraction of TM-polarized waves by a slit in a thick screen of infinite conductivity is treated. The case of an arbitrary incident beam wave is considered. We study the resonances that appear when the wavelength of the incident beam wave is larger than the slit width, i.e., the subwavelength regime where a one-mode model for the slit can be considered. High anomalous values (resonances) of the transmission coefficient, the angular diffracted energy, and the magnetic field within the slit are analyzed. A simple linear relationship to determine the resonant wavelengths is proposed. We show that the transmission coefficient, the normal diffracted energy, and the magnetic field within the cavity are linear functions of the resonant wavelength and the thickness of the screen. Additionally and surprisingly, we reveal that under certain conditions the incident beam wave via the diffraction can give a suppressed light transmission; i.e., a minimum in the transmission is obtained where a maximum is expected.

© 2007 Optical Society of America

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  1. 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, 667-668 (1998).
  2. D. Van Labeke, F. I. Baida, and J.-M. Vigoureux, "A new structure for enhanced transmission through a two-dimensional metallic grating," J. Microsc. 213, 140-143 (2004).
    [CrossRef]
  3. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
    [CrossRef]
  4. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
    [CrossRef]
  5. Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403-1-057403-4 (2002).
    [CrossRef]
  6. E. Popov, M. Nevière, J. Wenger, P. F. Lenne, H. Rigneault, and P. Chaumet, "Field enhancement in a single subwavelength aperture," J. Opt. Soc. Am. A 23, 2342-2348 (2006).
    [CrossRef]
  7. F. I. Baida, D. Van Labeke, and B. Guizal, "Enhanced confined light transmission by single subwavelength apertures in metallic films," Appl. Opt. 42, 6811-6815 (2003).
  8. Y. Takakura, "Optical resonance in a narrow slit in a thick metallic screen," Phys. Rev. Lett. 86, 5601-5603 (2001).
    [CrossRef]
  9. F. Yang and J. R. Sambles, "Determination of microwave permitivities using a metallic slit," J. Phys. D 35, 3049-3051 (2002).
    [CrossRef]
  10. F. Yang and J. R. Sambles, "Determination of the microwave permitivities of nematic liquid crystals using a single-metallic slit technique," Appl. Phys. Lett. 81, 2047-2049 (2002).
    [CrossRef]
  11. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
    [CrossRef]
  12. F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901-1-213901-4 (2003).
    [CrossRef]
  13. J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, "Transmission properties of a single metallic slit: from the subwavelength regime to the geometrical-optics limit," Phys. Rev. E 69, 026601-1-026601-6 (2004).
    [CrossRef]
  14. R. Gordon, "Light in a subwavelength slit in a metal: propagation and reflection," Phys. Rev. B 73, 153405-1-153405-3 (2006).
    [CrossRef]
  15. 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]
  16. O. Mata-Mendez, J. Avendaño, and F. Chavez-Rivas, "Rigorous theory of the diffraction of Gaussian beams by finite gratings: TM polarization," J. Opt. Soc. Am. A 23, 1889-1895 (2006).
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  20. O. Mata-Mendez and F. Chavez-Rivas, "Diffraction of Gaussian and Hermite-Gaussian beams by finite gratings," J. Opt. Soc. Am. A 18, 537-545 (2001).

2006 (4)

2004 (2)

D. Van Labeke, F. I. Baida, and J.-M. Vigoureux, "A new structure for enhanced transmission through a two-dimensional metallic grating," J. Microsc. 213, 140-143 (2004).
[CrossRef]

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, "Transmission properties of a single metallic slit: from the subwavelength regime to the geometrical-optics limit," Phys. Rev. E 69, 026601-1-026601-6 (2004).
[CrossRef]

2003 (3)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
[CrossRef]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901-1-213901-4 (2003).
[CrossRef]

F. I. Baida, D. Van Labeke, and B. Guizal, "Enhanced confined light transmission by single subwavelength apertures in metallic films," Appl. Opt. 42, 6811-6815 (2003).

2002 (3)

F. Yang and J. R. Sambles, "Determination of microwave permitivities using a metallic slit," J. Phys. D 35, 3049-3051 (2002).
[CrossRef]

F. Yang and J. R. Sambles, "Determination of the microwave permitivities of nematic liquid crystals using a single-metallic slit technique," Appl. Phys. Lett. 81, 2047-2049 (2002).
[CrossRef]

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403-1-057403-4 (2002).
[CrossRef]

2001 (2)

O. Mata-Mendez and F. Chavez-Rivas, "Diffraction of Gaussian and Hermite-Gaussian beams by finite gratings," J. Opt. Soc. Am. A 18, 537-545 (2001).

Y. Takakura, "Optical resonance in a narrow slit in a thick metallic screen," Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef]

2000 (1)

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

1999 (1)

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

1998 (2)

1995 (1)

1979 (1)

Avendaño, J.

Baida, F. I.

D. Van Labeke, F. I. Baida, and J.-M. Vigoureux, "A new structure for enhanced transmission through a two-dimensional metallic grating," J. Microsc. 213, 140-143 (2004).
[CrossRef]

F. I. Baida, D. Van Labeke, and B. Guizal, "Enhanced confined light transmission by single subwavelength apertures in metallic films," Appl. Opt. 42, 6811-6815 (2003).

Bravo-Abad, J.

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, "Transmission properties of a single metallic slit: from the subwavelength regime to the geometrical-optics limit," Phys. Rev. E 69, 026601-1-026601-6 (2004).
[CrossRef]

Cao, Q.

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403-1-057403-4 (2002).
[CrossRef]

Chaumet, P.

Chavez-Rivas, F.

Degiron, A.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
[CrossRef]

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
[CrossRef]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901-1-213901-4 (2003).
[CrossRef]

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, 667-668 (1998).

Enoch, S.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Foley, J. T.

García-Vidal, F. J.

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, "Transmission properties of a single metallic slit: from the subwavelength regime to the geometrical-optics limit," Phys. Rev. E 69, 026601-1-026601-6 (2004).
[CrossRef]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901-1-213901-4 (2003).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
[CrossRef]

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Ghaemi, H. F.

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, 667-668 (1998).

Gordon, R.

R. Gordon, "Light in a subwavelength slit in a metal: propagation and reflection," Phys. Rev. B 73, 153405-1-153405-3 (2006).
[CrossRef]

Guizal, B.

Hugonin, J. P.

Lalanne, P.

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]

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403-1-057403-4 (2002).
[CrossRef]

Lenne, P. F.

Lezec, H. J.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901-1-213901-4 (2003).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
[CrossRef]

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, 667-668 (1998).

Martín-Moreno, L.

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, "Transmission properties of a single metallic slit: from the subwavelength regime to the geometrical-optics limit," Phys. Rev. E 69, 026601-1-026601-6 (2004).
[CrossRef]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901-1-213901-4 (2003).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
[CrossRef]

Mata-Mendez, O.

Nevière, M.

E. Popov, M. Nevière, J. Wenger, P. F. Lenne, H. Rigneault, and P. Chaumet, "Field enhancement in a single subwavelength aperture," J. Opt. Soc. Am. A 23, 2342-2348 (2006).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Pendry, J. B.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Popov, E.

E. Popov, M. Nevière, J. Wenger, P. F. Lenne, H. Rigneault, and P. Chaumet, "Field enhancement in a single subwavelength aperture," J. Opt. Soc. Am. A 23, 2342-2348 (2006).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Porto, J. A.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Reinisch, R.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Rigneault, H.

Rodier, J. C.

Sambles, J. R.

F. Yang and J. R. Sambles, "Determination of microwave permitivities using a metallic slit," J. Phys. D 35, 3049-3051 (2002).
[CrossRef]

F. Yang and J. R. Sambles, "Determination of the microwave permitivities of nematic liquid crystals using a single-metallic slit technique," Appl. Phys. Lett. 81, 2047-2049 (2002).
[CrossRef]

Takakura, Y.

Y. Takakura, "Optical resonance in a narrow slit in a thick metallic screen," Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef]

Thio, T.

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, 667-668 (1998).

Van Labeke, D.

D. Van Labeke, F. I. Baida, and J.-M. Vigoureux, "A new structure for enhanced transmission through a two-dimensional metallic grating," J. Microsc. 213, 140-143 (2004).
[CrossRef]

F. I. Baida, D. Van Labeke, and B. Guizal, "Enhanced confined light transmission by single subwavelength apertures in metallic films," Appl. Opt. 42, 6811-6815 (2003).

Vigoureux, J.-M.

D. Van Labeke, F. I. Baida, and J.-M. Vigoureux, "A new structure for enhanced transmission through a two-dimensional metallic grating," J. Microsc. 213, 140-143 (2004).
[CrossRef]

Wenger, J.

Wolf, E.

Wolff, P. A.

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, 667-668 (1998).

Yang, F.

F. Yang and J. R. Sambles, "Determination of the microwave permitivities of nematic liquid crystals using a single-metallic slit technique," Appl. Phys. Lett. 81, 2047-2049 (2002).
[CrossRef]

F. Yang and J. R. Sambles, "Determination of microwave permitivities using a metallic slit," J. Phys. D 35, 3049-3051 (2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

F. Yang and J. R. Sambles, "Determination of the microwave permitivities of nematic liquid crystals using a single-metallic slit technique," Appl. Phys. Lett. 81, 2047-2049 (2002).
[CrossRef]

J. Microsc. (1)

D. Van Labeke, F. I. Baida, and J.-M. Vigoureux, "A new structure for enhanced transmission through a two-dimensional metallic grating," J. Microsc. 213, 140-143 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

J. Phys. D (1)

F. Yang and J. R. Sambles, "Determination of microwave permitivities using a metallic slit," J. Phys. D 35, 3049-3051 (2002).
[CrossRef]

Nature (London) (1)

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, 667-668 (1998).

Phys. Rev. B (2)

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

R. Gordon, "Light in a subwavelength slit in a metal: propagation and reflection," Phys. Rev. B 73, 153405-1-153405-3 (2006).
[CrossRef]

Phys. Rev. E (1)

J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, "Transmission properties of a single metallic slit: from the subwavelength regime to the geometrical-optics limit," Phys. Rev. E 69, 026601-1-026601-6 (2004).
[CrossRef]

Phys. Rev. Lett. (5)

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403-1-057403-4 (2002).
[CrossRef]

Y. Takakura, "Optical resonance in a narrow slit in a thick metallic screen," Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401-1-167401-4 (2003).
[CrossRef]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple paths to enhance optical transmission through a single subwavelength slit," Phys. Rev. Lett. 90, 213901-1-213901-4 (2003).
[CrossRef]

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