Abstract

Diffraction of TM-polarized Gaussian beams by N equally spaced slits (finite grating) in a planar perfectly conducting thick screen is treated. We extend to the TM polarization case the results of a previous paper where the TE polarization was considered [J. Opt. Soc. Am. A 20, 827 (2003). ]. The far-field diffraction patterns, the transmission coefficient τ, and the normally diffracted energy E as a function of several optogeometrical parameters are analyzed within the so-called vectorial region. The existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits is shown. In addition, the property E=Nτλ, valid in the scalar region, is extended to the TM polarization case in the vectorial region, λ being the wavelength. The coupling between slits is analyzed, giving an oscillating amplitude-decreasing function as the separation between slits increases, where the period for these oscillations is the wavelength λ. Finally, the extraordinary optical transmission phenomena that appear when the wavelength is larger than the slit width (subwavelength regime) are analyzed.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).
  2. C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-99 (1954).
    [CrossRef]
  3. K. Hongo, "Diffraction of an electromagnetic plane wave by a thick slit," IEEE Trans. Antennas Propag. AP-26, 494-499 (1978).
    [CrossRef]
  4. T. Otsuki, "Diffraction by two parallel slits in a plane," J. Math. Phys. 19, 911-915 (1978).
    [CrossRef]
  5. T. Otsuki, "Reexamination of diffraction problem of a slit by a method of Fourier orthogonal functions transformation," J. Phys. Soc. Jpn. 41, 2046-2051 (1976).
    [CrossRef]
  6. B. K. Sachdeva and R. A. Hurd, "Diffraction by multiple slits at the interface between two different media," Can. J. Phys. 53, 1013-1021 (1975).
    [CrossRef]
  7. A. S. Zil'bergleit, "Diffraction of electromagnetic waves by an ideal plate with an even number of symmetrically placed slits," Sov. Phys. Tech. Phys. 20, 292-295 (1975).
  8. T. Otsuki, "Diffraction by multiple slits," J. Opt. Soc. Am. A 7, 646-652 (1990).
    [CrossRef]
  9. H. A. Kalhor, "Diffraction of electromagnetic waves by plane metallic gratings," J. Opt. Soc. Am. 68, 1202-1205 (1978).
    [CrossRef]
  10. J. J. Stamnes and H. A. Eide, "Exact and approximate solutions for focusing of two-dimensional waves. I. Theory," J. Opt. Soc. Am. A 15, 1285-1291 (1998).
    [CrossRef]
  11. M. Wirgin, "Influence de l'épaisseur de l'écran sur la diffraction par une fente," C. R. Hebd. Seances Acad. Sci. 270, 1457-1460 (1970).
  12. H. Henke and H. Fruchting, "Irradiation in a slotted half space and diffraction by a slit in a thick screen," Nachrichtentechnik 29, 401-405 (1976).
  13. J. L. Roumiguieres, D. Maystre, R. Petit, and M. Cadilhac, "Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d'épaisseur quelconque," Opt. Commun. 9, 402-405 (1973).
    [CrossRef]
  14. F. L. Neerhoff and G. Mur, "Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media," Appl. Sci. Res. 28, 73-88 (1973).
  15. K. Hongo, "A method of evaluating the near diffracted field," IEEE Trans. Antennas Propag. AP-28, 409-412 (1980).
    [CrossRef]
  16. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1982).
  17. H. S. Tan, "On Kirchhoff's theory in non-planar scalar diffraction," Proc. Phys. Soc. London 91, 768-773 (1967).
    [CrossRef]
  18. O. Mata-Mendez, "Diffraction and beam-diameter measurement of Gaussian beams at optical and microwave frequencies," Opt. Lett. 16, 1629-1631 (1991).
    [CrossRef] [PubMed]
  19. 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).
    [CrossRef]
  20. O. Mata-Mendez, M. Cadilhac, and R. Petit, "Diffraction of a two-dimensional electromagnetic beam wave by a thick slit pierced in a perfectly conducting screen," J. Opt. Soc. Am. 73, 328-331 (1983).
    [CrossRef]
  21. O. Mata-Mendez and F. Chavez-Rivas, "Diffraction of Hermite-Gaussian beams by a slit," J. Opt. Soc. Am. A 12, 2440-2445 (1995).
    [CrossRef]
  22. G. A. Suedan and E. V. Jull, "Two-dimensional beam diffraction by a half-plane and wide slit," IEEE Trans. Antennas Propag. AP-35, 1077-1082 (1987).
    [CrossRef]
  23. R. A. Depine and D. C. Skigin, "Multilayer modal method for diffraction from dielectric inhomogeneous apertures," J. Opt. Soc. Am. A 15, 675-683 (1998).
    [CrossRef]
  24. D. C. Skigin and R. A. Depine, "Scattering by lossy inhomogeneous apertures in thick metallic screens," J. Opt. Soc. Am. A 15, 2089-2096 (1998).
    [CrossRef]
  25. O. Mata-Mendez and F. Chavez-Rivas, "New property in the diffraction of Hermite-Gaussian beams by a finite grating in the scalar diffraction regime: constant-intensity angles in the far field when the beam center is displaced through the grating," J. Opt. Soc. Am. A 15, 2698-2704 (1998).
    [CrossRef]
  26. H. K. Pak and S. H. Park, "Double slit with continuously variable width and center-to-center separation," Appl. Opt. 32, 3596-3597 (1993).
    [CrossRef] [PubMed]
  27. B. Guizal and D. Felbacq, "Electromagnetic beam diffraction by a finite strip grating," Opt. Commun. 165, 1-6 (1999).
    [CrossRef]
  28. Em. E. Kriezis, P. K. Pandelakis, and A. G. Papagiannakis, "Diffraction of a Gaussian beam from a periodic planar screen," J. Opt. Soc. Am. A 11, 630-636 (1994).
    [CrossRef]
  29. J.-I. Lee, C.-H. Lee, Y.-S. Lee, and Y.-K. Cho, "Diffraction of a Gaussian wave by finite periodic slots in a parallel-plate waveguide," IEICE Trans. Commun. E84-B, 95-99 (2001).
  30. J. Sumaya-Martinez, O. Mata-Mendez, and F. Chavez-Rivas, "Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization," J. Opt. Soc. Am. A 20, 827-835 (2003).
    [CrossRef]
  31. J. Huttunen, A. T. Friberg, and J. Turunen, "Scattering of partially coherent electromagnetic fields by microstructured media," Phys. Rev. E 52, 3081-3092 (1995).
    [CrossRef]
  32. 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]
  33. L. Martín-Moreno, F. J. García-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]
  34. 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]
  35. 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]
  36. M. M. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105-1-195105-11 (2002).
    [CrossRef]
  37. Y. Takakura, "Optical resonances in a narrow slit in a thick metallic screen," Phys. Rev. Lett. 86, 5601-5603 (2001).
    [CrossRef] [PubMed]
  38. 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]
  39. F. Yang and J. R. Sambles, "Determination of microwave permittivities using a metallic slit," J. Phys. D 35, 3049-3051 (2002).
    [CrossRef]
  40. F. Yang and J. R. Sambles, "Determination of the microwave permittivities of nematic liquid crystals using a single-metallic slit technique," Appl. Phys. Lett. 81, 2047-2049 (2002).
    [CrossRef]
  41. F. Yang and J. R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901-1-063901-3 (2002).
    [CrossRef]

2004 (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]

2003 (1)

2002 (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]

M. M. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105-1-195105-11 (2002).
[CrossRef]

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

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

F. Yang and J. R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901-1-063901-3 (2002).
[CrossRef]

2001 (4)

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

L. Martín-Moreno, F. J. García-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]

J.-I. Lee, C.-H. Lee, Y.-S. Lee, and Y.-K. Cho, "Diffraction of a Gaussian wave by finite periodic slots in a parallel-plate waveguide," IEICE Trans. Commun. E84-B, 95-99 (2001).

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).
[CrossRef]

1999 (2)

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]

B. Guizal and D. Felbacq, "Electromagnetic beam diffraction by a finite strip grating," Opt. Commun. 165, 1-6 (1999).
[CrossRef]

1998 (5)

1995 (2)

J. Huttunen, A. T. Friberg, and J. Turunen, "Scattering of partially coherent electromagnetic fields by microstructured media," Phys. Rev. E 52, 3081-3092 (1995).
[CrossRef]

O. Mata-Mendez and F. Chavez-Rivas, "Diffraction of Hermite-Gaussian beams by a slit," J. Opt. Soc. Am. A 12, 2440-2445 (1995).
[CrossRef]

1994 (1)

1993 (1)

1991 (1)

1990 (1)

1987 (1)

G. A. Suedan and E. V. Jull, "Two-dimensional beam diffraction by a half-plane and wide slit," IEEE Trans. Antennas Propag. AP-35, 1077-1082 (1987).
[CrossRef]

1983 (1)

1980 (1)

K. Hongo, "A method of evaluating the near diffracted field," IEEE Trans. Antennas Propag. AP-28, 409-412 (1980).
[CrossRef]

1978 (3)

H. A. Kalhor, "Diffraction of electromagnetic waves by plane metallic gratings," J. Opt. Soc. Am. 68, 1202-1205 (1978).
[CrossRef]

K. Hongo, "Diffraction of an electromagnetic plane wave by a thick slit," IEEE Trans. Antennas Propag. AP-26, 494-499 (1978).
[CrossRef]

T. Otsuki, "Diffraction by two parallel slits in a plane," J. Math. Phys. 19, 911-915 (1978).
[CrossRef]

1976 (2)

T. Otsuki, "Reexamination of diffraction problem of a slit by a method of Fourier orthogonal functions transformation," J. Phys. Soc. Jpn. 41, 2046-2051 (1976).
[CrossRef]

H. Henke and H. Fruchting, "Irradiation in a slotted half space and diffraction by a slit in a thick screen," Nachrichtentechnik 29, 401-405 (1976).

1975 (2)

B. K. Sachdeva and R. A. Hurd, "Diffraction by multiple slits at the interface between two different media," Can. J. Phys. 53, 1013-1021 (1975).
[CrossRef]

A. S. Zil'bergleit, "Diffraction of electromagnetic waves by an ideal plate with an even number of symmetrically placed slits," Sov. Phys. Tech. Phys. 20, 292-295 (1975).

1973 (2)

J. L. Roumiguieres, D. Maystre, R. Petit, and M. Cadilhac, "Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d'épaisseur quelconque," Opt. Commun. 9, 402-405 (1973).
[CrossRef]

F. L. Neerhoff and G. Mur, "Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media," Appl. Sci. Res. 28, 73-88 (1973).

1970 (1)

M. Wirgin, "Influence de l'épaisseur de l'écran sur la diffraction par une fente," C. R. Hebd. Seances Acad. Sci. 270, 1457-1460 (1970).

1967 (1)

H. S. Tan, "On Kirchhoff's theory in non-planar scalar diffraction," Proc. Phys. Soc. London 91, 768-773 (1967).
[CrossRef]

1954 (1)

C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-99 (1954).
[CrossRef]

Bouwkamp, C. J.

C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-99 (1954).
[CrossRef]

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]

Cadilhac, M.

O. Mata-Mendez, M. Cadilhac, and R. Petit, "Diffraction of a two-dimensional electromagnetic beam wave by a thick slit pierced in a perfectly conducting screen," J. Opt. Soc. Am. 73, 328-331 (1983).
[CrossRef]

J. L. Roumiguieres, D. Maystre, R. Petit, and M. Cadilhac, "Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d'épaisseur quelconque," Opt. Commun. 9, 402-405 (1973).
[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]

Chavez-Rivas, F.

Cho, Y.-K.

J.-I. Lee, C.-H. Lee, Y.-S. Lee, and Y.-K. Cho, "Diffraction of a Gaussian wave by finite periodic slots in a parallel-plate waveguide," IEICE Trans. Commun. E84-B, 95-99 (2001).

Depine, R. A.

Ebbesen, T. W.

L. Martín-Moreno, F. J. García-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. 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]

Eide, H. A.

Felbacq, D.

B. Guizal and D. Felbacq, "Electromagnetic beam diffraction by a finite strip grating," Opt. Commun. 165, 1-6 (1999).
[CrossRef]

Friberg, A. T.

J. Huttunen, A. T. Friberg, and J. Turunen, "Scattering of partially coherent electromagnetic fields by microstructured media," Phys. Rev. E 52, 3081-3092 (1995).
[CrossRef]

Fruchting, H.

H. Henke and H. Fruchting, "Irradiation in a slotted half space and diffraction by a slit in a thick screen," Nachrichtentechnik 29, 401-405 (1976).

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]

L. Martín-Moreno, F. J. García-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]

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, 667-669 (1998).
[CrossRef]

Guizal, B.

B. Guizal and D. Felbacq, "Electromagnetic beam diffraction by a finite strip grating," Opt. Commun. 165, 1-6 (1999).
[CrossRef]

Henke, H.

H. Henke and H. Fruchting, "Irradiation in a slotted half space and diffraction by a slit in a thick screen," Nachrichtentechnik 29, 401-405 (1976).

Hongo, K.

K. Hongo, "A method of evaluating the near diffracted field," IEEE Trans. Antennas Propag. AP-28, 409-412 (1980).
[CrossRef]

K. Hongo, "Diffraction of an electromagnetic plane wave by a thick slit," IEEE Trans. Antennas Propag. AP-26, 494-499 (1978).
[CrossRef]

Hurd, R. A.

B. K. Sachdeva and R. A. Hurd, "Diffraction by multiple slits at the interface between two different media," Can. J. Phys. 53, 1013-1021 (1975).
[CrossRef]

Huttunen, J.

J. Huttunen, A. T. Friberg, and J. Turunen, "Scattering of partially coherent electromagnetic fields by microstructured media," Phys. Rev. E 52, 3081-3092 (1995).
[CrossRef]

Jull, E. V.

G. A. Suedan and E. V. Jull, "Two-dimensional beam diffraction by a half-plane and wide slit," IEEE Trans. Antennas Propag. AP-35, 1077-1082 (1987).
[CrossRef]

Kalhor, H. A.

Kriezis, Em. E.

Lalanne, P.

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]

Lee, C.-H.

J.-I. Lee, C.-H. Lee, Y.-S. Lee, and Y.-K. Cho, "Diffraction of a Gaussian wave by finite periodic slots in a parallel-plate waveguide," IEICE Trans. Commun. E84-B, 95-99 (2001).

Lee, J.-I.

J.-I. Lee, C.-H. Lee, Y.-S. Lee, and Y.-K. Cho, "Diffraction of a Gaussian wave by finite periodic slots in a parallel-plate waveguide," IEICE Trans. Commun. E84-B, 95-99 (2001).

Lee, Y.-S.

J.-I. Lee, C.-H. Lee, Y.-S. Lee, and Y.-K. Cho, "Diffraction of a Gaussian wave by finite periodic slots in a parallel-plate waveguide," IEICE Trans. Commun. E84-B, 95-99 (2001).

Lezec, H. J.

L. Martín-Moreno, F. J. García-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. 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]

Loewen, E.

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1982).

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]

L. Martín-Moreno, F. J. García-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]

Mata-Mendez, O.

Maystre, D.

J. L. Roumiguieres, D. Maystre, R. Petit, and M. Cadilhac, "Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d'épaisseur quelconque," Opt. Commun. 9, 402-405 (1973).
[CrossRef]

Mur, G.

F. L. Neerhoff and G. Mur, "Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media," Appl. Sci. Res. 28, 73-88 (1973).

Neerhoff, F. L.

F. L. Neerhoff and G. Mur, "Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media," Appl. Sci. Res. 28, 73-88 (1973).

Otsuki, T.

T. Otsuki, "Diffraction by multiple slits," J. Opt. Soc. Am. A 7, 646-652 (1990).
[CrossRef]

T. Otsuki, "Diffraction by two parallel slits in a plane," J. Math. Phys. 19, 911-915 (1978).
[CrossRef]

T. Otsuki, "Reexamination of diffraction problem of a slit by a method of Fourier orthogonal functions transformation," J. Phys. Soc. Jpn. 41, 2046-2051 (1976).
[CrossRef]

Pak, H. K.

Pandelakis, P. K.

Papagiannakis, A. G.

Park, S. H.

Pellerin, K. M.

L. Martín-Moreno, F. J. García-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]

Pendry, J. B.

L. Martín-Moreno, F. J. García-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]

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]

Petit, R.

O. Mata-Mendez, M. Cadilhac, and R. Petit, "Diffraction of a two-dimensional electromagnetic beam wave by a thick slit pierced in a perfectly conducting screen," J. Opt. Soc. Am. 73, 328-331 (1983).
[CrossRef]

J. L. Roumiguieres, D. Maystre, R. Petit, and M. Cadilhac, "Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d'épaisseur quelconque," Opt. Commun. 9, 402-405 (1973).
[CrossRef]

Popov, E.

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

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]

Roumiguieres, J. L.

J. L. Roumiguieres, D. Maystre, R. Petit, and M. Cadilhac, "Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d'épaisseur quelconque," Opt. Commun. 9, 402-405 (1973).
[CrossRef]

Sachdeva, B. K.

B. K. Sachdeva and R. A. Hurd, "Diffraction by multiple slits at the interface between two different media," Can. J. Phys. 53, 1013-1021 (1975).
[CrossRef]

Sambles, J. R.

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

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

F. Yang and J. R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901-1-063901-3 (2002).
[CrossRef]

Skigin, D. C.

Stamnes, J. J.

Suedan, G. A.

G. A. Suedan and E. V. Jull, "Two-dimensional beam diffraction by a half-plane and wide slit," IEEE Trans. Antennas Propag. AP-35, 1077-1082 (1987).
[CrossRef]

Sumaya-Martinez, J.

Takakura, Y.

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

Tan, H. S.

H. S. Tan, "On Kirchhoff's theory in non-planar scalar diffraction," Proc. Phys. Soc. London 91, 768-773 (1967).
[CrossRef]

Thio, T.

L. Martín-Moreno, F. J. García-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. 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]

Treacy, M. M.

M. M. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105-1-195105-11 (2002).
[CrossRef]

Turunen, J.

J. Huttunen, A. T. Friberg, and J. Turunen, "Scattering of partially coherent electromagnetic fields by microstructured media," Phys. Rev. E 52, 3081-3092 (1995).
[CrossRef]

Wirgin, M.

M. Wirgin, "Influence de l'épaisseur de l'écran sur la diffraction par une fente," C. R. Hebd. Seances Acad. Sci. 270, 1457-1460 (1970).

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, 667-669 (1998).
[CrossRef]

Yang, F.

F. Yang and J. R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901-1-063901-3 (2002).
[CrossRef]

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

Zil'bergleit, A. S.

A. S. Zil'bergleit, "Diffraction of electromagnetic waves by an ideal plate with an even number of symmetrically placed slits," Sov. Phys. Tech. Phys. 20, 292-295 (1975).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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

Appl. Sci. Res. (1)

F. L. Neerhoff and G. Mur, "Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media," Appl. Sci. Res. 28, 73-88 (1973).

C. R. Hebd. Seances Acad. Sci. (1)

M. Wirgin, "Influence de l'épaisseur de l'écran sur la diffraction par une fente," C. R. Hebd. Seances Acad. Sci. 270, 1457-1460 (1970).

Can. J. Phys. (1)

B. K. Sachdeva and R. A. Hurd, "Diffraction by multiple slits at the interface between two different media," Can. J. Phys. 53, 1013-1021 (1975).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

K. Hongo, "Diffraction of an electromagnetic plane wave by a thick slit," IEEE Trans. Antennas Propag. AP-26, 494-499 (1978).
[CrossRef]

K. Hongo, "A method of evaluating the near diffracted field," IEEE Trans. Antennas Propag. AP-28, 409-412 (1980).
[CrossRef]

G. A. Suedan and E. V. Jull, "Two-dimensional beam diffraction by a half-plane and wide slit," IEEE Trans. Antennas Propag. AP-35, 1077-1082 (1987).
[CrossRef]

IEICE Trans. Commun. (1)

J.-I. Lee, C.-H. Lee, Y.-S. Lee, and Y.-K. Cho, "Diffraction of a Gaussian wave by finite periodic slots in a parallel-plate waveguide," IEICE Trans. Commun. E84-B, 95-99 (2001).

J. Math. Phys. (1)

T. Otsuki, "Diffraction by two parallel slits in a plane," J. Math. Phys. 19, 911-915 (1978).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (9)

O. Mata-Mendez and F. Chavez-Rivas, "Diffraction of Hermite-Gaussian beams by a slit," J. Opt. Soc. Am. A 12, 2440-2445 (1995).
[CrossRef]

R. A. Depine and D. C. Skigin, "Multilayer modal method for diffraction from dielectric inhomogeneous apertures," J. Opt. Soc. Am. A 15, 675-683 (1998).
[CrossRef]

D. C. Skigin and R. A. Depine, "Scattering by lossy inhomogeneous apertures in thick metallic screens," J. Opt. Soc. Am. A 15, 2089-2096 (1998).
[CrossRef]

O. Mata-Mendez and F. Chavez-Rivas, "New property in the diffraction of Hermite-Gaussian beams by a finite grating in the scalar diffraction regime: constant-intensity angles in the far field when the beam center is displaced through the grating," J. Opt. Soc. Am. A 15, 2698-2704 (1998).
[CrossRef]

J. Sumaya-Martinez, O. Mata-Mendez, and F. Chavez-Rivas, "Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization," J. Opt. Soc. Am. A 20, 827-835 (2003).
[CrossRef]

J. J. Stamnes and H. A. Eide, "Exact and approximate solutions for focusing of two-dimensional waves. I. Theory," J. Opt. Soc. Am. A 15, 1285-1291 (1998).
[CrossRef]

T. Otsuki, "Diffraction by multiple slits," J. Opt. Soc. Am. A 7, 646-652 (1990).
[CrossRef]

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).
[CrossRef]

Em. E. Kriezis, P. K. Pandelakis, and A. G. Papagiannakis, "Diffraction of a Gaussian beam from a periodic planar screen," J. Opt. Soc. Am. A 11, 630-636 (1994).
[CrossRef]

J. Phys. D (1)

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

J. Phys. Soc. Jpn. (1)

T. Otsuki, "Reexamination of diffraction problem of a slit by a method of Fourier orthogonal functions transformation," J. Phys. Soc. Jpn. 41, 2046-2051 (1976).
[CrossRef]

Nachrichtentechnik (1)

H. Henke and H. Fruchting, "Irradiation in a slotted half space and diffraction by a slit in a thick screen," Nachrichtentechnik 29, 401-405 (1976).

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, 667-669 (1998).
[CrossRef]

Opt. Commun. (2)

B. Guizal and D. Felbacq, "Electromagnetic beam diffraction by a finite strip grating," Opt. Commun. 165, 1-6 (1999).
[CrossRef]

J. L. Roumiguieres, D. Maystre, R. Petit, and M. Cadilhac, "Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d'épaisseur quelconque," Opt. Commun. 9, 402-405 (1973).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

M. M. Treacy, "Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings," Phys. Rev. B 66, 195105-1-195105-11 (2002).
[CrossRef]

Phys. Rev. E (2)

J. Huttunen, A. T. Friberg, and J. Turunen, "Scattering of partially coherent electromagnetic fields by microstructured media," Phys. Rev. E 52, 3081-3092 (1995).
[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]

Phys. Rev. Lett. (5)

F. Yang and J. R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Phys. Rev. Lett. 89, 063901-1-063901-3 (2002).
[CrossRef]

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

L. Martín-Moreno, F. J. García-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]

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]

Proc. Phys. Soc. London (1)

H. S. Tan, "On Kirchhoff's theory in non-planar scalar diffraction," Proc. Phys. Soc. London 91, 768-773 (1967).
[CrossRef]

Rep. Prog. Phys. (1)

C. J. Bouwkamp, "Diffraction theory," Rep. Prog. Phys. 17, 35-99 (1954).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

A. S. Zil'bergleit, "Diffraction of electromagnetic waves by an ideal plate with an even number of symmetrically placed slits," Sov. Phys. Tech. Phys. 20, 292-295 (1975).

Other (2)

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1982).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Our configuration composed of N slits of width l , separation d, and period D = d + l in an infinitely thick planar screen of thickness h. The slits are parallel to the O z axis.

Fig. 2
Fig. 2

Diffraction patterns of a finite grating with N = 10 and D l = 2.0 for a normally incident Gaussian beam with L l = 20 2 , b l = 9.5 , and wavelengths (a) λ l = 0.1 , (b) λ l = 0.8 , (c) λ l = 1.5 , and (d) λ l = 2.5 .

Fig. 3
Fig. 3

(a) Intensity diffracted at normal direction normalized to the total incident energy ( E I 0 ) and (b) transmission coefficient τ as a function of the wavelength λ l for finite gratings composed of two, three, four, five, and eight slits of period D l = 1.5 and for a normally incident Gaussian beam with width L l = 5 2 .

Fig. 4
Fig. 4

Transmission coefficient τ as a function of the normalized beam width L l for finite gratings with N = 2 , 3, 4, 5, 6, and 7 and period D l = 1.5 for a normally incident Gaussian beam with wavelength λ l = 0.9 whose beam waist is located at the middle of each finite grating.

Fig. 5
Fig. 5

Intensity diffracted at a normal direction normalized to the total incident energy ( E I 0 ) as a function of the beam width L l . Parameters are the same as those in Fig. 4.

Fig. 6
Fig. 6

Diffraction patterns from a finite grating when N = 15 , D l = 1.5 , and l = 1 for a normally incident Gaussian beam of wavelength λ l = 0.9 , beam position b l = 11 , and beam widths (a) L l = 7 2 , (b) L l = 10 2 , (c) L l = 45 2 2 , and (d) L l = 5000 2 .

Fig. 7
Fig. 7

(a) Intensity diffracted at a normal direction normalized to the total incident energy ( E I 0 ) and (b) the transmission coefficient τ versus the normalized beam position b l for a finite grating with N = 5 and period D l = 1.5 . A normally incident Gaussian beam, with wavelength λ l = 0.9 , beam width L l = 50 2 , and beam position b l = 3.5 , is assumed.

Fig. 8
Fig. 8

Coupling between slits. Transmission coefficient τ as a function of the normalized separation d l between slits for a finite grating with N = 5 , where a normally incident Gaussian beam, with wavelength λ l = 0.9 , beam width L l = 500 2 , and beam position b l = 0.5 , is considered.

Fig. 9
Fig. 9

Diffracted intensity normalized to the incident energy [ I ( θ ) I 0 ] for a finite grating with five slits of period D l = 1.5 , d l = 0.5 , when L l = 10 2 and λ l = 0.9 . Constant-intensity angles are pointed out by arrows.

Fig. 10
Fig. 10

Transmission coefficients in the subwavelength regime for three finite gratings composed of one, three, and ten slits of width l = 0.5 μ m , separation d = 0.2 μ m , and metallic screen thickness h = 8 μ m . The finite grating is illuminated by a normally incident Gaussian beam with width L = 15 2 μ m .

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

2 H x 2 + 2 H y 2 + k 0 2 H = 0 ,
H 1 ( x , y ) = 1 2 π k 0 k 0 A ( α ) exp [ i ( α x β y ) ] d α + 1 2 π B ( α ) exp [ i ( α x + β y ) ] d α ( y > h 2 ) ,
H 2 ( x , y ) = 1 2 π C ( α ) exp [ i ( α x β y ) ] d α ( y < h 2 ) ,
H 3 ( x , y ) = p = 1 N n = 0 [ a n p cos ( μ n y ) + b n p sin ( μ n y ) ] ϕ n p ( x ) ( h 2 < y < h 2 ) ,
ϕ n p ( x ) = { cos { [ x ( p 1 ) D ] n π l } if ( p 1 ) D x l + ( p 1 ) D 0 elsewhere } .
ϕ n p ( x ) , ϕ m q ( x ) = ϕ n p ( x ) [ ϕ m q ( x ) ] * d x = l 2 ( 1 + δ n 0 ) δ n m δ p q ,
H ̂ 1 ( α , h 2 ) H ̂ 3 ( α , h 2 ) , ϕ ̂ m q ( α ) = 0 ,
H ̂ 3 ( α , h 2 ) H ̂ 2 ( α , h 2 ) , ϕ ̂ m q ( α ) = 0 ,
2 A ( α ) exp ( i β h 2 ) , ϕ ̂ m q ( α ) = p = 1 N n = 0 { a n p [ μ n sin ( μ n h 2 ) i β ϕ ̂ n p ( α ) , ϕ ̂ m q ( α ) + cos ( μ n h 2 ) ϕ ̂ n p ( α ) , ϕ ̂ m q ( α ) ] + b n p [ μ n cos ( μ n h 2 ) × i β ϕ ̂ n p ( α ) , ϕ ̂ m q ( α ) + sin ( μ n h 2 ) ϕ ̂ n p ( α ) , ϕ ̂ m q ( α ) ] } ,
0 = p = 1 N n = 0 { a n p [ μ n sin ( μ n h 2 ) i β ϕ ̂ n p ( α ) , ϕ ̂ m q ( α ) + cos ( μ n h 2 ) ϕ ̂ n p ( α ) , ϕ ̂ m q ( α ) ] b n p { μ n cos ( μ n h 2 ) × i β ϕ ̂ n p ( α ) , ϕ ̂ m q ( α ) + sin ( μ n h 2 ) ϕ ̂ n p ( α ) , ϕ ̂ m q ( α ) ] } ,
A ( α ) + B ( α ) = C ( α ) ;
a n p = A ( α ) , ϕ ̂ n p ( α ) ϕ ̂ n p ( α ) , ϕ ̂ n p ( α ) = H i ( x , 0 ) , ϕ n p ( x ) l 2 ( 1 + δ n 0 ) ,
H 3 ( x , 0 ) = H i ( x , 0 ) ( x within the slits and h = 0 ) ;
I ( θ ) = 1 2 ϵ 0 ω H ̂ 3 y ( k 0 sin θ , h 2 ) 2 .
H i ( x , y = 0 ) = exp [ 2 ( x b ) 2 L 2 ] ,
A ( α ) = L 2 exp ( i α b ) exp ( α 2 L 2 8 ) .
( L l ) max = N D 2 .
E ( b ) = 0.75719 exp [ 3.9405 ( b 3.5 ) 2 L 2 ] ,
τ ( b ) = 0.143267 exp [ 3.8875 ( b 3.5 ) 2 L 2 ] ;
E = 0.9513 N τ λ .

Metrics