Abstract

A rigorous electromagnetic theory of the diffraction of radiation by a circular aperture in a thick screen is developed. In particular, the case of an incident plane wave is considered, and the effects of varying the thickness of the screen and of varying the wavelength, polarization, and angle of incidence of the incident wave on the reflection and transmission properties of the screen are investigated.

© 1987 Optical Society of America

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References

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  1. C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–402 (1950).
  2. D. S. Jones, “Diffraction of a high-frequency plane electromagnetic wave by a perfectly conducting circular disc,” Proc. Camb. Phil. Soc. 61, 247–270 (1965).
    [Crossref]
  3. J. Bazer, L. Rubenfeld, “Diffraction of electromagnetic waves by a circular aperture in an infinitely conducting plane screen,”J. Soc. Indust. Appl. Math. 13, 558–585 (1965).
    [Crossref]
  4. C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,”IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
    [Crossref]
  5. A. N. Akhiezer, “On the inclusion of the effect of the thickness of the screen in certain diffraction problems,” Zh. Tekh. Fiz. 27, 1294–1300 (1957).
  6. D. J. Bliek, L. C. Botten, R. Deleuil, R. C. McPhedran, D. Maystre, “Inductive grids in the region of diffraction anomalies: theory, experiment, and applications,” IEEE Trans. Microwave Theory Tech. MTT-28, 1119–1125 (1980).
    [Crossref]
  7. M. Wirgin, “Influence d l’épaisseur de l’écran sur la diffraction par une fente,”C. R. Acad. Sci. 270, 1457–1460 (1970).
  8. F. L. Neerhoff, 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).
  9. K. Hongo, G. Ishii, “Diffraction of an electromagnetic plane wave by a thick slit,”IEEE Trans. Antennas Propag. AP-26, 494–499 (1978).
    [Crossref]
  10. J. L. Roumiguières, D. Maystre, R. Petit, M. Cadilhac, “Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d’épaisseur quelconque,” Opt. Commun. 9, 368–373 (1973).
    [Crossref]
  11. O. Mata Mendez, M. Cadilhac, 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]
  12. L. N. Deriugin, “Reflection of a longitudinally polarized wave from a rectangular comb,” Radiotekhnika 15, 9–15 (1960).
  13. L. N. Deriugin, “The reflection of a plane transverse polarized wave from a rectangular comb,” Radiotekhnika 15, 15–26 (1960).
  14. A. Wirgin, “Considérations théoriques sur la diffraction par des réseaux,” Thèse d’Etat, Official Number 1429 (Faculté de Sciences d’Orsay, Orsay, France, 1967).
  15. A. Wirgin, R. Deleuil, “Theoretical and experimental investigation of a new type of blazed grating,”J. Opt. Soc. Am. 59, 1348–1357 (1969).
    [Crossref]
  16. D. Maystre, R. Petit, “Diffraction by an infinitely conducting lamellar grid,” Opt. Commun. 5, 90 (1972).
    [Crossref]
  17. N. Amitay, V. Galindo, “On the scalar product of certain circular and cartesian wave functions,” IEEE Trans. Microwave Theory Tech. MTT-16, 265–266 (1968).
    [Crossref]
  18. R. C. McPhedran, L. C. Botten, “Inductive grids with circular apertures,” (School of Physics, The University of Sydney, Sydney, Australia, 1977).
  19. R. C. McPhedran, D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
    [Crossref]
  20. W. Andrejewski, “Strenge Theorie der Beugung ebener elektromagnetischer Wellen an der vollkommen leitenden Kreisscheibe und an der kreisförmigen Öffnung im vollkommen leitenden ebenen Schirm,” Naturwissenschaften 38, 406–407 (1951).
    [Crossref]
  21. Y. Nomura, S. Katsura, “Diffraction of electromagnetic waves by circular plate and circular hole,” J. Phys. Soc. Jpn. 10, 285–304 (1955).
    [Crossref]
  22. J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
    [Crossref]
  23. J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
    [Crossref]
  24. H. Levine, J. Schwinger, “On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen,” Commun. Pure Appl. Math. 3, 355–391 (1950).
    [Crossref]
  25. C. Huang, R. D. Kodis, H. Levine, “Diffraction by apertures,” J. Appl. Phys. 26, 151–165 (1955).
    [Crossref]
  26. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), p. 401.
  27. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1958).

1983 (1)

1980 (1)

D. J. Bliek, L. C. Botten, R. Deleuil, R. C. McPhedran, D. Maystre, “Inductive grids in the region of diffraction anomalies: theory, experiment, and applications,” IEEE Trans. Microwave Theory Tech. MTT-28, 1119–1125 (1980).
[Crossref]

1979 (2)

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[Crossref]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[Crossref]

1978 (2)

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,”IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[Crossref]

K. Hongo, G. Ishii, “Diffraction of an electromagnetic plane wave by a thick slit,”IEEE Trans. Antennas Propag. AP-26, 494–499 (1978).
[Crossref]

1977 (1)

R. C. McPhedran, D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[Crossref]

1973 (2)

J. L. Roumiguières, D. Maystre, R. Petit, M. Cadilhac, “Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d’épaisseur quelconque,” Opt. Commun. 9, 368–373 (1973).
[Crossref]

F. L. Neerhoff, 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).

1972 (1)

D. Maystre, R. Petit, “Diffraction by an infinitely conducting lamellar grid,” Opt. Commun. 5, 90 (1972).
[Crossref]

1970 (1)

M. Wirgin, “Influence d l’épaisseur de l’écran sur la diffraction par une fente,”C. R. Acad. Sci. 270, 1457–1460 (1970).

1969 (1)

1968 (1)

N. Amitay, V. Galindo, “On the scalar product of certain circular and cartesian wave functions,” IEEE Trans. Microwave Theory Tech. MTT-16, 265–266 (1968).
[Crossref]

1965 (2)

D. S. Jones, “Diffraction of a high-frequency plane electromagnetic wave by a perfectly conducting circular disc,” Proc. Camb. Phil. Soc. 61, 247–270 (1965).
[Crossref]

J. Bazer, L. Rubenfeld, “Diffraction of electromagnetic waves by a circular aperture in an infinitely conducting plane screen,”J. Soc. Indust. Appl. Math. 13, 558–585 (1965).
[Crossref]

1960 (2)

L. N. Deriugin, “Reflection of a longitudinally polarized wave from a rectangular comb,” Radiotekhnika 15, 9–15 (1960).

L. N. Deriugin, “The reflection of a plane transverse polarized wave from a rectangular comb,” Radiotekhnika 15, 15–26 (1960).

1957 (1)

A. N. Akhiezer, “On the inclusion of the effect of the thickness of the screen in certain diffraction problems,” Zh. Tekh. Fiz. 27, 1294–1300 (1957).

1955 (2)

Y. Nomura, S. Katsura, “Diffraction of electromagnetic waves by circular plate and circular hole,” J. Phys. Soc. Jpn. 10, 285–304 (1955).
[Crossref]

C. Huang, R. D. Kodis, H. Levine, “Diffraction by apertures,” J. Appl. Phys. 26, 151–165 (1955).
[Crossref]

1951 (1)

W. Andrejewski, “Strenge Theorie der Beugung ebener elektromagnetischer Wellen an der vollkommen leitenden Kreisscheibe und an der kreisförmigen Öffnung im vollkommen leitenden ebenen Schirm,” Naturwissenschaften 38, 406–407 (1951).
[Crossref]

1950 (2)

C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–402 (1950).

H. Levine, J. Schwinger, “On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen,” Commun. Pure Appl. Math. 3, 355–391 (1950).
[Crossref]

Akhiezer, A. N.

A. N. Akhiezer, “On the inclusion of the effect of the thickness of the screen in certain diffraction problems,” Zh. Tekh. Fiz. 27, 1294–1300 (1957).

Amitay, N.

N. Amitay, V. Galindo, “On the scalar product of certain circular and cartesian wave functions,” IEEE Trans. Microwave Theory Tech. MTT-16, 265–266 (1968).
[Crossref]

Andrejewski, W.

W. Andrejewski, “Strenge Theorie der Beugung ebener elektromagnetischer Wellen an der vollkommen leitenden Kreisscheibe und an der kreisförmigen Öffnung im vollkommen leitenden ebenen Schirm,” Naturwissenschaften 38, 406–407 (1951).
[Crossref]

Andrewartha, J. R.

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[Crossref]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[Crossref]

Bazer, J.

J. Bazer, L. Rubenfeld, “Diffraction of electromagnetic waves by a circular aperture in an infinitely conducting plane screen,”J. Soc. Indust. Appl. Math. 13, 558–585 (1965).
[Crossref]

Bliek, D. J.

D. J. Bliek, L. C. Botten, R. Deleuil, R. C. McPhedran, D. Maystre, “Inductive grids in the region of diffraction anomalies: theory, experiment, and applications,” IEEE Trans. Microwave Theory Tech. MTT-28, 1119–1125 (1980).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), p. 401.

Botten, L. C.

D. J. Bliek, L. C. Botten, R. Deleuil, R. C. McPhedran, D. Maystre, “Inductive grids in the region of diffraction anomalies: theory, experiment, and applications,” IEEE Trans. Microwave Theory Tech. MTT-28, 1119–1125 (1980).
[Crossref]

R. C. McPhedran, L. C. Botten, “Inductive grids with circular apertures,” (School of Physics, The University of Sydney, Sydney, Australia, 1977).

Bouwkamp, C. J.

C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–402 (1950).

Butler, C. M.

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,”IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[Crossref]

Cadilhac, M.

O. Mata Mendez, M. Cadilhac, 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. Roumiguières, D. Maystre, R. Petit, M. Cadilhac, “Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d’épaisseur quelconque,” Opt. Commun. 9, 368–373 (1973).
[Crossref]

Deleuil, R.

D. J. Bliek, L. C. Botten, R. Deleuil, R. C. McPhedran, D. Maystre, “Inductive grids in the region of diffraction anomalies: theory, experiment, and applications,” IEEE Trans. Microwave Theory Tech. MTT-28, 1119–1125 (1980).
[Crossref]

A. Wirgin, R. Deleuil, “Theoretical and experimental investigation of a new type of blazed grating,”J. Opt. Soc. Am. 59, 1348–1357 (1969).
[Crossref]

Deriugin, L. N.

L. N. Deriugin, “Reflection of a longitudinally polarized wave from a rectangular comb,” Radiotekhnika 15, 9–15 (1960).

L. N. Deriugin, “The reflection of a plane transverse polarized wave from a rectangular comb,” Radiotekhnika 15, 15–26 (1960).

Fox, J. R.

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[Crossref]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[Crossref]

Galindo, V.

N. Amitay, V. Galindo, “On the scalar product of certain circular and cartesian wave functions,” IEEE Trans. Microwave Theory Tech. MTT-16, 265–266 (1968).
[Crossref]

Hongo, K.

K. Hongo, G. Ishii, “Diffraction of an electromagnetic plane wave by a thick slit,”IEEE Trans. Antennas Propag. AP-26, 494–499 (1978).
[Crossref]

Huang, C.

C. Huang, R. D. Kodis, H. Levine, “Diffraction by apertures,” J. Appl. Phys. 26, 151–165 (1955).
[Crossref]

Ishii, G.

K. Hongo, G. Ishii, “Diffraction of an electromagnetic plane wave by a thick slit,”IEEE Trans. Antennas Propag. AP-26, 494–499 (1978).
[Crossref]

Jones, D. S.

D. S. Jones, “Diffraction of a high-frequency plane electromagnetic wave by a perfectly conducting circular disc,” Proc. Camb. Phil. Soc. 61, 247–270 (1965).
[Crossref]

Katsura, S.

Y. Nomura, S. Katsura, “Diffraction of electromagnetic waves by circular plate and circular hole,” J. Phys. Soc. Jpn. 10, 285–304 (1955).
[Crossref]

Kodis, R. D.

C. Huang, R. D. Kodis, H. Levine, “Diffraction by apertures,” J. Appl. Phys. 26, 151–165 (1955).
[Crossref]

Levine, H.

C. Huang, R. D. Kodis, H. Levine, “Diffraction by apertures,” J. Appl. Phys. 26, 151–165 (1955).
[Crossref]

H. Levine, J. Schwinger, “On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen,” Commun. Pure Appl. Math. 3, 355–391 (1950).
[Crossref]

Mata Mendez, O.

Maystre, D.

D. J. Bliek, L. C. Botten, R. Deleuil, R. C. McPhedran, D. Maystre, “Inductive grids in the region of diffraction anomalies: theory, experiment, and applications,” IEEE Trans. Microwave Theory Tech. MTT-28, 1119–1125 (1980).
[Crossref]

R. C. McPhedran, D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[Crossref]

J. L. Roumiguières, D. Maystre, R. Petit, M. Cadilhac, “Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d’épaisseur quelconque,” Opt. Commun. 9, 368–373 (1973).
[Crossref]

D. Maystre, R. Petit, “Diffraction by an infinitely conducting lamellar grid,” Opt. Commun. 5, 90 (1972).
[Crossref]

McPhedran, R. C.

D. J. Bliek, L. C. Botten, R. Deleuil, R. C. McPhedran, D. Maystre, “Inductive grids in the region of diffraction anomalies: theory, experiment, and applications,” IEEE Trans. Microwave Theory Tech. MTT-28, 1119–1125 (1980).
[Crossref]

R. C. McPhedran, D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[Crossref]

R. C. McPhedran, L. C. Botten, “Inductive grids with circular apertures,” (School of Physics, The University of Sydney, Sydney, Australia, 1977).

Mittra, R.

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,”IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[Crossref]

Mur, G.

F. L. Neerhoff, 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, 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).

Nomura, Y.

Y. Nomura, S. Katsura, “Diffraction of electromagnetic waves by circular plate and circular hole,” J. Phys. Soc. Jpn. 10, 285–304 (1955).
[Crossref]

Petit, R.

O. Mata Mendez, M. Cadilhac, 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. Roumiguières, D. Maystre, R. Petit, M. Cadilhac, “Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d’épaisseur quelconque,” Opt. Commun. 9, 368–373 (1973).
[Crossref]

D. Maystre, R. Petit, “Diffraction by an infinitely conducting lamellar grid,” Opt. Commun. 5, 90 (1972).
[Crossref]

Rahmat-Samii, Y.

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,”IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[Crossref]

Roumiguières, J. L.

J. L. Roumiguières, D. Maystre, R. Petit, M. Cadilhac, “Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d’épaisseur quelconque,” Opt. Commun. 9, 368–373 (1973).
[Crossref]

Rubenfeld, L.

J. Bazer, L. Rubenfeld, “Diffraction of electromagnetic waves by a circular aperture in an infinitely conducting plane screen,”J. Soc. Indust. Appl. Math. 13, 558–585 (1965).
[Crossref]

Schwinger, J.

H. Levine, J. Schwinger, “On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen,” Commun. Pure Appl. Math. 3, 355–391 (1950).
[Crossref]

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1958).

Wilson, I. J.

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[Crossref]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[Crossref]

Wirgin, A.

A. Wirgin, R. Deleuil, “Theoretical and experimental investigation of a new type of blazed grating,”J. Opt. Soc. Am. 59, 1348–1357 (1969).
[Crossref]

A. Wirgin, “Considérations théoriques sur la diffraction par des réseaux,” Thèse d’Etat, Official Number 1429 (Faculté de Sciences d’Orsay, Orsay, France, 1967).

Wirgin, M.

M. Wirgin, “Influence d l’épaisseur de l’écran sur la diffraction par une fente,”C. R. Acad. Sci. 270, 1457–1460 (1970).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), p. 401.

Appl. Phys. (1)

R. C. McPhedran, D. Maystre, “On the theory and solar application of inductive grids,” Appl. Phys. 14, 1–20 (1977).
[Crossref]

Appl. Sci. Res. (1)

F. L. Neerhoff, 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. Acad. Sci. (1)

M. Wirgin, “Influence d l’épaisseur de l’écran sur la diffraction par une fente,”C. R. Acad. Sci. 270, 1457–1460 (1970).

Commun. Pure Appl. Math. (1)

H. Levine, J. Schwinger, “On the theory of electromagnetic wave diffraction by an aperture in an infinite plane conducting screen,” Commun. Pure Appl. Math. 3, 355–391 (1950).
[Crossref]

IEEE Trans. Antennas Propag. (2)

K. Hongo, G. Ishii, “Diffraction of an electromagnetic plane wave by a thick slit,”IEEE Trans. Antennas Propag. AP-26, 494–499 (1978).
[Crossref]

C. M. Butler, Y. Rahmat-Samii, R. Mittra, “Electromagnetic penetration through apertures in conducting surfaces,”IEEE Trans. Antennas Propag. AP-26, 82–93 (1978).
[Crossref]

IEEE Trans. Microwave Theory Tech. (2)

D. J. Bliek, L. C. Botten, R. Deleuil, R. C. McPhedran, D. Maystre, “Inductive grids in the region of diffraction anomalies: theory, experiment, and applications,” IEEE Trans. Microwave Theory Tech. MTT-28, 1119–1125 (1980).
[Crossref]

N. Amitay, V. Galindo, “On the scalar product of certain circular and cartesian wave functions,” IEEE Trans. Microwave Theory Tech. MTT-16, 265–266 (1968).
[Crossref]

J. Appl. Phys. (1)

C. Huang, R. D. Kodis, H. Levine, “Diffraction by apertures,” J. Appl. Phys. 26, 151–165 (1955).
[Crossref]

J. Opt. Soc. Am. (2)

J. Phys. Soc. Jpn. (1)

Y. Nomura, S. Katsura, “Diffraction of electromagnetic waves by circular plate and circular hole,” J. Phys. Soc. Jpn. 10, 285–304 (1955).
[Crossref]

J. Soc. Indust. Appl. Math. (1)

J. Bazer, L. Rubenfeld, “Diffraction of electromagnetic waves by a circular aperture in an infinitely conducting plane screen,”J. Soc. Indust. Appl. Math. 13, 558–585 (1965).
[Crossref]

Naturwissenschaften (1)

W. Andrejewski, “Strenge Theorie der Beugung ebener elektromagnetischer Wellen an der vollkommen leitenden Kreisscheibe und an der kreisförmigen Öffnung im vollkommen leitenden ebenen Schirm,” Naturwissenschaften 38, 406–407 (1951).
[Crossref]

Opt. Acta (2)

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Resonance anomalies in the lamellar grating,” Opt. Acta 26, 69–89 (1979).
[Crossref]

J. R. Andrewartha, J. R. Fox, I. J. Wilson, “Further properties of lamellar grating resonance anomalies,” Opt. Acta 26, 197–209 (1979).
[Crossref]

Opt. Commun. (2)

J. L. Roumiguières, D. Maystre, R. Petit, M. Cadilhac, “Etude de la diffraction par une fente pratiquée dans un écran infiniment conducteur d’épaisseur quelconque,” Opt. Commun. 9, 368–373 (1973).
[Crossref]

D. Maystre, R. Petit, “Diffraction by an infinitely conducting lamellar grid,” Opt. Commun. 5, 90 (1972).
[Crossref]

Philips Res. Rep. (1)

C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–402 (1950).

Proc. Camb. Phil. Soc. (1)

D. S. Jones, “Diffraction of a high-frequency plane electromagnetic wave by a perfectly conducting circular disc,” Proc. Camb. Phil. Soc. 61, 247–270 (1965).
[Crossref]

Radiotekhnika (2)

L. N. Deriugin, “Reflection of a longitudinally polarized wave from a rectangular comb,” Radiotekhnika 15, 9–15 (1960).

L. N. Deriugin, “The reflection of a plane transverse polarized wave from a rectangular comb,” Radiotekhnika 15, 15–26 (1960).

Zh. Tekh. Fiz. (1)

A. N. Akhiezer, “On the inclusion of the effect of the thickness of the screen in certain diffraction problems,” Zh. Tekh. Fiz. 27, 1294–1300 (1957).

Other (4)

A. Wirgin, “Considérations théoriques sur la diffraction par des réseaux,” Thèse d’Etat, Official Number 1429 (Faculté de Sciences d’Orsay, Orsay, France, 1967).

R. C. McPhedran, L. C. Botten, “Inductive grids with circular apertures,” (School of Physics, The University of Sydney, Sydney, Australia, 1977).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), p. 401.

G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1958).

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Figures (9)

Fig. 1
Fig. 1

Parameters used in the description of the aperture, screen, and incident radiation.

Fig. 2
Fig. 2

Cylindrical polar coordinate system used in the definition of the circular waveguide modes and field expansions within the aperture.

Fig. 3
Fig. 3

Transmission coefficient t plotted as a function of the dimensionless parameter k0a for two different screen thicknesses: h = 0 (solid line) and h = a (dashed line). Curves represent data calculated for (a) normally incident radiation and (b), (c) radiation incident at an angle of 30° to the normal for (b) TE or (c) TM polarization.

Fig. 4
Fig. 4

Transmission coefficient t versus k0a for a screen thickness of h = 10a and for (a) normally incident radiation and (b), (c) radiation at an angle of incidence of 30° and (b) TE and (c) TM polarizations.

Fig. 5
Fig. 5

Transmission coefficient t versus k0a for screen thicknesses of (a) h = 5a and (b) h = 10a. Also marked on the horizontal axis are values of k0ν201h, the phase difference between the upper and lower surfaces for the (0, 1) TM mode.

Fig. 6
Fig. 6

Transmission coefficient plotted as a function of screen thickness for (a) k0a = 1, (b) k0a = 5, and (c) k0a = 10 for TE-polarized (- - -) and TM-polarized (—) radiation at angles of incidence of 10° and 60°.

Fig. 7
Fig. 7

Diffraction patterns from an aperture with k0a ≡ 10 taken along a line parallel to the incident electric field for screen thicknesses of (a) h = 0, (b) h = a, and (c) h = 5a, using normally incident radiation.

Fig. 8
Fig. 8

Diffraction patterns obtained along lines that are (—) parallel to and (- - -) normal to the incident electric field vector for normal incidence and with k0a = 15. (a) Screen thickness of zero; (b) h = 5a.

Fig. 9
Fig. 9

Same as Fig. 8 but with k0a = 5 and, in (b), h = a.

Tables (1)

Tables Icon

Table 1 Angular Resolution of an Aperture with k0a = 10

Equations (104)

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R ( α , γ , x , y , z ) = k 0 2 π exp [ j k 0 ( α x + β y + γ z ) ] ,
β ( α , γ ) = { 1 - α 2 - γ 2 if α 2 + γ 2 1 j α 2 + γ 2 - 1 otherwise .
R ^ ( α , γ , x , y , z ) = k 0 2 π exp [ j k 0 ( α x - β y + γ z ) ] .
- - d x d z R ¯ ( α , γ , x , y , z ) R ( α , γ , x , y , z ) = - - d x d z R ¯ ( α , γ , x , y , z ) R ^ ( α , γ , x , y , z ) = δ ( α - α ) δ ( γ - γ ) .
Φ 1 ( α , γ , x , y , z ) = ( γ x ^ - α z ^ ) ξ R ( α , γ , x , y , z )
Φ 2 ( α , γ , x , y , z ) = ( α x ^ + γ z ^ ) ξ R ( α , γ , x , y , z ) ,
ξ = α 2 + γ 2 .
E t i = r = 1 2 d α d γ E r i ( α , γ ) Φ ^ r ( α , γ ) ,
Z 0 y ^ × H t i = r d α d γ Y r ( α , γ ) E r i ( α , γ ) Φ ^ r ( α , γ ) ,
Y 1 ( α , γ ) = β ( α , γ )
Y 2 ( α , γ ) = 1 β ( α , γ ) .
E t = E t i + r d α d γ E r ( α , γ ) Φ r ( α , γ )
Z 0 y ^ × H t = Z 0 y ^ × H t i - r d α d γ Y r ( α , γ ) E r ( α , γ ) Φ r ( α , γ ) .
E ^ t = r d α d γ E ^ r ( α , γ ) Φ ^ r ( α , γ )
Z 0 y ^ × H ^ t = r d α d γ Y r ( α , γ ) E ^ r ( α , γ ) Φ ^ r ( α , γ ) .
A Ψ s n m l · Ψ S N M L d A = δ s , S δ n , N δ m , M δ l , L ,
Ψ 1 n m 2 ( ρ , θ ) = g n m [ n a χ n m ρ J n ( χ n m ρ a ) cos ( n θ ) ρ ^ - J n ( χ n m ρ a ) sin ( n θ ) θ ^ ]
Ψ 2 n m 1 ( ρ , θ ) = h n m [ J n ( χ n m ρ a ) cos ( n θ ) ρ ^ - n a χ n m ρ J n ( χ n m ρ a ) sin ( n θ ) θ ^ ] ,
g n m = ( n π ) 1 / 2 χ n m a J n ( χ n m ) ( χ n m 2 - n 2 ) 1 / 2
h n m = ( n π ) 1 / 2 1 a J n - 1 ( χ n m ) .
Ψ 1 n m 1 ( ρ , θ ) = g n m [ n a χ n m ρ J n ( χ n m ρ a ) sin ( n θ ) ρ ^ + J n ( χ n m ρ a ) cos ( n θ ) θ ^ ]
Ψ 2 n m 2 ( ρ , θ ) = h n m [ J n ( χ n m ρ a ) sin ( n θ ) ρ ^ + n a χ n m ρ J n ( χ n m ρ a ) cos ( n θ ) θ ^ ] .
E t = s = 1 2 n = 0 m = 1 l = 1 2 [ a s n m l sin ( k 0 ν s n m y ) + b s n m l cos ( k 0 ν s n m y ) ] Ψ s n m l ( ρ , θ )
Z 0 y ^ × H ^ t = j s n m l { Y s n m [ a s n m l cos ( k 0 ν s n m y ) - b s n m l sin ( k 0 ν s n m y ) ] } Ψ s n m l ( ρ , θ ) ,
ν 1 n m = [ 1 - χ n m 2 ( k 0 a ) 2 ] 1 / 2 ,
ν 2 n m = [ 1 - χ n m 2 ( k 0 a ) 2 ] 1 / 2 ,
Y 1 n m = ν 1 n m ,
Y 2 n m = 1 ν 2 n m .
E r i * ( α , γ ) = E r i ( α , γ ) exp [ - j k 0 β ( α , γ ) h / 2 ] ,
E r * ( α , γ ) = E r ( α , γ ) exp [ j k 0 β ( α , γ ) h / 2 ] ,
E ^ r * ( α , γ ) = E ^ r ( α , γ ) exp [ j k 0 β ( α , γ ) h / 2 ] .
r d α d γ [ E r i * ( α , γ ) + E r * ( α , γ ) ] Φ r ( α , γ ) y = 0 = { s n m l [ a s n m l sin ( k 0 ν s n m h / 2 ) + b s n m l cos ( k 0 ν s n m h / 2 ) ] Ψ s n m l ( ρ , θ ) ( x , z ) A 0 ( x , z ) A ,
r d α d γ { Y r ( α , γ ) [ E r * ( α , γ ) - E r i * ( α , γ ) ] Φ r ( α , γ ) y = 0 } = j s n m l { Y s n m [ - a s n m l cos ( k 0 ν s n m h / 2 ) + b s n m l sin ( k 0 ν s n m h / 2 ) ] } Ψ s n m l ( ρ , θ )             ( x , z ) A ,
r d α d γ E ^ r * ( α , γ ) Φ r ( α , γ ) y = 0 = { s n m l [ b s n m l cos ( k 0 ν s n m h / 2 ) - a s n m l sin ( k 0 ν s n m h / 2 ) ] Ψ s n m l ( ρ , θ ) ( x , z ) A 0 ( x , z ) A ,
r d α d γ Y r ( α , γ ) E ^ r * ( α , γ ) Φ r ( α , γ ) y = 0 = j s n m l Y s n m [ b s n m l sin ( k 0 ν s n m h / 2 ) + a s n m l cos ( k 0 ν s n m h / 2 ) ] Ψ s n m l ( ρ , θ )             ( x , z ) A .
M r * ( α , γ ) = E r * ( α , γ ) - E ^ r * ( α , γ )
P r * ( α , γ ) = E r * ( α , γ ) + E ^ r * ( α , γ ) .
r d α d γ [ M r * ( α , γ ) + E r i * ( α , γ ) ] Φ r ( α , γ ) y = 0 = { 2 s n m l a s n m l sin ( k 0 ν s n m h / 2 ) Ψ s n m l ( ρ , θ ) ( x , z ) A 0 ( x , z ) A ,
r d α d γ Y r ( α , γ ) [ M r * ( α , γ ) - E r i * ( α , γ ) ] Φ r ( α , γ ) y = 0 = - 2 j s n m l Y s n m a s n m l cos ( k 0 ν s n m h / 2 ) Ψ s n m l ( ρ , θ )             ( x , z ) A
I s n m l r ( α , γ ) = Ψ s n m l ( ρ , θ ) · Φ ¯ r ( α , γ ) y = 0 d A .
M r * ( α , γ ) = - E r i * ( α , γ ) + 2 s n m l a s n m l sin ( k 0 ν s n m h / 2 ) I s n m l r ( α , γ ) .
r d α d γ Y r ( α , γ ) [ - E r i * ( α , γ ) + s n m l a s n m l sin ( k 0 ν s n m h / 2 ) I s n m l r ( α , γ ) ] Φ r ( α , γ ) y = 0 = - j s n m l Y s n m a s n m l cos ( k 0 ν s n m h / 2 ) Ψ s n m l ( ρ , θ ) .
s n m l a s n m l [ j Y s n m cos ( k 0 ν s n m h / 2 ) δ s , S δ m , M δ n , N δ l , L + sin ( k 0 ν s n m h / 2 ) r d α d γ Y r ( α , γ ) I s n m l r ( α , γ ) I ¯ S N M L r ( α , γ ) ] = r d α d γ Y r ( α , γ ) E r i * ( α , γ ) I ¯ S N M L r ( α , γ ) .
s n m l b s n m l [ - j Y s n m sin ( k 0 ν s n m h / 2 ) δ s , S δ n , N δ m , M δ I , L + cos ( k 0 ν s n m h / 2 ) r d α d γ Y r ( α , γ ) I s n m l r ( α , γ ) I ¯ S N M L r ( α , γ ) ] = r d α d γ Y r ( α , γ ) E r i * ( α , γ ) I ¯ S N M L r ( α , γ ) .
d α d γ Y r ( α , γ ) I s n m l r ( α , γ ) I ¯ S N M L r ( α , γ ) ,
E 1 i ( α , γ ) = - δ ( α - α 0 ) δ ( γ ) , E 2 i ( α , γ ) = 0 ,
E t i = k 0 2 π exp [ j k 0 ( α 0 x - β 0 y ) ] z ^ ,
E 2 i ( α , γ ) = β 0 δ ( α - α 0 ) δ ( γ ) , E 1 i ( α , γ ) = 0 ,
Z 0 y ^ × H t i = β 0 k 0 2 π exp [ j k 0 ( α 0 x - β 0 y ) ] z ^ .
W = s n m l E F s n m l ,
E F s n m l = { Y n m a s n m l b s n m l sin ( ψ b - ψ a ) 2 Z 0 Y s n m real i Y s n m a s n m l b s n m l cos ( ψ b - ψ a ) 2 Z 0 Y s n m imaginary .
W 0 = ( k 0 a ) 2 β 0 8 π Z 0
r Y r ( α 0 , γ 0 ) E r i E r ( - α 0 , - γ 0 ) = r Y r ( α , γ ) E r i E r ( α , γ ) ,
r d α d γ I s n m l r ( α , γ ) Φ r ( α , γ ) = { Ψ s n m l ( ρ , θ ) ( ρ , θ ) A 0 ( ρ , θ ) A .
Φ r ( α , γ ) ( ρ , θ ) = s n m l I ¯ s n m l r ( α , γ ) Ψ s n m l ( ρ , θ ) ,
r d α d γ I S N M L r ( α , γ ) I ¯ s n m l r ( α , γ ) = δ s , S δ n , N δ m , M δ l , L .
4 π ( k 0 a ) 2 s n m l I s n m l r ( α , γ ) 2 = 1.
m 2 χ 1 m 2 - 1 = 1.
lim k 0 a r d α d γ Y r ( α , γ ) I s n m l r ( α , γ ) I ¯ S N M L r ( α , γ ) = δ s , S δ n , N δ m , M δ l , L .
a 1 n m l - β ( α 0 , 0 ) I ¯ 1 n m l 1 ( α 0 , 0 ) exp ( - j k 0 β ( α 0 , 0 ) h / 2 ) j cos ( k 0 h / 2 ) + sin ( k 0 h / 2 ) , a 2 n m l 0 , b 1 n m l - β ( α 0 , 0 ) I ¯ 1 n m l 1 ( α 0 , 0 ) exp ( - j k 0 β ( α 0 , 0 ) h / 2 ) - j sin ( k 0 h / 2 ) + cos ( k 0 h / 2 ) = j a 1 n m l , b 2 n m l 0.
t 4 π ( k 0 a ) 2 n m l I 1 n m l 1 ( 0 , 0 ) 2 = 1
1 2 Z 0 r α 2 + γ 2 1 d α d γ Y r ( α , γ ) E ^ r * ( α , γ ) 2 .
r Y r ( α , γ ) E ^ r * ( α , γ ) 2 ,
I 1 n m 11 ( α , γ ) = ( n π ) 1 / 2 × ( - j ) n - 1 k 0 a cos [ n θ ( α , γ ) ] J n [ k 0 a ξ ( α , γ ) ] ( χ n m 2 - n 2 ) 1 / 2 { 1 - [ k 0 a ξ ( α , γ ) / χ n m ] 2 } ,
I 1 n m 21 ( α , γ ) = - tan [ n θ ( α , γ ) ] I 1 n m 11 ( α , γ ) ,
I 1 n m 12 ( α , γ ) = ( n π ) 1 / 2 × ( - j ) n - 1 n sin [ n θ ( α , γ ) ] J n [ k 0 a ξ ( α , γ ) ] ( χ n m 2 - n 2 ) 1 / 2 ξ ( α , γ ) ,
I 1 n m 22 ( α , γ ) = cot [ n θ ( α , γ ) ] I 1 n m 12 ,
I 2 n m l 1 = 0             n , m , l , α , γ ,
I 2 n m 12 ( α , γ ) = ( n π ) 1 / 2 × ( - j ) n - 1 cos [ n θ ( α , γ ) ] ξ ( α , γ ) J n [ k 0 a ξ ( α , γ ) ] ξ 2 ( α , γ ) - χ n m 2 / ( k 0 a ) 2 ,
I 2 n m 22 ( α , γ ) = tan [ n θ ( α , γ ) ] I 2 n m 12 ( α , γ ) ,
n = { 1 if n = 0 2 if n 0 ,
ξ ( α , γ ) = ( α 2 + γ 2 ) 1 / 2 ,
tan [ θ ( α , γ ) ] = α γ .
d α d γ Y 1 ( α , γ ) I 1 n m l 1 ( α , γ ) I ¯ 1 N M L 1 ( α , γ ) = 2 ( k 0 a ) 2 ( χ n m 2 - n 2 ) 1 / 2 ( χ n M 2 - n 2 ) 1 / 2 × 0 d ξ ξ ( 1 - ξ 2 ) 1 / 2 [ J n ( k 0 a ξ ) ] 2 [ 1 - ( k 0 a ξ / χ n m ) 2 ] [ 1 - ( k 0 a ξ / χ n M ) 2 ] δ l , L δ n , N ,
d α d γ Y 2 ( α , γ ) I 1 n m l 2 ( α , γ ) I ¯ 1 N M L 2 ( α , γ ) = 2 n 2 ( χ n m 2 - n 2 ) 1 / 2 ( χ n M 2 - n 2 ) 1 / 2 × 0 d ξ J n 2 ( k 0 a ξ ) ξ ( 1 - ξ 2 ) 1 / 2 δ n , N δ l , L ,
d α d γ Y 2 ( α , γ ) I 2 n m l 2 ( α , γ ) I ¯ 1 N M L 2 ( α , γ ) = 2 ( k 0 a ) 2 n ( χ n M 2 - n 2 ) 1 / 2 × 0 d ξ ξ J n 2 ( k 0 a ξ ) ( 1 - ξ 2 ) 1 / 2 [ ( k 0 a ξ ) 2 - χ n m 2 ] δ n , N ( 1 - δ l , L ) ,
d α d γ Y 2 ( α , γ ) I 2 n m l 2 ( α , γ ) I ¯ 2 N M L 2 ( α , γ ) = 2 ( k 0 a ) 4 0 d ξ × ξ 3 J n 2 ( k 0 a ξ ) ( 1 - ξ 2 ) 1 / 2 [ ( k 0 a ξ ) 2 - χ n m 2 ] [ ( k 0 a ξ ) 2 - χ n M 2 ] δ l , L δ n , N .
0 d ξ J n 2 ( k 0 a ξ ) ξ ( 1 - ξ 2 ) 1 / 2 = 1 2 n [ 1 - 1 k 0 a j = 1 n ( 2 j - 1 ) J 2 j - 1 ( 2 k 0 a ) + i ( - 1 ) n π × l = 0 n - 1 j = 0 l ( 2 n 2 l + 1 ) ( l j ) ( - 1 ) n - j - 1 × Γ ( n - j + ½ ) ( k 0 a ) n - j S n - j ( 2 k 0 a ) ] ,
d α d γ I 1 N M L 1 ( α , γ ) I ¯ 1 n m l 1 ( α , γ ) = 2 ( χ n m 2 - n 2 ) 1 / 2 ( χ n M 2 - n 2 ) 1 / 2 × 0 d u u [ J n ( u ) ] 2 ( 1 - u χ n m 2 ) ( 1 - u 2 χ n M 2 ) δ n , N δ l , L
2 ( χ n m 2 - n 2 ) 1 / 2 ( χ n M 2 - n 2 ) 1 / 2 χ n M 2 χ n m 2 χ n M 2 - χ n m 2 × { 0 d u u [ J n ( u ) ] 2 χ n m 2 - u 2 - 0 d u u [ J n ( u ) ] 2 χ n M 2 - u 2 } .
1 2 π i 0 [ C μ ( b x ) H ν ( 1 ) ( a x ) - e ρ π i C μ ( b x e i π ) H ν ( 1 ) ( a x e i π ) ] × x ρ - 1 ( x 2 - r 2 ) m + 1 d x = 1 2 m + 1 m ! ( d r d r ) [ r ρ - 1 C μ ( b r ) H ν ( 1 ) ( a r ) ] ,
R ( ν ) + R ( μ ) < R ( ρ ) < 2 m + 4.
0 J μ ( b x ) { cos [ ½ ( μ - ν ) π ] J ν ( a x ) + sin [ ½ ( μ - ν ) π ] Y ν ( a x ) } × x x 2 - r 2 d x = i π 2 [ ½ ( ν - μ ) π i ] J μ ( b r ) H ν ( 1 ) ( a r ) .
J n ( u ) = ½ [ J n - 1 ( u ) - J n + 1 ( u ) ]
0 d u u [ J n ( u ) ] 2 u 2 - r 2 = π i 8 [ J n + 1 ( r ) H n + 1 ( 1 ) ( r ) - 2 J n + 1 ( r ) × H n - 1 ( 1 ) ( r ) + J n - 1 ( r ) H n - 1 ( 1 ) ( r ) ]
0 d u u [ J n ( u ) ] 2 u 2 - χ n m 2 = π 4 χ n m n J n ( χ n m ) Y n ( χ n m )
p ν s ν - q ν r ν = 4 π 2 a b ,
p ν = J ν ( a ) Y ν ( b ) - J ν ( b ) Y ν ( a ) ,
q ν = J ν ( a ) Y ν ( b ) - J ν ( b ) Y ν ( a ) ,
r ν = J ν ( a ) Y ν ( b ) - J ν ( b ) Y ν ( a ) ,
s ν = J ν ( a ) Y ν ( b ) - J ν ( b ) Y ν ( a )
J n ( χ n m ) Y n ( χ n m ) = 2 π χ n m
- n ( χ n m 2 - n 2 ) 1 / 2 ( χ n M 2 - n 2 ) 1 / 2 .
0 J μ ( b x ) { cos [ ½ ( μ - ν ) π ] J ν ( a x ) + sin [ ½ ( μ - ν ) π ] Y ν ( a x ) } × x ( x 2 - r 2 ) d x = i π 4 r [ ½ ( ν - μ ) π i ] [ b J μ ( b r ) H ν ( 1 ) ( a r ) + a J μ ( b r ) H ν ( 1 ) ( a r ) ]
( 1 - n x n m 2 - n 2 ) δ n , N δ l , L .
d α d γ I 1 N M L 1 ( α , γ ) I ¯ 1 n m l 1 ( α , γ ) = [ δ m , M - n ( χ n m 2 - n 2 ) 1 / 2 ( χ n M 2 - n 2 ) 1 / 2 ] δ n , N δ l , L .
d α d γ I 1 N M L 2 ( α , γ ) I ¯ 1 n m l 2 ( α , γ ) = 2 n 2 ( χ n m 2 - n 2 ) 1 / 2 ( χ n M 2 - n 2 ) 1 / 2 0 d u J n 2 ( u ) u δ n , N δ l , L .
0 d u J n 2 ( u ) u = 1 2 n
r d α d γ I 1 N M L r ( α , γ ) I ¯ 1 n m l r ( α , γ ) = δ n , N δ m , M δ l , L ;
d α d γ I 1 N M L 2 ( α , γ ) I ¯ 2 n m l 2 ( α , γ ) = 2 n ( χ n M 2 - n 2 ) 1 / 2 0 d u u J n 2 ( u ) u 2 - χ n m 2 δ n , N ( 1 - δ l , L )
d α d γ I 2 N M L 2 ( α , γ ) I ¯ 2 n m l 2 ( α , γ ) = { 2 0 d u u 3 J n 2 ( u ) ( u 2 - χ n m 2 ) 2 δ n , N δ l , L if m = M 2 χ n m 2 - χ n M 2 [ χ n M 2 0 d u u J n 2 ( u ) u 2 - χ n m 2 - χ n m 2 0 d u u J n 2 ( u ) u 2 - χ n M 2 ] if m M .
0 d u u 3 J n 2 ( u ) ( u 2 - χ n m 2 ) 2 = - π 4 χ n m J n ( χ n m ) Y n ( χ n m ) = 1 / 2
r d α d γ I 2 N M L r ( α , γ ) I ¯ 2 n m l r ( α , γ ) = δ n , N δ m , M δ l , L .
r d α d γ I S N M L r ( α , γ ) I ¯ s n m l r ( α , γ ) = δ s , S δ n , N δ m , M δ n , N ,

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