Abstract

Rigorous diffraction theory is applied to compute the electromagnetic fields in the neighborhood of polygonal obstacles of three- and two-dimensional shape, including two-dimensional gratings. For obstacles such as a rectangular depression, a polygonal groove, or an array of grooves present in a metallic substrate, we calculate and measure significant departures from what a scalar diffraction approach would predict as soon as the width of the obstacle becomes smaller than one wavelength. For such widths, it is shown that the apparent depth of a groove can be smaller or larger than the geometrical depth, depending on the polarization of the incident light and on the optical constants of the substrate.

© 1979 Optical Society of America

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  1. J. J. M. Braat and G. Bouwhuis, Appl. Opt. 17, 2022 (1978).
  2. J. G. Dil and B. A. J. Jacobs, Digest of 1977, APS-URSI Symposium in Palo Alto, Ca., U.S.A., p. 44 (unpublished).
  3. A. Sommerfeld, Optics, (Academic, New York, 1964), pp 273–289.
  4. C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).
  5. A. T. De Hoop, Proc. Kon. Ned. Akad. Wet. B58, 1401 (1955).
  6. A. T. De Hoop, Modern Topics in Electromagnetics and Antennas, PPL Conference Publication 13, (Stevenage, Peter Peregrinus Ltd.,1977) Chap. 6.
  7. R. F. Harrington, Field computations by moment methods, (Mac-Millan, New York, 1968).
  8. W. Maue Phys. 126, 701 (1949).
  9. R. Petit, C. R. Acad. Sci. (Paris) 264, 1441 (1967).
  10. K. K. Mei and J. G. Van Bladel, IEEE AP-15, 795 (1967).
  11. G. A. Gray, and R. E. Kleinman, Proceedings 1977 URSI Symposium on Electromagnetic Wave Theory, 329 (1977) (unpublished).
  12. F. L. Neerhoff, Proc. R. Soc. Lond. A 342, 237 (1975).
  13. J. P. Hugonin and R. Petit, Opt. Commun. 22, 221 (1977).
  14. P. M. Van den Berg and J. C. M. Borburgh, Appl. Phys. 3, 55 (1974).
  15. A. A. Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975).
  16. J. P. J. Heemskerk and C. H. F. Velzel, Private communication on phase depths measurements, available in print at Philips Research Lab., Eindhoven, The Netherlands.
  17. B. A. J. Jacobs, Appl. Opt. 17, 2001 (1978).
  18. E. G. Loewen, M. Nevière, and D. Maystre, Appl. Opt. 16, 2711 (1977).
  19. T. B. A. Senior, Radio Sci. 10, 911 (1975).

Borburgh, J. C. M.

P. M. Van den Berg and J. C. M. Borburgh, Appl. Phys. 3, 55 (1974).

Bouwhuis, G.

J. J. M. Braat and G. Bouwhuis, Appl. Opt. 17, 2022 (1978).

Bouwkamp, C. J.

C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).

Braat, J. J. M.

J. J. M. Braat and G. Bouwhuis, Appl. Opt. 17, 2022 (1978).

De Hoop, A. T.

A. T. De Hoop, Proc. Kon. Ned. Akad. Wet. B58, 1401 (1955).

A. T. De Hoop, Modern Topics in Electromagnetics and Antennas, PPL Conference Publication 13, (Stevenage, Peter Peregrinus Ltd.,1977) Chap. 6.

Dil, J. G.

J. G. Dil and B. A. J. Jacobs, Digest of 1977, APS-URSI Symposium in Palo Alto, Ca., U.S.A., p. 44 (unpublished).

Gray, G. A.

G. A. Gray, and R. E. Kleinman, Proceedings 1977 URSI Symposium on Electromagnetic Wave Theory, 329 (1977) (unpublished).

Harrington, R. F.

R. F. Harrington, Field computations by moment methods, (Mac-Millan, New York, 1968).

Heemskerk, J. P. J.

J. P. J. Heemskerk and C. H. F. Velzel, Private communication on phase depths measurements, available in print at Philips Research Lab., Eindhoven, The Netherlands.

Hugonin, J. P.

J. P. Hugonin and R. Petit, Opt. Commun. 22, 221 (1977).

Jacobs, B. A. J.

J. G. Dil and B. A. J. Jacobs, Digest of 1977, APS-URSI Symposium in Palo Alto, Ca., U.S.A., p. 44 (unpublished).

B. A. J. Jacobs, Appl. Opt. 17, 2001 (1978).

Kleinman, R. E.

G. A. Gray, and R. E. Kleinman, Proceedings 1977 URSI Symposium on Electromagnetic Wave Theory, 329 (1977) (unpublished).

Loewen, E. G.

E. G. Loewen, M. Nevière, and D. Maystre, Appl. Opt. 16, 2711 (1977).

Maradudin, A. A.

A. A. Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975).

Maue, W.

W. Maue Phys. 126, 701 (1949).

Maystre, D.

E. G. Loewen, M. Nevière, and D. Maystre, Appl. Opt. 16, 2711 (1977).

Mei, K. K.

K. K. Mei and J. G. Van Bladel, IEEE AP-15, 795 (1967).

Mills, D. L.

A. A. Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975).

Neerhoff, F. L.

F. L. Neerhoff, Proc. R. Soc. Lond. A 342, 237 (1975).

Nevière, M.

E. G. Loewen, M. Nevière, and D. Maystre, Appl. Opt. 16, 2711 (1977).

Petit, R.

J. P. Hugonin and R. Petit, Opt. Commun. 22, 221 (1977).

R. Petit, C. R. Acad. Sci. (Paris) 264, 1441 (1967).

Senior, T. B. A.

T. B. A. Senior, Radio Sci. 10, 911 (1975).

Sommerfeld, A.

A. Sommerfeld, Optics, (Academic, New York, 1964), pp 273–289.

Van Bladel, J. G.

K. K. Mei and J. G. Van Bladel, IEEE AP-15, 795 (1967).

Van den Berg, P. M.

P. M. Van den Berg and J. C. M. Borburgh, Appl. Phys. 3, 55 (1974).

Velzel, C. H. F.

J. P. J. Heemskerk and C. H. F. Velzel, Private communication on phase depths measurements, available in print at Philips Research Lab., Eindhoven, The Netherlands.

Other (19)

J. J. M. Braat and G. Bouwhuis, Appl. Opt. 17, 2022 (1978).

J. G. Dil and B. A. J. Jacobs, Digest of 1977, APS-URSI Symposium in Palo Alto, Ca., U.S.A., p. 44 (unpublished).

A. Sommerfeld, Optics, (Academic, New York, 1964), pp 273–289.

C. J. Bouwkamp, Rep. Prog. Phys. 17, 35 (1954).

A. T. De Hoop, Proc. Kon. Ned. Akad. Wet. B58, 1401 (1955).

A. T. De Hoop, Modern Topics in Electromagnetics and Antennas, PPL Conference Publication 13, (Stevenage, Peter Peregrinus Ltd.,1977) Chap. 6.

R. F. Harrington, Field computations by moment methods, (Mac-Millan, New York, 1968).

W. Maue Phys. 126, 701 (1949).

R. Petit, C. R. Acad. Sci. (Paris) 264, 1441 (1967).

K. K. Mei and J. G. Van Bladel, IEEE AP-15, 795 (1967).

G. A. Gray, and R. E. Kleinman, Proceedings 1977 URSI Symposium on Electromagnetic Wave Theory, 329 (1977) (unpublished).

F. L. Neerhoff, Proc. R. Soc. Lond. A 342, 237 (1975).

J. P. Hugonin and R. Petit, Opt. Commun. 22, 221 (1977).

P. M. Van den Berg and J. C. M. Borburgh, Appl. Phys. 3, 55 (1974).

A. A. Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975).

J. P. J. Heemskerk and C. H. F. Velzel, Private communication on phase depths measurements, available in print at Philips Research Lab., Eindhoven, The Netherlands.

B. A. J. Jacobs, Appl. Opt. 17, 2001 (1978).

E. G. Loewen, M. Nevière, and D. Maystre, Appl. Opt. 16, 2711 (1977).

T. B. A. Senior, Radio Sci. 10, 911 (1975).

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