Abstract

The diffraction of a Gaussian beam normally incident on a circular aperture is investigated by using the boundary-diffraction-wave theory. With the help of the steepest-descent method, an asymptotic representation of the boundary diffraction wave is obtained. The diffracted field, which is the sum of the geometrical-optics component and the diffraction component, is shown to be continuous at the shadow boundary. The diffraction coefficient is compared with that used in Keller’s geometrical theory of diffraction for a plane wave. The error of the asymptotic approximation is also estimated.

© 1980 Optical Society of America

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  1. J. B. Keller, "Diffraction by an aperture," J. Appl. Phys. 28, 426–444 (1957).
  2. J. B. Keller, R. M. Lewis, and B. D. Seckler, "Diffraction by an aperture. II," J. Appl. Phys. 28, 570–579 (1957).
  3. R. G. Kouyoumjian and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE 62, 1448–1461 (1974).
  4. W. D. Wang and G. A. Deschamps, "Application of complex ray tracing to scattering problems," Proc. IEEE 62, 1541–1551 (1974).
  5. J.A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976),Chap. 2.
  6. S. Choudhary and L. B. Felsen, "Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking," Proc. IEEE 62, 1530–1541 (1974).
  7. H. L. Bertoni, A. C. Green, and L. B. Felsen, "Shadowing an inhomogeneous plane wave by an edge," J. Opt. Soc. Am. 68, 983–989 (1978).
  8. A. C. Green, H. L. Bertoni, and L. B. Felsen, "Properties of the shadow cast by a half-screen when illuminated by a Gaussian beam," J. Opt. Soc. Am. 69, 1503–1508 (1979).
  9. A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen," Ann. Phys. 53, 257–278 (1917).
  10. K. Miyamoto and E. Wolf, "Generalization of the Maggi-Rubinowicz theory of the boundary diffraction wave—Part I," J. Opt. Soc. Am. 52, 615–625 (1962).
  11. K. Miyamoto and E. Wolf, "Generalization of the Maggi-Rubinowicz theory of the boundary diffraction wave—Part II," J. Opt. Soc. Am. 52, 626–637 (1962).
  12. G. Otis, "Application of the boundary-diffraction-wave theory to Gaussian beams," J. Opt. Soc. Am. 64, 1545–1550 (1974).
  13. G. Otis, J.-L. Lachambre, J. W. Y. Lit, and P. Lavigne, "Diffracted waves in the shadow boundary region," J. Opt. Soc. Am. 67, 551–553 (1977).
  14. H. Kogelnik, "On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation," Appl. Opt. 4, 1562–1569 (1965).
  15. K. Tanaka, M. Shibukawa, and O. Fukumitsu, "Diffraction of a wave beam by an aperture," IEEE Trans. Microwave Theory Tech. MTT-20, 749–755 (1972).
  16. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4.

1979 (1)

1978 (1)

1977 (1)

1974 (1)

1972 (1)

K. Tanaka, M. Shibukawa, and O. Fukumitsu, "Diffraction of a wave beam by an aperture," IEEE Trans. Microwave Theory Tech. MTT-20, 749–755 (1972).

1965 (1)

1962 (2)

1957 (2)

J. B. Keller, "Diffraction by an aperture," J. Appl. Phys. 28, 426–444 (1957).

J. B. Keller, R. M. Lewis, and B. D. Seckler, "Diffraction by an aperture. II," J. Appl. Phys. 28, 570–579 (1957).

1917 (1)

A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen," Ann. Phys. 53, 257–278 (1917).

Arnaud, J. A.

J.A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976),Chap. 2.

Bertoni, H. L.

Choudhary, S.

S. Choudhary and L. B. Felsen, "Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking," Proc. IEEE 62, 1530–1541 (1974).

Deschamps, G. A.

W. D. Wang and G. A. Deschamps, "Application of complex ray tracing to scattering problems," Proc. IEEE 62, 1541–1551 (1974).

Felsen, L. B.

A. C. Green, H. L. Bertoni, and L. B. Felsen, "Properties of the shadow cast by a half-screen when illuminated by a Gaussian beam," J. Opt. Soc. Am. 69, 1503–1508 (1979).

H. L. Bertoni, A. C. Green, and L. B. Felsen, "Shadowing an inhomogeneous plane wave by an edge," J. Opt. Soc. Am. 68, 983–989 (1978).

S. Choudhary and L. B. Felsen, "Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking," Proc. IEEE 62, 1530–1541 (1974).

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4.

Fukumitsu, O.

K. Tanaka, M. Shibukawa, and O. Fukumitsu, "Diffraction of a wave beam by an aperture," IEEE Trans. Microwave Theory Tech. MTT-20, 749–755 (1972).

Green, A. C.

Keller, J. B.

J. B. Keller, "Diffraction by an aperture," J. Appl. Phys. 28, 426–444 (1957).

J. B. Keller, R. M. Lewis, and B. D. Seckler, "Diffraction by an aperture. II," J. Appl. Phys. 28, 570–579 (1957).

Kogelnik, H.

Kouyoumjian, R. G.

R. G. Kouyoumjian and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE 62, 1448–1461 (1974).

Lachambre, J.-L.

Lavigne, P.

Lewis, R. M.

J. B. Keller, R. M. Lewis, and B. D. Seckler, "Diffraction by an aperture. II," J. Appl. Phys. 28, 570–579 (1957).

Lit, J. W. Y.

Marcuvitz, N.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4.

Miyamoto, K.

Otis, G.

Pathak, P. H.

R. G. Kouyoumjian and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE 62, 1448–1461 (1974).

Rubinowicz, A.

A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen," Ann. Phys. 53, 257–278 (1917).

Seckler, B. D.

J. B. Keller, R. M. Lewis, and B. D. Seckler, "Diffraction by an aperture. II," J. Appl. Phys. 28, 570–579 (1957).

Shibukawa, M.

K. Tanaka, M. Shibukawa, and O. Fukumitsu, "Diffraction of a wave beam by an aperture," IEEE Trans. Microwave Theory Tech. MTT-20, 749–755 (1972).

Tanaka, K.

K. Tanaka, M. Shibukawa, and O. Fukumitsu, "Diffraction of a wave beam by an aperture," IEEE Trans. Microwave Theory Tech. MTT-20, 749–755 (1972).

Wang, W. D.

W. D. Wang and G. A. Deschamps, "Application of complex ray tracing to scattering problems," Proc. IEEE 62, 1541–1551 (1974).

Wolf, E.

Ann. Phys. (1)

A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen," Ann. Phys. 53, 257–278 (1917).

Appl. Opt. (1)

IEEE Trans. Microwave Theory Tech. (1)

K. Tanaka, M. Shibukawa, and O. Fukumitsu, "Diffraction of a wave beam by an aperture," IEEE Trans. Microwave Theory Tech. MTT-20, 749–755 (1972).

J. Appl. Phys. (2)

J. B. Keller, "Diffraction by an aperture," J. Appl. Phys. 28, 426–444 (1957).

J. B. Keller, R. M. Lewis, and B. D. Seckler, "Diffraction by an aperture. II," J. Appl. Phys. 28, 570–579 (1957).

J. Opt. Soc. Am. (6)

Other (5)

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4.

R. G. Kouyoumjian and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE 62, 1448–1461 (1974).

W. D. Wang and G. A. Deschamps, "Application of complex ray tracing to scattering problems," Proc. IEEE 62, 1541–1551 (1974).

J.A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976),Chap. 2.

S. Choudhary and L. B. Felsen, "Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking," Proc. IEEE 62, 1530–1541 (1974).

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