Abstract

The Braunbek method is applied to the generalized vector potential associated with the Maggi–Rubinowicz representation, and a closed-form expression for the vector potential is obtained. For observation points away from caustics or shadow boundaries, the field derived from this quantity is the same as that determined from the geometrical theory of diffraction on a singly diffracted edge ray. The paper concludes with an evaluation of the field for the simple case of a plane wave normally incident upon a circular aperture, showing that the field predicted by the Maggi–Rubinowicz theory is continuous across the shadow boundary.

© 1983 Optical Society of America

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  1. 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).
  2. 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).
  3. A. Rubinowicz, "The Miyamoto-Wolf diffraction wave," in Progress in Optics VI, E. Wolf, ed. (Wiley, New York, 1964), pp. 195–240.
  4. W. Braunbek, "Neue Näherungsmethode fülr die Beugung am ebenen Schrim," Z. Phys. 127, 381–390 (1950).
  5. C. J. Boukamp, "Diffraction theory," Rep. Prog. Phys. 17, 35–100 (1954).
  6. J. B. Keller, R. M. Lewis, and B. D. Seckler, "Diffraction by an aperture II," J. Appl. Phys. 28, 570–579 (1957).
  7. P. Wolfe, "A new approach to edge diffraction," SIAM J. Appl. Math. 15, 1434–1469 (1967).
  8. E. W. Marchand and E. Wolf, "Boundary diffraction wave in the domain of the Rayleigh—Kirchhoff diffraction theory," J. Opt. Soc. Am. 52, 761–767 (1962).
  9. G. L. James, Geometrical Theory of Diffraction (Peregrinus, Stevenage, England, 1976), Chap. 5.
  10. A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956), Chap. 2.
  11. F. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4.
  12. G. Otis, J. L Lachambre, J. W. Y. Lit, and P. Lavigne, "Diffracted waves in the shadow boundary region," J. Opt. Soc. Am. 67, 551–562 (1977).
  13. T. Takenaka, M. Kakeya, and O. Fukumitsu, "Asymptotic representation of the boundary diffraction wave for a Gaussian beam incident on a circular aperture," J. Opt. Soc. Am. 70, 1323–1328 (1980).
  14. R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1960), Chap. 7.

1980

1977

1967

P. Wolfe, "A new approach to edge diffraction," SIAM J. Appl. Math. 15, 1434–1469 (1967).

1962

1957

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

1954

C. J. Boukamp, "Diffraction theory," Rep. Prog. Phys. 17, 35–100 (1954).

1950

W. Braunbek, "Neue Näherungsmethode fülr die Beugung am ebenen Schrim," Z. Phys. 127, 381–390 (1950).

Boukamp, C. J.

C. J. Boukamp, "Diffraction theory," Rep. Prog. Phys. 17, 35–100 (1954).

Braunbek, W.

W. Braunbek, "Neue Näherungsmethode fülr die Beugung am ebenen Schrim," Z. Phys. 127, 381–390 (1950).

Churchill, R. V.

R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1960), Chap. 7.

Erdelyi, A.

A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956), Chap. 2.

Felsen, F. B.

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

Fukumitsu, O.

James, G. L.

G. L. James, Geometrical Theory of Diffraction (Peregrinus, Stevenage, England, 1976), Chap. 5.

Kakeya, M.

Keller, J. B.

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

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.

Marchand, E. W.

Marcuvitz, N.

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

Miyamoto, K.

Otis, G.

Rubinowicz, A.

A. Rubinowicz, "The Miyamoto-Wolf diffraction wave," in Progress in Optics VI, E. Wolf, ed. (Wiley, New York, 1964), pp. 195–240.

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).

Takenaka, T.

Wolf, E.

Wolfe, P.

P. Wolfe, "A new approach to edge diffraction," SIAM J. Appl. Math. 15, 1434–1469 (1967).

J. Appl. Phys.

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.

Rep. Prog. Phys.

C. J. Boukamp, "Diffraction theory," Rep. Prog. Phys. 17, 35–100 (1954).

SIAM J. Appl. Math.

P. Wolfe, "A new approach to edge diffraction," SIAM J. Appl. Math. 15, 1434–1469 (1967).

Z. Phys.

W. Braunbek, "Neue Näherungsmethode fülr die Beugung am ebenen Schrim," Z. Phys. 127, 381–390 (1950).

Other

A. Rubinowicz, "The Miyamoto-Wolf diffraction wave," in Progress in Optics VI, E. Wolf, ed. (Wiley, New York, 1964), pp. 195–240.

G. L. James, Geometrical Theory of Diffraction (Peregrinus, Stevenage, England, 1976), Chap. 5.

A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956), Chap. 2.

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

R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1960), Chap. 7.

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