Abstract

An exact decomposition of the diffracted field into a direct wave and a boundary diffraction wave is obtained for an incident inhomogeneous wave, namely, the complex-source-point spherical wave. Our result, in the paraxial approximation, is consistent with already published results on the diffraction of a Gaussian beam.

© 1983 Optical Society of America

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  1. T. Young, "Lectures on natural philosophy, diffraction," Phil. Trans. R. Soc. London 92, 12–49 (1802).
  2. G. A. Maggi, Ann. Mat. Ila, 16, 21 (1888).
  3. A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie des Beugungsercheinungen," Ann. Phys. 53, 257–278 (1917).
  4. 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).
  5. 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).
  6. E. Wolf, "Some recent research on diffraction of light," in Modern Optics (Polytechnic Institute of Brooklyn, New York, 1967), pp. 433–453.
  7. G. A. Deschamps, "Gaussian beam as a bundle of complex rays," Electron. Lett. 7, 684–685 (1971).
  8. L. B. Felsen, "Complex-source-point solutions of the field equations and their relation to the propagation and scattering of Gaussian beams," in Symposia Mathematica (Academic, New York, 1976), Vol. XVIII.
  9. M. Couture and P. A. Belanger, "From Gaussian beam to complex- source-point-spherical wave," Phys. Rev. A 24, 355–359 (1981).
  10. G. Otis, "Application of the boundary-diffraction wave theory to Gaussian beams," J. Opt. Soc. Am. 64, 1545–1550 (1974).
  11. 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).
  12. T. Takenaka and O. Fukumitsu, "Asymptotic representation of the boundary-diffraction wave for a three-dimensional Gaussian beam incident upon a Kirchhoff half-screen," J. Opt. Soc. Am. 72, 331–336 (1982).
  13. z0 is the Rayleigh range πW02/λ of the corresponding paraxial Gaussian beam of beam waist W0.
  14. The case in which the plane of the aperture is on the left-hand side of the plane z = 0 could also be analyzed in a way similar to that for a regular converging spherical wave.
  15. Note that, in order that Eqs. (3.4) and (3.5) be satisfied, a must always be smaller than z0.

1982

1981

M. Couture and P. A. Belanger, "From Gaussian beam to complex- source-point-spherical wave," Phys. Rev. A 24, 355–359 (1981).

1980

1974

1971

G. A. Deschamps, "Gaussian beam as a bundle of complex rays," Electron. Lett. 7, 684–685 (1971).

1962

1917

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

1802

T. Young, "Lectures on natural philosophy, diffraction," Phil. Trans. R. Soc. London 92, 12–49 (1802).

Belanger, P. A.

M. Couture and P. A. Belanger, "From Gaussian beam to complex- source-point-spherical wave," Phys. Rev. A 24, 355–359 (1981).

Couture, M.

M. Couture and P. A. Belanger, "From Gaussian beam to complex- source-point-spherical wave," Phys. Rev. A 24, 355–359 (1981).

Deschamps, G. A.

G. A. Deschamps, "Gaussian beam as a bundle of complex rays," Electron. Lett. 7, 684–685 (1971).

Felsen, L. B.

L. B. Felsen, "Complex-source-point solutions of the field equations and their relation to the propagation and scattering of Gaussian beams," in Symposia Mathematica (Academic, New York, 1976), Vol. XVIII.

Fukumitsu, O.

Kakeya, M.

Maggi, G. A.

G. A. Maggi, Ann. Mat. Ila, 16, 21 (1888).

Miyamoto, K.

Otis, G.

Rubinowicz, A.

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

Takenaka, T.

Wolf, E.

Young, T.

T. Young, "Lectures on natural philosophy, diffraction," Phil. Trans. R. Soc. London 92, 12–49 (1802).

Ann. Phys.

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

Electron. Lett.

G. A. Deschamps, "Gaussian beam as a bundle of complex rays," Electron. Lett. 7, 684–685 (1971).

J. Opt. Soc. Am.

Phil. Trans. R. Soc. London

T. Young, "Lectures on natural philosophy, diffraction," Phil. Trans. R. Soc. London 92, 12–49 (1802).

Phys. Rev.

M. Couture and P. A. Belanger, "From Gaussian beam to complex- source-point-spherical wave," Phys. Rev. A 24, 355–359 (1981).

Other

z0 is the Rayleigh range πW02/λ of the corresponding paraxial Gaussian beam of beam waist W0.

The case in which the plane of the aperture is on the left-hand side of the plane z = 0 could also be analyzed in a way similar to that for a regular converging spherical wave.

Note that, in order that Eqs. (3.4) and (3.5) be satisfied, a must always be smaller than z0.

G. A. Maggi, Ann. Mat. Ila, 16, 21 (1888).

E. Wolf, "Some recent research on diffraction of light," in Modern Optics (Polytechnic Institute of Brooklyn, New York, 1967), pp. 433–453.

L. B. Felsen, "Complex-source-point solutions of the field equations and their relation to the propagation and scattering of Gaussian beams," in Symposia Mathematica (Academic, New York, 1976), Vol. XVIII.

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