Abstract

The Rayleigh-Sommerfeld solutions and the Luneburg-Severin-Vasseur and Severin-Vasseur solutions of diffraction problems are shown to satisfy certain reciprocity theorems in the case of a spherical incident wave. These new reciprocity theorems have very simple relations to those known in Kirchhoff’s theory of diffraction.

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 2nd ed., p. 381.
  2. A. Rubinowicz, Die Beugungswelle in der Kirchhoƒƒschen Theorie der Beugung (Polska Akademia Nauk, Warszawa, 1957), p. 69; see also Acta Phys. Polon. 20, 9 (1961).
  3. F. Kottler, Ann. Physik. 71, 457 (1923).
  4. A. Kujawski, Acta Phys. Polon. 21, 597 (1962).
  5. A. Kujawski, Acta Phys. Polon. 25, 7 (1964).
  6. O. Laporte and J. Meixner, Z. Physik 153, 129 (1958).
  7. See, for example, Lord Rayleigh (J. W. Strutt), Phil. Mag. 43, 259 (1897); see also his Scientific Papers (Cambridge University Press, Cambridge, England, 1903), Vol. 4, p. 283.
  8. A. Sommerfeld, Optics (Academic Press Inc., New York, 1954), p. 199; see also Ref. 2, pp. 77–83.
  9. C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954).
  10. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., New York, 1962), p. 271.
  11. See Ref. 2, p. 242.
  12. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1964), p. 319.
  13. H. Severin, Z. Physik. 129, 426 (1951).
  14. J. P. Vasseur, Ann. Phys. (Paris) 7, 506 (1952).
  15. R. Barakat, J. Opt. Soc. Am. 55, 992 (1965).

Barakat, R.

R. Barakat, J. Opt. Soc. Am. 55, 992 (1965).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 2nd ed., p. 381.

Bouwkamp, C. J.

C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., New York, 1962), p. 271.

Kottler, F.

F. Kottler, Ann. Physik. 71, 457 (1923).

Kujawski, A.

A. Kujawski, Acta Phys. Polon. 21, 597 (1962).

A. Kujawski, Acta Phys. Polon. 25, 7 (1964).

Laporte, O.

O. Laporte and J. Meixner, Z. Physik 153, 129 (1958).

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1964), p. 319.

Meixner, J.

O. Laporte and J. Meixner, Z. Physik 153, 129 (1958).

Rayleigh, Lord

See, for example, Lord Rayleigh (J. W. Strutt), Phil. Mag. 43, 259 (1897); see also his Scientific Papers (Cambridge University Press, Cambridge, England, 1903), Vol. 4, p. 283.

Rubinowicz, A.

A. Rubinowicz, Die Beugungswelle in der Kirchhoƒƒschen Theorie der Beugung (Polska Akademia Nauk, Warszawa, 1957), p. 69; see also Acta Phys. Polon. 20, 9 (1961).

Severin, H.

H. Severin, Z. Physik. 129, 426 (1951).

Sommerfeld, A.

A. Sommerfeld, Optics (Academic Press Inc., New York, 1954), p. 199; see also Ref. 2, pp. 77–83.

Vasseur, J. P.

J. P. Vasseur, Ann. Phys. (Paris) 7, 506 (1952).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 2nd ed., p. 381.

Other (15)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 2nd ed., p. 381.

A. Rubinowicz, Die Beugungswelle in der Kirchhoƒƒschen Theorie der Beugung (Polska Akademia Nauk, Warszawa, 1957), p. 69; see also Acta Phys. Polon. 20, 9 (1961).

F. Kottler, Ann. Physik. 71, 457 (1923).

A. Kujawski, Acta Phys. Polon. 21, 597 (1962).

A. Kujawski, Acta Phys. Polon. 25, 7 (1964).

O. Laporte and J. Meixner, Z. Physik 153, 129 (1958).

See, for example, Lord Rayleigh (J. W. Strutt), Phil. Mag. 43, 259 (1897); see also his Scientific Papers (Cambridge University Press, Cambridge, England, 1903), Vol. 4, p. 283.

A. Sommerfeld, Optics (Academic Press Inc., New York, 1954), p. 199; see also Ref. 2, pp. 77–83.

C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954).

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., New York, 1962), p. 271.

See Ref. 2, p. 242.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1964), p. 319.

H. Severin, Z. Physik. 129, 426 (1951).

J. P. Vasseur, Ann. Phys. (Paris) 7, 506 (1952).

R. Barakat, J. Opt. Soc. Am. 55, 992 (1965).

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