Abstract

Theoretical and experimental aspects of the diffraction of gaussian laser beams by the straight edge bounding an opaque plane are investigated. Theoretical analysis is based upon the Kirchhoff scalar wave theory in the Fresnel limit, assuming an incident electromagnetic field having spatial amplitude and phase variation appropriate to a fundamental-mode gaussian beam. Experimental observation consisting of irradiance as a function of position is in good agreement with this theory. Both theoretical and experimental results are found to depend strongly on gaussian-beam parameters.

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  1. B. B. Baker and E. T. Copson, The Mathematical Theory of Huygens' Principle (Oxford University Press, New York, 1930), 2nd ed.
  2. A. Sommerfeld, Optics (Academic Press Inc., New York, 1954).
  3. E. Marom, J. Opt. Soc. Am. 57, 1390 (1967).
  4. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 3rd ed.
  5. G. Kirchhoff, Vorlesungen Über Math. Physik. 2 (Optik, Leipzig, 1891).
  6. E. Wolf and E. W. Marchand, J. Opt. Soc. Am. 54, 587 (1964).
  7. E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 56, 1712 (1966).
  8. C. W. Horton and R. B. Watson, J. Appl. Phys. 21, 16 (1950).
  9. R. D. Kodis, J. Appl. Phys. 23, 249 (1952).
  10. B. N. Harden, Proc. Inst. Elec. Engrs. Pt. III 99, 229 (1952).
  11. R. V. Row, J. Appl. Phys. 24, 1448 (1953).
  12. K. L. McDonald and F. S. Harris, Jr., J. Opt. Soc. Am. 42, 321 (1952).
  13. J. D. Barnett and F. S. Harris, Jr., J. Opt. Soc. Am. 52, 536 (1962).
  14. J. Komrska, V. Drahos, and A. Delong, Opt. Acta 11, 145 (1964).
  15. G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
  16. H. Kogelnik, Appl. Opt. 4, 1562 (1965).
  17. G. D. Boyd and H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).
  18. A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).
  19. W. R. Bennett, Jr. and J. W. Knutson, Jr., Bull. Am. Phys. Soc. 9, 500 (1964).
  20. W. R. Bennett, Jr., Appl. Opt., Suppl. 2, 3 (1965).
  21. The detail and rapid oscillations in the curves of Fig. 2 can best be appreciated by referring to the expanded-scale figures in the experimental section of this paper.
  22. See K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615, 626 (1962) for a mathematical formulation of Young's theory.
  23. From a superficial examination of Fig. 2, it appears that diffraction in the limit of small beam sizes is not purely an edge effect as predicted by Huygens' principle. It is possible to show, however, (see Refs. 6, 7, 22) that, even for small incident beams, diffraction is an edge effect. The size and rate of expansion of the beam play ever-increasing roles in determining the exact nature of the diffraction pattern as the beam size is reduced.
  24. H. Kogelnik, Bell System Tech. J. 44, 455 (1965).

Baker, B. B.

B. B. Baker and E. T. Copson, The Mathematical Theory of Huygens' Principle (Oxford University Press, New York, 1930), 2nd ed.

Barnett, J. D.

J. D. Barnett and F. S. Harris, Jr., J. Opt. Soc. Am. 52, 536 (1962).

Bennett, Jr., W. R.

W. R. Bennett, Jr. and J. W. Knutson, Jr., Bull. Am. Phys. Soc. 9, 500 (1964).

W. R. Bennett, Jr., Appl. Opt., Suppl. 2, 3 (1965).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 3rd ed.

Boyd, G. D.

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).

G. D. Boyd and H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).

Copson, E. T.

B. B. Baker and E. T. Copson, The Mathematical Theory of Huygens' Principle (Oxford University Press, New York, 1930), 2nd ed.

Delong, A.

J. Komrska, V. Drahos, and A. Delong, Opt. Acta 11, 145 (1964).

Drahos, V.

J. Komrska, V. Drahos, and A. Delong, Opt. Acta 11, 145 (1964).

Fox, A. G.

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).

Gordon, J. P.

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).

Harden, B. N.

B. N. Harden, Proc. Inst. Elec. Engrs. Pt. III 99, 229 (1952).

Harris, F. S.

J. D. Barnett and F. S. Harris, Jr., J. Opt. Soc. Am. 52, 536 (1962).

K. L. McDonald and F. S. Harris, Jr., J. Opt. Soc. Am. 42, 321 (1952).

Horton, C. W.

C. W. Horton and R. B. Watson, J. Appl. Phys. 21, 16 (1950).

Kirchhoff, G.

G. Kirchhoff, Vorlesungen Über Math. Physik. 2 (Optik, Leipzig, 1891).

Knutson, Jr., J. W.

W. R. Bennett, Jr. and J. W. Knutson, Jr., Bull. Am. Phys. Soc. 9, 500 (1964).

Kodis, R. D.

R. D. Kodis, J. Appl. Phys. 23, 249 (1952).

Kogelnik, H.

H. Kogelnik, Appl. Opt. 4, 1562 (1965).

G. D. Boyd and H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).

H. Kogelnik, Bell System Tech. J. 44, 455 (1965).

Komrska, J.

J. Komrska, V. Drahos, and A. Delong, Opt. Acta 11, 145 (1964).

Li, T.

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).

Marchand, E. W.

E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 56, 1712 (1966).

E. Wolf and E. W. Marchand, J. Opt. Soc. Am. 54, 587 (1964).

Marom, E.

E. Marom, J. Opt. Soc. Am. 57, 1390 (1967).

McDonald, K. L.

K. L. McDonald and F. S. Harris, Jr., J. Opt. Soc. Am. 42, 321 (1952).

Miyamoto, K.

See K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615, 626 (1962) for a mathematical formulation of Young's theory.

Row, R. V.

R. V. Row, J. Appl. Phys. 24, 1448 (1953).

Sommerfeld, A.

A. Sommerfeld, Optics (Academic Press Inc., New York, 1954).

Watson, R. B.

C. W. Horton and R. B. Watson, J. Appl. Phys. 21, 16 (1950).

Wolf, E.

See K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615, 626 (1962) for a mathematical formulation of Young's theory.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 3rd ed.

E. Wolf and E. W. Marchand, J. Opt. Soc. Am. 54, 587 (1964).

E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 56, 1712 (1966).

Other

B. B. Baker and E. T. Copson, The Mathematical Theory of Huygens' Principle (Oxford University Press, New York, 1930), 2nd ed.

A. Sommerfeld, Optics (Academic Press Inc., New York, 1954).

E. Marom, J. Opt. Soc. Am. 57, 1390 (1967).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 3rd ed.

G. Kirchhoff, Vorlesungen Über Math. Physik. 2 (Optik, Leipzig, 1891).

E. Wolf and E. W. Marchand, J. Opt. Soc. Am. 54, 587 (1964).

E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 56, 1712 (1966).

C. W. Horton and R. B. Watson, J. Appl. Phys. 21, 16 (1950).

R. D. Kodis, J. Appl. Phys. 23, 249 (1952).

B. N. Harden, Proc. Inst. Elec. Engrs. Pt. III 99, 229 (1952).

R. V. Row, J. Appl. Phys. 24, 1448 (1953).

K. L. McDonald and F. S. Harris, Jr., J. Opt. Soc. Am. 42, 321 (1952).

J. D. Barnett and F. S. Harris, Jr., J. Opt. Soc. Am. 52, 536 (1962).

J. Komrska, V. Drahos, and A. Delong, Opt. Acta 11, 145 (1964).

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).

H. Kogelnik, Appl. Opt. 4, 1562 (1965).

G. D. Boyd and H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).

W. R. Bennett, Jr. and J. W. Knutson, Jr., Bull. Am. Phys. Soc. 9, 500 (1964).

W. R. Bennett, Jr., Appl. Opt., Suppl. 2, 3 (1965).

The detail and rapid oscillations in the curves of Fig. 2 can best be appreciated by referring to the expanded-scale figures in the experimental section of this paper.

See K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615, 626 (1962) for a mathematical formulation of Young's theory.

From a superficial examination of Fig. 2, it appears that diffraction in the limit of small beam sizes is not purely an edge effect as predicted by Huygens' principle. It is possible to show, however, (see Refs. 6, 7, 22) that, even for small incident beams, diffraction is an edge effect. The size and rate of expansion of the beam play ever-increasing roles in determining the exact nature of the diffraction pattern as the beam size is reduced.

H. Kogelnik, Bell System Tech. J. 44, 455 (1965).

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