Abstract

A simple, single-mode, coherent Gaussian laser beam with wavefronts that are spherical as they pass through a reference plane is assumed, and then by using only the Huygen’s principle and scalar diffraction theory, the propagation characteristics are found, and the formulas for the beam at a distance from the reference plane are derived. The action of a lens on a wavefront is discussed, and the lens formula is derived.

© 1973 Optical Society of America

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  1. G. D. Boyd, J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).
  2. A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).
  3. G. D. Boyd, H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).
  4. A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
    [CrossRef]
  5. S. A. Collins, Appl. Opt. 3, 1263 (1964).
    [CrossRef]
  6. T. Li, Appl. Opt. 3, 1315 (1964).
    [CrossRef]
  7. G. Seifert, Appl. Opt. 7, 337 (1968).
    [CrossRef] [PubMed]
  8. H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).
  9. H. Kogelnik, “Modes in Optical Resonators,” in Advances in Lasers, A. K. Levine, Ed. (Marcel Dekker, New York, 1966).
  10. G. Goubau, F. Schwering, Trans. IRE AP-9, 248 (1961).
  11. J. R. Pierce, Proc. Nat. Acad. Sci. 47, 1808 (1961).
    [CrossRef] [PubMed]
  12. G. Goubau, “Optical Relations for Coherent Wave Beams,” in Electromagnetic Theory and Antennas (Macmillan, New York, 1963), Vol. 2, p. 907.
  13. A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963).
    [CrossRef]
  14. H. Kogelnik, Appl. Opt. 4, 1562 (1965).
    [CrossRef]
  15. T. S. Chu, Bell Syst. Tech. J. 45, 287 (1966).
  16. L. Levey, S. Maurer, J. Opt. Soc. Am. 61, 1699 (1971).
    [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965).
  18. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  19. C. S. Williams, O. A. Becklund, Optics (Wiley, New York, 1972), pp. 130–134.
  20. T. Miyamoto, K. Yasuura, Appl. Opt. 10, 161 (1971) [also see Appl. Opt. 10, 1518 (1971)].
    [CrossRef] [PubMed]
  21. L. M. Vallese, Appl. Opt. 10, 959 (1971).
    [CrossRef] [PubMed]

1971 (3)

1968 (1)

1966 (1)

T. S. Chu, Bell Syst. Tech. J. 45, 287 (1966).

1965 (2)

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

H. Kogelnik, Appl. Opt. 4, 1562 (1965).
[CrossRef]

1964 (2)

1963 (2)

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[CrossRef]

A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963).
[CrossRef]

1962 (1)

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

1961 (4)

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

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

G. Goubau, F. Schwering, Trans. IRE AP-9, 248 (1961).

J. R. Pierce, Proc. Nat. Acad. Sci. 47, 1808 (1961).
[CrossRef] [PubMed]

Becklund, O. A.

C. S. Williams, O. A. Becklund, Optics (Wiley, New York, 1972), pp. 130–134.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965).

Boyd, G. D.

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

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

Chu, T. S.

T. S. Chu, Bell Syst. Tech. J. 45, 287 (1966).

Collins, S. A.

Fox, A. G.

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[CrossRef]

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

Gordon, J. P.

A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963).
[CrossRef]

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

Goubau, G.

G. Goubau, F. Schwering, Trans. IRE AP-9, 248 (1961).

G. Goubau, “Optical Relations for Coherent Wave Beams,” in Electromagnetic Theory and Antennas (Macmillan, New York, 1963), Vol. 2, p. 907.

Kogelnik, H.

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

H. Kogelnik, Appl. Opt. 4, 1562 (1965).
[CrossRef]

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

H. Kogelnik, “Modes in Optical Resonators,” in Advances in Lasers, A. K. Levine, Ed. (Marcel Dekker, New York, 1966).

Levey, L.

Li, T.

T. Li, Appl. Opt. 3, 1315 (1964).
[CrossRef]

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[CrossRef]

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

Maurer, S.

Miyamoto, T.

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

Pierce, J. R.

J. R. Pierce, Proc. Nat. Acad. Sci. 47, 1808 (1961).
[CrossRef] [PubMed]

Schwering, F.

G. Goubau, F. Schwering, Trans. IRE AP-9, 248 (1961).

Seifert, G.

Vallese, L. M.

Williams, C. S.

C. S. Williams, O. A. Becklund, Optics (Wiley, New York, 1972), pp. 130–134.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965).

Yariv, A.

A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963).
[CrossRef]

Yasuura, K.

Appl. Opt. (6)

Bell Syst. Tech. J. (5)

T. S. Chu, Bell Syst. Tech. J. 45, 287 (1966).

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

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

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

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

J. Opt. Soc. Am. (1)

Proc. IEEE (2)

A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963).
[CrossRef]

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[CrossRef]

Proc. Nat. Acad. Sci. (1)

J. R. Pierce, Proc. Nat. Acad. Sci. 47, 1808 (1961).
[CrossRef] [PubMed]

Trans. IRE AP-9 (1)

G. Goubau, F. Schwering, Trans. IRE AP-9, 248 (1961).

Other (5)

G. Goubau, “Optical Relations for Coherent Wave Beams,” in Electromagnetic Theory and Antennas (Macmillan, New York, 1963), Vol. 2, p. 907.

H. Kogelnik, “Modes in Optical Resonators,” in Advances in Lasers, A. K. Levine, Ed. (Marcel Dekker, New York, 1966).

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1965).

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

C. S. Williams, O. A. Becklund, Optics (Wiley, New York, 1972), pp. 130–134.

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