Abstract

Near-field irradiance patterns have been calculated for plane-wave gaussian beams truncated by circular apertures. The Kirchhoff diffraction integral was integrated numerically, using the small-angle Fresnel approximation. The effect of truncation was important when the aperture radius was less than twice the spot size of the gaussian beam.

© 1969 Optical Society of America

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References

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  1. In this paper“irradiance” is to be understood in the sense of the square of wave amplitude. Formerly, the word “intensity” was commonly used for this sense, but confusion over such a usage has arisen.See J. Opt. Soc. Am. 57, 854 (1967).
  2. A. Yariv, Quantum Electronics (John Wiley & Sons, Inc., New York, 1967), Ch. 14.
  3. G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
    [Crossref]
  4. S. E. Miller and L. C. Tillotson, Appl. Opt. 5, 1538 (1966) and references therein.
    [Crossref] [PubMed]
  5. W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968); and references therein.
    [Crossref]
  6. J. F. Kauffman, IEEE Trans. Ant. and Prop. AP-13, 473 (1965).
    [Crossref]
  7. A. L. Buck, Proc. IEEE 55, 450 (1967).
    [Crossref]
  8. A. L. Bloom, Gas Lasers (John Wiley & Sons, Inc., New York, 1968), p. 114.
  9. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., New York, 1962), Ch. 9.
  10. S. Silver, J. Opt. Soc. Am. 52, 131 (1962).
    [Crossref] [PubMed]
  11. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Ltd., Oxford, 1965).
  12. P. M. Morse and H. Feshback, Methods of Theoretical Physics (McGraw–Hill Book Co., New York, 1953), Vol. I, p. 621.

1968 (1)

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968); and references therein.
[Crossref]

1967 (2)

1966 (1)

1965 (1)

J. F. Kauffman, IEEE Trans. Ant. and Prop. AP-13, 473 (1965).
[Crossref]

1962 (1)

1961 (1)

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

Bloom, A. L.

A. L. Bloom, Gas Lasers (John Wiley & Sons, Inc., New York, 1968), p. 114.

Born, M.

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

Boyd, G. D.

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

Buck, A. L.

A. L. Buck, Proc. IEEE 55, 450 (1967).
[Crossref]

Feshback, H.

P. M. Morse and H. Feshback, Methods of Theoretical Physics (McGraw–Hill Book Co., New York, 1953), Vol. I, p. 621.

Gordon, J. P.

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

Haus, H. A.

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968); and references therein.
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., New York, 1962), Ch. 9.

Kauffman, J. F.

J. F. Kauffman, IEEE Trans. Ant. and Prop. AP-13, 473 (1965).
[Crossref]

Marburger, J. H.

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968); and references therein.
[Crossref]

Miller, S. E.

Morse, P. M.

P. M. Morse and H. Feshback, Methods of Theoretical Physics (McGraw–Hill Book Co., New York, 1953), Vol. I, p. 621.

Silver, S.

Tillotson, L. C.

Wagner, W. G.

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968); and references therein.
[Crossref]

Wolf, E.

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

Yariv, A.

A. Yariv, Quantum Electronics (John Wiley & Sons, Inc., New York, 1967), Ch. 14.

Appl. Opt. (1)

Bell System Tech. J. (1)

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

IEEE Trans. Ant. and Prop. (1)

J. F. Kauffman, IEEE Trans. Ant. and Prop. AP-13, 473 (1965).
[Crossref]

J. Opt. Soc. Am. (2)

Phys. Rev. (1)

W. G. Wagner, H. A. Haus, and J. H. Marburger, Phys. Rev. 175, 256 (1968); and references therein.
[Crossref]

Proc. IEEE (1)

A. L. Buck, Proc. IEEE 55, 450 (1967).
[Crossref]

Other (5)

A. L. Bloom, Gas Lasers (John Wiley & Sons, Inc., New York, 1968), p. 114.

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, Inc., New York, 1962), Ch. 9.

A. Yariv, Quantum Electronics (John Wiley & Sons, Inc., New York, 1967), Ch. 14.

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

P. M. Morse and H. Feshback, Methods of Theoretical Physics (McGraw–Hill Book Co., New York, 1953), Vol. I, p. 621.

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Figures (4)

F. 1
F. 1

Geometry and coordinates.

F. 2
F. 2

Axial irradiance vs distance for various illumination-spot sizes at constant aperture radius (a = 700 wavelengths).

F. 3
F. 3

Irradiance vs distance off axis for various illumination-spot sizes (aperture radius a = 700 wavelengths, axial distance R = 230a).

F. 4
F. 4

Irradiance vs distance off axis for various illumination-spot sizes (aperture radius a = 700 wavelengths, axial distance R = 375a).

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

u ( x , y , R ) = K U ( ξ , η ) e iks s ( 1 + cos β ) d ξ d η .
s = r ρ x cos θ r + ρ 2 2 r ( 1 x 2 cos 2 θ r 2 ) + ρ 3 x cos θ 2 r 3 ( 1 x 2 cos 2 θ r 2 ) + .
u ( x , R ) = K r 0 a { ρ U ( ρ ) exp ( i k ρ 2 / 2 r ) × π π exp [ ( i k ρ x cos θ ) / r ] d θ } d ρ ,
u ( x , R ) = K r 0 a ρ U ( ρ ) J 0 ( k ρ x r ) exp ( i k ρ 2 / 2 r ) d ρ .
U ( ρ ) = exp [ ( ρ / w ) 2 ] ,
u ( x , R ) = K r 0 a ρ J 0 ( k ρ x r ) exp [ ( i k 2 r w 2 ) ρ 2 ] d ρ .