Abstract

The behavior of the diffraction field of a Gaussian beam through an aperture depends on incidence conditions and aperture radius. The field spread in the Fraunhofer region varies with the curvature of the equiphase surface of the incident beam as well as the ratio of the aperture radius to the spot size. The divergence angle obtained from the field spread is considered and an approximation method to the diffracted beam by one Gaussian beam is proposed. And the effect of curvature of the incident equiphase surface is also discussed.

© 1985 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. G. Schell, G. Tyras, “Irradiance from Truncated-Gaussian Field,” J. Opt. Soc. Am 61, 31 (1971).
    [CrossRef]
  2. D. A. Holmes, J. E. Korka, P. V. Avizonis, “Parametric Study of Apertured Focused Gaussian Beams,” Appl. Opt. 11, 565 (1972).
    [CrossRef] [PubMed]
  3. K. Tanaka, M. Shibukawa, O. Kukumitsu, “Diffraction of a Wave Beam by an Aperture,” IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972).
    [CrossRef]
  4. P. Belland, J. P. Crenn, “Changes in the Characteristics of a Gaussian Beam Weakly Diffracted by a Circular Aperture,” Appl. Opt. 21, 522 (1982).
    [CrossRef] [PubMed]
  5. V. N. Mahajan, “Axial Irradiance and Optimum Focusing of Laser Beams,” Appl. Opt. 22, 3042 (1983).
    [CrossRef] [PubMed]

1983 (1)

1982 (1)

1972 (2)

D. A. Holmes, J. E. Korka, P. V. Avizonis, “Parametric Study of Apertured Focused Gaussian Beams,” Appl. Opt. 11, 565 (1972).
[CrossRef] [PubMed]

K. Tanaka, M. Shibukawa, O. Kukumitsu, “Diffraction of a Wave Beam by an Aperture,” IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972).
[CrossRef]

1971 (1)

R. G. Schell, G. Tyras, “Irradiance from Truncated-Gaussian Field,” J. Opt. Soc. Am 61, 31 (1971).
[CrossRef]

Avizonis, P. V.

Belland, P.

Crenn, J. P.

Holmes, D. A.

Korka, J. E.

Kukumitsu, O.

K. Tanaka, M. Shibukawa, O. Kukumitsu, “Diffraction of a Wave Beam by an Aperture,” IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972).
[CrossRef]

Mahajan, V. N.

Schell, R. G.

R. G. Schell, G. Tyras, “Irradiance from Truncated-Gaussian Field,” J. Opt. Soc. Am 61, 31 (1971).
[CrossRef]

Shibukawa, M.

K. Tanaka, M. Shibukawa, O. Kukumitsu, “Diffraction of a Wave Beam by an Aperture,” IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972).
[CrossRef]

Tanaka, K.

K. Tanaka, M. Shibukawa, O. Kukumitsu, “Diffraction of a Wave Beam by an Aperture,” IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972).
[CrossRef]

Tyras, G.

R. G. Schell, G. Tyras, “Irradiance from Truncated-Gaussian Field,” J. Opt. Soc. Am 61, 31 (1971).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Microwave Theory Tech. (1)

K. Tanaka, M. Shibukawa, O. Kukumitsu, “Diffraction of a Wave Beam by an Aperture,” IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972).
[CrossRef]

J. Opt. Soc. Am (1)

R. G. Schell, G. Tyras, “Irradiance from Truncated-Gaussian Field,” J. Opt. Soc. Am 61, 31 (1971).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Incident Gaussian beam, the aperture, and the definition of parameters.

Fig. 2
Fig. 2

Divergence angle of a Gaussian beam.

Fig. 3
Fig. 3

Divergence angle of a diffracted Gaussian beam as a function of the ratio of aperture radius a to the intensity spot size r0 with p = l λ / r m 2 as a parameter. The angle is calculated by - - -, beam mode expansion method; -·-, Belland and Crenn's method; –‥–‥ –, calculation of the diffraction field Eq. (4); —, received energy: (a) p = 0; (b) p = 1; (c) p = 5; (d) p = 7; (e) p = 10; (f) p = 20; (g) p = 30.

Fig. 4
Fig. 4

Transverse intensity distribution in the Fraunhofer region for spherical wave incidence, normalized by the maximum intensity of each distribution. The parameter Δ is given by Δ = d/λ, where d is the path difference between the center and the edge of the aperture.

Equations (15)

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

ψ 00 ( ρ , z ) = κ π exp [ i k ( z z s ) ½ κ 2 σ 2 ρ 2 + i tan 1 ξ ] ,
ξ = 2 ( z z s ) k w s 2 , κ = 2 w s 1 + ξ 2 , σ 2 = 1 + i ξ .
U 00 ( ρ , z ) = i k κ 0 π ( z l ) exp [ i k ( z l ) + i tan 1 ξ 0 i k ρ 2 2 ( z l ) ] 0 a J 0 ( k ρ ρ 0 z l ) exp ( ½ κ 0 2 σ 0 2 ρ 0 2 ) ρ 0 d ρ 0 ,
N a = k a 2 z 1 , x = κ 0 a = a r 0 , p = 2 l λ w s 2 = l λ r m 2 ,
I ( ρ , z ) = N a 2 κ 0 2 π { [ 0 1 R 0 J 0 ( N a R 0 R ) exp ( ½ x 2 R 0 2 ) × cos ( p 4 π x 2 R 0 2 ) d R 0 ] 2 + [ 0 1 R 0 J 0 ( N a R 0 R ) exp ( ½ x 2 R 0 2 ) × sin ( p 4 π x 2 R 0 2 ) d R 0 ] 2 } .
θ m tan θ m = r z .
θ m = r z ,
θ m θ m = r / z r / z = r r = r / a r / a .
U 00 ( ρ , z ) = n = 0 C ̅ 0 n ψ ̅ 0 n ( ρ , z ) .
U 00 ( ρ , z ) C ̅ 00 ψ ̅ 00 ( ρ , z ) .
0 0 2 π | U 00 ( ρ , z ) C ̅ 00 ψ ̅ 00 | 2 r d r d θ .
ξ 0 κ 0 2 a 2 = ξ ̅ 0 κ ̅ 0 2 a 2 ,
( κ 0 2 a 2 κ ̅ 0 2 a 2 ) { 1 exp [ ½ κ 0 2 a 2 + κ ̅ 0 2 a 2 ] } + κ ̅ 0 2 a 2 ( κ 0 2 a 2 + κ ̅ 0 2 a 2 ) exp [ ½ κ 0 2 a 2 + κ ̅ 0 2 a 2 ] = 0 ,
w ̅ s a = 2 κ ̅ 0 a 1 + ξ ̅ 0 2 , z ̅ s = k ξ ̅ 0 a 2 κ ̅ 0 2 a 2 ( 1 + ξ ̅ 0 2 ) z 0 .
P = 1 exp ( ρ 2 / r 2 ) .

Metrics