Abstract

Simple procedures and formulas for tracing the characteristics of a spherical Gaussian beam through a train of lenses or mirrors are described which are analogous to those used in geometrical optics to trace repeated images through an optical train.

© 1983 Optical Society of America

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References

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  1. W. H. Carter, Appl. Opt. 21, 1989 (1982).
    [CrossRef] [PubMed]
  2. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 8.
  3. S. A. Self, “Focusing of Gaussian Laser Beams,” High-Temperature Gasdynamics Laboratory Memorandum Report No. 3, August1976 (unpublished).
  4. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), Chap. 4.

1982

Carter, W. H.

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), Chap. 4.

Self, S. A.

S. A. Self, “Focusing of Gaussian Laser Beams,” High-Temperature Gasdynamics Laboratory Memorandum Report No. 3, August1976 (unpublished).

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 8.

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), Chap. 4.

Appl. Opt.

Other

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 8.

S. A. Self, “Focusing of Gaussian Laser Beams,” High-Temperature Gasdynamics Laboratory Memorandum Report No. 3, August1976 (unpublished).

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), Chap. 4.

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Figures (5)

Fig. 1
Fig. 1

Cartesian plot of the lens formula of geometrical optics. Solid lines show normalized image distance vs normalized object distance. Broken lines show the magnification. Below are sketched ray diagrams illustrating the situations for points on branch (1) and on the segments (2) and (3) of the second branch.

Fig. 2
Fig. 2

Geometry of a spherical Gaussian beam.

Fig. 3
Fig. 3

Geometry of the imaging of a Gaussian beam by a lens shown for the case of a positive lens and real object and image waists.

Fig. 4
Fig. 4

Cartesian plot of the lens formula for Gaussian beams showing normalized image distance vs normalized object distance, with normalized Rayleigh range of the input beam as the parameter.

Fig. 5
Fig. 5

Graph of magnification for a Gaussian beam vs normalized object distance, with normalized Rayleigh range of the input beam as the parameter.

Equations (18)

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1 s + 1 s = 1 f ,
1 ( s / f ) + 1 ( s / f ) = 1
m = | s s | = 1 | 1 ( s / f ) | ,
I ( r , z ) = ( 2 / π w 2 ) exp 2 ( r / w ) 2 ,
w ( z ) = w 0 [ 1 + ( z / z R ) 2 ] 1 / 2 .
z R ( π w 0 2 / λ )
R ( z ) = z [ 1 + ( z R / z ) 2 ] .
w F F w 0 ( z / z R ) = λ z / π w 0 .
θ F F = w F F / z = λ / π w 0 .
1 s + z R 2 / ( s f ) + 1 s = 1 f .
1 ( s / f ) + ( z R / f ) 2 / ( s / f 1 ) + 1 ( s / f ) = 1 ,
( s / f ) = 1 + [ ( s / f ) 1 ] [ ( s / f ) 1 ] 2 + ( z R / f ) 2 ,
( s / f ) = 1 + 1 [ ( s / f ) 1 ] .
( s / f ) max = 1 + 1 2 ( z R / f ) at ( s / f ) = 1 + ( z R / f ) ;
( s / f ) min = 1 1 2 ( z R / f ) at ( s / f ) = 1 ( z R / f ) .
m = w 0 w 0 = 1 { [ 1 ( s / f ) 2 ] + ( z R / f ) 2 } 1 / 2 ,
z R = m 2 z R .
1 s + 1 s + z R 2 / ( s f ) = 1 f .

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