Abstract

Solutions of problems on the propagation and matching of Gaussian laser beams can be found graphically by means of circle diagrams called Gaussian beam charts. It is the purpose of this paper to propose a logarithmic version of this chart that covers a much wider region.

© 1968 Optical Society of America

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References

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  1. S. A. Collins, Appl. Opt. 3, 1263 (1964).
    [CrossRef]
  2. T. Li, Appl. Opt. 3, 1315 (1964).
    [CrossRef]
  3. O. Zinke, Archiv Elektr. Übertragung 18, 331 (1964).
  4. H. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]

1966

1964

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Figures (3)

Fig. 1
Fig. 1

Logarithmic Gaussian beam chart.

Fig. 2
Fig. 2

Solution of the mode matching problem given by Fig. 2. b ¯ was chosen to be 1 m. The heavy curves pertain to the coordinates −z/ b ¯ and b/2 b ¯ = w02k/2 b ¯, the dotted ones to b ¯/r and 2 b ¯/kw2.

Fig. 3
Fig. 3

Matching of a gas laser to a beam waveguide.

Equations (4)

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ln | 2 b ¯ k w 2 + j b ¯ r | ,
ln | w o 2 k 2 b ¯ - j z b ¯ | ,
α = arc tan [ b ¯ r / 2 b ¯ k w 2 ] or arc tan [ - z b / w 0 2 k 2 b ¯ ] ,
2 b ¯ k w 2 + j ( b ¯ / r ) = 1 ( w 0 2 k / 2 b ¯ ) - j ( z / b ¯ ) .

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