Abstract

Measurements of higher-order CO2 laser beam spot size have been made and found in good agreement with a Hermite-Gaussian rectangular beam propagation model. A modified working definition of spot size is introduced, and a useful depth of focus relationship is presented. It is shown that a single measurement of spot size for any higher-order mode is all that is required to reasonably predict spot size for the same laser operating in different modes. Alternatively, beam size can be predicted theoretically on the basis of the optical cavity parameters.

© 1981 Optical Society of America

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References

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  1. W. H. Carter, Appl. Opt. 19, 1027 (1980).
    [CrossRef] [PubMed]
  2. J. T. Luxon, D. E. Parker, Appl. Opt. 20, 1933 (1981).
    [CrossRef] [PubMed]
  3. H. W. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

R6(z)X (half the distance between outer irradiance peaks in the X direction) vs z, measured and calculated.

Fig. 2
Fig. 2

R4(z)Y (half the distance between irradiance peaks in the Y direction) vs z, measured and calculated.

Tables (1)

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Table I Ratio of Half the Distance between Outside Irradlance Peaks to Standard Deviation for Hermite-Gaussian Laser Beam Model (Rsis) and its Reciprocal Ksl

Equations (8)

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σ s ( z ) l = σ s ( o ) ( 2 l + 1 ) 1 / 2 ( 1 + ( z 2 / z o s 2 ) 1 / 2 ,
z o s = ( 2 π / λ ) σ s 2 ( o ) .
R s ( z ) l = R s ( o ) ( 2 l + 1 ) 1 / 2 ( 1 + C s z 2 ) 1 / 2 ,
C s = [ λ / 2 π K l 2 R s 2 ( o ) ] 2 ,
K s l R s ( o ) = σ s ( o ) .
R s ( o ) = λ f ( 2 l + 1 ) 1 / 2 / 2 π K s l 2 S ,
d = ± [ ( ρ 2 1 ) / C s ] 1 / 2 = ± ( ρ 2 1 ) 1 / 2 2 π K s l 2 R s 2 ( o ) / λ ± 2 π ( ρ 2 1 ) 1 / 2 K s l 2 R s 2 ( o ) l / ( 2 l + 1 ) .
D s ( o ) l = ( λ L 2 π ) 1 / 2 ( 2 l + 1 ) 1 / 2 K s l [ g 1 g 2 ( 1 g 1 g 2 ) ] 1 / 4 ( g 1 + g 2 2 g 1 g 2 ) 1 / 2 ,

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