Abstract

A new definition of the pointing stability of a laser beam is proposed. It is derived from the superposition integral between the optical field and a misaligned version of itself. This approach permits the characterization of the pointing stability with a single number, while taking into account the intensity and phase features of the beam. This pointing stability criterion is invariant under propagation and can be related to the moment definitions of beam size, divergence, and quality. The definition is also suggestive of an experimental measurement procedure.

© 1994 Optical Society of America

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References

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  1. A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).
  2. P. A. Bélanger, Opt. Lett. 16, 196 (1991).
    [CrossRef] [PubMed]
  3. A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
    [CrossRef]
  4. W. B. Joyce, B. C. DeLoach, Appl. Opt. 23, 4187 (1984).
    [CrossRef] [PubMed]
  5. S. A. Collins, J. Opt. Soc. Am. 60, 1168 (1970).
    [CrossRef]
  6. M. A. Porras, J. Alda, E. Bernabeu, Appl. Opt. 31, 6389 (1992).
    [CrossRef] [PubMed]

1992 (1)

1991 (2)

P. A. Bélanger, Opt. Lett. 16, 196 (1991).
[CrossRef] [PubMed]

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[CrossRef]

1990 (1)

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

1984 (1)

1970 (1)

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

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Figures (1)

Fig. 1.
Fig. 1.

Accuracy of the second-order approximation of the misalignment figure |ηm|2 for unidimensional Hermite-Gaussian beams of order n = 0 and n = 6.

Equations (18)

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η = U 1 ( x ) U 2 * ( x ) d x [ | U 1 ( x ) | 2 d x ] 1 / 2 [ | U 2 ( x ) | 2 d x ] 1 / 2 .
η m = 1 I U ( x ) [ U ( x δ ) exp ( j k α x ) ] * d x ,
I = | U ( x ) | 2 d x .
η m 1 I U ( x ) [ U * ( x ) δ d U * ( x ) d x + δ 2 2 d 2 U * ( x ) d x 2 ] × [ 1 + j k α x ( k α x ) 2 2 ] d x .
η m 1 + j k α x ¯ j k δ θ ¯ k 2 α 2 x 2 ¯ 2 k 2 δ 2 θ 2 ¯ 2 j k α δ I x U ( x ) d U * ( x ) d x d x ,
x n ¯ = 1 I x n | U ( x ) | 2 d x , n = 1 , 2 ,
θ n ¯ = 1 I ( j k ) n U ( x ) d n U * ( x ) d x n d x , n = 1 , 2 ,
| η m | 2 1 k 2 α 2 x 2 ¯ k 2 δ 2 θ 2 ¯ + j k α δ I x [ U * ( x ) d U ( x ) d x U ( x ) d U * ( x ) d x ] d x .
| η m | 2 1 k 2 4 ( α 2 W 2 + δ 2 θ d 2 2 α δ W 2 R ) ,
1 R = j λ π W 2 I x [ U * ( x ) d U ( x ) d x U ( x ) d U * ( x ) d x ] d x
| η m | 2 1 ( M 2 ) 2 ( α 2 θ d 2 + δ 2 W 0 2 ) ,
M 2 = π θ d W 0 λ .
P s = 1 T 0 T | η m ( t ) | 2 d t ,
P s = 1 ( M 2 ) 2 [ ( Δ θ ¯ rms ) 2 θ d 2 + ( Δ x ¯ rms ) 2 W 0 2 ] ,
| U ( x ) | 2 = [ H n ( 2 x ω 0 ) ] 2 exp ( 2 x 2 ω 0 2 ) .
| η m | 2 = exp ( υ ) [ L n ( υ ) ] 2 ,
| η m | appx 2 = 1 ( 2 n + 1 ) υ ,
υ = ( δ ω 0 ) 2 + ( k α ω 0 2 ) 2 .

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