Abstract

The optical quality of a pulsed atmospheric CO2 electric laser is investigated. The density disturbances in the optical cavity are caused by edge waves originating at the anode and cathode. Volumetric heating effects associated with a nonuniform electric discharge are shown to be negligible. The disturbance propagating from the cathode results from a discontinuity in the spatial heating and the cathode fall. The wave emanating from the anode is associated with the presence of a solid surface that prevents the gas from expanding. As a result, lasers have to be designed with pulse durations much less than the acoustic transit time across the cavity.

© 1974 Optical Society of America

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References

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  1. J. D. Daugherty, E. R. Pugh, D. H. Douglas-Hamilton, Bull. Am. Phys. Soc. 16, 399 (1971); C. A. Fernstermacher, M. J. Nutter, J. P. Rink, K. Boyer, Bull. Am. Phys. Soc. 16, 42 (1971).
  2. J. Wallace, M. Camac, J. Opt. Soc. Am. 60, 1587 (1970).
    [CrossRef]
  3. J. H. Jacob, J. P. Reilly, E. R. Pugh, J. Appl. Phys. 45, 2609 (1974).
    [CrossRef]
  4. D. B. Henderson, J. Appl. Phys. 44, 1513 (1973); J. H. Jacob, J. Appl. Phys. 45, 467 (1974).
    [CrossRef]

1974

J. H. Jacob, J. P. Reilly, E. R. Pugh, J. Appl. Phys. 45, 2609 (1974).
[CrossRef]

1973

D. B. Henderson, J. Appl. Phys. 44, 1513 (1973); J. H. Jacob, J. Appl. Phys. 45, 467 (1974).
[CrossRef]

1971

J. D. Daugherty, E. R. Pugh, D. H. Douglas-Hamilton, Bull. Am. Phys. Soc. 16, 399 (1971); C. A. Fernstermacher, M. J. Nutter, J. P. Rink, K. Boyer, Bull. Am. Phys. Soc. 16, 42 (1971).

1970

Camac, M.

Daugherty, J. D.

J. D. Daugherty, E. R. Pugh, D. H. Douglas-Hamilton, Bull. Am. Phys. Soc. 16, 399 (1971); C. A. Fernstermacher, M. J. Nutter, J. P. Rink, K. Boyer, Bull. Am. Phys. Soc. 16, 42 (1971).

Douglas-Hamilton, D. H.

J. D. Daugherty, E. R. Pugh, D. H. Douglas-Hamilton, Bull. Am. Phys. Soc. 16, 399 (1971); C. A. Fernstermacher, M. J. Nutter, J. P. Rink, K. Boyer, Bull. Am. Phys. Soc. 16, 42 (1971).

Henderson, D. B.

D. B. Henderson, J. Appl. Phys. 44, 1513 (1973); J. H. Jacob, J. Appl. Phys. 45, 467 (1974).
[CrossRef]

Jacob, J. H.

J. H. Jacob, J. P. Reilly, E. R. Pugh, J. Appl. Phys. 45, 2609 (1974).
[CrossRef]

Pugh, E. R.

J. H. Jacob, J. P. Reilly, E. R. Pugh, J. Appl. Phys. 45, 2609 (1974).
[CrossRef]

J. D. Daugherty, E. R. Pugh, D. H. Douglas-Hamilton, Bull. Am. Phys. Soc. 16, 399 (1971); C. A. Fernstermacher, M. J. Nutter, J. P. Rink, K. Boyer, Bull. Am. Phys. Soc. 16, 42 (1971).

Reilly, J. P.

J. H. Jacob, J. P. Reilly, E. R. Pugh, J. Appl. Phys. 45, 2609 (1974).
[CrossRef]

Wallace, J.

Bull. Am. Phys. Soc.

J. D. Daugherty, E. R. Pugh, D. H. Douglas-Hamilton, Bull. Am. Phys. Soc. 16, 399 (1971); C. A. Fernstermacher, M. J. Nutter, J. P. Rink, K. Boyer, Bull. Am. Phys. Soc. 16, 42 (1971).

J. Appl. Phys.

J. H. Jacob, J. P. Reilly, E. R. Pugh, J. Appl. Phys. 45, 2609 (1974).
[CrossRef]

D. B. Henderson, J. Appl. Phys. 44, 1513 (1973); J. H. Jacob, J. Appl. Phys. 45, 467 (1974).
[CrossRef]

J. Opt. Soc. Am.

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Figures (10)

Fig. 1
Fig. 1

Schematic of electron beam ionizer-sustainer laser.

Fig. 2
Fig. 2

The spatial variation of the energy deposition that gives rise to density gradients in the optical cavity.

Fig. 3
Fig. 3

Time dependence of acoustic disturbances caused by the heating profile shown in Fig. 2.

Fig. 4
Fig. 4

Time dependence of the acoustic disturbances for a Gaussian beam. Comparison with Fig. 3 illustrates the ∇2Q effect along with the edge waves.

Fig. 5
Fig. 5

Schematic of Mach–Zender interferometric apparatus.

Fig. 6
Fig. 6

A finite fringe pattern taken in the central portion of the laser cavity under typical operating conditions.

Fig. 7
Fig. 7

Same as Fig. 6, except that the energy input was decreased. Notice the similarity between a fringe and the early time disturbance shown in Fig. 3.

Fig. 8
Fig. 8

Current and voltage waveforms. These traces were used to calculate the decay rate of the energy deposited in the laser cavity.

Fig. 9
Fig. 9

A moiré fringe pattern of Fig. 5 that facilitates the counting of fringe shifts.

Fig. 10
Fig. 10

Comparison between the predicted disturbance and experimental results. The solid line is a plot of Eq. (18). The crosses are experimental results obtained from Fig. 9. The dashed curves are the predicted disturbances for impulsive heating and step-function heat input.

Equations (21)

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( ρ / t ) + ρ 0 · v = 0 .
ρ 0 ( v / t ) = p .
ρ 0 ( h / t ) ( p / t ) = Q .
h = [ γ / ( γ 1 ) ] [ ( p / ρ 0 ) ( p 0 ρ / ρ 0 2 ) ] ,
ρ , p , v = 0 at t = 0
n · v = 0 ,
v = ( N d / t d ) ψ ,
2 ψ ( 2 ψ / τ 2 ) = Q ¯ ,
ψ ( x , y , z , 0 ) = ( ψ / τ ) ( x , y , z , 0 ) = 0.
ρ ρ 0 = N d a 0 t d ( 0 τ Q ¯ d t + ψ τ ) .
Q = E · J = σ ( E · E ) .
Δ ϕ = 2 π ( n 0 1 ) λ 0 2 l ρ ρ 0 ( x , y , z ) d z π .
ρ ρ 0 = N d a 0 t d 0 τ ( τ τ ) 2 2 2 Q ¯ d τ 1.0.
Q Q 0 = ( ( A + B ξ ) / 2 · { 1 erf [ ( ξ 1 ) / ] } + [ Q c / ( π ) 1 / 2 ] exp [ ( ξ 1 ) 2 / ] ) f ( τ ) ,
ψ ( ξ , τ ) = 1 ( 2 π ) 0 ψ ( p , τ ) cos p ξ d p ,
ψ ( p , τ ) = 0 τ f ( t ) sin p ( τ t ) p [ 0 Q ( x ) cos p ξ d ξ ] d t .
ρ ρ 0 = ( N d a 0 t d ) { 0 τ Q ( ξ ) f ( t ) d t 1 2 0 τ [ Q ( | ξ + τ t | ) + Q ( | ξ τ + t | ) ] f ( t ) d t } .
V s = V 0 exp ( τ / t d 1 ) ; I s = I 0 exp ( τ / t d 2 ) , 1 / t d 1 = 0.56 ; 1 / t d 2 = 1.35.
1 / t d = ( 1 / t d 1 + 1 / t d 2 ) = 1.9.
ρ / ρ 0 = 0.95 [ 1.9 ( 1 η ) 1 + exp { 1.9 ( 1 η ) } ] θ ( 1 η ) ,
ρ / ρ 0 = ( F m ) / F ,

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