Abstract

A Nd:YAG crystal 7.6 cm long and 6.35 mm in diameter was pumped by two krypton filled arc lamps in a double elliptical pumping cavity. The pump radiation absorbed and the heat dissipated by the Nd:YAG crystal were measured. This was done by a calorimetric measurement of the heat removed from the YAG crystal cooling loop and by monitoring the laser output power. In separate experiments the pump cavity transfer efficiency and the optical losses of the resonator were determined. The results of these measurements show that in the case of a high powered YAG system having an output power of 250 W at 12 kW input, which is six times threshold, 7.5% of the electrical input to the lamp is being absorbed by the crystal, and 40% of the absorbed pump power leaves the crystal as stimulated emission. The experiments revealed that 15% of the electrical input into the krypton arc lamps is emitted into the absorption bands of Nd:YAG crystal. The temperature profile and the associated stress components in the YAG crystal are calculated from the experimental data.

© 1970 Optical Society of America

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References

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  1. C. Bowness, Appl. Opt. 4, 103 (1965).
    [CrossRef]
  2. K. Kamiryo et al., Japan J. Appl. Phys. 5, 1217 (1966).
    [CrossRef]
  3. E. Matovich, Autonetics, private communication.
  4. R. A. Brandewie, C. L. Telk, J. Opt. Soc. Amer. 57, 1221 (1967).
    [CrossRef]
  5. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, London, 1948), p. 191.
  6. S. T. Hsu, Engineering Heat Transfer (D. Van Nostrand Company, Princeton, N. J., 1963), Chap. 9.
  7. YAG:Nd Data Brochure, Union Carbide Corporation, Crystal Products Department.
  8. S. Timoshenko, J. N. Goodier, Theory of Elasticity, (McGraw-Hill Book Co., New York, 1951).

1967 (1)

R. A. Brandewie, C. L. Telk, J. Opt. Soc. Amer. 57, 1221 (1967).
[CrossRef]

1966 (1)

K. Kamiryo et al., Japan J. Appl. Phys. 5, 1217 (1966).
[CrossRef]

1965 (1)

Bowness, C.

Brandewie, R. A.

R. A. Brandewie, C. L. Telk, J. Opt. Soc. Amer. 57, 1221 (1967).
[CrossRef]

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, London, 1948), p. 191.

Goodier, J. N.

S. Timoshenko, J. N. Goodier, Theory of Elasticity, (McGraw-Hill Book Co., New York, 1951).

Hsu, S. T.

S. T. Hsu, Engineering Heat Transfer (D. Van Nostrand Company, Princeton, N. J., 1963), Chap. 9.

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, London, 1948), p. 191.

Kamiryo, K.

K. Kamiryo et al., Japan J. Appl. Phys. 5, 1217 (1966).
[CrossRef]

Matovich, E.

E. Matovich, Autonetics, private communication.

Telk, C. L.

R. A. Brandewie, C. L. Telk, J. Opt. Soc. Amer. 57, 1221 (1967).
[CrossRef]

Timoshenko, S.

S. Timoshenko, J. N. Goodier, Theory of Elasticity, (McGraw-Hill Book Co., New York, 1951).

Appl. Opt. (1)

J. Opt. Soc. Amer. (1)

R. A. Brandewie, C. L. Telk, J. Opt. Soc. Amer. 57, 1221 (1967).
[CrossRef]

Japan J. Appl. Phys. (1)

K. Kamiryo et al., Japan J. Appl. Phys. 5, 1217 (1966).
[CrossRef]

Other (5)

E. Matovich, Autonetics, private communication.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, London, 1948), p. 191.

S. T. Hsu, Engineering Heat Transfer (D. Van Nostrand Company, Princeton, N. J., 1963), Chap. 9.

YAG:Nd Data Brochure, Union Carbide Corporation, Crystal Products Department.

S. Timoshenko, J. N. Goodier, Theory of Elasticity, (McGraw-Hill Book Co., New York, 1951).

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Figures (5)

Fig. 1
Fig. 1

Heat dissipated by a Nd:YAG crystal as a function of input lamp power.

Fig. 2
Fig. 2

Total absorbed pump power by the Nd:YAG crystal.

Fig. 3
Fig. 3

Annular cooling configuration.

Fig. 4
Fig. 4

Radial temperature distribution within the crystal as a function of radius. TF is the temperature of coolant entering flow tube assembly, ΔTF is the axial temperature gradient and T(r0) is the rod surface temperature.

Fig. 5
Fig. 5

Radial (σr), tangential (σӨ) and axial (σz) stress components within the crystal as a function of radius.

Tables (1)

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Table I Optical Efficiencies in the Pump Cavity of a High Powered cw Operated Nd:YAG Laser

Equations (27)

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η 3 = η 0 ( λ ) w ( λ ) ( λ ) d λ ,
η 3 = η 0 ( W 1 1 + W 2 2 + W 3 3 + W 4 4 )
η 3 = η 0 eff ,
d 2 T d r 2 + 1 r d T d r + A 0 K = 0.
T ( r ) = T ( r 0 ) + ( A 0 / 4 K ) ( r 0 2 r 2 ) .
A 0 = P a / π r 0 2 L ,
T ( 0 ) T ( r 0 ) = P a / 4 π K L .
P a = 0 L h π D 1 ( T R T F ) d x ,
P a = h π D 1 L ( T R T F ) ;
T R T F = P a / A h .
Δ T R Δ T F = P a / m * C P ,
T ( 0 ) max = T F + P a ( 1 4 π K L + 1 A h + 1 m * C P ) .
h 1 = 1.02 K w D 2 D 1 N Re 0.45 N Pr 0.5 N Gr 0.05 ( D 2 D 1 L ) 0.4 ( D 2 D 1 ) 0.8 .
h t = 0.02 K w D 2 D 1 ( N Re ) 0.8 ( N Pr ) 0.33 ( D 2 D 1 ) 0.53 ;
N Re = ( D 2 D 1 ) G / μ ,
G = 4 m * / π ( D 2 2 D 1 2 ) .
N Pr = C p μ / K ,
N Gr = ( D 2 D 1 ) 3 ρ 2 g γ ( T R T F ) / μ 2 ,
N Re = 8750 , N Pr = 7.4 , N Gr = 1200 ;
h 1 = 0.36 cal / cm 2 sec ° C , and h t = 0.18 cal / cm 2 sec ° C .
Δ T F Δ T R = 1 ° C ; T R T F = 36 ° C ; T ( 0 ) T ( r 0 ) = 57 ° C .
σ ˙ r = α E 1 ν ( 1 r 0 2 0 r 0 T r d r 1 r 2 0 r T r d r )
σ θ = α E 1 ν ( 1 r 0 2 0 r 0 T r d r + 1 r 2 0 r T r T )
σ z = α E 1 ν ( 2 r 0 2 0 r 0 T r d r T ) ,
σ r = [ P a α E / 16 ( 1 ν ) K π L ] [ 1 + ( r 2 / r 0 2 ) ]
σ θ = [ P a α E / 16 ( 1 ν ) K π L ] [ 1 + 3 ( r 2 / r 0 2 ) ]
σ z = [ P a α E / 4 ( 1 ν ) K π L ] [ 1 2 + ( r 2 / r 0 2 ) ] .

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