Abstract

A study of the temperature dependence on an absorption coefficient is presented. We describe the absorption spectrum measurement of the laser material Yb:YAG that was performed over a wide temperature range. As the temperature increases from 23°Cto300°C, the central wavelength of the Yb:YAG absorption spectrum at 940nm varies slightly from 941.2nmto941.1nm, and the maximal absorption cross section drops dramatically from 7.89×1021cm2to4.23×1021cm2. According to our experimental results, we have presented an analytic description of temperature distribution with the numerical iterative method and have investigated the pumping optimization and laser oscillator performance, taking into account that the absorption coefficient is strongly influenced by temperature. Our analyses also include the effect of pump absorption saturation and the temperature dependence of Boltzmann population fractions, stimulated emission cross section, and thermal conductivity. We have shown that the predicted laser output power exceeds the actual value if the temperature dependence of Yb:YAG’s absorption coefficient is neglected.

© 2007 Optical Society of America

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References

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  1. W. F. Krupke and L. L. Chase, "Ground state depleted solid-state lasers: principles, characteristics and scaling," Opt. Quantum Electron. 22, S1-S22 (1989).
    [CrossRef]
  2. A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, "Scalable concept for diode-pumped high power solid-state lasers," Appl. Phys. B 58, 365-372 (1994).
    [CrossRef]
  3. T. S. Rutherford, W. M. Tulloch, E. K. Gustafson, and R. L. Byer, "Demonstration and scaling of edge-pumped zigzag slab lasers," in Advanced Solid State Lasers, Vol. 34 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), paper MA2-1.
  4. H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, "Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers," IEEE J. Sel. Top. Quantum Electron. 3, pp. 105-116 (1997).
    [CrossRef]
  5. C. Bibeau, R. J. Beach, S. C. Mitchell, M. A. Emanuel, J. A. Skidmore, C. A. Ebbers, S. B. Sutton, and K. S. Jancaitis, "High-average-power 1 μm performance and frequency conversion of a diode-end-pumped Yb:YAG laser," IEEE J. Quantum Electron. 34, pp. 2010-2019 (1998).
    [CrossRef]
  6. H. W. Bruesselbach, presented at the Optical Society of America 2001 Annual Meeting, Long Beach, Calif., October 14-18, 2001.
  7. T. S. Rutherford, W. M. Tulloch, E. K. Gustafson, and R. L. Byer, "Edge-pumped quasi-three-level slab lasers: design and power scaling," IEEE J. Quantum Electron. 36, 205-219 (2000).
    [CrossRef]
  8. J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser--Part I: theory," IEEE J. Quantum Electron. QE-20, 289-300 (1984).
    [CrossRef]
  9. T. J. Kane, J. M. Eggleston, and R. L. Byer, "The slab geometry laser--Part II: thermal effects in a finite slab," IEEE J. Quantum Electron. QE-21, 1195-1210 (1985).
    [CrossRef]
  10. P. Hello, E. Durand, P. K. Fritschel, and C. N. Man, "Thermal effects in Nd:YAG slabs 3D modeling and comparison with experiments," J. Mod. Opt. 41, 1371-1390 (1994).
    [CrossRef]
  11. T. S. Rutherford, W. M. Tulloch, S. Sinha, and R. L. Byer, "Yb:YAG and Nd:YAG edge-pumped slab lasers," Opt. Lett. 26, 986-988 (2001).
    [CrossRef]
  12. W. M. Tulloch, T. S. Rutherford, E. K. Gustafson, and R. L. Byer, "CW, high-power, conduction-cooled, edge-pumped slab laser," Proc. SPIE 3613, 2-7 (1999).
    [CrossRef]
  13. B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, "Thermal lensing of edge-pumped slab lasers--I," Appl. Phys. B 82, 413-418 (2006).
    [CrossRef]
  14. T. Y. Fan, "Heat generation in Nd:YAG and Yb:YAG," IEEE J. Quantum Electron. 29, 1457-1459 (1993).
    [CrossRef]
  15. M. Bass, "Modeling high-power solid-state lasers," Photonics Spectra 39, 110-112 (2005).
  16. B. Chen, Y. Chen, and M. Bass, "Edge-and end-pumped slab lasers with both efficient and uniform pumping," IEEE J. Quantum Electron. 42, 483-489 (2006).
    [CrossRef]
  17. B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, "Modeling of high power solid-state slab lasers," Proc. SPIE 4968, p. 1-10 (2003).
    [CrossRef]
  18. W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer-Verlag, 1999).
  19. D. C. Brown, "Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers," IEEE J. Quantum Electron. 33, 861-873 (1997).
    [CrossRef]
  20. R. J. Beach, "CW theory of quasi-three level end-pumped laser oscillators," Opt. Commun. 123, 385-393 (1996).
    [CrossRef]

2006

B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, "Thermal lensing of edge-pumped slab lasers--I," Appl. Phys. B 82, 413-418 (2006).
[CrossRef]

B. Chen, Y. Chen, and M. Bass, "Edge-and end-pumped slab lasers with both efficient and uniform pumping," IEEE J. Quantum Electron. 42, 483-489 (2006).
[CrossRef]

2005

M. Bass, "Modeling high-power solid-state lasers," Photonics Spectra 39, 110-112 (2005).

2003

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, "Modeling of high power solid-state slab lasers," Proc. SPIE 4968, p. 1-10 (2003).
[CrossRef]

2001

2000

T. S. Rutherford, W. M. Tulloch, E. K. Gustafson, and R. L. Byer, "Edge-pumped quasi-three-level slab lasers: design and power scaling," IEEE J. Quantum Electron. 36, 205-219 (2000).
[CrossRef]

1999

W. M. Tulloch, T. S. Rutherford, E. K. Gustafson, and R. L. Byer, "CW, high-power, conduction-cooled, edge-pumped slab laser," Proc. SPIE 3613, 2-7 (1999).
[CrossRef]

1998

C. Bibeau, R. J. Beach, S. C. Mitchell, M. A. Emanuel, J. A. Skidmore, C. A. Ebbers, S. B. Sutton, and K. S. Jancaitis, "High-average-power 1 μm performance and frequency conversion of a diode-end-pumped Yb:YAG laser," IEEE J. Quantum Electron. 34, pp. 2010-2019 (1998).
[CrossRef]

1997

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, "Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers," IEEE J. Sel. Top. Quantum Electron. 3, pp. 105-116 (1997).
[CrossRef]

D. C. Brown, "Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers," IEEE J. Quantum Electron. 33, 861-873 (1997).
[CrossRef]

1996

R. J. Beach, "CW theory of quasi-three level end-pumped laser oscillators," Opt. Commun. 123, 385-393 (1996).
[CrossRef]

1994

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, "Scalable concept for diode-pumped high power solid-state lasers," Appl. Phys. B 58, 365-372 (1994).
[CrossRef]

P. Hello, E. Durand, P. K. Fritschel, and C. N. Man, "Thermal effects in Nd:YAG slabs 3D modeling and comparison with experiments," J. Mod. Opt. 41, 1371-1390 (1994).
[CrossRef]

1993

T. Y. Fan, "Heat generation in Nd:YAG and Yb:YAG," IEEE J. Quantum Electron. 29, 1457-1459 (1993).
[CrossRef]

1989

W. F. Krupke and L. L. Chase, "Ground state depleted solid-state lasers: principles, characteristics and scaling," Opt. Quantum Electron. 22, S1-S22 (1989).
[CrossRef]

1985

T. J. Kane, J. M. Eggleston, and R. L. Byer, "The slab geometry laser--Part II: thermal effects in a finite slab," IEEE J. Quantum Electron. QE-21, 1195-1210 (1985).
[CrossRef]

1984

J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser--Part I: theory," IEEE J. Quantum Electron. QE-20, 289-300 (1984).
[CrossRef]

Appl. Phys. B

A. Giesen, H. Hugel, A. Voss, K. Witting, U. Brauch, and H. Opower, "Scalable concept for diode-pumped high power solid-state lasers," Appl. Phys. B 58, 365-372 (1994).
[CrossRef]

B. Chen, Y. Chen, J. Simmons, T. Y. Chung, and M. Bass, "Thermal lensing of edge-pumped slab lasers--I," Appl. Phys. B 82, 413-418 (2006).
[CrossRef]

IEEE J. Quantum Electron.

T. Y. Fan, "Heat generation in Nd:YAG and Yb:YAG," IEEE J. Quantum Electron. 29, 1457-1459 (1993).
[CrossRef]

C. Bibeau, R. J. Beach, S. C. Mitchell, M. A. Emanuel, J. A. Skidmore, C. A. Ebbers, S. B. Sutton, and K. S. Jancaitis, "High-average-power 1 μm performance and frequency conversion of a diode-end-pumped Yb:YAG laser," IEEE J. Quantum Electron. 34, pp. 2010-2019 (1998).
[CrossRef]

B. Chen, Y. Chen, and M. Bass, "Edge-and end-pumped slab lasers with both efficient and uniform pumping," IEEE J. Quantum Electron. 42, 483-489 (2006).
[CrossRef]

D. C. Brown, "Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers," IEEE J. Quantum Electron. 33, 861-873 (1997).
[CrossRef]

T. S. Rutherford, W. M. Tulloch, E. K. Gustafson, and R. L. Byer, "Edge-pumped quasi-three-level slab lasers: design and power scaling," IEEE J. Quantum Electron. 36, 205-219 (2000).
[CrossRef]

J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternahrer, and R. L. Byer, "The slab geometry laser--Part I: theory," IEEE J. Quantum Electron. QE-20, 289-300 (1984).
[CrossRef]

T. J. Kane, J. M. Eggleston, and R. L. Byer, "The slab geometry laser--Part II: thermal effects in a finite slab," IEEE J. Quantum Electron. QE-21, 1195-1210 (1985).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, "Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers," IEEE J. Sel. Top. Quantum Electron. 3, pp. 105-116 (1997).
[CrossRef]

J. Mod. Opt.

P. Hello, E. Durand, P. K. Fritschel, and C. N. Man, "Thermal effects in Nd:YAG slabs 3D modeling and comparison with experiments," J. Mod. Opt. 41, 1371-1390 (1994).
[CrossRef]

Opt. Commun.

R. J. Beach, "CW theory of quasi-three level end-pumped laser oscillators," Opt. Commun. 123, 385-393 (1996).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

W. F. Krupke and L. L. Chase, "Ground state depleted solid-state lasers: principles, characteristics and scaling," Opt. Quantum Electron. 22, S1-S22 (1989).
[CrossRef]

Photonics Spectra

M. Bass, "Modeling high-power solid-state lasers," Photonics Spectra 39, 110-112 (2005).

Proc. SPIE

B. Chen, J. Dong, M. Patel, Y. Chen, A. Kar, and M. Bass, "Modeling of high power solid-state slab lasers," Proc. SPIE 4968, p. 1-10 (2003).
[CrossRef]

W. M. Tulloch, T. S. Rutherford, E. K. Gustafson, and R. L. Byer, "CW, high-power, conduction-cooled, edge-pumped slab laser," Proc. SPIE 3613, 2-7 (1999).
[CrossRef]

Other

T. S. Rutherford, W. M. Tulloch, E. K. Gustafson, and R. L. Byer, "Demonstration and scaling of edge-pumped zigzag slab lasers," in Advanced Solid State Lasers, Vol. 34 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), paper MA2-1.

W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer-Verlag, 1999).

H. W. Bruesselbach, presented at the Optical Society of America 2001 Annual Meeting, Long Beach, Calif., October 14-18, 2001.

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Figures (9)

Fig. 1
Fig. 1

(a) Measured transmittance spectrum of Yb:YAG at different temperatures from 27 ° C to 300 ° C ; (b) calculated absorption spectrum of Yb:YAG at different temperatures from 27 ° C to 300 ° C .

Fig. 2
Fig. 2

Absorption cross section of Yb:YAG as a function of temperature. The indicated exponential decay fit was obtained by the least-squares method.

Fig. 3
Fig. 3

Pump and cooling configurations of an edge-pumped slab laser.

Fig. 4
Fig. 4

(a) Temperature distribution in the Yb:YAG slab along the thickness at x = 0.16 , z = 0 ; (b) Temperature distribution in the slab along the width at y = 0 , z = 0 ; initial distribution and results after iterations are shown in both figures.

Fig. 5
Fig. 5

(a) Temperature distribution in the cross section of an edge-pumped slab assuming that absorption coefficient is constant (initial distribution), with 1 kW pump power and 300 K coolant temperature; (b) temperature distribution of the slab cross section with the temperature-dependent absorption coefficient (stationary distribution after iterations); (c) absorption coefficient distribution in the slab; (d); difference between initial temperature distribution and iterated temperature distribution.

Fig. 6
Fig. 6

(a) Absorbed pump power density distribution in the slab with constant absorption coefficient (initial distribution); (b) absorbed pump power density distribution in the slab with temperature-dependent absorption coefficient (iterated distribution).

Fig. 7
Fig. 7

Pump figure of merit along the width with same product α w . The square (∎) with the discontinuous and continuous curves individually represents the initial and iterated distribution for the case α w = 1 ; the circle (●) with discontinuous and continuous curves individually represents the case for α w = 1.5 ; the pentacle (★) with discontinuous and continuous curves individually represents the case for α w = 2 .

Fig. 8
Fig. 8

Pump absorption efficiency, pump absorption uniformity, and pumping figure of merit in initial and iterated distribution for the case R p = 0.6 ; (a) as a function of the slab width with n d = 4.5 at. % ; (b) as a function of the dopant concentration with w = 0.32 cm .

Fig. 9
Fig. 9

(a) Predicted laser oscillator performance for a 1 kW edge-pumped Yb:YAG slab laser; f represents the Boltzmann population fractions ( f a , f b , f a , and f b ); (b) temperature dependence of parameters in the oscillator model.

Tables (2)

Tables Icon

Table 1 Design Parameters for Edge-Pumped Yb:YAG Slab Laser in the Numerical Computation

Tables Icon

Table 2 Laser Output Power with Different Temperature Dependence of Parameters

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

σ a = ln T n d L ,
σ a = [ 2.07 + 6.37 exp ( T 288 ) ] 10 21 cm 2 .
2 T ( x , y ) = Q ( x ) k ,
T x = 0 , for x = ± w 2 ,
k T y + λ head T = 0 , for y = t 2 ,
k T y + λ head T = 0 , for y = t 2 ,
Q ( x ) = η h ρ abs ( x ) = η h α P p t L exp ( α w 2 ) 1 R p e α w cos h ( α x ) ,
T ( x , y ) = T c + Q 0 t 2 8 k ( 1 + 4 k λ head t ( 2 y t ) 2 ) + 2 Q 0 t n = 1 ( 1 ) n β n 2 ( α w ) 2 ( α w ) 2 + 4 n 2 π 2 [ 1 cosh ( β n y ) k β n λ head sinh ( β n t 2 ) + cos h ( β n t 2 ) ] cos ( β n x ) ,
η abs = 1 exp ( α w ) 1 R p exp ( α w )
k ( T ) = a ( ln ( b T ) ) c d T ,
ρ abs ( x ) = α P p t L exp ( α w 2 ) 1 R p exp ( α w ) cosh ( α x ) ,
η abs = t L w 2 w 2 ρ abs ( x ) d x P p = 1 exp ( α w ) 1 R p exp ( α w ) .
U = ρ abs ( 0 ) ρ abs ( w 2 ) = sech ( α w 2 ) ,
F = U η abs = 1 exp ( α w ) 1 R p exp ( α w ) sech ( α w 2 ) .
α = α 0 1 1 + ( I 0 I sat ) ,
P out = η slope ( η abs P p P 0 ) ,
η slope = η mod e ν L ν P 1 R oc 1 R oc + R oc ( 1 1 δ + δ 1 ) ,
η abs = 1 e σ a Δ n eff w 1 R P e σ a Δ n eff w ,
P 0 = h ν P τ w t L n U ,
n U = 1 2 f β σ e l eff ln [ 1 R oc ( 1 δ ) 2 ] + f a f n d ,
Δ n eff = f a n d ( f a + f b ) n U = f a f f a f f n d f f 1 2 β σ e l eff ln [ 1 R oc ( 1 δ ) 2 ] ,
f a = exp ( E a l k T ) i exp ( E i k T ) , f b = exp ( E b l k T ) j exp ( E j k T ) ,
f a = exp ( E a p k T ) i exp ( E i k T ) , f b = exp ( E b p k T ) j exp ( E j k T ) ,
σ e = 0.95334 + 33.608 exp ( T 92.82465 ) 10 20 cm 2 .

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