Abstract

A detailed 3-dimensional calculation of the temperature field of a laser crystal pumped with high average power is presented. The pump configuration, the anisotropy of a Brewster-angle-cut Ti:Sapphire crystal, and the temperature dependence of the thermal conductivity are taken into account. The corresponding focal length of the thermal lens is calculated for pump levels up to 100 W. This refined thermal model is the basis for a optimized resonator design of a high-average power differential absorption lidar system transmitter.

© 2005 Optical Society of America

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References

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  1. M. Endemann, P. Dubock, P. Ingmann, R. Wimmer, D. Morancais and D. Demuth, �??The ADM-Aelous Mission - The First Wind-Lidar In Space,�?? in Reviewed and Revised Papers Presented at the 22nd International Laser Radar Conference, ILRC 2004, Matera, Italy, G. Pappalardo, A. Amodeo, eds. (ESA Publication Division, ESTEC, Noordwijk, The Netherlands, 2004), pp. 953�??956.
  2. V. Wulfmeyer, H. Bauer, P. Di Girolamo and C. Serio, �??Comparison of active and passive water vapor remote sensing from space: An analysis based on the simulated performance of IASI and space borne differential absorption lidar,�?? Remote Sens. Environ. 95, 211�??230 (2005).
    [CrossRef]
  3. P. Di Girolamo, A. Behrendt and V. Wulfmeyer, �??Pure rotational Raman lidar measurements of atmospheric temperature, relative humidity and extinction from space: performance simulations,�?? submitted to Appl. Opt. (2005).
  4. National Science Foundation (NSF, USA) and National Center for Atmospheric Research (NCAR, USA), �??HIAPER - High-Performance Instrumented Airborne Platform for Enviromental Research,�?? Project Office Home Page, <a href="http://www.hiaper.ucar.edu/">http://www.hiaper.ucar.edu/</a>.
  5. German aerospace center (DLR), �??HALO - High Altitude and Long Range Research Aircraft,�?? Project Office Home Page, <a href="http://www.pa.op.dlr.de/halo/">http://www.pa.op.dlr.de/halo/</a>.
  6. V. Wulfmeyer, �??Ground-based differential absorption lidar for water-vapor and temperature profiling: development and specifications of a high-performance laser transmitter,�?? Appl. Opt. 37, 304�??324 (1998).
    [CrossRef]
  7. V. Wulfmeyer, H.-S. Bauer, S. Crewell, G. Ehret, O. Reitebuch, C. Werner, M. Wirth, D. Engelbart, A. Rhodin, W. Wergen, A. Giesen, H. Grassl, G. Huber, H. Klingenberg, P. Mahnke, U. Kummer, C. Wührer, P. Ritter, R. Wallenstein and U. Wandinger, �??Lidar Research NetworkWater Vapor andWind,�?? Meteorol. Z. 12, 5�??24 (2003).
    [CrossRef]
  8. ESA, �??WALES - WAter vapour Lidar Experiment in Space,�?? in ESA SP-1257(2) - Report for Assessment, P. Ingmann and A. Hélière, eds. (ESA Publication Division, ESTEC, Noordwijk, The Netherlands, 2001)
  9. A. Behrendt, �??Temperature Measurements with Lidar,�?? in Lidar - Range Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer Series in Optical Sciences 102, New York, 2005), pp. 273�??305.
  10. M. Ostermeyer, P. Kappe, R. Menzel and V. Wulfmeyer, �??Diode-pumped Nd:YAG master oscillator power amplifier with high pulse energy, excellent beam quality, and frequency-stabilized master oscillator as a basis for a next-generation lidar system,�?? Appl. Opt. 44, 582�??590 (2005).
    [CrossRef] [PubMed]
  11. A. Suda, A. Kadoi, K. Nagasaka, H, Tashiro and K. Midorikawa, �??Absorption and Oscillation Characteristics of a Pulsed Cr4+:YAG Laser Investigated by a Double-Pulse Pumping Technique,�?? IEEE J. Quantum Electron. 35, 1548�??1553 (1999).
    [CrossRef]
  12. P. F. Moulton, �??Spectroscopic and laser characteristics of Ti:Al2O3,�?? J. Opt. Soc. Am. B 3, 125�??133 (1986).
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  13. Recommended values of �??Thermal Conductivity of Aluminium Oxide (Sapphire),�?? in Thermophysical Properties of Matter, Y. S. Touloukian and C. Y. Ho, eds. (IFI/Plenum TPRC Data Series 2, New York, 1972), pp. 93�??97.
  14. R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos and H. P. Weber, �??Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,�?? IEEE J. Quantum Electron. 34, 1047�??1053 (1998).
    [CrossRef]
  15. F. P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer (John Wiley & Sons, Hoboken (NJ), 2002)
  16. K. Frauchiger, P. Albers and H. P. Weber, �??Modeling of Thermal Lensing and Higher Order Ring Mode Oscillation in End-Pumped CW Nd:YAG Lasers,�?? IEEE J. Quantum Electron. 28, 1046�??1056 (1992).
    [CrossRef]
  17. M. E. Innocenzi, H. T. Yura, C. L. Fincher and R. A. Fields, �??Thermal Modeling of Continous-Wave End-Pumped Solid-State Lasers,�?? Appl. Phys. Lett. 56, 1831�??1833 (1990).
    [CrossRef]
  18. W. Koechner, �??Thermo-Optic Effects and Heat Removal,�?? in Solid-State Laser Engineering, A. L. Schawlow, A. E. Siegman and T. Tamir, eds. (Springer Series in Optical Sciences 1, New York, 1999), pp. 406�??468.
  19. N.W. Rimington, S. L. Schieffer,W. A. Schroeder and B. K. Brikeen, �??Thermal lens shaping in a Brewster-Gain Media: A high-power, diode-pumped Nd:GdVO4 laser�?? Opt. Express 12, 1426�??1436 (2004).
    [CrossRef] [PubMed]
  20. A. E. Siegman, �??Ray Optics and Ray Matrices,�?? in Lasers, A. Kelly, ed. (University Science Books, Sausalito (CA), 1986), pp. 581�??625.

Appl. Opt.

P. Di Girolamo, A. Behrendt and V. Wulfmeyer, �??Pure rotational Raman lidar measurements of atmospheric temperature, relative humidity and extinction from space: performance simulations,�?? submitted to Appl. Opt. (2005).

V. Wulfmeyer, �??Ground-based differential absorption lidar for water-vapor and temperature profiling: development and specifications of a high-performance laser transmitter,�?? Appl. Opt. 37, 304�??324 (1998).
[CrossRef]

M. Ostermeyer, P. Kappe, R. Menzel and V. Wulfmeyer, �??Diode-pumped Nd:YAG master oscillator power amplifier with high pulse energy, excellent beam quality, and frequency-stabilized master oscillator as a basis for a next-generation lidar system,�?? Appl. Opt. 44, 582�??590 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett.

M. E. Innocenzi, H. T. Yura, C. L. Fincher and R. A. Fields, �??Thermal Modeling of Continous-Wave End-Pumped Solid-State Lasers,�?? Appl. Phys. Lett. 56, 1831�??1833 (1990).
[CrossRef]

ESA SP-1257(2)

ESA, �??WALES - WAter vapour Lidar Experiment in Space,�?? in ESA SP-1257(2) - Report for Assessment, P. Ingmann and A. Hélière, eds. (ESA Publication Division, ESTEC, Noordwijk, The Netherlands, 2001)

IEEE J. Quantum Electron.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos and H. P. Weber, �??Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,�?? IEEE J. Quantum Electron. 34, 1047�??1053 (1998).
[CrossRef]

A. Suda, A. Kadoi, K. Nagasaka, H, Tashiro and K. Midorikawa, �??Absorption and Oscillation Characteristics of a Pulsed Cr4+:YAG Laser Investigated by a Double-Pulse Pumping Technique,�?? IEEE J. Quantum Electron. 35, 1548�??1553 (1999).
[CrossRef]

K. Frauchiger, P. Albers and H. P. Weber, �??Modeling of Thermal Lensing and Higher Order Ring Mode Oscillation in End-Pumped CW Nd:YAG Lasers,�?? IEEE J. Quantum Electron. 28, 1046�??1056 (1992).
[CrossRef]

Int'l Laser Radar Conference 2004

M. Endemann, P. Dubock, P. Ingmann, R. Wimmer, D. Morancais and D. Demuth, �??The ADM-Aelous Mission - The First Wind-Lidar In Space,�?? in Reviewed and Revised Papers Presented at the 22nd International Laser Radar Conference, ILRC 2004, Matera, Italy, G. Pappalardo, A. Amodeo, eds. (ESA Publication Division, ESTEC, Noordwijk, The Netherlands, 2004), pp. 953�??956.

J. Opt. Soc. Am. B

Lasers

A. E. Siegman, �??Ray Optics and Ray Matrices,�?? in Lasers, A. Kelly, ed. (University Science Books, Sausalito (CA), 1986), pp. 581�??625.

Lidar - Range Resolved Optical Remote Se

A. Behrendt, �??Temperature Measurements with Lidar,�?? in Lidar - Range Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer Series in Optical Sciences 102, New York, 2005), pp. 273�??305.

Meteorol. Z.

V. Wulfmeyer, H.-S. Bauer, S. Crewell, G. Ehret, O. Reitebuch, C. Werner, M. Wirth, D. Engelbart, A. Rhodin, W. Wergen, A. Giesen, H. Grassl, G. Huber, H. Klingenberg, P. Mahnke, U. Kummer, C. Wührer, P. Ritter, R. Wallenstein and U. Wandinger, �??Lidar Research NetworkWater Vapor andWind,�?? Meteorol. Z. 12, 5�??24 (2003).
[CrossRef]

Opt. Express

Remote Sens. Environ.

V. Wulfmeyer, H. Bauer, P. Di Girolamo and C. Serio, �??Comparison of active and passive water vapor remote sensing from space: An analysis based on the simulated performance of IASI and space borne differential absorption lidar,�?? Remote Sens. Environ. 95, 211�??230 (2005).
[CrossRef]

Solid-State Laser Engineering

W. Koechner, �??Thermo-Optic Effects and Heat Removal,�?? in Solid-State Laser Engineering, A. L. Schawlow, A. E. Siegman and T. Tamir, eds. (Springer Series in Optical Sciences 1, New York, 1999), pp. 406�??468.

Thermophysical Properties of Matter

Recommended values of �??Thermal Conductivity of Aluminium Oxide (Sapphire),�?? in Thermophysical Properties of Matter, Y. S. Touloukian and C. Y. Ho, eds. (IFI/Plenum TPRC Data Series 2, New York, 1972), pp. 93�??97.

Other

F. P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer (John Wiley & Sons, Hoboken (NJ), 2002)

National Science Foundation (NSF, USA) and National Center for Atmospheric Research (NCAR, USA), �??HIAPER - High-Performance Instrumented Airborne Platform for Enviromental Research,�?? Project Office Home Page, <a href="http://www.hiaper.ucar.edu/">http://www.hiaper.ucar.edu/</a>.

German aerospace center (DLR), �??HALO - High Altitude and Long Range Research Aircraft,�?? Project Office Home Page, <a href="http://www.pa.op.dlr.de/halo/">http://www.pa.op.dlr.de/halo/</a>.

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Figures (9)

Fig. 1.
Fig. 1.

Cooler of two-side pumped Titanium-Sapphire crystal.

Fig. 2.
Fig. 2.

2-d cross-section through the calculated 3-d temperature field of a plane-parallel crystal pumped with 25 W each side.

Fig. 3.
Fig. 3.

2-d cross-section through the calculated 3-d temperature field of Brewster-cut crystal pumped with 25 W each side.

Fig. 4.
Fig. 4.

Calculated temperature at center towards surface for Brewster-cut crystal. The temperature distribution for both planes is nearly the same at crystal center.

Fig. 5.
Fig. 5.

Calculated temperature along the optical axis of the crystal for Brewster-cut crystal.

Fig. 6.
Fig. 6.

Calculated temperature (blue line) and its parabolic approximation (red line).

Fig. 7.
Fig. 7.

Calculated focal lengths of thermal lens for Brewster-cut crystal.

Fig. 8.
Fig. 8.

Sagittal and tangential plane beam propagation of a high-power Ti:Sapphire ring resonator.

Fig. 9.
Fig. 9.

Stability zone of a high-power Ti:Sapphire ring resonator.

Tables (1)

Tables Icon

Table 1. WALES mission requirements for laser transmitter.

Equations (18)

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E Fl , sat = h ν σ gs ,
α = n 0 σ g s ,
η = E photon , 532 nm E photon , 935 nm E photon , 532 nm = 1 h ν 935 h ν 532 ,
[ κ ( T ( x , y , z , t ) ) T ( x , y , z , t ) ] = H ( x , y , z , t )
H ( x , y , z , t ) = p ( t ) 2 η P π ω p 2 α 1 exp ( α l ) exp ( 2 x 2 ω p 2 ) exp ( 2 y 2 ω p 2 )
× [ exp ( α z ) + exp ( α ( z l ) ) ] .
M t , T L = M T 2 M T L x , i = m M T L x , i = 1 M T 1
= ( 1 n 0 cos Θ B n sin Θ B cos Θ B sin Θ B R x n ) ( cos b x , i ( d n x , i ) ( sin b x , i b x , i ) ( n x , i d ) b x , i sin b x , i cos b x , i ) i = 1 m
( n 0 n sin Θ B cos Θ B cos Θ B sin Θ B R x 1 n )
M s , T L = M S 2 M T L y , i = m M T L y , i = 1 M S 1
= ( 1 0 n sin Θ B cos Θ B R y 1 ) ( cos b y , i ( d n y , i ) ( sin b y , i b y , i ) ( n y , i d ) b y , i sin b y , i cos b y , i ) i = 1 m
( 1 0 cos Θ B n sin Θ B R y 1 )
b [ x , y ] , i = d 2 γ [ x , y ] , i n [ x , y ] , i .
M t , T L , R x = = ( 1 n 0 0 n ) ( cos b x , i ( d n x , i ) ( sin b x , i b x , i ) ( n x , i d ) b x , i sin b x , i cos b x , i ) i = 1 m
( n 0 0 1 n )
M s , T L , R y = = ( 1 0 0 1 ) ( cos b y , i ( d n y , i ) ( sin b y , i b y , i ) ( n y , i d ) b y , i sin b y , i cos b y , i ) i = 1 m
( 1 0 0 1 )
b [ x , y ] , i = d 2 γ [ x , y ] , i n [ x , y ] , i .

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