Abstract

We have studied the amplification characteristics of a cryogenically cooled Yb3+:YAG total-reflection active-mirror (TRAM) ceramic laser including wavefront distortion, birefringence loss, small signal gain (SSG), and temperature rise for developing high-performance master oscillator power amplifier (MOPA) systems. A 0.6 mm thick Yb3+:YAG ceramic sample was used, and maximum pump intensity 10kW/cm2 was reached. The transmitted wavefront was measured by using a Shack–Hartmann wavefront sensor, and we evaluated the thermal lens focal length and Strehl ratio for different pump conditions. We have also observed a butterfly-like leakage profile of thermally induced birefringence loss at the maximum pump intensity. From SSG measurements, we obtained moderate laser gain of G=3 for one bounce with a near aberration-free wavefront. Gain calculations, which included also temperature dependence of the emission cross section and reabsorption of Yb3+:YAG, were in good agreement with the experiments. These experimental results will be useful as benchmark data for numerical simulations of temperature distribution in TRAM and for designing multikilowatt-class high-performance MOPA systems.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013

2012

2011

2010

D. Harvilla and R. Brockmann, “Latest advances in high power disk lasers,” Proc. SPIE 7578, 75780C (2010).

2009

2008

2007

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

2005

S. Tokita, J. Kawanaka, M. Fujita, T. Kawashima, and Y. Izawa, “Sapphire-conductive end-cooling of high power cryogenic Yb:YAG lasers,” Appl. Phys. B 80, 635–638 (2005).
[CrossRef]

2004

S. Chenais, F. Balembois, F. Druon, G. L. Leclin, and P. Georges, “Thermal lensing in diode-pumped ytterbium lasers—part I: theoretical analysis and wavefront measurements,” IEEE J. Quantum Electron. 40, 1217–1234 (2004).
[CrossRef]

2003

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

J. Dong, M. Bass, Y. Mao, P. Deng, and F. Gan, “Dependence of the Yb3+ emission cross section and lifetime on temperature and concentration in yttrium aluminum garnet,” J. Opt. Soc. Am. B 20, 1975–1979 (2003).
[CrossRef]

1999

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Electron. 29, 697–703 (1999).
[CrossRef]

1994

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

1990

K. Okuyama and Y. Iida, “Transient boiling heat transfer characteristics of nitrogen (bubble behavior and heat transfer rate at stepwise heat generation),” Int. J. Heat Mass Transf. 33, 2065–2071 (1990).
[CrossRef]

Aka, G. P.

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

Albach, D.

Asman, C. P.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Balembois, F.

S. Chenais, F. Balembois, F. Druon, G. L. Leclin, and P. Georges, “Thermal lensing in diode-pumped ytterbium lasers—part I: theoretical analysis and wavefront measurements,” IEEE J. Quantum Electron. 40, 1217–1234 (2004).
[CrossRef]

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

Bass, M.

Bisson, J. F.

Brauch, U.

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

Brockmann, R.

D. Harvilla and R. Brockmann, “Latest advances in high power disk lasers,” Proc. SPIE 7578, 75780C (2010).

Burchman, D.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Chanteloup, J. C.

Chenais, S.

S. Chenais, F. Balembois, F. Druon, G. L. Leclin, and P. Georges, “Thermal lensing in diode-pumped ytterbium lasers—part I: theoretical analysis and wavefront measurements,” IEEE J. Quantum Electron. 40, 1217–1234 (2004).
[CrossRef]

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

Chosrowjan, H.

Contag, K.

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Electron. 29, 697–703 (1999).
[CrossRef]

Deng, P.

Dong, J.

Druon, F.

S. Chenais, F. Balembois, F. Druon, G. L. Leclin, and P. Georges, “Thermal lensing in diode-pumped ytterbium lasers—part I: theoretical analysis and wavefront measurements,” IEEE J. Quantum Electron. 40, 1217–1234 (2004).
[CrossRef]

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

Fichot, Y.

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

Fomin, V.

V. Gapontsev, V. Fomin, and A. Yusim, “Recent progress in scaling high power fiber lasers at IPG photonics,” presented at the 22nd Annual Solid State and Diode Laser Technology Review, Newton, Massachusetts, June29–July 2 (2009).

Fujita, M.

Furuse, H.

Gan, F.

Gapontsev, V.

V. Gapontsev, V. Fomin, and A. Yusim, “Recent progress in scaling high power fiber lasers at IPG photonics,” presented at the 22nd Annual Solid State and Diode Laser Technology Review, Newton, Massachusetts, June29–July 2 (2009).

Gaume, R.

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

Georges, P.

S. Chenais, F. Balembois, F. Druon, G. L. Leclin, and P. Georges, “Thermal lensing in diode-pumped ytterbium lasers—part I: theoretical analysis and wavefront measurements,” IEEE J. Quantum Electron. 40, 1217–1234 (2004).
[CrossRef]

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

Giesen, A.

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Electron. 29, 697–703 (1999).
[CrossRef]

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

Harvilla, D.

D. Harvilla and R. Brockmann, “Latest advances in high power disk lasers,” Proc. SPIE 7578, 75780C (2010).

Hugel, H.

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Electron. 29, 697–703 (1999).
[CrossRef]

Hügel, H.

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

Iida, Y.

K. Okuyama and Y. Iida, “Transient boiling heat transfer characteristics of nitrogen (bubble behavior and heat transfer rate at stepwise heat generation),” Int. J. Heat Mass Transf. 33, 2065–2071 (1990).
[CrossRef]

Imasaki, K.

Injeyan, H.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Ishii, S.

Izawa, Y.

Jankevics, A.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Johnson, A. M. F.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Jones, G. C.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Karszewski, M.

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Electron. 29, 697–703 (1999).
[CrossRef]

Kawanaka, J.

Kawashima, T.

S. Tokita, J. Kawanaka, M. Fujita, T. Kawashima, and Y. Izawa, “Sapphire-conductive end-cooling of high power cryogenic Yb:YAG lasers,” Appl. Phys. B 80, 635–638 (2005).
[CrossRef]

Komine, H.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Kouznetsov, D.

Leclin, G. L.

S. Chenais, F. Balembois, F. Druon, G. L. Leclin, and P. Georges, “Thermal lensing in diode-pumped ytterbium lasers—part I: theoretical analysis and wavefront measurements,” IEEE J. Quantum Electron. 40, 1217–1234 (2004).
[CrossRef]

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

LeTouze, G.

Machan, J.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Mao, Y.

Marmo, J.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

McClellan, M.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

McNaught, S. J.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Miyanaga, N.

Okuyama, K.

K. Okuyama and Y. Iida, “Transient boiling heat transfer characteristics of nitrogen (bubble behavior and heat transfer rate at stepwise heat generation),” Int. J. Heat Mass Transf. 33, 2065–2071 (1990).
[CrossRef]

Opower, H.

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

Saiki, T.

Simpson, R.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Sollee, J.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Speiser, J.

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13, 598–609 (2007).
[CrossRef]

Stewen, C.

K. Contag, M. Karszewski, C. Stewen, A. Giesen, and H. Hugel, “Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser,” Quantum Electron. 29, 697–703 (1999).
[CrossRef]

Takeshita, K.

Tokita, S.

S. Tokita, J. Kawanaka, M. Fujita, T. Kawashima, and Y. Izawa, “Sapphire-conductive end-cooling of high power cryogenic Yb:YAG lasers,” Appl. Phys. B 80, 635–638 (2005).
[CrossRef]

Valley, M. M.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Viana, B.

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

Vivien, D.

S. Chenais, F. Druon, F. Balembois, G. L. Leclin, Y. Fichot, P. Georges, R. Gaume, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[CrossRef]

Voss, A.

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

Weber, M.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Weiss, S. B.

S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

Wittig, K.

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

Yusim, A.

V. Gapontsev, V. Fomin, and A. Yusim, “Recent progress in scaling high power fiber lasers at IPG photonics,” presented at the 22nd Annual Solid State and Diode Laser Technology Review, Newton, Massachusetts, June29–July 2 (2009).

Appl. Phys. B

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S. J. McNaught, H. Komine, S. B. Weiss, R. Simpson, A. M. F. Johnson, J. Machan, C. P. Asman, M. Weber, G. C. Jones, M. M. Valley, A. Jankevics, D. Burchman, M. McClellan, J. Sollee, J. Marmo, and H. Injeyan, “100  kW coherently combined slab MOPAs,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2009), paper CThA1.

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Figures (9)

Fig. 1.
Fig. 1.

Experimental setup for wavefront measurements. HR, high reflection mirror; GTP, Glan–Thompson polarizer; DM, dichroic mirror; LN2, liquid nitrogen.

Fig. 2.
Fig. 2.

Wavefront distortion of 0.6 mm thick TRAM at 450 W pump power for pump spot diameter of 4 mm.

Fig. 3.
Fig. 3.

Zernike polynomials at several pump intensities for 4 mm pump beam diameter.

Fig. 4.
Fig. 4.

Thermal lens focal length estimated from the defocus components of Zernike polynomials for 2.4, 4, and 6 mm pump beam diameters, respectively. Solid line is a fitting curve of all experimental data below 700W/cm2 pump intensities. Dashed lines are fitting curves at higher pump intensities corresponding to different pump beam sizes.

Fig. 5.
Fig. 5.

Strehl ratio evaluated from Zernike polynomials as a function of the pump intensity for 2.4, 4, and 6 mm pump beam diameters, respectively. The defocus component was ignored in the presented evaluations.

Fig. 6.
Fig. 6.

Thermally induced depolarization of 0.6 mm thick TRAM sample for 2.4, 4, and 6 mm pump beam diameters. The inset shows the leakage pattern at 450 W pump power for 2.4 mm pump beam diameter.

Fig. 7.
Fig. 7.

Experimental setup for single-pass amplification. SP, spectrometer; HR, high-reflection mirror; AP, aperture; DM, dichroic mirror; PD, photodiode.

Fig. 8.
Fig. 8.

SSG for one bounce and inferred Yb:YAG temperature as a function of pump power for 4 mm pump beam diameter. Circles and triangles show the experimental and calculated results of the SSG, respectively. In the calculations inferred temperature (squares) was used for evaluating gain and reabsorption coefficients.

Fig. 9.
Fig. 9.

M2-fit data of the seed (w/o pump) and amplified beams at pump power of 280 W and 4 mm pump beam diameter (2.2kW/cm2 pump intensity). The inset shows the far field pattern (FFP) of amplified signal.

Equations (4)

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|f|=rp243λZdef,
G=exp[(g0(T)α0(T))l],
g0(T)=σemi(T)τfηtηQηSηaηBPV1hν,
α0(T)=σemi(T)flN0.

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