Abstract

A theoretical model of continuous-wave Yb3+-doped microchip lasers based on a quasi-four-level system is proposed, and it is applied to the Yb:YAG microchip laser. The theoretical results of calculations are in agreement with those of experiments. Several ways to improve the properties of Yb3+-doped microchip lasers are described. This model is applicable not only to Yb3+-doped microchip lasers but also to other quasi-four-level microchip lasers.

© 2003 Optical Society of America

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  1. P. Wang, J. M. Dawes, P. Dekker, and J. A. Piper, “Highly efficient diode-pumped ytterbium-doped yttrium aluminum borate laser,” Opt. Commun. 174, 467–470 (2000).
    [CrossRef]
  2. A. Brenier and G. Boulon, “Overview of the best Yb3+-doped laser crystals,” J. Alloys Compd. 323–324, 210–213 (2001).
    [CrossRef]
  3. H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
    [CrossRef]
  4. P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
    [CrossRef]
  5. F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37, 135–144 (2001).
    [CrossRef]
  6. P. Yang, P. Deng, J. Xu, and Z. Yin, “Growth of high doping Yb:YAG and its laser performance,” J. Chin. Ceram. Soc. 28, 566–569 (2000).
  7. V. V. Ter-Mikirtychev and V. A. Fromzel, “Directly single-mode-pumped continuous-wave Yb3+:YAG laser tunable in the 1047–1051-nm wavelength range,” Appl. Opt. 39, 4964–4969 (2000).
    [CrossRef]
  8. T. Kasamatsu, H. Sekita, and Y. Kuwano, “Temperature dependence and optimization of 970-nm diode-pumped Yb:YAG and Yb:LuAG lasers,” Appl. Opt. 38, 5149–5153 (1999).
    [CrossRef]
  9. P. Yang, P. Deng, J. Xu, W. Chen, J. Qiao, and G. Huang, “Spectroscopy and laser performance of Yb3+ doped YAG crystal,” Acta Opt. Sin. 19, 132–135 (1999).
  10. P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Efficient output of a Ti:sapphire laser pumped Yb:YAG thin chip cw laser at 1.053 μm,” Chin. J. Lasers 26, 865–868 (1999).
  11. P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Ti:sapphire pumped 10-at. % Yb:YAG thin chip with 320-mW cw laser output of 1.053 μm,” Chin. J. Lasers 9, 8–10 (2000).
  12. H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
    [CrossRef]
  13. H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
    [CrossRef]
  14. K. I. Schaffers, L. D. Deloach, and S. A. Payne, “Crystal growth, frequency doubling, and infrared laser performance of Yb3+:BaCaBO3F,” IEEE J. Quantum Electron. 32, 741–748 (1996).
    [CrossRef]
  15. A. A. Lagatsky, A. Abdolvand, and N. V. Kuleshov, “Passive Q switching and self-frequency Raman conversion in a diode-pumped Yb:KGd(WO4)2 laser,” Opt. Lett. 25, 616–618 (2000).
    [CrossRef]
  16. F. Brunner, G. J. Spuhler, J. Aus der Au, L. Krainer, F. Morier-Genoud, R. Paschotta, N. Lichtenstein, S. Weiss, C. Harder, A. A. Lagatsky, A. Abdolvand, N. V. Kuleshov, and U. Keller, “Diode-pumped femtosecond Yb:KGd(WO4)2 laser with 1.1-W average power,” Opt. Lett. 25, 1119–1121 (2000).
    [CrossRef]
  17. F. Druon, F. Balembois, P. Georges, A. Brun, A. Courjaud, C. Honninger, F. Salin, A. Aron, F. Mougel, G. Aka, and D. Vivien, “Generation of 90-fs pulses from a mode-locked diode-pumped Yb3+:Ca4GdO(BO3)3 laser,” Opt. Lett. 25, 423–425 (2000).
    [CrossRef]
  18. E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
    [CrossRef]
  19. E. Montoya, J. Capmany, L. E. Bausa, T. Kellner, A. Diening, and G. Huber, “Infrared and self-frequency doubled laser action in Yb3+-doped LiNbO3:MgO,” Appl. Phys. Lett. 74, 3113–3115 (1999).
    [CrossRef]
  20. A. N. P. Bustamante, D. A. Hammons, R. E. Peale, B. H. T. Chai, M. Richardson, and A. Chin, “Simultaneous cw dual-wavelength laser action and tunability performance of diode-pumped Yb3+:Sr5(VO4)3F,” Opt. Commun. 192, 309–313 (2001).
    [CrossRef]
  21. L. D. Deloach, S. A. Payne, L. K. Smith, W. L. Kway, and W. F. Krupke, “Laser and spectroscopic properties of Sr5(PO4)3F:Yb,” J. Opt. Soc. Am. B 11, 269–276 (1994).
    [CrossRef]
  22. C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
    [CrossRef]
  23. J. J. Zayhowski and A. Mooradian, “Single-frequency microchip Nd lasers,” Opt. Lett. 14, 24–26 (1989).
    [CrossRef] [PubMed]
  24. N. Pavel, J. Saikawa, S. Kurimura, and Taira, “Microchip high power radially pumped composite Yb:YAG laser,” in ROMOPTO 2000: Sixth Conference on Optics, V.I. Vlad, ed., Proc. SPIE 4430, 27–34 (2001).
    [CrossRef]
  25. P. Laporta, S. Longhi, G. Sorbello, S. Taccheo, and C. Svelto, “Erbium-ytterbium miniaturized laser devices for optical communications,” in Rare-Earth-Doped Materials and Devices III, S. Jiang and S. Honkanen, eds., Proc. SPIE 3622, 82–91 (1999).
    [CrossRef]
  26. A. Chardon, F. Sanchez, and G. M. Stephan, “Polarization switching of an Er.Yb:Cr:phosphate glass microchip laser,” Ann. Telecommun. 52, 588–593 (1997).
  27. N. Pavel, J. Saikawa, S. Kurimura, and T. Taira, “Continuous-wave diode radial-pumped composite Yb:YAG laser,” in Proceedings of the International Conference on Lasers 2000, V. J. Corcoran and T. A. Corcoran, eds. (STS Press, McLean, Va., pp. 790–795.
  28. H. Hu and L. Zhang, “A new microlaser material rare-earth doped glasses,” J. Chin. Ceram. Soc. 29, 460–465 (2001).
  29. T. Y. Fan and R. L. Byer, “Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron. QE-23, 605–612 (1987).
  30. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5, 1412–1423 (1988).
    [CrossRef]
  31. A. Brenier, “A new evaluation of Yb3+-doped crystals for laser applications,” J. Lumin. 92, 199–204 (2001).
    [CrossRef]
  32. G. L. Bourdet, “Gain and absorption saturation coupling in end pumped Tm:YVO4 and Tm, Ho:YLF cw amplifiers,” Opt. Commun. 173, 333–340 (2000).
    [CrossRef]
  33. G. L. Bourdet, “Theoretical investigation of quasi-three-level longitudinally pumped continuous wave lasers,” Appl. Opt. 39, 966–971 (2000).
    [CrossRef]
  34. G. L. Bourdet and G. Lescroart, “Theoretical modeling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
    [CrossRef]
  35. G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
    [CrossRef]
  36. A. J. Alfrey, “Modeling of longitudinally pumped cw Ti:sapphire laser oscillators,” IEEE J. Quantum Electron. 25, 760–766 (1989).
    [CrossRef]
  37. Y. Zhou, X. Chen, D. Tang, Z. Luo, and W. Yang, “Investigation of the spectroscopic properties of acentric orthorhombic Nd3+:Gd2(MoO4)3 crystals,” Opt. Commun. 167, 99–104 (1999).
    [CrossRef]
  38. N. MacKinnon and B. D. Sinclair, “Pump power induced cavity stability in lithium neodymium tetraphosphate (LNP) microchip lasers,” Opt. Commun. 94, 281–288 (1992).
    [CrossRef]
  39. C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
    [CrossRef]
  40. R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11, 245–254 (1999).
    [CrossRef]
  41. Z. Luo and Y. Huang, “An empirical relationship between laser threshold and chemical composition of laser crystals,” Opt. Commun. 206, 159–164 (2002).
    [CrossRef]
  42. T. Omatsu, Y. Kato, M. Shimosegawa, A. Hasegawa, and I. Ogura, “Thermal effects in laser diode pumped self-frequency-doubled NdxY1−xAl3(BO3)4 (NYAB) microchip laser,” Opt. Commun. 118, 302–308 (1995).
    [CrossRef]

2002 (3)

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
[CrossRef]

P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
[CrossRef]

Z. Luo and Y. Huang, “An empirical relationship between laser threshold and chemical composition of laser crystals,” Opt. Commun. 206, 159–164 (2002).
[CrossRef]

2001 (7)

A. Brenier, “A new evaluation of Yb3+-doped crystals for laser applications,” J. Lumin. 92, 199–204 (2001).
[CrossRef]

H. Hu and L. Zhang, “A new microlaser material rare-earth doped glasses,” J. Chin. Ceram. Soc. 29, 460–465 (2001).

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37, 135–144 (2001).
[CrossRef]

A. N. P. Bustamante, D. A. Hammons, R. E. Peale, B. H. T. Chai, M. Richardson, and A. Chin, “Simultaneous cw dual-wavelength laser action and tunability performance of diode-pumped Yb3+:Sr5(VO4)3F,” Opt. Commun. 192, 309–313 (2001).
[CrossRef]

N. Pavel, J. Saikawa, S. Kurimura, and Taira, “Microchip high power radially pumped composite Yb:YAG laser,” in ROMOPTO 2000: Sixth Conference on Optics, V.I. Vlad, ed., Proc. SPIE 4430, 27–34 (2001).
[CrossRef]

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

A. Brenier and G. Boulon, “Overview of the best Yb3+-doped laser crystals,” J. Alloys Compd. 323–324, 210–213 (2001).
[CrossRef]

2000 (10)

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Ti:sapphire pumped 10-at. % Yb:YAG thin chip with 320-mW cw laser output of 1.053 μm,” Chin. J. Lasers 9, 8–10 (2000).

P. Wang, J. M. Dawes, P. Dekker, and J. A. Piper, “Highly efficient diode-pumped ytterbium-doped yttrium aluminum borate laser,” Opt. Commun. 174, 467–470 (2000).
[CrossRef]

P. Yang, P. Deng, J. Xu, and Z. Yin, “Growth of high doping Yb:YAG and its laser performance,” J. Chin. Ceram. Soc. 28, 566–569 (2000).

E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
[CrossRef]

G. L. Bourdet, “Gain and absorption saturation coupling in end pumped Tm:YVO4 and Tm, Ho:YLF cw amplifiers,” Opt. Commun. 173, 333–340 (2000).
[CrossRef]

F. Druon, F. Balembois, P. Georges, A. Brun, A. Courjaud, C. Honninger, F. Salin, A. Aron, F. Mougel, G. Aka, and D. Vivien, “Generation of 90-fs pulses from a mode-locked diode-pumped Yb3+:Ca4GdO(BO3)3 laser,” Opt. Lett. 25, 423–425 (2000).
[CrossRef]

A. A. Lagatsky, A. Abdolvand, and N. V. Kuleshov, “Passive Q switching and self-frequency Raman conversion in a diode-pumped Yb:KGd(WO4)2 laser,” Opt. Lett. 25, 616–618 (2000).
[CrossRef]

G. L. Bourdet, “Theoretical investigation of quasi-three-level longitudinally pumped continuous wave lasers,” Appl. Opt. 39, 966–971 (2000).
[CrossRef]

F. Brunner, G. J. Spuhler, J. Aus der Au, L. Krainer, F. Morier-Genoud, R. Paschotta, N. Lichtenstein, S. Weiss, C. Harder, A. A. Lagatsky, A. Abdolvand, N. V. Kuleshov, and U. Keller, “Diode-pumped femtosecond Yb:KGd(WO4)2 laser with 1.1-W average power,” Opt. Lett. 25, 1119–1121 (2000).
[CrossRef]

V. V. Ter-Mikirtychev and V. A. Fromzel, “Directly single-mode-pumped continuous-wave Yb3+:YAG laser tunable in the 1047–1051-nm wavelength range,” Appl. Opt. 39, 4964–4969 (2000).
[CrossRef]

1999 (8)

T. Kasamatsu, H. Sekita, and Y. Kuwano, “Temperature dependence and optimization of 970-nm diode-pumped Yb:YAG and Yb:LuAG lasers,” Appl. Opt. 38, 5149–5153 (1999).
[CrossRef]

Y. Zhou, X. Chen, D. Tang, Z. Luo, and W. Yang, “Investigation of the spectroscopic properties of acentric orthorhombic Nd3+:Gd2(MoO4)3 crystals,” Opt. Commun. 167, 99–104 (1999).
[CrossRef]

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11, 245–254 (1999).
[CrossRef]

E. Montoya, J. Capmany, L. E. Bausa, T. Kellner, A. Diening, and G. Huber, “Infrared and self-frequency doubled laser action in Yb3+-doped LiNbO3:MgO,” Appl. Phys. Lett. 74, 3113–3115 (1999).
[CrossRef]

P. Laporta, S. Longhi, G. Sorbello, S. Taccheo, and C. Svelto, “Erbium-ytterbium miniaturized laser devices for optical communications,” in Rare-Earth-Doped Materials and Devices III, S. Jiang and S. Honkanen, eds., Proc. SPIE 3622, 82–91 (1999).
[CrossRef]

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

P. Yang, P. Deng, J. Xu, W. Chen, J. Qiao, and G. Huang, “Spectroscopy and laser performance of Yb3+ doped YAG crystal,” Acta Opt. Sin. 19, 132–135 (1999).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Efficient output of a Ti:sapphire laser pumped Yb:YAG thin chip cw laser at 1.053 μm,” Chin. J. Lasers 26, 865–868 (1999).

1998 (2)

G. L. Bourdet and G. Lescroart, “Theoretical modeling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
[CrossRef]

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
[CrossRef]

1997 (1)

A. Chardon, F. Sanchez, and G. M. Stephan, “Polarization switching of an Er.Yb:Cr:phosphate glass microchip laser,” Ann. Telecommun. 52, 588–593 (1997).

1996 (2)

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

K. I. Schaffers, L. D. Deloach, and S. A. Payne, “Crystal growth, frequency doubling, and infrared laser performance of Yb3+:BaCaBO3F,” IEEE J. Quantum Electron. 32, 741–748 (1996).
[CrossRef]

1995 (1)

T. Omatsu, Y. Kato, M. Shimosegawa, A. Hasegawa, and I. Ogura, “Thermal effects in laser diode pumped self-frequency-doubled NdxY1−xAl3(BO3)4 (NYAB) microchip laser,” Opt. Commun. 118, 302–308 (1995).
[CrossRef]

1994 (2)

L. D. Deloach, S. A. Payne, L. K. Smith, W. L. Kway, and W. F. Krupke, “Laser and spectroscopic properties of Sr5(PO4)3F:Yb,” J. Opt. Soc. Am. B 11, 269–276 (1994).
[CrossRef]

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

1992 (1)

N. MacKinnon and B. D. Sinclair, “Pump power induced cavity stability in lithium neodymium tetraphosphate (LNP) microchip lasers,” Opt. Commun. 94, 281–288 (1992).
[CrossRef]

1989 (2)

A. J. Alfrey, “Modeling of longitudinally pumped cw Ti:sapphire laser oscillators,” IEEE J. Quantum Electron. 25, 760–766 (1989).
[CrossRef]

J. J. Zayhowski and A. Mooradian, “Single-frequency microchip Nd lasers,” Opt. Lett. 14, 24–26 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (1)

T. Y. Fan and R. L. Byer, “Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron. QE-23, 605–612 (1987).

Abdolvand, A.

Aka, G.

Alfrey, A. J.

A. J. Alfrey, “Modeling of longitudinally pumped cw Ti:sapphire laser oscillators,” IEEE J. Quantum Electron. 25, 760–766 (1989).
[CrossRef]

Aron, A.

Aus der Au, J.

Balembois, F.

Bausa, L. E.

E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
[CrossRef]

E. Montoya, J. Capmany, L. E. Bausa, T. Kellner, A. Diening, and G. Huber, “Infrared and self-frequency doubled laser action in Yb3+-doped LiNbO3:MgO,” Appl. Phys. Lett. 74, 3113–3115 (1999).
[CrossRef]

Beach, R. J.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Boulon, G.

A. Brenier and G. Boulon, “Overview of the best Yb3+-doped laser crystals,” J. Alloys Compd. 323–324, 210–213 (2001).
[CrossRef]

Bourdet, G. L.

G. L. Bourdet, “Gain and absorption saturation coupling in end pumped Tm:YVO4 and Tm, Ho:YLF cw amplifiers,” Opt. Commun. 173, 333–340 (2000).
[CrossRef]

G. L. Bourdet, “Theoretical investigation of quasi-three-level longitudinally pumped continuous wave lasers,” Appl. Opt. 39, 966–971 (2000).
[CrossRef]

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
[CrossRef]

G. L. Bourdet and G. Lescroart, “Theoretical modeling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
[CrossRef]

Brenier, A.

A. Brenier and G. Boulon, “Overview of the best Yb3+-doped laser crystals,” J. Alloys Compd. 323–324, 210–213 (2001).
[CrossRef]

A. Brenier, “A new evaluation of Yb3+-doped crystals for laser applications,” J. Lumin. 92, 199–204 (2001).
[CrossRef]

Brun, A.

Brunner, F.

Bustamante, A. N. P.

A. N. P. Bustamante, D. A. Hammons, R. E. Peale, B. H. T. Chai, M. Richardson, and A. Chin, “Simultaneous cw dual-wavelength laser action and tunability performance of diode-pumped Yb3+:Sr5(VO4)3F,” Opt. Commun. 192, 309–313 (2001).
[CrossRef]

Byer, R. L.

T. Y. Fan and R. L. Byer, “Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron. QE-23, 605–612 (1987).

Capmany, J.

E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
[CrossRef]

E. Montoya, J. Capmany, L. E. Bausa, T. Kellner, A. Diening, and G. Huber, “Infrared and self-frequency doubled laser action in Yb3+-doped LiNbO3:MgO,” Appl. Phys. Lett. 74, 3113–3115 (1999).
[CrossRef]

Chai, B. H. T.

A. N. P. Bustamante, D. A. Hammons, R. E. Peale, B. H. T. Chai, M. Richardson, and A. Chin, “Simultaneous cw dual-wavelength laser action and tunability performance of diode-pumped Yb3+:Sr5(VO4)3F,” Opt. Commun. 192, 309–313 (2001).
[CrossRef]

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Chardon, A.

A. Chardon, F. Sanchez, and G. M. Stephan, “Polarization switching of an Er.Yb:Cr:phosphate glass microchip laser,” Ann. Telecommun. 52, 588–593 (1997).

Chen, W.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
[CrossRef]

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Ti:sapphire pumped 10-at. % Yb:YAG thin chip with 320-mW cw laser output of 1.053 μm,” Chin. J. Lasers 9, 8–10 (2000).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Efficient output of a Ti:sapphire laser pumped Yb:YAG thin chip cw laser at 1.053 μm,” Chin. J. Lasers 26, 865–868 (1999).

P. Yang, P. Deng, J. Xu, W. Chen, J. Qiao, and G. Huang, “Spectroscopy and laser performance of Yb3+ doped YAG crystal,” Acta Opt. Sin. 19, 132–135 (1999).

Chen, X.

Y. Zhou, X. Chen, D. Tang, Z. Luo, and W. Yang, “Investigation of the spectroscopic properties of acentric orthorhombic Nd3+:Gd2(MoO4)3 crystals,” Opt. Commun. 167, 99–104 (1999).
[CrossRef]

Cheng, R.

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Chin, A.

A. N. P. Bustamante, D. A. Hammons, R. E. Peale, B. H. T. Chai, M. Richardson, and A. Chin, “Simultaneous cw dual-wavelength laser action and tunability performance of diode-pumped Yb3+:Sr5(VO4)3F,” Opt. Commun. 192, 309–313 (2001).
[CrossRef]

Courjaud, A.

Dawes, J.

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Dawes, J. M.

P. Wang, J. M. Dawes, P. Dekker, and J. A. Piper, “Highly efficient diode-pumped ytterbium-doped yttrium aluminum borate laser,” Opt. Commun. 174, 467–470 (2000).
[CrossRef]

Dekker, P.

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

P. Wang, J. M. Dawes, P. Dekker, and J. A. Piper, “Highly efficient diode-pumped ytterbium-doped yttrium aluminum borate laser,” Opt. Commun. 174, 467–470 (2000).
[CrossRef]

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Deloach, L. D.

K. I. Schaffers, L. D. Deloach, and S. A. Payne, “Crystal growth, frequency doubling, and infrared laser performance of Yb3+:BaCaBO3F,” IEEE J. Quantum Electron. 32, 741–748 (1996).
[CrossRef]

L. D. Deloach, S. A. Payne, L. K. Smith, W. L. Kway, and W. F. Krupke, “Laser and spectroscopic properties of Sr5(PO4)3F:Yb,” J. Opt. Soc. Am. B 11, 269–276 (1994).
[CrossRef]

Deng, P.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
[CrossRef]

P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
[CrossRef]

P. Yang, P. Deng, J. Xu, and Z. Yin, “Growth of high doping Yb:YAG and its laser performance,” J. Chin. Ceram. Soc. 28, 566–569 (2000).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Ti:sapphire pumped 10-at. % Yb:YAG thin chip with 320-mW cw laser output of 1.053 μm,” Chin. J. Lasers 9, 8–10 (2000).

P. Yang, P. Deng, J. Xu, W. Chen, J. Qiao, and G. Huang, “Spectroscopy and laser performance of Yb3+ doped YAG crystal,” Acta Opt. Sin. 19, 132–135 (1999).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Efficient output of a Ti:sapphire laser pumped Yb:YAG thin chip cw laser at 1.053 μm,” Chin. J. Lasers 26, 865–868 (1999).

Diening, A.

E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
[CrossRef]

E. Montoya, J. Capmany, L. E. Bausa, T. Kellner, A. Diening, and G. Huber, “Infrared and self-frequency doubled laser action in Yb3+-doped LiNbO3:MgO,” Appl. Phys. Lett. 74, 3113–3115 (1999).
[CrossRef]

Dong, J.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
[CrossRef]

Druon, F.

Emanuel, M. A.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Equall, R.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37, 135–144 (2001).
[CrossRef]

Fan, T. Y.

T. Y. Fan and R. L. Byer, “Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron. QE-23, 605–612 (1987).

Fromzel, V. A.

Georges, P.

Gruber, R.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Hammons, D. A.

A. N. P. Bustamante, D. A. Hammons, R. E. Peale, B. H. T. Chai, M. Richardson, and A. Chin, “Simultaneous cw dual-wavelength laser action and tunability performance of diode-pumped Yb3+:Sr5(VO4)3F,” Opt. Commun. 192, 309–313 (2001).
[CrossRef]

Harder, C.

Hasegawa, A.

T. Omatsu, Y. Kato, M. Shimosegawa, A. Hasegawa, and I. Ogura, “Thermal effects in laser diode pumped self-frequency-doubled NdxY1−xAl3(BO3)4 (NYAB) microchip laser,” Opt. Commun. 118, 302–308 (1995).
[CrossRef]

Honea, E. C.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37, 135–144 (2001).
[CrossRef]

Hong, L.

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

Honninger, C.

Hu, H.

H. Hu and L. Zhang, “A new microlaser material rare-earth doped glasses,” J. Chin. Ceram. Soc. 29, 460–465 (2001).

Hu, X.

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

Huang, G.

P. Yang, P. Deng, J. Xu, W. Chen, J. Qiao, and G. Huang, “Spectroscopy and laser performance of Yb3+ doped YAG crystal,” Acta Opt. Sin. 19, 132–135 (1999).

Huang, Y.

Z. Luo and Y. Huang, “An empirical relationship between laser threshold and chemical composition of laser crystals,” Opt. Commun. 206, 159–164 (2002).
[CrossRef]

Huber, G.

E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
[CrossRef]

E. Montoya, J. Capmany, L. E. Bausa, T. Kellner, A. Diening, and G. Huber, “Infrared and self-frequency doubled laser action in Yb3+-doped LiNbO3:MgO,” Appl. Phys. Lett. 74, 3113–3115 (1999).
[CrossRef]

Hutcheson, R.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37, 135–144 (2001).
[CrossRef]

Jiang, H.

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

Kasamatsu, T.

Kato, Y.

T. Omatsu, Y. Kato, M. Shimosegawa, A. Hasegawa, and I. Ogura, “Thermal effects in laser diode pumped self-frequency-doubled NdxY1−xAl3(BO3)4 (NYAB) microchip laser,” Opt. Commun. 118, 302–308 (1995).
[CrossRef]

Keller, U.

Kellner, T.

E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
[CrossRef]

E. Montoya, J. Capmany, L. E. Bausa, T. Kellner, A. Diening, and G. Huber, “Infrared and self-frequency doubled laser action in Yb3+-doped LiNbO3:MgO,” Appl. Phys. Lett. 74, 3113–3115 (1999).
[CrossRef]

Krainer, L.

Krupke, W. F.

Kuleshov, N. V.

Kurimura, S.

N. Pavel, J. Saikawa, S. Kurimura, and Taira, “Microchip high power radially pumped composite Yb:YAG laser,” in ROMOPTO 2000: Sixth Conference on Optics, V.I. Vlad, ed., Proc. SPIE 4430, 27–34 (2001).
[CrossRef]

Kuwano, Y.

Kway, W. L.

Lagatsky, A. A.

Laporta, P.

P. Laporta, S. Longhi, G. Sorbello, S. Taccheo, and C. Svelto, “Erbium-ytterbium miniaturized laser devices for optical communications,” in Rare-Earth-Doped Materials and Devices III, S. Jiang and S. Honkanen, eds., Proc. SPIE 3622, 82–91 (1999).
[CrossRef]

Lescroart, G.

G. L. Bourdet and G. Lescroart, “Theoretical modeling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
[CrossRef]

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
[CrossRef]

Li, J.

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

Lichtenstein, N.

Liu, X.

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Liu, Y.

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Ti:sapphire pumped 10-at. % Yb:YAG thin chip with 320-mW cw laser output of 1.053 μm,” Chin. J. Lasers 9, 8–10 (2000).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Efficient output of a Ti:sapphire laser pumped Yb:YAG thin chip cw laser at 1.053 μm,” Chin. J. Lasers 26, 865–868 (1999).

Longhi, S.

P. Laporta, S. Longhi, G. Sorbello, S. Taccheo, and C. Svelto, “Erbium-ytterbium miniaturized laser devices for optical communications,” in Rare-Earth-Doped Materials and Devices III, S. Jiang and S. Honkanen, eds., Proc. SPIE 3622, 82–91 (1999).
[CrossRef]

Luo, Z.

Z. Luo and Y. Huang, “An empirical relationship between laser threshold and chemical composition of laser crystals,” Opt. Commun. 206, 159–164 (2002).
[CrossRef]

Y. Zhou, X. Chen, D. Tang, Z. Luo, and W. Yang, “Investigation of the spectroscopic properties of acentric orthorhombic Nd3+:Gd2(MoO4)3 crystals,” Opt. Commun. 167, 99–104 (1999).
[CrossRef]

MacKinnon, N.

N. MacKinnon and B. D. Sinclair, “Pump power induced cavity stability in lithium neodymium tetraphosphate (LNP) microchip lasers,” Opt. Commun. 94, 281–288 (1992).
[CrossRef]

Marshall, C. D.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Meng, X.

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Merazzi, S.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Montoya, E.

E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
[CrossRef]

E. Montoya, J. Capmany, L. E. Bausa, T. Kellner, A. Diening, and G. Huber, “Infrared and self-frequency doubled laser action in Yb3+-doped LiNbO3:MgO,” Appl. Phys. Lett. 74, 3113–3115 (1999).
[CrossRef]

Mooradian, A.

Morier-Genoud, F.

Mougel, F.

Neuenschwander, B.

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11, 245–254 (1999).
[CrossRef]

Ogura, I.

T. Omatsu, Y. Kato, M. Shimosegawa, A. Hasegawa, and I. Ogura, “Thermal effects in laser diode pumped self-frequency-doubled NdxY1−xAl3(BO3)4 (NYAB) microchip laser,” Opt. Commun. 118, 302–308 (1995).
[CrossRef]

Omatsu, T.

T. Omatsu, Y. Kato, M. Shimosegawa, A. Hasegawa, and I. Ogura, “Thermal effects in laser diode pumped self-frequency-doubled NdxY1−xAl3(BO3)4 (NYAB) microchip laser,” Opt. Commun. 118, 302–308 (1995).
[CrossRef]

Paschotta, R.

Patel, F. D.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37, 135–144 (2001).
[CrossRef]

Pavel, N.

N. Pavel, J. Saikawa, S. Kurimura, and Taira, “Microchip high power radially pumped composite Yb:YAG laser,” in ROMOPTO 2000: Sixth Conference on Optics, V.I. Vlad, ed., Proc. SPIE 4430, 27–34 (2001).
[CrossRef]

Payne, S. A.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37, 135–144 (2001).
[CrossRef]

K. I. Schaffers, L. D. Deloach, and S. A. Payne, “Crystal growth, frequency doubling, and infrared laser performance of Yb3+:BaCaBO3F,” IEEE J. Quantum Electron. 32, 741–748 (1996).
[CrossRef]

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

L. D. Deloach, S. A. Payne, L. K. Smith, W. L. Kway, and W. F. Krupke, “Laser and spectroscopic properties of Sr5(PO4)3F:Yb,” J. Opt. Soc. Am. B 11, 269–276 (1994).
[CrossRef]

Peale, R. E.

A. N. P. Bustamante, D. A. Hammons, R. E. Peale, B. H. T. Chai, M. Richardson, and A. Chin, “Simultaneous cw dual-wavelength laser action and tunability performance of diode-pumped Yb3+:Sr5(VO4)3F,” Opt. Commun. 192, 309–313 (2001).
[CrossRef]

Pfistner, C.

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Piper, J. A.

P. Wang, J. M. Dawes, P. Dekker, and J. A. Piper, “Highly efficient diode-pumped ytterbium-doped yttrium aluminum borate laser,” Opt. Commun. 174, 467–470 (2000).
[CrossRef]

Qiao, J.

P. Yang, P. Deng, J. Xu, W. Chen, J. Qiao, and G. Huang, “Spectroscopy and laser performance of Yb3+ doped YAG crystal,” Acta Opt. Sin. 19, 132–135 (1999).

Qiu, H.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
[CrossRef]

Richardson, M.

A. N. P. Bustamante, D. A. Hammons, R. E. Peale, B. H. T. Chai, M. Richardson, and A. Chin, “Simultaneous cw dual-wavelength laser action and tunability performance of diode-pumped Yb3+:Sr5(VO4)3F,” Opt. Commun. 192, 309–313 (2001).
[CrossRef]

Risk, W. P.

Saikawa, J.

N. Pavel, J. Saikawa, S. Kurimura, and Taira, “Microchip high power radially pumped composite Yb:YAG laser,” in ROMOPTO 2000: Sixth Conference on Optics, V.I. Vlad, ed., Proc. SPIE 4430, 27–34 (2001).
[CrossRef]

Salin, F.

Sanchez, F.

A. Chardon, F. Sanchez, and G. M. Stephan, “Polarization switching of an Er.Yb:Cr:phosphate glass microchip laser,” Ann. Telecommun. 52, 588–593 (1997).

Sanz-Garcia, J. A.

E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
[CrossRef]

Schaffers, K. I.

K. I. Schaffers, L. D. Deloach, and S. A. Payne, “Crystal growth, frequency doubling, and infrared laser performance of Yb3+:BaCaBO3F,” IEEE J. Quantum Electron. 32, 741–748 (1996).
[CrossRef]

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Sekita, H.

Shimosegawa, M.

T. Omatsu, Y. Kato, M. Shimosegawa, A. Hasegawa, and I. Ogura, “Thermal effects in laser diode pumped self-frequency-doubled NdxY1−xAl3(BO3)4 (NYAB) microchip laser,” Opt. Commun. 118, 302–308 (1995).
[CrossRef]

Sinclair, B. D.

N. MacKinnon and B. D. Sinclair, “Pump power induced cavity stability in lithium neodymium tetraphosphate (LNP) microchip lasers,” Opt. Commun. 94, 281–288 (1992).
[CrossRef]

Skidmore, J.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Smith, L. K.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

L. D. Deloach, S. A. Payne, L. K. Smith, W. L. Kway, and W. F. Krupke, “Laser and spectroscopic properties of Sr5(PO4)3F:Yb,” J. Opt. Soc. Am. B 11, 269–276 (1994).
[CrossRef]

Sorbello, G.

P. Laporta, S. Longhi, G. Sorbello, S. Taccheo, and C. Svelto, “Erbium-ytterbium miniaturized laser devices for optical communications,” in Rare-Earth-Doped Materials and Devices III, S. Jiang and S. Honkanen, eds., Proc. SPIE 3622, 82–91 (1999).
[CrossRef]

Speth, J.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37, 135–144 (2001).
[CrossRef]

Spuhler, G. J.

Stephan, G. M.

A. Chardon, F. Sanchez, and G. M. Stephan, “Polarization switching of an Er.Yb:Cr:phosphate glass microchip laser,” Ann. Telecommun. 52, 588–593 (1997).

Sun, L.

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Svelto, C.

P. Laporta, S. Longhi, G. Sorbello, S. Taccheo, and C. Svelto, “Erbium-ytterbium miniaturized laser devices for optical communications,” in Rare-Earth-Doped Materials and Devices III, S. Jiang and S. Honkanen, eds., Proc. SPIE 3622, 82–91 (1999).
[CrossRef]

Taccheo, S.

P. Laporta, S. Longhi, G. Sorbello, S. Taccheo, and C. Svelto, “Erbium-ytterbium miniaturized laser devices for optical communications,” in Rare-Earth-Doped Materials and Devices III, S. Jiang and S. Honkanen, eds., Proc. SPIE 3622, 82–91 (1999).
[CrossRef]

Taira,

N. Pavel, J. Saikawa, S. Kurimura, and Taira, “Microchip high power radially pumped composite Yb:YAG laser,” in ROMOPTO 2000: Sixth Conference on Optics, V.I. Vlad, ed., Proc. SPIE 4430, 27–34 (2001).
[CrossRef]

Tang, D.

Y. Zhou, X. Chen, D. Tang, Z. Luo, and W. Yang, “Investigation of the spectroscopic properties of acentric orthorhombic Nd3+:Gd2(MoO4)3 crystals,” Opt. Commun. 167, 99–104 (1999).
[CrossRef]

Teng, B.

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

Ter-Mikirtychev, V. V.

Vivien, D.

Wang, J.

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

Wang, P.

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

P. Wang, J. M. Dawes, P. Dekker, and J. A. Piper, “Highly efficient diode-pumped ytterbium-doped yttrium aluminum borate laser,” Opt. Commun. 174, 467–470 (2000).
[CrossRef]

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Weber, H. P.

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11, 245–254 (1999).
[CrossRef]

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Weber, R.

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11, 245–254 (1999).
[CrossRef]

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

Weiss, S.

Xu, J.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
[CrossRef]

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Ti:sapphire pumped 10-at. % Yb:YAG thin chip with 320-mW cw laser output of 1.053 μm,” Chin. J. Lasers 9, 8–10 (2000).

P. Yang, P. Deng, J. Xu, and Z. Yin, “Growth of high doping Yb:YAG and its laser performance,” J. Chin. Ceram. Soc. 28, 566–569 (2000).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Efficient output of a Ti:sapphire laser pumped Yb:YAG thin chip cw laser at 1.053 μm,” Chin. J. Lasers 26, 865–868 (1999).

P. Yang, P. Deng, J. Xu, W. Chen, J. Qiao, and G. Huang, “Spectroscopy and laser performance of Yb3+ doped YAG crystal,” Acta Opt. Sin. 19, 132–135 (1999).

Yang, P.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
[CrossRef]

P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
[CrossRef]

P. Yang, P. Deng, J. Xu, and Z. Yin, “Growth of high doping Yb:YAG and its laser performance,” J. Chin. Ceram. Soc. 28, 566–569 (2000).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Ti:sapphire pumped 10-at. % Yb:YAG thin chip with 320-mW cw laser output of 1.053 μm,” Chin. J. Lasers 9, 8–10 (2000).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Efficient output of a Ti:sapphire laser pumped Yb:YAG thin chip cw laser at 1.053 μm,” Chin. J. Lasers 26, 865–868 (1999).

P. Yang, P. Deng, J. Xu, W. Chen, J. Qiao, and G. Huang, “Spectroscopy and laser performance of Yb3+ doped YAG crystal,” Acta Opt. Sin. 19, 132–135 (1999).

Yang, W.

Y. Zhou, X. Chen, D. Tang, Z. Luo, and W. Yang, “Investigation of the spectroscopic properties of acentric orthorhombic Nd3+:Gd2(MoO4)3 crystals,” Opt. Commun. 167, 99–104 (1999).
[CrossRef]

Yin, Z.

P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
[CrossRef]

P. Yang, P. Deng, J. Xu, and Z. Yin, “Growth of high doping Yb:YAG and its laser performance,” J. Chin. Ceram. Soc. 28, 566–569 (2000).

Zayhowski, J. J.

Zhang, C.

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

Zhang, H.

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Zhang, L.

H. Hu and L. Zhang, “A new microlaser material rare-earth doped glasses,” J. Chin. Ceram. Soc. 29, 460–465 (2001).

Zhang, S.

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Zhang, Y.

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Ti:sapphire pumped 10-at. % Yb:YAG thin chip with 320-mW cw laser output of 1.053 μm,” Chin. J. Lasers 9, 8–10 (2000).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Efficient output of a Ti:sapphire laser pumped Yb:YAG thin chip cw laser at 1.053 μm,” Chin. J. Lasers 26, 865–868 (1999).

Zhou, Y.

Y. Zhou, X. Chen, D. Tang, Z. Luo, and W. Yang, “Investigation of the spectroscopic properties of acentric orthorhombic Nd3+:Gd2(MoO4)3 crystals,” Opt. Commun. 167, 99–104 (1999).
[CrossRef]

Zhu, L.

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Acta Opt. Sin. (1)

P. Yang, P. Deng, J. Xu, W. Chen, J. Qiao, and G. Huang, “Spectroscopy and laser performance of Yb3+ doped YAG crystal,” Acta Opt. Sin. 19, 132–135 (1999).

Ann. Telecommun. (1)

A. Chardon, F. Sanchez, and G. M. Stephan, “Polarization switching of an Er.Yb:Cr:phosphate glass microchip laser,” Ann. Telecommun. 52, 588–593 (1997).

Appl. Opt. (3)

Appl. Phys. B (1)

H. Zhang, X. Meng, P. Wang, L. Zhu, X. Liu, R. Cheng, J. Dawes, P. Dekker, S. Zhang, and L. Sun, “Slope efficiency of up to 73% for Yb:Ca4YO(BO3)3 crystal laser pumped by a laser diode,” Appl. Phys. B 68, 1147–1149 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

E. Montoya, J. Capmany, L. E. Bausa, T. Kellner, A. Diening, and G. Huber, “Infrared and self-frequency doubled laser action in Yb3+-doped LiNbO3:MgO,” Appl. Phys. Lett. 74, 3113–3115 (1999).
[CrossRef]

Chin. J. Lasers (2)

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Efficient output of a Ti:sapphire laser pumped Yb:YAG thin chip cw laser at 1.053 μm,” Chin. J. Lasers 26, 865–868 (1999).

P. Yang, P. Deng, Y. Liu, Y. Zhang, W. Chen, and J. Xu, “Ti:sapphire pumped 10-at. % Yb:YAG thin chip with 320-mW cw laser output of 1.053 μm,” Chin. J. Lasers 9, 8–10 (2000).

IEEE J. Quantum Electron. (6)

K. I. Schaffers, L. D. Deloach, and S. A. Payne, “Crystal growth, frequency doubling, and infrared laser performance of Yb3+:BaCaBO3F,” IEEE J. Quantum Electron. 32, 741–748 (1996).
[CrossRef]

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, and B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, “Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG,” IEEE J. Quantum Electron. 37, 135–144 (2001).
[CrossRef]

T. Y. Fan and R. L. Byer, “Modeling and cw operation of a quasi-three-level 946 nm Nd:YAG laser,” IEEE J. Quantum Electron. QE-23, 605–612 (1987).

A. J. Alfrey, “Modeling of longitudinally pumped cw Ti:sapphire laser oscillators,” IEEE J. Quantum Electron. 25, 760–766 (1989).
[CrossRef]

C. Pfistner, R. Weber, H. P. Weber, S. Merazzi, and R. Gruber, “Thermal beam distortions in end-pumped Nd:YAG, Nd:GSGG, and Nd:YLF rods,” IEEE J. Quantum Electron. 30, 1605–1615 (1994).
[CrossRef]

J. Alloys Compd. (1)

A. Brenier and G. Boulon, “Overview of the best Yb3+-doped laser crystals,” J. Alloys Compd. 323–324, 210–213 (2001).
[CrossRef]

J. Appl. Phys. (1)

E. Montoya, J. A. Sanz-Garcia, J. Capmany, L. E. Bausa, A. Diening, T. Kellner, and G. Huber, “Continuous wave infrared laser action, self-frequency doubling, and tunability of Yb3+:MgO:LiNbO3,” J. Appl. Phys. 87, 4056–4062 (2000).
[CrossRef]

J. Chin. Ceram. Soc. (2)

H. Hu and L. Zhang, “A new microlaser material rare-earth doped glasses,” J. Chin. Ceram. Soc. 29, 460–465 (2001).

P. Yang, P. Deng, J. Xu, and Z. Yin, “Growth of high doping Yb:YAG and its laser performance,” J. Chin. Ceram. Soc. 28, 566–569 (2000).

J. Cryst. Growth (1)

H. Jiang, J. Li, J. Wang, X. Hu, L. Hong, B. Teng, C. Zhang, P. Dekker, and P. Wang, “Growth of Yb:YAl3(BO3)4 crystals and their optical and self-frequency-doubling properties,” J. Cryst. Growth 233, 248–252 (2001).
[CrossRef]

J. Lumin. (2)

P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
[CrossRef]

A. Brenier, “A new evaluation of Yb3+-doped crystals for laser applications,” J. Lumin. 92, 199–204 (2001).
[CrossRef]

J. Opt. Soc. Am. B (2)

Mater. Lett. (1)

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser Yb:YAG,” Mater. Lett. 55, 1–7 (2002).
[CrossRef]

Opt. Commun. (9)

P. Wang, J. M. Dawes, P. Dekker, and J. A. Piper, “Highly efficient diode-pumped ytterbium-doped yttrium aluminum borate laser,” Opt. Commun. 174, 467–470 (2000).
[CrossRef]

A. N. P. Bustamante, D. A. Hammons, R. E. Peale, B. H. T. Chai, M. Richardson, and A. Chin, “Simultaneous cw dual-wavelength laser action and tunability performance of diode-pumped Yb3+:Sr5(VO4)3F,” Opt. Commun. 192, 309–313 (2001).
[CrossRef]

G. L. Bourdet, “Gain and absorption saturation coupling in end pumped Tm:YVO4 and Tm, Ho:YLF cw amplifiers,” Opt. Commun. 173, 333–340 (2000).
[CrossRef]

Z. Luo and Y. Huang, “An empirical relationship between laser threshold and chemical composition of laser crystals,” Opt. Commun. 206, 159–164 (2002).
[CrossRef]

T. Omatsu, Y. Kato, M. Shimosegawa, A. Hasegawa, and I. Ogura, “Thermal effects in laser diode pumped self-frequency-doubled NdxY1−xAl3(BO3)4 (NYAB) microchip laser,” Opt. Commun. 118, 302–308 (1995).
[CrossRef]

Y. Zhou, X. Chen, D. Tang, Z. Luo, and W. Yang, “Investigation of the spectroscopic properties of acentric orthorhombic Nd3+:Gd2(MoO4)3 crystals,” Opt. Commun. 167, 99–104 (1999).
[CrossRef]

N. MacKinnon and B. D. Sinclair, “Pump power induced cavity stability in lithium neodymium tetraphosphate (LNP) microchip lasers,” Opt. Commun. 94, 281–288 (1992).
[CrossRef]

G. L. Bourdet and G. Lescroart, “Theoretical modeling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
[CrossRef]

G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
[CrossRef]

Opt. Lett. (4)

Opt. Mater. (1)

R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11, 245–254 (1999).
[CrossRef]

Proc. SPIE (2)

N. Pavel, J. Saikawa, S. Kurimura, and Taira, “Microchip high power radially pumped composite Yb:YAG laser,” in ROMOPTO 2000: Sixth Conference on Optics, V.I. Vlad, ed., Proc. SPIE 4430, 27–34 (2001).
[CrossRef]

P. Laporta, S. Longhi, G. Sorbello, S. Taccheo, and C. Svelto, “Erbium-ytterbium miniaturized laser devices for optical communications,” in Rare-Earth-Doped Materials and Devices III, S. Jiang and S. Honkanen, eds., Proc. SPIE 3622, 82–91 (1999).
[CrossRef]

Other (1)

N. Pavel, J. Saikawa, S. Kurimura, and T. Taira, “Continuous-wave diode radial-pumped composite Yb:YAG laser,” in Proceedings of the International Conference on Lasers 2000, V. J. Corcoran and T. A. Corcoran, eds. (STS Press, McLean, Va., pp. 790–795.

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Figures (4)

Fig. 1
Fig. 1

Energy-level diagram of the Yb3+:YAG crystal.

Fig. 2
Fig. 2

Output power of the Yb3+:YAG microchip laser versus absorbed pump power for a sample with N0=20 at. %, L=0.5 mm, and δ=0.06 cm-1.

Fig. 3
Fig. 3

Pump threshold of the Yb3+:YAG microchip laser as a function of doping concentration and crystal thickness. The transmission of the output coupler was set to 0.0426, and the internal loss per unit crystal length was assumed to be 0.06 cm-1.

Fig. 4
Fig. 4

Output power of the Yb3+:YAG microchip laser as a function of doping concentration and crystal thickness with an incident pump power of 1.0 W. The internal loss per unit crystal length was assumed to be 0.06 cm-1, and the transmission of the output coupler was set to 0.0426.

Tables (2)

Tables Icon

Table 1 Values of the Nonadjustable Parameters for Yb3+:YAG Microchip Lasers

Tables Icon

Table 2 Comparison of Experimental and Calculated Results for the Yb3+:YAG Microchip Laser a

Equations (27)

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

wp2(z)=wp021+λp2(z-z0)2π2wp04np2,
wc2(z)=wc021+λc2(z-z0)2π2wc04nc2,
 flow=exp(-E4/kT)exp(-E1/kT)+exp(-E2/kT)+exp(-E3/kT)+exp(-E4/kT),
rp(r, z)=2αpπwp02ηaexp-2r2wp02{exp(-αpz)+exp[-αp(2L-z)]},
ϕc(r, z)=2πwc02Lexp-2r2wc02,
dNup(r, z)dt=Rrp(r, z)-Nup(r, z)-Nup0τf(N0)-cσeΔN(r, z)nc Φϕc(r, z)=0,
dNlow(r, z)dt=-flowRrp(r, z)-Nlow(r, z)-Nlow0τf(N0)+flowcσeΔN(r, z)nc Φϕc(r, z)=0.
dΔN(r, z)dt=fRrp(r, z)-ΔN(r, z)-ΔN0τf(N0)-fcσeΔN(r, z)nc Φϕc(r, z)=0,
A exp-2r2wp02{exp(-αpz)+exp[-αp(2L-z)]}
-ΔN(r, z)+flowN0τf(N0)
-BPcΔN(r, z)exp-2r2wc02=0,
A=2Pp0αpfπwp02hνp,
B=4σefπwc02hνc.
ΔN(r, z)=Aτf(N0)exp(-2r2/wp02){exp(-αpz)+exp[-αp(2L-z)]}-N0flow1+Bτf(N0)Pcexp(-2r2/wc02).
dΦdt=cσencΔN(r, z)Φϕc(r, z)dV-Φτq=0,
τq=2ncLc(2δL+T2),
2πσe00LΔN(r, z)ϕc(r, z)rdrdz=12L (2δL+T2).
4σewc0200LAτf(N0)exp(-2r2/wp02){exp(-αpz)+exp[-αp(2L-z)]}-N0flow1+Bτf(N0)Pcexp(-2r2/wc02)exp-2r2wc02rdrdz=12 (2δL+T2).
x=2r2wc02,a=wc02wp02.
σe00LAτf(N0)exp(-ax){exp(-αpz)+exp[-αp(2L-z)]}-N0flow1+Bτf(N0)Pcexp(-x)exp(-x)dxdz=12 (2δL+T2).
 σe010LAτf(N0)ya{exp(-αpz)+exp[-αp(2L-z)]}-N0flow1+Bτf(N0)Pcydydz=12 (2δL+T2).
σe01Pp0Aτf(N0)ya[1-exp(-2αpL)]-N0flowL1+Bτf(N0)Pcydy
=12 (2δL+T2),
A=AαpPp0=2fπwp02hνp;
Pp0=12σe (2δL+T2)+01{N0flowL/[1+Bτf(N0)Pcy]}dy01{Aτf(N0)yaηa/[1+Bτf(N0)Pcy]}dy.
Pth=2δL+T2+2σeN0flowL2σe01Aτf(N0)yaηady.
Pth=(2δL+T2+2σeN0flowL)(a+1)2σeAτf(N0)ηa.

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