Abstract

A simple optical model of K DPAL, where Gaussian spatial shapes of the pump and laser intensities in any cross section of the beams are assumed, is reported. The model, applied to the recently reported highly efficient static, pulsed K DPAL [Zhdanov et al, Optics Express 22, 17266 (2014)], shows good agreement between the calculated and measured dependence of the laser power on the incident pump power. In particular, the model reproduces the observed threshold pump power, 22 W (corresponding to pump intensity of 4 kW/cm2), which is much higher than that predicted by the standard semi-analytical models of the DPAL. The reason for the large values of the threshold power is that the volume occupied by the excited K atoms contributing to the spontaneous emission is much larger than the volumes of the pump and laser beams in the laser cell, resulting in very large energy losses due to the spontaneous emission. To reduce the adverse effect of the high threshold power, high pump power is needed, and therefore gas flow with high gas velocity to avoid heating the gas has to be applied. Thus, for obtaining high power, highly efficient K DPAL, subsonic or supersonic flowing-gas device is needed.

© 2015 Optical Society of America

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References

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  1. W. F. Krupke, “Diode pumped alkali lasers (DPALs) — A review (rev1),” J. Prog. Quantum Electron. 36(1), 4–28 (2012).
    [Crossref]
  2. B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2012).
    [Crossref]
  3. B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Efficient potassium diode pumped alkali laser operating in pulsed mode,” Opt. Express 22(14), 17266–17270 (2014).
    [Crossref] [PubMed]
  4. G. D. Hager and G. P. Perram, “A three-level analytic model for alkali metal vapor lasers: part I. Narrowband optical pumping,” Appl. Phys. B 101(1-2), 45–56 (2010).
    [Crossref]
  5. G. D. Hager and G. P. Perram, “A three-level model for alkali metal vapor lasers. Part II: broadband optical pumping,” Appl. Phys. B 112(4), 507–520 (2013).
    [Crossref]
  6. B. D. Barmashenko and S. Rosenwaks, “Detailed analysis of kinetic and fluid dynamic processes in diode-pumped alkali lasers,” J. Opt. Soc. Am. B 30(5), 1118–1126 (2013).
    [Crossref]
  7. K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Computational fluid dynamics modeling of subsonic flowing-gas diode pumped alkali lasers: comparison with semi-analytical model calculations and with experimental results,” J. Opt. Soc. Am. B 31(11), 2628–2637 (2014).
    [Crossref]
  8. A. M. Komashko and J. Zweiback, “Modeling laser performance of scalable side-pumped alkali laser,” Proc. SPIE 7581, 75810H (2010).
    [Crossref]
  9. R. J. Knize, B. V. Zhdanov, and M. K. Shaffer, “Photoionization in alkali lasers,” Opt. Express 19(8), 7894–7902 (2011).
    [Crossref] [PubMed]
  10. B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013).
    [Crossref]
  11. B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Power degradation due to thermal effects in Potassium Diode Pumped Alkali Laser,” Opt. Commun. 341, 97–100 (2015).
    [Crossref]
  12. H. Wang, P. L. Gould, and W. C. Stwalleya, “Long-range interaction of the 39K(4s)+ 39K(4p) asymptote by photoassociative spectroscopy. I. The 0 g pure long-range state and the long-range potential constants,” J. Chem. Phys. 106(19), 7899–7912 (1997).
    [Crossref]
  13. Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
    [Crossref]
  14. J. Ciuryelo and L. Krause, “42P1/2 → 42P3/2 mixing in potassium induced in collisions with noble gas atoms,” J. Quant. Spectrosc. Radiat. Transf. 28(6), 457–461 (1982).
    [Crossref]
  15. P. Ya. Kantor, N. P. Penkin, and L. N. Shabanov, “Broadening of the K I 769.9 and 766.5-nm lines by inert gases,” Opt. Spectrosc. (USSR) 59(2), 151–156 (1985).
  16. K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “CFD assisted simulation of temperature distribution and laser power in pulsed and CW pumped static gas DPALs,” Proc. SPIE (to be published).
  17. B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Study of potassium DPAL operation in pulsed and CW mode,” Proc. SPIE 9251, 92510Y (2014).

2015 (1)

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Power degradation due to thermal effects in Potassium Diode Pumped Alkali Laser,” Opt. Commun. 341, 97–100 (2015).
[Crossref]

2014 (3)

2013 (3)

B. D. Barmashenko and S. Rosenwaks, “Detailed analysis of kinetic and fluid dynamic processes in diode-pumped alkali lasers,” J. Opt. Soc. Am. B 30(5), 1118–1126 (2013).
[Crossref]

B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013).
[Crossref]

G. D. Hager and G. P. Perram, “A three-level model for alkali metal vapor lasers. Part II: broadband optical pumping,” Appl. Phys. B 112(4), 507–520 (2013).
[Crossref]

2012 (2)

W. F. Krupke, “Diode pumped alkali lasers (DPALs) — A review (rev1),” J. Prog. Quantum Electron. 36(1), 4–28 (2012).
[Crossref]

B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2012).
[Crossref]

2011 (2)

R. J. Knize, B. V. Zhdanov, and M. K. Shaffer, “Photoionization in alkali lasers,” Opt. Express 19(8), 7894–7902 (2011).
[Crossref] [PubMed]

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

2010 (2)

A. M. Komashko and J. Zweiback, “Modeling laser performance of scalable side-pumped alkali laser,” Proc. SPIE 7581, 75810H (2010).
[Crossref]

G. D. Hager and G. P. Perram, “A three-level analytic model for alkali metal vapor lasers: part I. Narrowband optical pumping,” Appl. Phys. B 101(1-2), 45–56 (2010).
[Crossref]

1997 (1)

H. Wang, P. L. Gould, and W. C. Stwalleya, “Long-range interaction of the 39K(4s)+ 39K(4p) asymptote by photoassociative spectroscopy. I. The 0 g pure long-range state and the long-range potential constants,” J. Chem. Phys. 106(19), 7899–7912 (1997).
[Crossref]

1985 (1)

P. Ya. Kantor, N. P. Penkin, and L. N. Shabanov, “Broadening of the K I 769.9 and 766.5-nm lines by inert gases,” Opt. Spectrosc. (USSR) 59(2), 151–156 (1985).

1982 (1)

J. Ciuryelo and L. Krause, “42P1/2 → 42P3/2 mixing in potassium induced in collisions with noble gas atoms,” J. Quant. Spectrosc. Radiat. Transf. 28(6), 457–461 (1982).
[Crossref]

Barmashenko, B. D.

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Computational fluid dynamics modeling of subsonic flowing-gas diode pumped alkali lasers: comparison with semi-analytical model calculations and with experimental results,” J. Opt. Soc. Am. B 31(11), 2628–2637 (2014).
[Crossref]

B. D. Barmashenko and S. Rosenwaks, “Detailed analysis of kinetic and fluid dynamic processes in diode-pumped alkali lasers,” J. Opt. Soc. Am. B 30(5), 1118–1126 (2013).
[Crossref]

B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013).
[Crossref]

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “CFD assisted simulation of temperature distribution and laser power in pulsed and CW pumped static gas DPALs,” Proc. SPIE (to be published).

Chen, J.

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

Ciuryelo, J.

J. Ciuryelo and L. Krause, “42P1/2 → 42P3/2 mixing in potassium induced in collisions with noble gas atoms,” J. Quant. Spectrosc. Radiat. Transf. 28(6), 457–461 (1982).
[Crossref]

Gould, P. L.

H. Wang, P. L. Gould, and W. C. Stwalleya, “Long-range interaction of the 39K(4s)+ 39K(4p) asymptote by photoassociative spectroscopy. I. The 0 g pure long-range state and the long-range potential constants,” J. Chem. Phys. 106(19), 7899–7912 (1997).
[Crossref]

Hager, G. D.

G. D. Hager and G. P. Perram, “A three-level model for alkali metal vapor lasers. Part II: broadband optical pumping,” Appl. Phys. B 112(4), 507–520 (2013).
[Crossref]

G. D. Hager and G. P. Perram, “A three-level analytic model for alkali metal vapor lasers: part I. Narrowband optical pumping,” Appl. Phys. B 101(1-2), 45–56 (2010).
[Crossref]

Hua, W.

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

Kantor, P. Ya.

P. Ya. Kantor, N. P. Penkin, and L. N. Shabanov, “Broadening of the K I 769.9 and 766.5-nm lines by inert gases,” Opt. Spectrosc. (USSR) 59(2), 151–156 (1985).

Knize, R. J.

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Power degradation due to thermal effects in Potassium Diode Pumped Alkali Laser,” Opt. Commun. 341, 97–100 (2015).
[Crossref]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Study of potassium DPAL operation in pulsed and CW mode,” Proc. SPIE 9251, 92510Y (2014).

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Efficient potassium diode pumped alkali laser operating in pulsed mode,” Opt. Express 22(14), 17266–17270 (2014).
[Crossref] [PubMed]

B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2012).
[Crossref]

R. J. Knize, B. V. Zhdanov, and M. K. Shaffer, “Photoionization in alkali lasers,” Opt. Express 19(8), 7894–7902 (2011).
[Crossref] [PubMed]

Komashko, A. M.

A. M. Komashko and J. Zweiback, “Modeling laser performance of scalable side-pumped alkali laser,” Proc. SPIE 7581, 75810H (2010).
[Crossref]

Krause, L.

J. Ciuryelo and L. Krause, “42P1/2 → 42P3/2 mixing in potassium induced in collisions with noble gas atoms,” J. Quant. Spectrosc. Radiat. Transf. 28(6), 457–461 (1982).
[Crossref]

Krupke, W. F.

W. F. Krupke, “Diode pumped alkali lasers (DPALs) — A review (rev1),” J. Prog. Quantum Electron. 36(1), 4–28 (2012).
[Crossref]

Li, Y.

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

Liu, L.

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

Lu, Q.

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

Penkin, N. P.

P. Ya. Kantor, N. P. Penkin, and L. N. Shabanov, “Broadening of the K I 769.9 and 766.5-nm lines by inert gases,” Opt. Spectrosc. (USSR) 59(2), 151–156 (1985).

Perram, G. P.

G. D. Hager and G. P. Perram, “A three-level model for alkali metal vapor lasers. Part II: broadband optical pumping,” Appl. Phys. B 112(4), 507–520 (2013).
[Crossref]

G. D. Hager and G. P. Perram, “A three-level analytic model for alkali metal vapor lasers: part I. Narrowband optical pumping,” Appl. Phys. B 101(1-2), 45–56 (2010).
[Crossref]

Rosenwaks, S.

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Computational fluid dynamics modeling of subsonic flowing-gas diode pumped alkali lasers: comparison with semi-analytical model calculations and with experimental results,” J. Opt. Soc. Am. B 31(11), 2628–2637 (2014).
[Crossref]

B. D. Barmashenko and S. Rosenwaks, “Detailed analysis of kinetic and fluid dynamic processes in diode-pumped alkali lasers,” J. Opt. Soc. Am. B 30(5), 1118–1126 (2013).
[Crossref]

B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013).
[Crossref]

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “CFD assisted simulation of temperature distribution and laser power in pulsed and CW pumped static gas DPALs,” Proc. SPIE (to be published).

Rotondaro, M. D.

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Power degradation due to thermal effects in Potassium Diode Pumped Alkali Laser,” Opt. Commun. 341, 97–100 (2015).
[Crossref]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Study of potassium DPAL operation in pulsed and CW mode,” Proc. SPIE 9251, 92510Y (2014).

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Efficient potassium diode pumped alkali laser operating in pulsed mode,” Opt. Express 22(14), 17266–17270 (2014).
[Crossref] [PubMed]

Shabanov, L. N.

P. Ya. Kantor, N. P. Penkin, and L. N. Shabanov, “Broadening of the K I 769.9 and 766.5-nm lines by inert gases,” Opt. Spectrosc. (USSR) 59(2), 151–156 (1985).

Shaffer, M. K.

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Power degradation due to thermal effects in Potassium Diode Pumped Alkali Laser,” Opt. Commun. 341, 97–100 (2015).
[Crossref]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Study of potassium DPAL operation in pulsed and CW mode,” Proc. SPIE 9251, 92510Y (2014).

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Efficient potassium diode pumped alkali laser operating in pulsed mode,” Opt. Express 22(14), 17266–17270 (2014).
[Crossref] [PubMed]

R. J. Knize, B. V. Zhdanov, and M. K. Shaffer, “Photoionization in alkali lasers,” Opt. Express 19(8), 7894–7902 (2011).
[Crossref] [PubMed]

Stwalleya, W. C.

H. Wang, P. L. Gould, and W. C. Stwalleya, “Long-range interaction of the 39K(4s)+ 39K(4p) asymptote by photoassociative spectroscopy. I. The 0 g pure long-range state and the long-range potential constants,” J. Chem. Phys. 106(19), 7899–7912 (1997).
[Crossref]

Waichman, K.

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Computational fluid dynamics modeling of subsonic flowing-gas diode pumped alkali lasers: comparison with semi-analytical model calculations and with experimental results,” J. Opt. Soc. Am. B 31(11), 2628–2637 (2014).
[Crossref]

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “CFD assisted simulation of temperature distribution and laser power in pulsed and CW pumped static gas DPALs,” Proc. SPIE (to be published).

Wang, H.

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

H. Wang, P. L. Gould, and W. C. Stwalleya, “Long-range interaction of the 39K(4s)+ 39K(4p) asymptote by photoassociative spectroscopy. I. The 0 g pure long-range state and the long-range potential constants,” J. Chem. Phys. 106(19), 7899–7912 (1997).
[Crossref]

Xu, X.

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

Yang, Z.

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

Zhdanov, B. V.

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Power degradation due to thermal effects in Potassium Diode Pumped Alkali Laser,” Opt. Commun. 341, 97–100 (2015).
[Crossref]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Study of potassium DPAL operation in pulsed and CW mode,” Proc. SPIE 9251, 92510Y (2014).

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Efficient potassium diode pumped alkali laser operating in pulsed mode,” Opt. Express 22(14), 17266–17270 (2014).
[Crossref] [PubMed]

B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2012).
[Crossref]

R. J. Knize, B. V. Zhdanov, and M. K. Shaffer, “Photoionization in alkali lasers,” Opt. Express 19(8), 7894–7902 (2011).
[Crossref] [PubMed]

Zweiback, J.

A. M. Komashko and J. Zweiback, “Modeling laser performance of scalable side-pumped alkali laser,” Proc. SPIE 7581, 75810H (2010).
[Crossref]

Appl. Phys. B (2)

G. D. Hager and G. P. Perram, “A three-level analytic model for alkali metal vapor lasers: part I. Narrowband optical pumping,” Appl. Phys. B 101(1-2), 45–56 (2010).
[Crossref]

G. D. Hager and G. P. Perram, “A three-level model for alkali metal vapor lasers. Part II: broadband optical pumping,” Appl. Phys. B 112(4), 507–520 (2013).
[Crossref]

Appl. Phys. Lett. (1)

B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013).
[Crossref]

J. Chem. Phys. (1)

H. Wang, P. L. Gould, and W. C. Stwalleya, “Long-range interaction of the 39K(4s)+ 39K(4p) asymptote by photoassociative spectroscopy. I. The 0 g pure long-range state and the long-range potential constants,” J. Chem. Phys. 106(19), 7899–7912 (1997).
[Crossref]

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

J. Phys. At. Mol. Opt. Phys. (1)

Z. Yang, H. Wang, Q. Lu, L. Liu, Y. Li, W. Hua, X. Xu, and J. Chen, “Theoretical model and novel numerical approach of a broadband optically pumped three-level alkali vapour laser,” J. Phys. At. Mol. Opt. Phys. 44(8), 085401 (2011).
[Crossref]

J. Prog. Quantum Electron. (1)

W. F. Krupke, “Diode pumped alkali lasers (DPALs) — A review (rev1),” J. Prog. Quantum Electron. 36(1), 4–28 (2012).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (1)

J. Ciuryelo and L. Krause, “42P1/2 → 42P3/2 mixing in potassium induced in collisions with noble gas atoms,” J. Quant. Spectrosc. Radiat. Transf. 28(6), 457–461 (1982).
[Crossref]

Opt. Commun. (1)

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Power degradation due to thermal effects in Potassium Diode Pumped Alkali Laser,” Opt. Commun. 341, 97–100 (2015).
[Crossref]

Opt. Eng. (1)

B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2012).
[Crossref]

Opt. Express (2)

Opt. Spectrosc. (USSR) (1)

P. Ya. Kantor, N. P. Penkin, and L. N. Shabanov, “Broadening of the K I 769.9 and 766.5-nm lines by inert gases,” Opt. Spectrosc. (USSR) 59(2), 151–156 (1985).

Proc. SPIE (2)

A. M. Komashko and J. Zweiback, “Modeling laser performance of scalable side-pumped alkali laser,” Proc. SPIE 7581, 75810H (2010).
[Crossref]

B. V. Zhdanov, M. D. Rotondaro, M. K. Shaffer, and R. J. Knize, “Study of potassium DPAL operation in pulsed and CW mode,” Proc. SPIE 9251, 92510Y (2014).

Other (1)

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “CFD assisted simulation of temperature distribution and laser power in pulsed and CW pumped static gas DPALs,” Proc. SPIE (to be published).

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Figures (6)

Fig. 1
Fig. 1 Schematics of K DPAL studied in [3].
Fig. 2
Fig. 2 Normalized spectral distributions of the pump laser, gp(ν), obtained by measurements and of the absorption on the D2 transition.
Fig. 3
Fig. 3 Dependence of the pumping and laser beam sizes (HWHM) on the distance z along the optical axis.
Fig. 4
Fig. 4 Calculated and measured small signal transmission of the K vapor cell for the pump wavelength at different temperatures. Pump intensity is 1 W/cm2.
Fig. 5
Fig. 5 Measured [3] and calculated dependence of the output laser power Plase on the incident pump power Pp,0 for different temperatures and pump and laser beams spatial distributions in the transverse direction.
Fig. 6
Fig. 6 Spatial distribution of the spontaneous emission, pump and laser intensities in the y direction at x = 0 and Pp,0 = 45 W. The vertical axis shows Ip/Ip(y = 0), Il/Il(y = 0) and Isp(103 W/cm3).

Tables (1)

Tables Icon

Table 1 Parameters of K DPAL Used in the Calculations

Equations (21)

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I p (x,y,z,ν)= P p (z,ν) f p (x,y,z),
I l ± (x,y,z)= P l ± (z) f l (x,y,z),
<x,y< dxdy f p,l (x,y,z)=1 .
d P p (z,ν) dz =α(z,ν) P p (z,ν),
d P l ± (z) dz =±β(z) P l ± (z),
α(z,ν)= -<x,y< dxdy σ D 2 (ν)( n 1 n 3 2 ) f p (x,y,z)
β(z)= -<x,y< dxdy σ D 1 ( ν l )( n 2 n 1 ) f l (x,y,z)
σ D 1 ( ν l )= σ D 1 ,at Δ ν D 1 ,n Δ ν D 1
σ D 2 (ν)= σ D 2 ,at Δ ν D 2 ,n Δ ν D 2 ( Δ ν D 2 /2 ) 2 ( ν ν p ) 2 + ( Δ ν D 2 /2 ) 2
n 1 = n 0 Φ s (1+Y F s +Y τ R )+ F s (K+Y)+1+K τ R +Y τ R 1+K τ R +Y τ R + F s (2+3K+3Y)+ Φ s (4Y F s +2Y τ R +1) ,
n 2 = n 0 Φ s (1+Y F s +Y τ R )+2 F s 1+K τ R +Y τ R + F s (2+3K+3Y)+ Φ s (4Y F s +2Y τ R +1) ,
n 3 = n 0 Φ s (2Y F s +K)+2 F s (Y+K) 1+K τ R +Y τ R + F s (2+3K+3Y)+ Φ s (4Y F s +2Y τ R +1) ,
P p (0,ν)= P p,0 t g p (ν),
f p (x,y,z)= ln2 π w x (z) w y (z) exp[ ln2( x 2 w x 2 (z) + y 2 w y 2 (z) ) ],
f l (x,y)= ln2 π w l 2 (z) exp[ ln2 x 2 + y 2 w l 2 (z) ],
Tr= 0 P p (z=l,ν)dν / 0 P p (z=0,ν) dν,
f p (x,y,z)= 1 4 w x (z) w y (z) for | x | w x (z) and | y | w y (z); f p (x,y,z)=0 for | x |> w x (z) and | y |> w y (z),
f p (r)= 1 π r p 2 for r r p 4 w ¯ x w ¯ y π , f p (r)=0 for r> r p ;
f l (r)= 1 π r l 2 for r r l w ¯ l , f l (r)=0 for r> r l ,
P th =h ν p V ( n 2 / τ D 1 + n 3 / τ D 2 ) / ( η abs t) ,
I sp (x,y)= 0 l h ν p ( n 2 / τ D 1 + n 3 / τ D 2 ) dz l

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