Abstract

As a new kind of optically pumped gaseous lasers, diode pumped metastable rare gas lasers (OPRGLs) show potential in high power operation. In this paper, a multi-level rate equation based model of OPRGL is established. A qualitative agreement between simulation and Rawlins et al.’s experimental result shows the validity of the model. The key parameters’ influences and energy distribution characteristics are theoretically studied, which is useful for the optimized design of high efficient OPRGLs.

© 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),” 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 (2013).
    [Crossref]
  3. J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G(2010).
    [Crossref]
  4. 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]
  5. A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
    [Crossref]
  6. B. Zhdanov and R. J. Knize, “Diode-pumped 10 W continuous wave cesium laser,” Opt. Lett. 32(15), 2167–2169 (2007).
    [Crossref] [PubMed]
  7. L. Zhiyong, T. Rongqing, H. Wei, and Z. Dandan, “Quasicontinuous wave linearly polarized rubidium vapor laser pumped by a 5-bar laser diode stack,” Opt. Eng. 53(11), 116113 (2014).
    [Crossref]
  8. L. O. Quarrie, “The effect of atomic rubidium vapor on the performance of optical windows in diode pumped alkali laser (DPALs),” Opt. Mater. 35(5), 843–851 (2013).
    [Crossref]
  9. S. S. Q. Wu, T. F. Soules, R. H. Page, S. C. Mitchell, V. K. Kanz, and R. J. Beach, “Hydrocarbon-free resonance transition 795-nm rubidium laser,” Opt. Lett. 32(16), 2423–2425 (2007).
    [Crossref] [PubMed]
  10. J. P. Nole, “Nanotextured optical surfaces advance laser power and reliability,” Laser Focus World. 50, 38–43 (2014).
  11. J. Han and M. C. Heaven, “Gain and lasing of optically pumped metastable rare gas atoms,” Opt. Lett. 37(11), 2157–2159 (2012).
    [Crossref] [PubMed]
  12. J. Han, L. Glebov, G. Venus, and M. C. Heaven, “Demonstration of a diode-pumped metastable Ar laser,” Opt. Lett. 38(24), 5458–5461 (2013).
    [Crossref] [PubMed]
  13. W. T. Rawlins, K. L. Galbally-Kinney, S. J. Davis, A. R. Hoskinson, J. A. Hopwood, and M. C. Heaven, “Optically pumped microplasma rare gas laser,” Opt. Express 23(4), 4804–4813 (2015).
    [Crossref] [PubMed]
  14. J. Han, M. C. Heaven, G. D. Hager, G. B. Venus, and L. B. Glebov, “Kinetics of an optically pumped metastable Ar laser,” Proc. SPIE 8962, 896202 (2014).
    [Crossref]
  15. A. V. Demyanov, I. V. Kochetov, and P. A. Mikheyev, “Kinetic study of a cw optically pumped laser with metastable rare gas atoms produced in an electric discharge,” J. Phys. D Appl. Phys. 46(37), 375202 (2013).
    [Crossref]
  16. A. Kramida and Y. Ralchenko, J. Reader and NIST ASD Team (2013). NIST Atomic Spectra Database. Available: http://physics.nist.gov/asd .
  17. R. S. F. Chang and D. W. Setser, “Radiative lifetimes and twobody deactivation rate constants for Ar (3p5, 4p) and Ar (3p5, 4p’) states,” J. Chem. Phys. 69(9), 3885–3897 (1978).
    [Crossref]
  18. J. Han and M. C. Heaven, “Kinetics of optically pumped Ar metastables,” Opt. Lett. 39(22), 6541–6544 (2014).
    [Crossref] [PubMed]
  19. W. Wieme and J. Lenaerts, “Excimer formation in argon, krypton, and xenon discharge afterglows between 200 and 400K,” J. Chem. Phys. 74(1), 483–493 (1981).
    [Crossref]
  20. R. J. Beach, W. F. Krupke, V. K. Kanz, S. A. Payne, M. A. Dubinskii, and L. D. Merkle, “End-pumped continuous-wave alkali vapor lasers: experiment, model, and power scaling,” J. Opt. Soc. Am. B 21(12), 2151–2163 (2004).
    [Crossref]

2015 (1)

2014 (4)

J. Han, M. C. Heaven, G. D. Hager, G. B. Venus, and L. B. Glebov, “Kinetics of an optically pumped metastable Ar laser,” Proc. SPIE 8962, 896202 (2014).
[Crossref]

J. Han and M. C. Heaven, “Kinetics of optically pumped Ar metastables,” Opt. Lett. 39(22), 6541–6544 (2014).
[Crossref] [PubMed]

L. Zhiyong, T. Rongqing, H. Wei, and Z. Dandan, “Quasicontinuous wave linearly polarized rubidium vapor laser pumped by a 5-bar laser diode stack,” Opt. Eng. 53(11), 116113 (2014).
[Crossref]

J. P. Nole, “Nanotextured optical surfaces advance laser power and reliability,” Laser Focus World. 50, 38–43 (2014).

2013 (5)

L. O. Quarrie, “The effect of atomic rubidium vapor on the performance of optical windows in diode pumped alkali laser (DPALs),” Opt. Mater. 35(5), 843–851 (2013).
[Crossref]

B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2013).
[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]

J. Han, L. Glebov, G. Venus, and M. C. Heaven, “Demonstration of a diode-pumped metastable Ar laser,” Opt. Lett. 38(24), 5458–5461 (2013).
[Crossref] [PubMed]

A. V. Demyanov, I. V. Kochetov, and P. A. Mikheyev, “Kinetic study of a cw optically pumped laser with metastable rare gas atoms produced in an electric discharge,” J. Phys. D Appl. Phys. 46(37), 375202 (2013).
[Crossref]

2012 (3)

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

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

J. Han and M. C. Heaven, “Gain and lasing of optically pumped metastable rare gas atoms,” Opt. Lett. 37(11), 2157–2159 (2012).
[Crossref] [PubMed]

2010 (1)

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G(2010).
[Crossref]

2007 (2)

2004 (1)

1981 (1)

W. Wieme and J. Lenaerts, “Excimer formation in argon, krypton, and xenon discharge afterglows between 200 and 400K,” J. Chem. Phys. 74(1), 483–493 (1981).
[Crossref]

1978 (1)

R. S. F. Chang and D. W. Setser, “Radiative lifetimes and twobody deactivation rate constants for Ar (3p5, 4p) and Ar (3p5, 4p’) states,” J. Chem. Phys. 69(9), 3885–3897 (1978).
[Crossref]

Barmashenko, B. D.

Beach, R. J.

Bogachev, A. V.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Chang, R. S. F.

R. S. F. Chang and D. W. Setser, “Radiative lifetimes and twobody deactivation rate constants for Ar (3p5, 4p) and Ar (3p5, 4p’) states,” J. Chem. Phys. 69(9), 3885–3897 (1978).
[Crossref]

Dandan, Z.

L. Zhiyong, T. Rongqing, H. Wei, and Z. Dandan, “Quasicontinuous wave linearly polarized rubidium vapor laser pumped by a 5-bar laser diode stack,” Opt. Eng. 53(11), 116113 (2014).
[Crossref]

Davis, S. J.

Demyanov, A. V.

A. V. Demyanov, I. V. Kochetov, and P. A. Mikheyev, “Kinetic study of a cw optically pumped laser with metastable rare gas atoms produced in an electric discharge,” J. Phys. D Appl. Phys. 46(37), 375202 (2013).
[Crossref]

Dubinskii, M. A.

Dudov, A. M.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Galbally-Kinney, K. L.

Garanin, S. G.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Glebov, L.

Glebov, L. B.

J. Han, M. C. Heaven, G. D. Hager, G. B. Venus, and L. B. Glebov, “Kinetics of an optically pumped metastable Ar laser,” Proc. SPIE 8962, 896202 (2014).
[Crossref]

Hager, G. D.

J. Han, M. C. Heaven, G. D. Hager, G. B. Venus, and L. B. Glebov, “Kinetics of an optically pumped metastable Ar laser,” Proc. SPIE 8962, 896202 (2014).
[Crossref]

Han, J.

Heaven, M. C.

Hopwood, J. A.

Hoskinson, A. R.

Kanz, V. K.

Knize, R. J.

B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2013).
[Crossref]

B. Zhdanov and R. J. Knize, “Diode-pumped 10 W continuous wave cesium laser,” Opt. Lett. 32(15), 2167–2169 (2007).
[Crossref] [PubMed]

Kochetov, I. V.

A. V. Demyanov, I. V. Kochetov, and P. A. Mikheyev, “Kinetic study of a cw optically pumped laser with metastable rare gas atoms produced in an electric discharge,” J. Phys. D Appl. Phys. 46(37), 375202 (2013).
[Crossref]

Komashko, A.

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G(2010).
[Crossref]

Krupke, W. F.

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

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G(2010).
[Crossref]

R. J. Beach, W. F. Krupke, V. K. Kanz, S. A. Payne, M. A. Dubinskii, and L. D. Merkle, “End-pumped continuous-wave alkali vapor lasers: experiment, model, and power scaling,” J. Opt. Soc. Am. B 21(12), 2151–2163 (2004).
[Crossref]

Kulikov, S. M.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Lenaerts, J.

W. Wieme and J. Lenaerts, “Excimer formation in argon, krypton, and xenon discharge afterglows between 200 and 400K,” J. Chem. Phys. 74(1), 483–493 (1981).
[Crossref]

Merkle, L. D.

Mikaelian, G. T.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Mikheyev, P. A.

A. V. Demyanov, I. V. Kochetov, and P. A. Mikheyev, “Kinetic study of a cw optically pumped laser with metastable rare gas atoms produced in an electric discharge,” J. Phys. D Appl. Phys. 46(37), 375202 (2013).
[Crossref]

Mitchell, S. C.

Nole, J. P.

J. P. Nole, “Nanotextured optical surfaces advance laser power and reliability,” Laser Focus World. 50, 38–43 (2014).

Page, R. H.

Panarin, V. A.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Pautov, V. O.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Payne, S. A.

Quarrie, L. O.

L. O. Quarrie, “The effect of atomic rubidium vapor on the performance of optical windows in diode pumped alkali laser (DPALs),” Opt. Mater. 35(5), 843–851 (2013).
[Crossref]

Rawlins, W. T.

Rongqing, T.

L. Zhiyong, T. Rongqing, H. Wei, and Z. Dandan, “Quasicontinuous wave linearly polarized rubidium vapor laser pumped by a 5-bar laser diode stack,” Opt. Eng. 53(11), 116113 (2014).
[Crossref]

Rosenwaks, S.

Rus, A. V.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Setser, D. W.

R. S. F. Chang and D. W. Setser, “Radiative lifetimes and twobody deactivation rate constants for Ar (3p5, 4p) and Ar (3p5, 4p’) states,” J. Chem. Phys. 69(9), 3885–3897 (1978).
[Crossref]

Soules, T. F.

Sukharev, S. A.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Venus, G.

Venus, G. B.

J. Han, M. C. Heaven, G. D. Hager, G. B. Venus, and L. B. Glebov, “Kinetics of an optically pumped metastable Ar laser,” Proc. SPIE 8962, 896202 (2014).
[Crossref]

Wei, H.

L. Zhiyong, T. Rongqing, H. Wei, and Z. Dandan, “Quasicontinuous wave linearly polarized rubidium vapor laser pumped by a 5-bar laser diode stack,” Opt. Eng. 53(11), 116113 (2014).
[Crossref]

Wieme, W.

W. Wieme and J. Lenaerts, “Excimer formation in argon, krypton, and xenon discharge afterglows between 200 and 400K,” J. Chem. Phys. 74(1), 483–493 (1981).
[Crossref]

Wu, S. S. Q.

Yeroshenko, V. A.

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Zhdanov, B.

Zhdanov, B. V.

B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2013).
[Crossref]

Zhiyong, L.

L. Zhiyong, T. Rongqing, H. Wei, and Z. Dandan, “Quasicontinuous wave linearly polarized rubidium vapor laser pumped by a 5-bar laser diode stack,” Opt. Eng. 53(11), 116113 (2014).
[Crossref]

Zweiback, J.

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G(2010).
[Crossref]

J. Chem. Phys. (2)

R. S. F. Chang and D. W. Setser, “Radiative lifetimes and twobody deactivation rate constants for Ar (3p5, 4p) and Ar (3p5, 4p’) states,” J. Chem. Phys. 69(9), 3885–3897 (1978).
[Crossref]

W. Wieme and J. Lenaerts, “Excimer formation in argon, krypton, and xenon discharge afterglows between 200 and 400K,” J. Chem. Phys. 74(1), 483–493 (1981).
[Crossref]

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

J. Phys. D Appl. Phys. (1)

A. V. Demyanov, I. V. Kochetov, and P. A. Mikheyev, “Kinetic study of a cw optically pumped laser with metastable rare gas atoms produced in an electric discharge,” J. Phys. D Appl. Phys. 46(37), 375202 (2013).
[Crossref]

J. Quantum Electron. (1)

A. V. Bogachev, S. G. Garanin, A. M. Dudov, V. A. Yeroshenko, S. M. Kulikov, G. T. Mikaelian, V. A. Panarin, V. O. Pautov, A. V. Rus, and S. A. Sukharev, “Diode-pumped caesium vapour laser with closed-cycle laser-active medium circulation,” J. Quantum Electron. 42(2), 95–98 (2012).
[Crossref]

Laser Focus World. (1)

J. P. Nole, “Nanotextured optical surfaces advance laser power and reliability,” Laser Focus World. 50, 38–43 (2014).

Opt. Eng. (2)

L. Zhiyong, T. Rongqing, H. Wei, and Z. Dandan, “Quasicontinuous wave linearly polarized rubidium vapor laser pumped by a 5-bar laser diode stack,” Opt. Eng. 53(11), 116113 (2014).
[Crossref]

B. V. Zhdanov and R. J. Knize, “Review of alkali laser research and development,” Opt. Eng. 52(2), 021010 (2013).
[Crossref]

Opt. Express (1)

Opt. Lett. (5)

Opt. Mater. (1)

L. O. Quarrie, “The effect of atomic rubidium vapor on the performance of optical windows in diode pumped alkali laser (DPALs),” Opt. Mater. 35(5), 843–851 (2013).
[Crossref]

Proc. SPIE (2)

J. Zweiback, A. Komashko, and W. F. Krupke, “Alkali vapor lasers,” Proc. SPIE 7581, 75810G(2010).
[Crossref]

J. Han, M. C. Heaven, G. D. Hager, G. B. Venus, and L. B. Glebov, “Kinetics of an optically pumped metastable Ar laser,” Proc. SPIE 8962, 896202 (2014).
[Crossref]

Prog. Quantum Electron. (1)

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

Other (1)

A. Kramida and Y. Ralchenko, J. Reader and NIST ASD Team (2013). NIST Atomic Spectra Database. Available: http://physics.nist.gov/asd .

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Figures (7)

Fig. 1
Fig. 1 Energy levels and population transfer channels in OPRGLs.
Fig. 2
Fig. 2 Influence of k21 on laser performance. The solid circle dot line and solid diamond dot line represent Ilaser vs IPump at different Ar 1s5 concentration at realistic k21 value, while the hollow circle dot line represents the performance at infinite k21 value
Fig. 3
Fig. 3 Influence of Ar (1s5) concentration on optical conversion efficiency at different pump intensities.
Fig. 4
Fig. 4 Influence of Ar (1s5) concentration on optical conversion efficiency at different gain length, pump intensity 5kW/cm2.
Fig. 5
Fig. 5 Influence of helium pressure (with constant Ar partial pressure of 20torr) on optical conversion efficiency at different pump intensity and Ar (1s5) concentration.
Fig. 6
Fig. 6 Influence of helium pressure (with constant Ar partial pressure of 20torr) on pump absorption efficiency ( η pump absorption ), optical conversion efficiency ( η laser ), optical conversion efficiency relative to absorbed pump power ( η laserabs ), fluorescence efficiency relative to absorbed pump power ( η fluorescenceabs ) and heat efficiency relative to absorbed pump power ( η heatabs ).
Fig. 7
Fig. 7 Absorbed pump power distribution of a diode pumped Ar metastable laser.

Tables (1)

Tables Icon

Table 1 Collisional relaxation processes that involved in the model.

Equations (13)

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d n 1 dt = W pump + W laser + k 21 [ n 2 g 2 g 1 n 1 exp( Δ E 21 kT ) ]+ n 3 ( A 31 + k 31 )+ n 4 ( A 41 + k 41 ) + n 5 ( A 51 + k 51 ) n 1 k A r 2 * ,
d n 2 dt = n 3 A 32 + n 5 A 52 k 21 [ n 2 g 2 g 1 n 1 exp( Δ E 21 kT ) ] n 2 A 20 eff ,
d n 3 dt = W laser + k 43 [ n 4 g 4 g 3 n 3 exp( Δ E 43 kT ) ]+ k 53 [ n 5 g 5 g 3 n 3 exp( Δ E 53 kT ) ] n 3 ( A 31 + A 32 + A p10s2 + A p10s3 + k 31 ),
d n 4 dt = W pump + k 54 [ n 5 g 5 g 4 n 4 exp( Δ E 54 kT ) ] k 43 [ n 4 g 4 g 3 n 3 exp( Δ E 43 kT ) ] n 4 ( A 41 + k 41 ),
d n 5 dt = k 54 [ n 5 g 5 g 4 n 4 exp( Δ E 54 kT ) ] k 53 [ n 5 g 5 g 3 n 3 exp( Δ E 53 kT ) ] n 5 ( A 51 + A 52 + A p8s2 + k 51 ),
d I L dt = c 2 l cavity { R L R OC T r 2 exp[ 2( n 3 g 3 g 1 n 1 ) σ 31 broadened l gain ]1 } I L .
W pump = η del η mode l gain dλ 1 h v P I P g P (λ) { 1exp[ ( n 1 g 1 g 4 n 4 ) σ 14 broadened (λ) l gain ] } { 1+ R P T r 2 exp[ ( n 1 g 1 g 4 n 4 ) σ 14 broadened (λ) l gain ] },
W laser = 1 l gain I L h ν L R OC 1 R OC ( 1 T r R L R OC 1 )( 1+ T r R L R OC ),
P laser = I laser S,
P fluorescence = V gain ( n 3 A 31 Δ E 31 + n 3 A 32 Δ E 32 + n 4 A 41 Δ E 41 + n 5 A 51 Δ E 51 + n 5 A 52 Δ E 52 ),
P heat = V gain { n 3 k 31 Δ E 31 + n 4 k 41 Δ E 41 + n 5 k 51 Δ E 51 + k 21 Δ E 21 [ n 2 g 2 g 1 n 1 exp( Δ E 21 kT ) ] + k 43 Δ E 43 [ n 4 g 4 g 3 n 3 exp( Δ E 43 kT ) ]+ k 54 Δ E 54 [ n 5 g 5 g 4 n 4 exp( Δ E 54 kT ) ] + k 53 Δ E 53 [ n 5 g 5 g 3 n 3 exp( Δ E 53 kT ) ] },
P scatter = P laser [ R OC /(1 R OC )1/ R L R OC T r 2 ][ (1 T r )+ T r (1 R L )+ T r R L (1 T r ) ],
P additional loss = V gain [ n 2 A 20 Δ E 21 + n 3 ( A p10s2 + A p10s3 )Δ E 31 + n 5 A p8s2 Δ E 51 ].

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