Abstract

We derive the analytical expressions for the output Stokes pulse energy extracted from Q-switched lasers with intracavity Raman conversion. It has been shown that the problem of Stokes-pulse-energy optimization in Q-switched lasers is closely related to the optimization of intracavity photon-number density at a fundamental frequency in such lasers without the intracavity Raman conversion, although it has been found that at fixed laser parameters there is an optimum value of the cavity-mirror reflectivity at a Stokes frequency that maximizes the output Stokes pulse energy. These results have been applied for the Stokes-pulse-energy optimization of microchip solid-state lasers.

© 2005 Optical Society of America

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  1. Y. R. Shen, Principles of Nonlinear Optics (Wiley, 1984).
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    [Crossref]
  3. J. K. Brasseur, K. S. Repasky, and J. L. Carlsten, “Continuous-wave Raman laser in H2,” Opt. Lett.  23, 367–369 (1998).
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  4. L. S. Meng, P. A. Roos, and J. L. Carlsten, “Continuous-wave rotational Raman laser in H2,” Opt. Lett.  27, 1226–1228 (2002).
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  5. A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, G. I. Ryabtsev, V. A. Orlovich, and A. A. Demidovich, “Stimulated Raman scattering in Nd:KGW laser with diode pumping,” J. Alloys Compd.300–301, 300–302 (2000).
  6. J. Findeisen, H. J. Eichler, and P. Peuser, “Self-stimulating, transversely diode pumped Nd3+:KGd(WO4)2 Raman laser,” Opt. Commun.  181, 129–133 (2000).
    [Crossref]
  7. W. Chen, Yu. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd3+:PbWO4 Raman laser,” Opt. Commun.  194, 401–407 (2001).
    [Crossref]
  8. P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun.  209, 403–409 (2002).
    [Crossref]
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    [Crossref]
  10. W. Koechner, Solid State Laser Engineering (Springer–Verlag, 1979).
  11. Y. Kalisky, “New trends in lasers and laser crystals,” Opt. Mater. (Amsterdam, Neth.)  13, 135–139 (1999).
    [Crossref]
  12. H. M. Pask, “The design and operation of solid-state Raman lasers,” Prog. Quantum Electron.  27, 3–56 (2003).
    [Crossref]
  13. P. Mandel, Theoretical Problems in Cavity Nonlinear Optics (Cambridge U. Press, 1997).
    [Crossref]
  14. J. J. Degnan, “Theory of the optimally coupled Q-switched laser,” IEEE J. Quantum Electron.  QE-25, 214–220 (1989).
    [Crossref]
  15. J. J. Zayhowski and P. L. Kelley, “Optimization of Q-switched lasers,” IEEE J. Quantum Electron.  QE-27, 2220–2225 (1991).
    [Crossref]
  16. J. J. Degnan, “Optimization of passively Q-switched lasers,” IEEE J. Quantum Electron.  QE-31, 1890–1901 (1995).
    [Crossref]
  17. J. J. Degnan, D. B. Coyle, and R. B. Kay, “Effects of thermalization on Q-switched laser properties,” IEEE J. Quantum Electron.  QE-34, 887–899 (1998).
    [Crossref]
  18. G. Xiao and M. Bass, “A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber,” IEEE J. Quantum Electron.  QE-33, 41–44 (1997).
    [Crossref]
  19. P. Peterson and A. Gavrielides, “Pulse train characteristics of a passively Q-switched microchip laser,” Opt. Express  5, 149–156 (1999).
    [Crossref] [PubMed]
  20. J. Liu, D. Shen, S.-Ch. Tam, and Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron.  QE-37, 888–896 (2001).
  21. J. K. Brasseur, P. A. Roos, K. S. Repasky, and J. L. Carlsten, “Characterization of a continuous-wave Raman laser in H2,” J. Opt. Soc. Am. B  16, 1305–1312 (1999).
    [Crossref]
  22. J. C. Bienfang, W. Rudolph, P. A. Roos, L. S. Meng, and J. L. Carlsten, “Steady state thermo-optic model of a continuous-wave Raman laser,” J. Opt. Soc. Am. B  19, 1318–1325 (2002).
    [Crossref]
  23. P. A. Roos, L. S. Meng, and J. L. Carlsten, “Optimization of a far-off-resonance continuous-wave Raman laser,” J. Opt. Soc. Am. B  19, 1310–1317 (2002).
    [Crossref]
  24. Yu. V. Loiko, A. A. Demidovich, V. A. Lisinetskii (B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Nezaleznasti Avenue 68, 220072 Minsk, Belarus), and A. P. Voitovich are preparing a manuscript to be called “Analytical treatment of Q-switched lasers with intracavity Raman conversion.”
  25. T.T.Basiev and R.C.Powell, eds., “Special issue on solid-state Raman lasers,” Opt. Mater. 11, 301–390 (1999).
  26. J. P. Meyn, T. Jensen, and G. Hubner, “Spectroscopic properties and efficient diode-pumped laser operation of Neodymium-doped Lanthanum Scandium Borate,” IEEE J. Quantum Electron.  QE-30, 913–917 (1994).
    [Crossref]

2003 (2)

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

H. M. Pask, “The design and operation of solid-state Raman lasers,” Prog. Quantum Electron.  27, 3–56 (2003).
[Crossref]

2002 (4)

2001 (2)

W. Chen, Yu. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd3+:PbWO4 Raman laser,” Opt. Commun.  194, 401–407 (2001).
[Crossref]

J. Liu, D. Shen, S.-Ch. Tam, and Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron.  QE-37, 888–896 (2001).

2000 (1)

J. Findeisen, H. J. Eichler, and P. Peuser, “Self-stimulating, transversely diode pumped Nd3+:KGd(WO4)2 Raman laser,” Opt. Commun.  181, 129–133 (2000).
[Crossref]

1999 (3)

1998 (2)

J. J. Degnan, D. B. Coyle, and R. B. Kay, “Effects of thermalization on Q-switched laser properties,” IEEE J. Quantum Electron.  QE-34, 887–899 (1998).
[Crossref]

J. K. Brasseur, K. S. Repasky, and J. L. Carlsten, “Continuous-wave Raman laser in H2,” Opt. Lett.  23, 367–369 (1998).
[Crossref]

1997 (1)

G. Xiao and M. Bass, “A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber,” IEEE J. Quantum Electron.  QE-33, 41–44 (1997).
[Crossref]

1995 (1)

J. J. Degnan, “Optimization of passively Q-switched lasers,” IEEE J. Quantum Electron.  QE-31, 1890–1901 (1995).
[Crossref]

1994 (1)

J. P. Meyn, T. Jensen, and G. Hubner, “Spectroscopic properties and efficient diode-pumped laser operation of Neodymium-doped Lanthanum Scandium Borate,” IEEE J. Quantum Electron.  QE-30, 913–917 (1994).
[Crossref]

1991 (1)

J. J. Zayhowski and P. L. Kelley, “Optimization of Q-switched lasers,” IEEE J. Quantum Electron.  QE-27, 2220–2225 (1991).
[Crossref]

1989 (1)

J. J. Degnan, “Theory of the optimally coupled Q-switched laser,” IEEE J. Quantum Electron.  QE-25, 214–220 (1989).
[Crossref]

1979 (1)

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron.  6, 55–140 (1979).
[Crossref]

Apanasevich, P. A.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

Bass, M.

G. Xiao and M. Bass, “A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber,” IEEE J. Quantum Electron.  QE-33, 41–44 (1997).
[Crossref]

Batay, L. E.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

Bienfang, J. C.

Brasseur, J. K.

Carlsten, J. L.

Cerny, P.

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun.  209, 403–409 (2002).
[Crossref]

Chen, W.

W. Chen, Yu. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd3+:PbWO4 Raman laser,” Opt. Commun.  194, 401–407 (2001).
[Crossref]

Coyle, D. B.

J. J. Degnan, D. B. Coyle, and R. B. Kay, “Effects of thermalization on Q-switched laser properties,” IEEE J. Quantum Electron.  QE-34, 887–899 (1998).
[Crossref]

Danailov, M. B.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

Degnan, J. J.

J. J. Degnan, D. B. Coyle, and R. B. Kay, “Effects of thermalization on Q-switched laser properties,” IEEE J. Quantum Electron.  QE-34, 887–899 (1998).
[Crossref]

J. J. Degnan, “Optimization of passively Q-switched lasers,” IEEE J. Quantum Electron.  QE-31, 1890–1901 (1995).
[Crossref]

J. J. Degnan, “Theory of the optimally coupled Q-switched laser,” IEEE J. Quantum Electron.  QE-25, 214–220 (1989).
[Crossref]

Demidovich, A. A.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, G. I. Ryabtsev, V. A. Orlovich, and A. A. Demidovich, “Stimulated Raman scattering in Nd:KGW laser with diode pumping,” J. Alloys Compd.300–301, 300–302 (2000).

Yu. V. Loiko, A. A. Demidovich, V. A. Lisinetskii (B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Nezaleznasti Avenue 68, 220072 Minsk, Belarus), and A. P. Voitovich are preparing a manuscript to be called “Analytical treatment of Q-switched lasers with intracavity Raman conversion.”

Eichler, H. J.

J. Findeisen, H. J. Eichler, and P. Peuser, “Self-stimulating, transversely diode pumped Nd3+:KGd(WO4)2 Raman laser,” Opt. Commun.  181, 129–133 (2000).
[Crossref]

Findeisen, J.

J. Findeisen, H. J. Eichler, and P. Peuser, “Self-stimulating, transversely diode pumped Nd3+:KGd(WO4)2 Raman laser,” Opt. Commun.  181, 129–133 (2000).
[Crossref]

Gavrielides, A.

Grabtchikov, A. S.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, G. I. Ryabtsev, V. A. Orlovich, and A. A. Demidovich, “Stimulated Raman scattering in Nd:KGW laser with diode pumping,” J. Alloys Compd.300–301, 300–302 (2000).

Hait, V. L.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

Hubner, G.

J. P. Meyn, T. Jensen, and G. Hubner, “Spectroscopic properties and efficient diode-pumped laser operation of Neodymium-doped Lanthanum Scandium Borate,” IEEE J. Quantum Electron.  QE-30, 913–917 (1994).
[Crossref]

Inagawa, Yu.

W. Chen, Yu. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd3+:PbWO4 Raman laser,” Opt. Commun.  194, 401–407 (2001).
[Crossref]

Jabczynski, J.

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun.  209, 403–409 (2002).
[Crossref]

Jelinkova, H.

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun.  209, 403–409 (2002).
[Crossref]

Jensen, T.

J. P. Meyn, T. Jensen, and G. Hubner, “Spectroscopic properties and efficient diode-pumped laser operation of Neodymium-doped Lanthanum Scandium Borate,” IEEE J. Quantum Electron.  QE-30, 913–917 (1994).
[Crossref]

Kaiser, W.

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron.  6, 55–140 (1979).
[Crossref]

Kalisky, Y.

Y. Kalisky, “New trends in lasers and laser crystals,” Opt. Mater. (Amsterdam, Neth.)  13, 135–139 (1999).
[Crossref]

Kay, R. B.

J. J. Degnan, D. B. Coyle, and R. B. Kay, “Effects of thermalization on Q-switched laser properties,” IEEE J. Quantum Electron.  QE-34, 887–899 (1998).
[Crossref]

Kelley, P. L.

J. J. Zayhowski and P. L. Kelley, “Optimization of Q-switched lasers,” IEEE J. Quantum Electron.  QE-27, 2220–2225 (1991).
[Crossref]

Kiefer, W.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

Koechner, W.

W. Koechner, Solid State Laser Engineering (Springer–Verlag, 1979).

Kopczynski, K.

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun.  209, 403–409 (2002).
[Crossref]

Kuzmin, A. N.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, G. I. Ryabtsev, V. A. Orlovich, and A. A. Demidovich, “Stimulated Raman scattering in Nd:KGW laser with diode pumping,” J. Alloys Compd.300–301, 300–302 (2000).

Kuzmin, O. V.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

Lam, Y.-L.

J. Liu, D. Shen, S.-Ch. Tam, and Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron.  QE-37, 888–896 (2001).

Laubereau, A.

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron.  6, 55–140 (1979).
[Crossref]

Lisinetskii, V. A.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, G. I. Ryabtsev, V. A. Orlovich, and A. A. Demidovich, “Stimulated Raman scattering in Nd:KGW laser with diode pumping,” J. Alloys Compd.300–301, 300–302 (2000).

Yu. V. Loiko, A. A. Demidovich, V. A. Lisinetskii (B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Nezaleznasti Avenue 68, 220072 Minsk, Belarus), and A. P. Voitovich are preparing a manuscript to be called “Analytical treatment of Q-switched lasers with intracavity Raman conversion.”

Liu, J.

J. Liu, D. Shen, S.-Ch. Tam, and Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron.  QE-37, 888–896 (2001).

Loiko, Yu. V.

Yu. V. Loiko, A. A. Demidovich, V. A. Lisinetskii (B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Nezaleznasti Avenue 68, 220072 Minsk, Belarus), and A. P. Voitovich are preparing a manuscript to be called “Analytical treatment of Q-switched lasers with intracavity Raman conversion.”

Mandel, P.

P. Mandel, Theoretical Problems in Cavity Nonlinear Optics (Cambridge U. Press, 1997).
[Crossref]

Meng, L. S.

Meyn, J. P.

J. P. Meyn, T. Jensen, and G. Hubner, “Spectroscopic properties and efficient diode-pumped laser operation of Neodymium-doped Lanthanum Scandium Borate,” IEEE J. Quantum Electron.  QE-30, 913–917 (1994).
[Crossref]

Omatsu, T.

W. Chen, Yu. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd3+:PbWO4 Raman laser,” Opt. Commun.  194, 401–407 (2001).
[Crossref]

Orlovich, V. A.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, G. I. Ryabtsev, V. A. Orlovich, and A. A. Demidovich, “Stimulated Raman scattering in Nd:KGW laser with diode pumping,” J. Alloys Compd.300–301, 300–302 (2000).

Pask, H. M.

H. M. Pask, “The design and operation of solid-state Raman lasers,” Prog. Quantum Electron.  27, 3–56 (2003).
[Crossref]

Penzkofer, A.

A. Penzkofer, A. Laubereau, and W. Kaiser, “High intensity Raman interactions,” Prog. Quantum Electron.  6, 55–140 (1979).
[Crossref]

Peterson, P.

Peuser, P.

J. Findeisen, H. J. Eichler, and P. Peuser, “Self-stimulating, transversely diode pumped Nd3+:KGd(WO4)2 Raman laser,” Opt. Commun.  181, 129–133 (2000).
[Crossref]

Repasky, K. S.

Roos, P. A.

Rudolph, W.

Ryabtsev, G. I.

A. A. Demidovich, P. A. Apanasevich, L. E. Batay, A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, V. A. Orlovich, G. I. Ryabtsev, O. V. Kuzmin, V. L. Hait, W. Kiefer, and M. B. Danailov, “Sub-nanosecond microchip laser with intracavity Raman conversion,” Appl. Phys. B  76, 509–514 (2003).
[Crossref]

A. S. Grabtchikov, A. N. Kuzmin, V. A. Lisinetskii, G. I. Ryabtsev, V. A. Orlovich, and A. A. Demidovich, “Stimulated Raman scattering in Nd:KGW laser with diode pumping,” J. Alloys Compd.300–301, 300–302 (2000).

Shen, D.

J. Liu, D. Shen, S.-Ch. Tam, and Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron.  QE-37, 888–896 (2001).

Shen, Y. R.

Y. R. Shen, Principles of Nonlinear Optics (Wiley, 1984).

Sulc, J.

P. Cerny, W. Zendzian, J. Jabczynski, H. Jelinkova, J. Sulc, and K. Kopczynski, “Efficient diode-pumped passively Q-switched Raman laser on barium tungstate crystal,” Opt. Commun.  209, 403–409 (2002).
[Crossref]

Takeuchi, N.

W. Chen, Yu. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd3+:PbWO4 Raman laser,” Opt. Commun.  194, 401–407 (2001).
[Crossref]

Tam, S.-Ch.

J. Liu, D. Shen, S.-Ch. Tam, and Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron.  QE-37, 888–896 (2001).

Tateda, M.

W. Chen, Yu. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd3+:PbWO4 Raman laser,” Opt. Commun.  194, 401–407 (2001).
[Crossref]

Usuki, Y.

W. Chen, Yu. Inagawa, T. Omatsu, M. Tateda, N. Takeuchi, and Y. Usuki, “Diode-pumped, self-stimulating, passively Q-switched Nd3+:PbWO4 Raman laser,” Opt. Commun.  194, 401–407 (2001).
[Crossref]

Voitovich, A. P.

Yu. V. Loiko, A. A. Demidovich, V. A. Lisinetskii (B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Nezaleznasti Avenue 68, 220072 Minsk, Belarus), and A. P. Voitovich are preparing a manuscript to be called “Analytical treatment of Q-switched lasers with intracavity Raman conversion.”

Xiao, G.

G. Xiao and M. Bass, “A generalized model for passively Q-switched lasers including excited state absorption in the saturable absorber,” IEEE J. Quantum Electron.  QE-33, 41–44 (1997).
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Figures (1)

Fig. 1
Fig. 1

Energy extracted by the Stokes pulse from Nd:LSB microchip lasers with Cr 4 + : YAG as the SA and Ba ( N O 3 ) 2 as the Raman medium. The dependences of the output Stokes pulse energy on the output mirror reflectivity at Stokes frequency R 2 at two different small-signal transmissions of SA, which are equal to (a) T 0 = 0.90 ( l a = 0.35 mm , t r 1 = t r 2 = 40 ps ), Ǝ 1 = 0.01 , Ǝ 2 = 0.07 and (b) T 0 = 0.85 ( l a = 0.56 mm , t r 1 = t r 2 = 43 ps ), Ǝ 1 = 0.04 , Ǝ 2 = 0.02 . (c) The dependence of the optimized output Stokes pulse energy on the mirror reflectivity at fundamental frequency ( R 1 ) ; (d) the curves in the plane of the coupling factors R 1 and R 2 which optimize (maximize) output Stokes pulse energy. Dashed and solid curves represent the results obtained by the numerical integration of the model [Eq. (1)] and by the analytical expression [Eq. (16)], respectively. Solid (open) squares and circles represent the optimized value of Stokes pulse energy obtained analytically (numerically) at T 0 = 0.90 and T 0 = 0.85 , respectively. Crosses denote the data obtained experimentally at R 1 = 0.97 with the other parameters as given in Table 1.

Tables (1)

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Table 1 Laser Parameters

Equations (38)

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d N 1 d t = 1 t r 1 N 1 [ k 1 + 2 l g σ g n 2 l a σ a n a 2 l a σ ESA ( n ¯ a n a ) ] N 1 ( G R t r 2 N 2 + G ) ,
d N 2 d t = 1 t r 2 N 2 ( k 2 + G R N 1 ) + G N 1 ,
d n d t = γ ( n n ¯ ) r c σ g n N 1 ,
d n a d t = γ a ( n a n ¯ a ) r a c σ a n a N 1 ,
d N 1 d n = 1 t r 1 r c σ g 1 n [ k 1 2 l g σ g n + 2 l a σ a n a + 2 l a σ ESA ( n ¯ a n a ) + t r 1 G R t r 2 N 2 + t r 1 G ] ,
d N 2 d n = 1 t r 2 r c σ g 1 n ( k 2 N 2 N 1 G R N 2 ) 1 n G r c σ g ,
d n d t = r c σ g n N 1 ,
d n a d t = r a c σ a n a N 1 .
n a = n a 0 ( n n 0 ) r a σ a r σ g ,
d N 1 d x = 1 x [ ( ρ 1 + L 1 ) z g x + z a ( x ) α ] + 1 x z R N 2 + 1 x z sp ,
d N 2 d x = 1 x [ ( ρ 2 + L 2 ) 1 N 1 z R ] N 2 1 x z sp .
x = n n 0 , α = r a σ a r σ g ,
z R = G R t r 2 r c σ g = 1 2 h c λ 1 2 l R g R t r 2 r σ g , z sp = G r c σ g ,
z g = 2 l g σ g n 0 t r 1 r c σ g , z a = 2 ln T 0 1 t r 1 r c σ g ( 1 σ ESA σ a ) ,
ln T 0 1 = l a σ a n a 0 ,
k 1 ( 2 ) = [ ρ 1 ( 2 ) + L 1 ( 2 ) ] t r 1 ( r 2 ) r c σ g ,
ρ 1 ( 2 ) = ln [ 1 R 1 ( 2 ) ] t r 1 ( r 2 ) r c σ g ,
L 1 = Θ 1 t r 1 r c σ g + 2 ln T 0 1 t r 1 r c σ g σ ESA σ a , L 2 = Θ 2 t r 2 r c σ g ,
N 1 FFL ( x ) = ( ρ 1 + L 1 ) ln x z g ( x 1 ) + α 1 z a ( x α 1 ) .
N 1 ( exact ) ( x ) = N 1 FFL ( x ) N 20 ( x x 1 ) z R ,
N 2 ( exact ) ( x ) = N 20 ( x x 1 ) z R ,
E FL ( a , b ) = t a t b P FL ( t ) d t = h ν 1 A 1 l 1 t r 1 ln ( 1 R 1 ) t a t b N 1 ( t ) d t = h ν 1 A 1 l 1 t r 1 r c σ g ln ( 1 R 1 ) ln x a x b ,
E FL = h ν 1 A 1 l 1 t r 1 r c σ g ln ( 1 R 1 ) ln 1 x 2 f ,
E R ( a , b ) = t a t b P R ( t ) d t = h ν 2 A 2 l 2 t r 2 ln ( 1 R 2 ) t a t b N 2 ( t ) d t = h ν 2 A 2 l 2 t r 2 r c σ g ln ( 1 R 2 ) x b x a N 2 ( x ) N 1 ( x ) d x x .
d N 1 d x = d N 1 FFL d x d N 2 d x + ( ρ 2 + L 2 ) 1 x N 2 ( x ) N 1 ( x ) .
E R ( a , b ) = h ν 2 A 2 l 2 t r 2 r c σ g ln ( 1 R 2 ) ( ρ 2 + L 2 ) x b x a ( d N 1 d N 1 FFL + d N 2 ) = h ν 2 A 2 l 2 t r 2 r c σ g ln ( 1 R 2 ) ( ρ 2 + L 2 ) { [ N 1 FEL ( x b ) N 1 ( x b ) N 2 ( x b ) ] [ N 1 FFL ( x a ) N 1 ( x a ) N 2 ( x a ) ] } .
E R = h ν 2 A 2 l 2 t r 2 r c σ g ln ( 1 R 2 ) ( ρ 2 + L 2 ) { [ N 1 FFL ( x 2 f ) N 1 ( x 2 f ) N 2 ( x 2 f ) ] [ N 1 FFL ( x 0 ) N 1 ( x 0 ) N 2 ( x 0 ) ] } .
N 1 ( x 2 f ) = N 2 ( x 2 f ) = N 1 FFL ( x 0 ) = N 1 ( x 0 ) = N 2 ( x 0 ) = 0 .
E R ( front ) = h ν 2 A 2 l 2 t r 2 r c σ g ln ( 1 R 2 ) ( ρ 2 + L 2 ) [ N 1 FFL ( x 2 m ) N 1 ( x 2 m ) N 2 ( x 2 m ) ] ,
E R ( tail ) = h ν 2 A 2 l 2 t r 2 r c σ g ln ( 1 R 2 ) ( ρ 2 + L 2 ) { N 1 FFL ( x 2 f ) [ N 1 FFL ( x 2 m ) N 1 ( x 2 m ) N 2 ( x 2 m ) ] } .
E R = h ν 2 A 2 l 2 t r 2 r c σ g ln ( 1 R 2 ) ( ρ 2 + L 2 ) N 1 FFL ( x 2 f ) = ( h ν 2 A 2 l 2 ) × ρ 2 ( ρ 2 + L 2 ) N 1 FFL ( x 2 f ) ,
x 2 f = exp ( E FL h ν 1 A 1 l 1 t r 1 r c σ g ln 1 R 1 ) .
E R = h ν 2 A 2 l 2 t r 2 r c σ g ln ( 1 R 2 ) ( ρ 2 + L 2 ) N 1 FFL [ exp ( E F L h ν 1 A 1 l 1 t r 1 r c σ g ln 1 R 1 ) ] ,
E R h ν 2 A 2 l 2 ( ρ 2 + L 2 ) ρ 2 = E F L h ν 1 A 1 l 1 ( ρ 1 + L 1 ) ρ 1 z g [ exp ( E FL h ν 1 A 1 l 1 1 ρ 1 ) 1 ] + z a α [ exp ( α E FL h ν 1 A 1 l 1 1 ρ 1 ) 1 ] .
E R max = ( h ν 2 A 2 l 2 ) max [ N 1 FFL ( x 2 f ) ] ,
d N 1 d t = 1 t r 1 N 1 [ k 1 + 2 l g σ g n 2 l a σ a n a 2 l a σ ESA ( n ¯ a n a ) ] a t r 2 N 1 N 2 Q sin ( φ 2 φ 1 + φ Q ) ,
d N 2 d t = 1 t r 2 [ k 2 N 2 + a N 1 N 2 Q sin ( φ 2 φ 1 + φ Q ) ] ,
d Q d t = 2 Γ Q Q + b N 1 N 2 Q sin ( φ 2 φ 1 + φ Q ) ,

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