Abstract

An analytical model is developed for optimizing two key parameters of an external passive Q-switch in a fiber laser from the criterion of the minimum average mode area inside the saturable absorber. One parameter is the optimum focal position that is analytically derived to be a function of the thickness and initial transmission of the saturable absorber. The other parameter is the optimum magnification of the reimaging optics that is analytically derived to be in terms of the numerical aperture and core radius of the laser fiber as well as the thickness and initial transmission of the saturable absorber. To demonstrate the utilization of the present model, an experiment on the subject of the passively Q-switched fiber laser is performed and optimized.

© 2008 Optical Society of America

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References

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  1. L. Zenteno, “High-power double-clad fiber lasers,” J. Lightwave Technol. 11, 1435-1446 (1993).
    [CrossRef]
  2. M. J. F. Digonnet, Rare-Earth-Doped Fiber Lasers and Amplifiers, 2nd ed. (Marcel Dekker, 2001).
    [CrossRef]
  3. Z. J. Chen, A. B. Grudinin, J. Porta, and J. D. Minelly, “Enhanced Q-switching in double-clad fiber lasers,” Opt. Lett. 23, 454-456 (1998).
    [CrossRef]
  4. J. A. Alvarez-Chavez, H. L. Offerhaus, J. Nilson, P. W. Turner, W. A. Clarkson, and D. J. Richardson, “High-energy high-power ytterbium-doped Q-switched fiber laser,” Opt. Lett. 25, 37-39 (2000).
    [CrossRef]
  5. Y. X. Fan, F. Y. Lu, S. L. Hu, K. C. Lu, H. J. Wang, X. Y. Dong, J. L. He, and H. T. Wang, “Tunable high-peak-power, high-energy hybrid Q-switched double-clad fiber laser,” Opt. Lett. 29, 724-726 (2004).
    [CrossRef] [PubMed]
  6. B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, K. Thyagarajan, M. R. Shenoy, and S. M. Oak, “Mechanisms of generation of multi-peak and mode-locked resembling pulses in Q-switched Yb-doped fiber lasers,” Opt. Express 15, 11576-11588 (2007).
    [CrossRef] [PubMed]
  7. T. Tordella, H. Djellout, B. Dussardier, A. Saïssy, and G. Monnom, “High repetition rate passively Q-switched Nd3+:Cr4+ all-fibre laser,” Electron. Lett. 39, 1307-1308(2003).
    [CrossRef]
  8. A. Fotiadi, A. Kurkov, and I. Razdobreev, “All-fiber passively Q-switched ytterbium laser,” in CLEO/Europe-EQEC 2005, Technical Digest, CJ 2-3 (IEEE, 2005).
    [CrossRef]
  9. P. Adel, M. Auerbach, C. Fallnich, S. Unger, H.-R. Müller, and J. Kirchhof, “Passive Q-switching by Tm3+ co-doping of a Yb3+-fiber laser,” Opt. Express 11, 2730-2735 (2003).
    [CrossRef] [PubMed]
  10. M. Laroche, A. M. Chardon, J. Nilsson, D. P. Shepherd, W. A. Clarkson, S. Girard, and R. Moncorgé, “Compact diode-pumped passively Q-switched tunable Er-Yb double-clad fiber laser,” Opt. Lett. 27, 1980-1982 (2002).
    [CrossRef]
  11. V. N. Philippov, A. V. Kiryanov, and S. Unger, “Advanced configuration of erbium fiber passively Q-switched laser with Co2+:ZnSe crystal as saturable absorber,” IEEE Photonics Technol. Lett. 16, 57-59 (2004).
    [CrossRef]
  12. F. Z. Qamar and T. A. King, “Passive Q-switching of the Tm-silica fiber laser near 2 μm by Cr2+:ZnSe saturable absorber crystal,” Opt. Commun. 248, 501-505 (2005).
    [CrossRef]
  13. M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, “Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber,” IEEE Photon. Technol. Lett. 18, 764-766 (2006).
    [CrossRef]
  14. R. Paschotta, R. Häring, E. Gini, H. Melchior, U. Keller, H. L. Offerhaus, and D. J. Richardson, “Passively Q-switched 0.1 mJ fiber laser system at 1.53 μm,” Opt. Lett. 24, 388-390(1999).
    [CrossRef]
  15. Y. Wang and C. Q. Xu, “Modeling and optimization of Q-switched double-clad fiber lasers,” Appl. Opt. 45, 2058-2071(2006).
    [CrossRef] [PubMed]
  16. Y. F. Chen, Y. P. Lan, and H. L. Chang, “Analytical model for design criteria of passively Q-switched lasers,” IEEE J. Quantum Electron. 37, 462-468 (2001).
    [CrossRef]
  17. J. J. Degnan, “Optimization of passively Q-switched lasers,” IEEE J. Quantum Electron. 31, 1890-1901 (1995).
    [CrossRef]
  18. G. Xiao and M. Bass, “A generalized model Q-switched lasers including excited state absorption in the saturable absorber,” IEEE J. Quantum Electron. 33, 41-44 (1997).
    [CrossRef]
  19. X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
    [CrossRef]
  20. M. Hercher, “An analysis of saturable absorbers,” Appl. Opt. 6, 947-954 (1967).
    [CrossRef] [PubMed]
  21. A. E. Siegman, Lasers (University Science Books, 1986).
  22. K. Lu and N. K. Dutta, “Spectroscopic properties of Yb-doped silica glass,” J. Apl. Phys. 91, 576-581 (2002).
    [CrossRef]
  23. Y. Shimony, Z, Burshtein, and Y. Kalisky, “Cr4+:YAG as passive Q-switch and Brewster plate in a pulsed Nd:YAG laser,” IEEE J. Quantum Electron. 31, 1738-1741 (1995).
    [CrossRef]

2007

2006

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, “Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber,” IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

Y. Wang and C. Q. Xu, “Modeling and optimization of Q-switched double-clad fiber lasers,” Appl. Opt. 45, 2058-2071(2006).
[CrossRef] [PubMed]

2005

A. Fotiadi, A. Kurkov, and I. Razdobreev, “All-fiber passively Q-switched ytterbium laser,” in CLEO/Europe-EQEC 2005, Technical Digest, CJ 2-3 (IEEE, 2005).
[CrossRef]

F. Z. Qamar and T. A. King, “Passive Q-switching of the Tm-silica fiber laser near 2 μm by Cr2+:ZnSe saturable absorber crystal,” Opt. Commun. 248, 501-505 (2005).
[CrossRef]

2004

Y. X. Fan, F. Y. Lu, S. L. Hu, K. C. Lu, H. J. Wang, X. Y. Dong, J. L. He, and H. T. Wang, “Tunable high-peak-power, high-energy hybrid Q-switched double-clad fiber laser,” Opt. Lett. 29, 724-726 (2004).
[CrossRef] [PubMed]

V. N. Philippov, A. V. Kiryanov, and S. Unger, “Advanced configuration of erbium fiber passively Q-switched laser with Co2+:ZnSe crystal as saturable absorber,” IEEE Photonics Technol. Lett. 16, 57-59 (2004).
[CrossRef]

2003

P. Adel, M. Auerbach, C. Fallnich, S. Unger, H.-R. Müller, and J. Kirchhof, “Passive Q-switching by Tm3+ co-doping of a Yb3+-fiber laser,” Opt. Express 11, 2730-2735 (2003).
[CrossRef] [PubMed]

T. Tordella, H. Djellout, B. Dussardier, A. Saïssy, and G. Monnom, “High repetition rate passively Q-switched Nd3+:Cr4+ all-fibre laser,” Electron. Lett. 39, 1307-1308(2003).
[CrossRef]

2002

2001

M. J. F. Digonnet, Rare-Earth-Doped Fiber Lasers and Amplifiers, 2nd ed. (Marcel Dekker, 2001).
[CrossRef]

Y. F. Chen, Y. P. Lan, and H. L. Chang, “Analytical model for design criteria of passively Q-switched lasers,” IEEE J. Quantum Electron. 37, 462-468 (2001).
[CrossRef]

2000

1999

1998

1997

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

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

1995

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

Y. Shimony, Z, Burshtein, and Y. Kalisky, “Cr4+:YAG as passive Q-switch and Brewster plate in a pulsed Nd:YAG laser,” IEEE J. Quantum Electron. 31, 1738-1741 (1995).
[CrossRef]

1993

L. Zenteno, “High-power double-clad fiber lasers,” J. Lightwave Technol. 11, 1435-1446 (1993).
[CrossRef]

1986

A. E. Siegman, Lasers (University Science Books, 1986).

1967

Adel, P.

Aït-Ameur, K.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, “Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber,” IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

Alvarez-Chavez, J. A.

Auerbach, M.

Bass, M.

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

Burshtein,

Y. Shimony, Z, Burshtein, and Y. Kalisky, “Cr4+:YAG as passive Q-switch and Brewster plate in a pulsed Nd:YAG laser,” IEEE J. Quantum Electron. 31, 1738-1741 (1995).
[CrossRef]

Chakravarty, U.

Chang, H. L.

Y. F. Chen, Y. P. Lan, and H. L. Chang, “Analytical model for design criteria of passively Q-switched lasers,” IEEE J. Quantum Electron. 37, 462-468 (2001).
[CrossRef]

Chardon, A. M.

Chen, Y. F.

Y. F. Chen, Y. P. Lan, and H. L. Chang, “Analytical model for design criteria of passively Q-switched lasers,” IEEE J. Quantum Electron. 37, 462-468 (2001).
[CrossRef]

Chen, Z. J.

Clarkson, W. A.

Degnan, J. J.

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

Digonnet, M. J. F.

M. J. F. Digonnet, Rare-Earth-Doped Fiber Lasers and Amplifiers, 2nd ed. (Marcel Dekker, 2001).
[CrossRef]

Djellout, H.

T. Tordella, H. Djellout, B. Dussardier, A. Saïssy, and G. Monnom, “High repetition rate passively Q-switched Nd3+:Cr4+ all-fibre laser,” Electron. Lett. 39, 1307-1308(2003).
[CrossRef]

Dong, X. Y.

Dussardier, B.

T. Tordella, H. Djellout, B. Dussardier, A. Saïssy, and G. Monnom, “High repetition rate passively Q-switched Nd3+:Cr4+ all-fibre laser,” Electron. Lett. 39, 1307-1308(2003).
[CrossRef]

Dutta, N. K.

K. Lu and N. K. Dutta, “Spectroscopic properties of Yb-doped silica glass,” J. Apl. Phys. 91, 576-581 (2002).
[CrossRef]

Fallnich, C.

Fan, Y. X.

Fotiadi, A.

A. Fotiadi, A. Kurkov, and I. Razdobreev, “All-fiber passively Q-switched ytterbium laser,” in CLEO/Europe-EQEC 2005, Technical Digest, CJ 2-3 (IEEE, 2005).
[CrossRef]

Gilles, H.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, “Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber,” IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

Gini, E.

Girard, S.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, “Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber,” IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

M. Laroche, A. M. Chardon, J. Nilsson, D. P. Shepherd, W. A. Clarkson, S. Girard, and R. Moncorgé, “Compact diode-pumped passively Q-switched tunable Er-Yb double-clad fiber laser,” Opt. Lett. 27, 1980-1982 (2002).
[CrossRef]

Grudinin, A. B.

Häring, R.

He, J. L.

Hercher, M.

Hu, S. L.

Kalisky, Y.

Y. Shimony, Z, Burshtein, and Y. Kalisky, “Cr4+:YAG as passive Q-switch and Brewster plate in a pulsed Nd:YAG laser,” IEEE J. Quantum Electron. 31, 1738-1741 (1995).
[CrossRef]

Keller, U.

King, T. A.

F. Z. Qamar and T. A. King, “Passive Q-switching of the Tm-silica fiber laser near 2 μm by Cr2+:ZnSe saturable absorber crystal,” Opt. Commun. 248, 501-505 (2005).
[CrossRef]

Kirchhof, J.

Kiryanov, A. V.

V. N. Philippov, A. V. Kiryanov, and S. Unger, “Advanced configuration of erbium fiber passively Q-switched laser with Co2+:ZnSe crystal as saturable absorber,” IEEE Photonics Technol. Lett. 16, 57-59 (2004).
[CrossRef]

Kurkov, A.

A. Fotiadi, A. Kurkov, and I. Razdobreev, “All-fiber passively Q-switched ytterbium laser,” in CLEO/Europe-EQEC 2005, Technical Digest, CJ 2-3 (IEEE, 2005).
[CrossRef]

Kuruvilla, A.

Lan, Y. P.

Y. F. Chen, Y. P. Lan, and H. L. Chang, “Analytical model for design criteria of passively Q-switched lasers,” IEEE J. Quantum Electron. 37, 462-468 (2001).
[CrossRef]

Laroche, M.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, “Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber,” IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

M. Laroche, A. M. Chardon, J. Nilsson, D. P. Shepherd, W. A. Clarkson, S. Girard, and R. Moncorgé, “Compact diode-pumped passively Q-switched tunable Er-Yb double-clad fiber laser,” Opt. Lett. 27, 1980-1982 (2002).
[CrossRef]

Lu, F. Y.

Lu, K.

K. Lu and N. K. Dutta, “Spectroscopic properties of Yb-doped silica glass,” J. Apl. Phys. 91, 576-581 (2002).
[CrossRef]

Lu, K. C.

Melchior, H.

Minelly, J. D.

Moncorgé, R.

Monnom, G.

T. Tordella, H. Djellout, B. Dussardier, A. Saïssy, and G. Monnom, “High repetition rate passively Q-switched Nd3+:Cr4+ all-fibre laser,” Electron. Lett. 39, 1307-1308(2003).
[CrossRef]

Müller, H.-R.

Nilson, J.

Nilsson, J.

Oak, S. M.

Offerhaus, H. L.

Paschotta, R.

Passilly, N.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, “Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber,” IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

Philippov, V. N.

V. N. Philippov, A. V. Kiryanov, and S. Unger, “Advanced configuration of erbium fiber passively Q-switched laser with Co2+:ZnSe crystal as saturable absorber,” IEEE Photonics Technol. Lett. 16, 57-59 (2004).
[CrossRef]

Porta, J.

Qamar, F. Z.

F. Z. Qamar and T. A. King, “Passive Q-switching of the Tm-silica fiber laser near 2 μm by Cr2+:ZnSe saturable absorber crystal,” Opt. Commun. 248, 501-505 (2005).
[CrossRef]

Razdobreev, I.

A. Fotiadi, A. Kurkov, and I. Razdobreev, “All-fiber passively Q-switched ytterbium laser,” in CLEO/Europe-EQEC 2005, Technical Digest, CJ 2-3 (IEEE, 2005).
[CrossRef]

Richardson, D. J.

Saïssy, A.

T. Tordella, H. Djellout, B. Dussardier, A. Saïssy, and G. Monnom, “High repetition rate passively Q-switched Nd3+:Cr4+ all-fibre laser,” Electron. Lett. 39, 1307-1308(2003).
[CrossRef]

Shenoy, M. R.

Shepherd, D. P.

Shimony, Y.

Y. Shimony, Z, Burshtein, and Y. Kalisky, “Cr4+:YAG as passive Q-switch and Brewster plate in a pulsed Nd:YAG laser,” IEEE J. Quantum Electron. 31, 1738-1741 (1995).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Sun, L.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Thyagarajan, K.

Tordella, T.

T. Tordella, H. Djellout, B. Dussardier, A. Saïssy, and G. Monnom, “High repetition rate passively Q-switched Nd3+:Cr4+ all-fibre laser,” Electron. Lett. 39, 1307-1308(2003).
[CrossRef]

Turner, P. W.

Unger, S.

V. N. Philippov, A. V. Kiryanov, and S. Unger, “Advanced configuration of erbium fiber passively Q-switched laser with Co2+:ZnSe crystal as saturable absorber,” IEEE Photonics Technol. Lett. 16, 57-59 (2004).
[CrossRef]

P. Adel, M. Auerbach, C. Fallnich, S. Unger, H.-R. Müller, and J. Kirchhof, “Passive Q-switching by Tm3+ co-doping of a Yb3+-fiber laser,” Opt. Express 11, 2730-2735 (2003).
[CrossRef] [PubMed]

Upadhyaya, B. N.

Wang, H. J.

Wang, H. T.

Wang, Q.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Wang, Y.

Xiao, G.

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

Xu, C. Q.

Z,

Y. Shimony, Z, Burshtein, and Y. Kalisky, “Cr4+:YAG as passive Q-switch and Brewster plate in a pulsed Nd:YAG laser,” IEEE J. Quantum Electron. 31, 1738-1741 (1995).
[CrossRef]

Zenteno, L.

L. Zenteno, “High-power double-clad fiber lasers,” J. Lightwave Technol. 11, 1435-1446 (1993).
[CrossRef]

Zhang, Q.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Zhang, S.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Zhang, X.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Zhao, S.

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Appl. Opt.

Electron. Lett.

T. Tordella, H. Djellout, B. Dussardier, A. Saïssy, and G. Monnom, “High repetition rate passively Q-switched Nd3+:Cr4+ all-fibre laser,” Electron. Lett. 39, 1307-1308(2003).
[CrossRef]

IEEE J. Quantum Electron.

Y. F. Chen, Y. P. Lan, and H. L. Chang, “Analytical model for design criteria of passively Q-switched lasers,” IEEE J. Quantum Electron. 37, 462-468 (2001).
[CrossRef]

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

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

X. Zhang, S. Zhao, Q. Wang, Q. Zhang, L. Sun, and S. Zhang, “Optimization of Cr4+-doped saturable-absorber Q-switched lasers,” IEEE J. Quantum Electron. 33, 2286-2294 (1997).
[CrossRef]

Y. Shimony, Z, Burshtein, and Y. Kalisky, “Cr4+:YAG as passive Q-switch and Brewster plate in a pulsed Nd:YAG laser,” IEEE J. Quantum Electron. 31, 1738-1741 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Laroche, H. Gilles, S. Girard, N. Passilly, and K. Aït-Ameur, “Nanosecond pulse generation in a passively Q-switched Yb-doped fiber laser by Cr4+:YAG saturable absorber,” IEEE Photon. Technol. Lett. 18, 764-766 (2006).
[CrossRef]

IEEE Photonics Technol. Lett.

V. N. Philippov, A. V. Kiryanov, and S. Unger, “Advanced configuration of erbium fiber passively Q-switched laser with Co2+:ZnSe crystal as saturable absorber,” IEEE Photonics Technol. Lett. 16, 57-59 (2004).
[CrossRef]

J. Apl. Phys.

K. Lu and N. K. Dutta, “Spectroscopic properties of Yb-doped silica glass,” J. Apl. Phys. 91, 576-581 (2002).
[CrossRef]

J. Lightwave Technol.

L. Zenteno, “High-power double-clad fiber lasers,” J. Lightwave Technol. 11, 1435-1446 (1993).
[CrossRef]

Opt. Commun.

F. Z. Qamar and T. A. King, “Passive Q-switching of the Tm-silica fiber laser near 2 μm by Cr2+:ZnSe saturable absorber crystal,” Opt. Commun. 248, 501-505 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Other

M. J. F. Digonnet, Rare-Earth-Doped Fiber Lasers and Amplifiers, 2nd ed. (Marcel Dekker, 2001).
[CrossRef]

A. Fotiadi, A. Kurkov, and I. Razdobreev, “All-fiber passively Q-switched ytterbium laser,” in CLEO/Europe-EQEC 2005, Technical Digest, CJ 2-3 (IEEE, 2005).
[CrossRef]

A. E. Siegman, Lasers (University Science Books, 1986).

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Figures (9)

Fig. 1
Fig. 1

Schematic illustration of the external cavity in a passively Q-switched fiber laser. ω o is the beam waist of the laser mode; z o is the position of the beam waist.

Fig. 2
Fig. 2

A comparison for the calculated results ω s 2 obtained with Eqs. (16, 17) for a typical case with the parameters of N A = 0.04 , r c = 12.5 μm , n r = 1.82 , T o = 0.4 , and l a = 2 mm .

Fig. 3
Fig. 3

Dependence of the average mode area on the focal position for several T o values; the results are calculated with Eq. (18) and the parameters of N A = 0.04 , r c = 12.5 μm , n r = 1.82 , and l a = 2 mm .

Fig. 4
Fig. 4

Dependence of the average mode area on the magnification for several l a values; the results are calculated with Eq. (22) and the parameters of N A = 0.04 , r c = 12.5 μm , n r = 1.82 , and T o = 0.5 .

Fig. 5
Fig. 5

Schematic setup of a diode-pumped passively Q-switched Yb-doped double-clad fiber laser. HR: high reflection; HT: high transmission.

Fig. 6
Fig. 6

Experimental and theoretical results for the output pulse energy as a function of the focal position. Symbols are experimental data. Solid line is calculated results using Eqs. (8, 9).

Fig. 7
Fig. 7

Average output powers versus the incident pump power for CW lasing between facets, CW lasing with the external high-reflection cavity, and passive Q-switching operation with the external high-reflection cavity and the saturable absorber at the optimum focal position.

Fig. 8
Fig. 8

Pulse repetition rate and pulse energy versus the incident pump power at the optimum focal position.

Fig. 9
Fig. 9

Experimental and theoretical results for the dependence of the output pulse energy on the focal position at an incident pump power of 10 W . Symbols are experimental data. Solid line is calculated results using Eqs. (8, 9).

Equations (23)

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

d ϕ d t = ϕ t r [ 2 σ n l 2 σ gs n gs l s 2 σ es n es l s ( ln ( 1 R ) + L ) ] ,
d n d t = γ c σ ϕ n ,
d n gs d t = A A s c σ gs ϕ n gs ,
n gs + n es = n so ,
d n gs d n = A A s 1 γ σ gs σ n gs n .
n gs = n so ( n n i ) α ,
α = 1 γ σ gs σ A A s .
E = h v A 2 σ γ ln ( 1 R ) x ,
1 e x x + ( 1 σ es / σ gs ) ln ( 1 / T o 2 ) ln ( 1 / T o 2 ) + ln ( 1 / R ) + L ( x 1 e α x α ) = 0.
ω s ( z ) = ω o 1 + [ C ( z z o ) ] 2 ,
C = M 2 λ π n r ω o 2 ,
ω o = M a r c .
M 2 = ( NA · r c ) ( π / λ ) ,
C = NA n r M a 2 r c .
A s = π ω s 2
ω s 2 = 0 l a ω s 2 ( z ) [ e n so σ gs z + e n so σ gs ( 2 l a z ) ] d z 0 l a [ e n so σ gs z + e n so σ gs ( 2 l a z ) ] d z ,
ω s 2 = 0 l a ω s 2 ( z ) e n so σ gs z d z 0 l a e n so σ gs z d z .
A s = π ω o 2 C 2 { z o 2 2 z o l a [ 1 ln ( 1 / T o ) T o 1 T o ] + [ 1 C 2 + 2 l a 2 ( ln ( 1 / T o ) ) 2 l a 2 ( T o 1 T o ) ( 1 + 2 ln ( 1 / T o ) ) ] } ,
A s z o | z o = z opt = 2 π ω o 2 C 2 × { z opt l a [ 1 ln ( 1 / T o ) T o 1 T o ] } = 0 .
z opt = l a [ 1 ln ( 1 / T o ) T o 1 T o ] .
A s = π { M a 2 r c 2 + ( NA ) 2 l a 2 n r 2 M a 2 [ 1 ( ln ( 1 / T o ) ) 2 T o ( 1 T o ) 2 ] } .
A s M a | M a = M opt = π { 2 M opt r c 2 2 ( NA ) 2 l a 2 n r 2 M opt 3 [ 1 ( ln ( 1 / T o ) ) 2 T o ( 1 T o ) 2 ] } = 0 .
M opt = { ( NA ) 2 l a 2 n r 2 r c 2 [ 1 ( ln ( 1 / T o ) ) 2 T o ( 1 T o ) 2 ] } 1 / 4 .

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