Abstract

We describe a systematic, rigorous procedure for the determination of the optical absorption saturation parameters for Cr4+:YAG and Cr4+:forsterite crystals at 1064nm. A rate-equation approach was used to analyze the cw and pulsed transmission data of several crystals by accounting for the transverse as well as longitudinal variation of the beam intensity, saturation effects, and excited-state absorption. Use of an iterative procedure whereby the cw and pulsed data were simultaneously analyzed led to a considerable reduction in the error for the determination of cross sections. The average value of the absorption cross section σa and the normalized excited-state absorption cross section fp=σesaσa were determined to be 6.13×1019cm2 and 0.45, respectively, for Cr4+:forsterite and 19.6×1019cm2 and 0.06, respectively, for Cr4+:YAG. Detailed comparison was also made with previous saturation measurements in the literature. Our results further show that lumped models based on the thin-length approximation should be used with caution in the determination of cross sections, especially when the pump beam is tightly focused inside the absorber.

© 2006 Optical Society of America

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  1. A. Sennaroglu, "Broadly tunable Cr4+-doped solid-state lasers in the near infrared and visible," Prog. Quantum Electron. 26, 287-352 (2002).
    [CrossRef]
  2. M. I. Demchuk, V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, P. V. Prokoshin, K. V. Yumashev, M. G. Livshits, and B. I. Minkov, "Chromium-doped forsterite as solid-state saturable absorber," Opt. Lett. 17, 929-930 (1992).
    [CrossRef] [PubMed]
  3. H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, "Saturation of 1.064 µm absorption in Cr,Ca:Y3Al5O12 crystals," Appl. Phys. Lett. 61, 2958-2960 (1992).
    [CrossRef]
  4. J. J. Zayhowski and C. Dill, "Diode-pumped passively Q-switiched picosecond microchip lasers," Opt. Lett. 19, 1427-1429 (1994).
    [CrossRef] [PubMed]
  5. 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]
  6. Y.-F. Chen and S. W. Tsai, "Simultaneous Q switching and mode-locking in a diode-pumped Nd:YVO 4-Cr4+:YAG laser," IEEE J. Quantum Electron. 37, 580-586 (2001).
    [CrossRef]
  7. Y. Kalisky, "Cr4+-doped crystals: their use as lasers and passive Q switches," Prog. Quantum Electron. 28, 249-303 (2004).
    [CrossRef]
  8. H. R. Verdun and L. Merkle, "Evidence of excited-state absorption of pump radiation in the Cr:forsterite laser," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).
  9. V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).
  10. K. Spariosu, W. Chen, R. Stultz, and M. Birnbaum, "Dual Q switching and laser action at 1.06 and 1.44µm in a Nd3+:YAG-Cr4+:YAG oscillator at 300 K," Opt. Lett. 18, 814-816 (1993).
    [CrossRef] [PubMed]
  11. M. I. Demchuk, N. V. Kuleshov, and V. P. Mikhailov, "Saturable absorbers based on impurity and defect centers in crystals," IEEE J. Quantum Electron. 30, 2120-2126 (1994).
    [CrossRef]
  12. A. Sennaroglu, C. R. Pollock, and H. Nathel, "Efficient continuous-wave chromium-doped YAG laser," J. Opt. Soc. Am. B 12, 930-937 (1995).
    [CrossRef]
  13. A. Sennaroglu, "Continuous wave thermal loading in saturable absorbers: theory and experiment," Appl. Opt. 36, 9528-9535 (1997).
    [CrossRef]
  14. A. Sennaroglu and B. Pekerten, "Experimental and numerical investigation of thermal effects in end-pumped Cr4+:forsterite lasers near room temperature," IEEE J. Quantum Electron. 34, 1996-2005 (1998).
    [CrossRef]
  15. Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kokta, "Excited-state absorption studies of Cr4+ ions in several garnet host crystals," IEEE J. Quantum Electron. 34, 292-299 (1998).
    [CrossRef]
  16. N. V. Kuleshov, A. V. Podlipensky, V. G. Shcherbitsky, A. A. Lagatsky, and V. P. Mikhailov, "Excited-state absorption in the range of pumping and laser efficiency of Cr4+:fosterite," Opt. Lett. 23, 1028-1030 (1998).
    [CrossRef]
  17. T. Togashi, Y. Nabekawa, T. Sekikawa, and S. Watanabe, "High-peak power femtosecond Cr:forsterite laser system," Appl. Phys. B: Photophys. Laser Chem. 68, 169-175 (1999).
    [CrossRef]
  18. G. Xiao, J. H. Lim, S. Yang, E. V. Stryland, M. Bass, and L. Weichman, "Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet," IEEE J. Quantum Electron. 35, 1086-1091 (1999).
    [CrossRef]
  19. A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, "Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a double-pulse pumping technique," IEEE J. Quantum Electron. 35, 1548-1553 (1999).
    [CrossRef]
  20. A. G. Okhrimchuk and A. V. Shestakov, "Absorption saturation mechanism for YAG:Cr4+ crystals," Phys. Rev. B 61, 988-995 (2000).
    [CrossRef]
  21. A. Sennaroglu, "Analysis and optimization of lifetime thermal loading in continuous-wave Cr4+-doped solid-state lasers," J. Opt. Soc. Am. B 18, 1578-1586 (2001).
    [CrossRef]
  22. A. Sennaroglu, A. Kurt, and S. Buhours, "Analysis and optimization of diode end-pumped solid-state lasers: Application to Nd3+:YVO4 lasers at 1064 and 1342 nm," Opt. Eng. 44, 054202 (2005).
    [CrossRef]
  23. A. Sennaroglu and B. Pekerten, "Determination of the optimum absorption coefficient in Cr4+:forsterite lasers under thermal loading," Opt. Lett. 23, 361-363 (1998).
    [CrossRef]
  24. Y. Kalisky, R. Moncorge, Y. Guyot, and M. Kokta, "Laser operation and Q-switching properties of (Cr4+,Mg2+):YAG crystal," in Advanced Solid-State Lasers, Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998).
  25. S. Kück, K. Petermann, and G. Huber, "Spectroscopic investigation of the Cr4+-center in YAG," in Advanced Solid-State Lasers (Optical Society of America, 1991).
  26. N. I. Borodin, V. A. Zhitnyuk, A. G. Okhrimchuk, and A. V. Shestakov, "Oscillation of a Y3Al5O12:Cr4+ laser in wave length region of 1.34-1.6 mm," Izv. Akad. Nauk SSSR Ser. Fiz. 54, 1500-1506 (1990).
  27. S. Naumov, E. Sorokin, and I. T. Sorokina, "Measurement of the excited state absorption cross-section in Cr4+:YAG using relaxation oscillations study," in Advanced Solid-State Photonics, Vol. 98 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2005).
  28. J. Chen, H.-F. Yau, H.-P. Liu, T.-C. Chen, C.-C. Cheng, and F.-M. Liu, "Passive Q-switch and mode-locking modulators for Nd:hosted lasers," Opt. Laser Technol. 32, 215-219 (2000).
    [CrossRef]
  29. T. Dascalu, G. Philipps, and H. Weber, "Investigation of a Cr4+:YAG passive Q-switch in cw pumped Nd: YAG lasers," Opt. Laser Technol. 29, 145-149 (1997).
    [CrossRef]

2005 (1)

A. Sennaroglu, A. Kurt, and S. Buhours, "Analysis and optimization of diode end-pumped solid-state lasers: Application to Nd3+:YVO4 lasers at 1064 and 1342 nm," Opt. Eng. 44, 054202 (2005).
[CrossRef]

2004 (1)

Y. Kalisky, "Cr4+-doped crystals: their use as lasers and passive Q switches," Prog. Quantum Electron. 28, 249-303 (2004).
[CrossRef]

2002 (1)

A. Sennaroglu, "Broadly tunable Cr4+-doped solid-state lasers in the near infrared and visible," Prog. Quantum Electron. 26, 287-352 (2002).
[CrossRef]

2001 (2)

Y.-F. Chen and S. W. Tsai, "Simultaneous Q switching and mode-locking in a diode-pumped Nd:YVO 4-Cr4+:YAG laser," IEEE J. Quantum Electron. 37, 580-586 (2001).
[CrossRef]

A. Sennaroglu, "Analysis and optimization of lifetime thermal loading in continuous-wave Cr4+-doped solid-state lasers," J. Opt. Soc. Am. B 18, 1578-1586 (2001).
[CrossRef]

2000 (2)

A. G. Okhrimchuk and A. V. Shestakov, "Absorption saturation mechanism for YAG:Cr4+ crystals," Phys. Rev. B 61, 988-995 (2000).
[CrossRef]

J. Chen, H.-F. Yau, H.-P. Liu, T.-C. Chen, C.-C. Cheng, and F.-M. Liu, "Passive Q-switch and mode-locking modulators for Nd:hosted lasers," Opt. Laser Technol. 32, 215-219 (2000).
[CrossRef]

1999 (3)

T. Togashi, Y. Nabekawa, T. Sekikawa, and S. Watanabe, "High-peak power femtosecond Cr:forsterite laser system," Appl. Phys. B: Photophys. Laser Chem. 68, 169-175 (1999).
[CrossRef]

G. Xiao, J. H. Lim, S. Yang, E. V. Stryland, M. Bass, and L. Weichman, "Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet," IEEE J. Quantum Electron. 35, 1086-1091 (1999).
[CrossRef]

A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, "Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a double-pulse pumping technique," IEEE J. Quantum Electron. 35, 1548-1553 (1999).
[CrossRef]

1998 (4)

A. Sennaroglu and B. Pekerten, "Experimental and numerical investigation of thermal effects in end-pumped Cr4+:forsterite lasers near room temperature," IEEE J. Quantum Electron. 34, 1996-2005 (1998).
[CrossRef]

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kokta, "Excited-state absorption studies of Cr4+ ions in several garnet host crystals," IEEE J. Quantum Electron. 34, 292-299 (1998).
[CrossRef]

N. V. Kuleshov, A. V. Podlipensky, V. G. Shcherbitsky, A. A. Lagatsky, and V. P. Mikhailov, "Excited-state absorption in the range of pumping and laser efficiency of Cr4+:fosterite," Opt. Lett. 23, 1028-1030 (1998).
[CrossRef]

A. Sennaroglu and B. Pekerten, "Determination of the optimum absorption coefficient in Cr4+:forsterite lasers under thermal loading," Opt. Lett. 23, 361-363 (1998).
[CrossRef]

1997 (2)

T. Dascalu, G. Philipps, and H. Weber, "Investigation of a Cr4+:YAG passive Q-switch in cw pumped Nd: YAG lasers," Opt. Laser Technol. 29, 145-149 (1997).
[CrossRef]

A. Sennaroglu, "Continuous wave thermal loading in saturable absorbers: theory and experiment," Appl. Opt. 36, 9528-9535 (1997).
[CrossRef]

1995 (2)

A. Sennaroglu, C. R. Pollock, and H. Nathel, "Efficient continuous-wave chromium-doped YAG laser," J. Opt. Soc. Am. B 12, 930-937 (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]

1994 (2)

J. J. Zayhowski and C. Dill, "Diode-pumped passively Q-switiched picosecond microchip lasers," Opt. Lett. 19, 1427-1429 (1994).
[CrossRef] [PubMed]

M. I. Demchuk, N. V. Kuleshov, and V. P. Mikhailov, "Saturable absorbers based on impurity and defect centers in crystals," IEEE J. Quantum Electron. 30, 2120-2126 (1994).
[CrossRef]

1993 (1)

1992 (2)

M. I. Demchuk, V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, P. V. Prokoshin, K. V. Yumashev, M. G. Livshits, and B. I. Minkov, "Chromium-doped forsterite as solid-state saturable absorber," Opt. Lett. 17, 929-930 (1992).
[CrossRef] [PubMed]

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, "Saturation of 1.064 µm absorption in Cr,Ca:Y3Al5O12 crystals," Appl. Phys. Lett. 61, 2958-2960 (1992).
[CrossRef]

1990 (1)

N. I. Borodin, V. A. Zhitnyuk, A. G. Okhrimchuk, and A. V. Shestakov, "Oscillation of a Y3Al5O12:Cr4+ laser in wave length region of 1.34-1.6 mm," Izv. Akad. Nauk SSSR Ser. Fiz. 54, 1500-1506 (1990).

Baryshevski, V. G.

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Bass, M.

G. Xiao, J. H. Lim, S. Yang, E. V. Stryland, M. Bass, and L. Weichman, "Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet," IEEE J. Quantum Electron. 35, 1086-1091 (1999).
[CrossRef]

Birnbaum, M.

Blau, P.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kokta, "Excited-state absorption studies of Cr4+ ions in several garnet host crystals," IEEE J. Quantum Electron. 34, 292-299 (1998).
[CrossRef]

Borodin, N. I.

N. I. Borodin, V. A. Zhitnyuk, A. G. Okhrimchuk, and A. V. Shestakov, "Oscillation of a Y3Al5O12:Cr4+ laser in wave length region of 1.34-1.6 mm," Izv. Akad. Nauk SSSR Ser. Fiz. 54, 1500-1506 (1990).

Buhours, S.

A. Sennaroglu, A. Kurt, and S. Buhours, "Analysis and optimization of diode end-pumped solid-state lasers: Application to Nd3+:YVO4 lasers at 1064 and 1342 nm," Opt. Eng. 44, 054202 (2005).
[CrossRef]

Burshtein, Z.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kokta, "Excited-state absorption studies of Cr4+ ions in several garnet host crystals," IEEE J. Quantum Electron. 34, 292-299 (1998).
[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]

Chen, J.

J. Chen, H.-F. Yau, H.-P. Liu, T.-C. Chen, C.-C. Cheng, and F.-M. Liu, "Passive Q-switch and mode-locking modulators for Nd:hosted lasers," Opt. Laser Technol. 32, 215-219 (2000).
[CrossRef]

Chen, T.-C.

J. Chen, H.-F. Yau, H.-P. Liu, T.-C. Chen, C.-C. Cheng, and F.-M. Liu, "Passive Q-switch and mode-locking modulators for Nd:hosted lasers," Opt. Laser Technol. 32, 215-219 (2000).
[CrossRef]

Chen, W.

Chen, Y.-F.

Y.-F. Chen and S. W. Tsai, "Simultaneous Q switching and mode-locking in a diode-pumped Nd:YVO 4-Cr4+:YAG laser," IEEE J. Quantum Electron. 37, 580-586 (2001).
[CrossRef]

Cheng, C.-C.

J. Chen, H.-F. Yau, H.-P. Liu, T.-C. Chen, C.-C. Cheng, and F.-M. Liu, "Passive Q-switch and mode-locking modulators for Nd:hosted lasers," Opt. Laser Technol. 32, 215-219 (2000).
[CrossRef]

Dascalu, T.

T. Dascalu, G. Philipps, and H. Weber, "Investigation of a Cr4+:YAG passive Q-switch in cw pumped Nd: YAG lasers," Opt. Laser Technol. 29, 145-149 (1997).
[CrossRef]

Demchuk, M. I.

M. I. Demchuk, N. V. Kuleshov, and V. P. Mikhailov, "Saturable absorbers based on impurity and defect centers in crystals," IEEE J. Quantum Electron. 30, 2120-2126 (1994).
[CrossRef]

M. I. Demchuk, V. P. Mikhailov, N. I. Zhavoronkov, N. V. Kuleshov, P. V. Prokoshin, K. V. Yumashev, M. G. Livshits, and B. I. Minkov, "Chromium-doped forsterite as solid-state saturable absorber," Opt. Lett. 17, 929-930 (1992).
[CrossRef] [PubMed]

Dennis, W. M.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, "Saturation of 1.064 µm absorption in Cr,Ca:Y3Al5O12 crystals," Appl. Phys. Lett. 61, 2958-2960 (1992).
[CrossRef]

Dill, C.

Eilers, H.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, "Saturation of 1.064 µm absorption in Cr,Ca:Y3Al5O12 crystals," Appl. Phys. Lett. 61, 2958-2960 (1992).
[CrossRef]

Guyot, Y.

Y. Kalisky, R. Moncorge, Y. Guyot, and M. Kokta, "Laser operation and Q-switching properties of (Cr4+,Mg2+):YAG crystal," in Advanced Solid-State Lasers, Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998).

Hoffman, K. R.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, "Saturation of 1.064 µm absorption in Cr,Ca:Y3Al5O12 crystals," Appl. Phys. Lett. 61, 2958-2960 (1992).
[CrossRef]

Huber, G.

S. Kück, K. Petermann, and G. Huber, "Spectroscopic investigation of the Cr4+-center in YAG," in Advanced Solid-State Lasers (Optical Society of America, 1991).

Jacobsen, S. M.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, "Saturation of 1.064 µm absorption in Cr,Ca:Y3Al5O12 crystals," Appl. Phys. Lett. 61, 2958-2960 (1992).
[CrossRef]

Kadoi, A.

A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, "Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a double-pulse pumping technique," IEEE J. Quantum Electron. 35, 1548-1553 (1999).
[CrossRef]

Kalisky, Y.

Y. Kalisky, "Cr4+-doped crystals: their use as lasers and passive Q switches," Prog. Quantum Electron. 28, 249-303 (2004).
[CrossRef]

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kokta, "Excited-state absorption studies of Cr4+ ions in several garnet host crystals," IEEE J. Quantum Electron. 34, 292-299 (1998).
[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]

Y. Kalisky, R. Moncorge, Y. Guyot, and M. Kokta, "Laser operation and Q-switching properties of (Cr4+,Mg2+):YAG crystal," in Advanced Solid-State Lasers, Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998).

Kimaev, A. E.

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Kokta, M.

Y. Kalisky, R. Moncorge, Y. Guyot, and M. Kokta, "Laser operation and Q-switching properties of (Cr4+,Mg2+):YAG crystal," in Advanced Solid-State Lasers, Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998).

Kokta, M. R.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kokta, "Excited-state absorption studies of Cr4+ ions in several garnet host crystals," IEEE J. Quantum Electron. 34, 292-299 (1998).
[CrossRef]

Korzhik, M. V.

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Kück, S.

S. Kück, K. Petermann, and G. Huber, "Spectroscopic investigation of the Cr4+-center in YAG," in Advanced Solid-State Lasers (Optical Society of America, 1991).

Kuleshov, N. V.

Kurt, A.

A. Sennaroglu, A. Kurt, and S. Buhours, "Analysis and optimization of diode end-pumped solid-state lasers: Application to Nd3+:YVO4 lasers at 1064 and 1342 nm," Opt. Eng. 44, 054202 (2005).
[CrossRef]

Lagatsky, A. A.

Lim, J. H.

G. Xiao, J. H. Lim, S. Yang, E. V. Stryland, M. Bass, and L. Weichman, "Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet," IEEE J. Quantum Electron. 35, 1086-1091 (1999).
[CrossRef]

Liu, F.-M.

J. Chen, H.-F. Yau, H.-P. Liu, T.-C. Chen, C.-C. Cheng, and F.-M. Liu, "Passive Q-switch and mode-locking modulators for Nd:hosted lasers," Opt. Laser Technol. 32, 215-219 (2000).
[CrossRef]

Liu, H.-P.

J. Chen, H.-F. Yau, H.-P. Liu, T.-C. Chen, C.-C. Cheng, and F.-M. Liu, "Passive Q-switch and mode-locking modulators for Nd:hosted lasers," Opt. Laser Technol. 32, 215-219 (2000).
[CrossRef]

Livshits, M. G.

Livshitz, M. G.

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Meilman, M. L.

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Merkle, L.

H. R. Verdun and L. Merkle, "Evidence of excited-state absorption of pump radiation in the Cr:forsterite laser," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Midorikawa, K.

A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, "Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a double-pulse pumping technique," IEEE J. Quantum Electron. 35, 1548-1553 (1999).
[CrossRef]

Mikhailov, V. P.

Minkov, B. I.

Minkov, B. J.

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Mishkel, I. I.

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Moncorge, R.

Y. Kalisky, R. Moncorge, Y. Guyot, and M. Kokta, "Laser operation and Q-switching properties of (Cr4+,Mg2+):YAG crystal," in Advanced Solid-State Lasers, Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998).

Nabekawa, Y.

T. Togashi, Y. Nabekawa, T. Sekikawa, and S. Watanabe, "High-peak power femtosecond Cr:forsterite laser system," Appl. Phys. B: Photophys. Laser Chem. 68, 169-175 (1999).
[CrossRef]

Nagasaka, K.

A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, "Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a double-pulse pumping technique," IEEE J. Quantum Electron. 35, 1548-1553 (1999).
[CrossRef]

Nathel, H.

Naumov, S.

S. Naumov, E. Sorokin, and I. T. Sorokina, "Measurement of the excited state absorption cross-section in Cr4+:YAG using relaxation oscillations study," in Advanced Solid-State Photonics, Vol. 98 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2005).

Okhrimchuk, A. G.

A. G. Okhrimchuk and A. V. Shestakov, "Absorption saturation mechanism for YAG:Cr4+ crystals," Phys. Rev. B 61, 988-995 (2000).
[CrossRef]

N. I. Borodin, V. A. Zhitnyuk, A. G. Okhrimchuk, and A. V. Shestakov, "Oscillation of a Y3Al5O12:Cr4+ laser in wave length region of 1.34-1.6 mm," Izv. Akad. Nauk SSSR Ser. Fiz. 54, 1500-1506 (1990).

Pekerten, B.

A. Sennaroglu and B. Pekerten, "Determination of the optimum absorption coefficient in Cr4+:forsterite lasers under thermal loading," Opt. Lett. 23, 361-363 (1998).
[CrossRef]

A. Sennaroglu and B. Pekerten, "Experimental and numerical investigation of thermal effects in end-pumped Cr4+:forsterite lasers near room temperature," IEEE J. Quantum Electron. 34, 1996-2005 (1998).
[CrossRef]

Petermann, K.

S. Kück, K. Petermann, and G. Huber, "Spectroscopic investigation of the Cr4+-center in YAG," in Advanced Solid-State Lasers (Optical Society of America, 1991).

Philipps, G.

T. Dascalu, G. Philipps, and H. Weber, "Investigation of a Cr4+:YAG passive Q-switch in cw pumped Nd: YAG lasers," Opt. Laser Technol. 29, 145-149 (1997).
[CrossRef]

Podlipensky, A. V.

Pollock, C. R.

Prokoshin, P. V.

Sekikawa, T.

T. Togashi, Y. Nabekawa, T. Sekikawa, and S. Watanabe, "High-peak power femtosecond Cr:forsterite laser system," Appl. Phys. B: Photophys. Laser Chem. 68, 169-175 (1999).
[CrossRef]

Sennaroglu, A.

A. Sennaroglu, A. Kurt, and S. Buhours, "Analysis and optimization of diode end-pumped solid-state lasers: Application to Nd3+:YVO4 lasers at 1064 and 1342 nm," Opt. Eng. 44, 054202 (2005).
[CrossRef]

A. Sennaroglu, "Broadly tunable Cr4+-doped solid-state lasers in the near infrared and visible," Prog. Quantum Electron. 26, 287-352 (2002).
[CrossRef]

A. Sennaroglu, "Analysis and optimization of lifetime thermal loading in continuous-wave Cr4+-doped solid-state lasers," J. Opt. Soc. Am. B 18, 1578-1586 (2001).
[CrossRef]

A. Sennaroglu and B. Pekerten, "Determination of the optimum absorption coefficient in Cr4+:forsterite lasers under thermal loading," Opt. Lett. 23, 361-363 (1998).
[CrossRef]

A. Sennaroglu and B. Pekerten, "Experimental and numerical investigation of thermal effects in end-pumped Cr4+:forsterite lasers near room temperature," IEEE J. Quantum Electron. 34, 1996-2005 (1998).
[CrossRef]

A. Sennaroglu, "Continuous wave thermal loading in saturable absorbers: theory and experiment," Appl. Opt. 36, 9528-9535 (1997).
[CrossRef]

A. Sennaroglu, C. R. Pollock, and H. Nathel, "Efficient continuous-wave chromium-doped YAG laser," J. Opt. Soc. Am. B 12, 930-937 (1995).
[CrossRef]

Shcherbitsky, V. G.

Shestakov, A. V.

A. G. Okhrimchuk and A. V. Shestakov, "Absorption saturation mechanism for YAG:Cr4+ crystals," Phys. Rev. B 61, 988-995 (2000).
[CrossRef]

N. I. Borodin, V. A. Zhitnyuk, A. G. Okhrimchuk, and A. V. Shestakov, "Oscillation of a Y3Al5O12:Cr4+ laser in wave length region of 1.34-1.6 mm," Izv. Akad. Nauk SSSR Ser. Fiz. 54, 1500-1506 (1990).

Shimony, Y.

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kokta, "Excited-state absorption studies of Cr4+ ions in several garnet host crystals," IEEE J. Quantum Electron. 34, 292-299 (1998).
[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]

Shkadarevich, A. P.

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Sorokin, E.

S. Naumov, E. Sorokin, and I. T. Sorokina, "Measurement of the excited state absorption cross-section in Cr4+:YAG using relaxation oscillations study," in Advanced Solid-State Photonics, Vol. 98 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2005).

Sorokina, I. T.

S. Naumov, E. Sorokin, and I. T. Sorokina, "Measurement of the excited state absorption cross-section in Cr4+:YAG using relaxation oscillations study," in Advanced Solid-State Photonics, Vol. 98 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2005).

Spariosu, K.

Stryland, E. V.

G. Xiao, J. H. Lim, S. Yang, E. V. Stryland, M. Bass, and L. Weichman, "Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet," IEEE J. Quantum Electron. 35, 1086-1091 (1999).
[CrossRef]

Stultz, R.

Suda, A.

A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, "Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a double-pulse pumping technique," IEEE J. Quantum Electron. 35, 1548-1553 (1999).
[CrossRef]

Tarasov, A. A.

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Tashiro, H.

A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, "Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a double-pulse pumping technique," IEEE J. Quantum Electron. 35, 1548-1553 (1999).
[CrossRef]

Togashi, T.

T. Togashi, Y. Nabekawa, T. Sekikawa, and S. Watanabe, "High-peak power femtosecond Cr:forsterite laser system," Appl. Phys. B: Photophys. Laser Chem. 68, 169-175 (1999).
[CrossRef]

Tsai, S. W.

Y.-F. Chen and S. W. Tsai, "Simultaneous Q switching and mode-locking in a diode-pumped Nd:YVO 4-Cr4+:YAG laser," IEEE J. Quantum Electron. 37, 580-586 (2001).
[CrossRef]

Verdun, H. R.

H. R. Verdun and L. Merkle, "Evidence of excited-state absorption of pump radiation in the Cr:forsterite laser," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Watanabe, S.

T. Togashi, Y. Nabekawa, T. Sekikawa, and S. Watanabe, "High-peak power femtosecond Cr:forsterite laser system," Appl. Phys. B: Photophys. Laser Chem. 68, 169-175 (1999).
[CrossRef]

Weber, H.

T. Dascalu, G. Philipps, and H. Weber, "Investigation of a Cr4+:YAG passive Q-switch in cw pumped Nd: YAG lasers," Opt. Laser Technol. 29, 145-149 (1997).
[CrossRef]

Weichman, L.

G. Xiao, J. H. Lim, S. Yang, E. V. Stryland, M. Bass, and L. Weichman, "Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet," IEEE J. Quantum Electron. 35, 1086-1091 (1999).
[CrossRef]

Xiao, G.

G. Xiao, J. H. Lim, S. Yang, E. V. Stryland, M. Bass, and L. Weichman, "Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet," IEEE J. Quantum Electron. 35, 1086-1091 (1999).
[CrossRef]

Yang, S.

G. Xiao, J. H. Lim, S. Yang, E. V. Stryland, M. Bass, and L. Weichman, "Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet," IEEE J. Quantum Electron. 35, 1086-1091 (1999).
[CrossRef]

Yau, H.-F.

J. Chen, H.-F. Yau, H.-P. Liu, T.-C. Chen, C.-C. Cheng, and F.-M. Liu, "Passive Q-switch and mode-locking modulators for Nd:hosted lasers," Opt. Laser Technol. 32, 215-219 (2000).
[CrossRef]

Yen, W. M.

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, "Saturation of 1.064 µm absorption in Cr,Ca:Y3Al5O12 crystals," Appl. Phys. Lett. 61, 2958-2960 (1992).
[CrossRef]

Yumashev, K. V.

Zayhowski, J. J.

Zhavoronkov, N. I.

Zhitnyuk, V. A.

N. I. Borodin, V. A. Zhitnyuk, A. G. Okhrimchuk, and A. V. Shestakov, "Oscillation of a Y3Al5O12:Cr4+ laser in wave length region of 1.34-1.6 mm," Izv. Akad. Nauk SSSR Ser. Fiz. 54, 1500-1506 (1990).

Appl. Opt. (1)

Appl. Phys. B: Photophys. Laser Chem. (1)

T. Togashi, Y. Nabekawa, T. Sekikawa, and S. Watanabe, "High-peak power femtosecond Cr:forsterite laser system," Appl. Phys. B: Photophys. Laser Chem. 68, 169-175 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

H. Eilers, K. R. Hoffman, W. M. Dennis, S. M. Jacobsen, and W. M. Yen, "Saturation of 1.064 µm absorption in Cr,Ca:Y3Al5O12 crystals," Appl. Phys. Lett. 61, 2958-2960 (1992).
[CrossRef]

IEEE J. Quantum Electron. (7)

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]

Y.-F. Chen and S. W. Tsai, "Simultaneous Q switching and mode-locking in a diode-pumped Nd:YVO 4-Cr4+:YAG laser," IEEE J. Quantum Electron. 37, 580-586 (2001).
[CrossRef]

G. Xiao, J. H. Lim, S. Yang, E. V. Stryland, M. Bass, and L. Weichman, "Z-scan measurement of the ground and excited state absorption cross sections of Cr4+ in yttrium aluminum garnet," IEEE J. Quantum Electron. 35, 1086-1091 (1999).
[CrossRef]

A. Suda, A. Kadoi, K. Nagasaka, H. Tashiro, and K. Midorikawa, "Absorption and oscillation characteristics of a pulsed Cr4+:YAG laser investigated by a double-pulse pumping technique," IEEE J. Quantum Electron. 35, 1548-1553 (1999).
[CrossRef]

A. Sennaroglu and B. Pekerten, "Experimental and numerical investigation of thermal effects in end-pumped Cr4+:forsterite lasers near room temperature," IEEE J. Quantum Electron. 34, 1996-2005 (1998).
[CrossRef]

Z. Burshtein, P. Blau, Y. Kalisky, Y. Shimony, and M. R. Kokta, "Excited-state absorption studies of Cr4+ ions in several garnet host crystals," IEEE J. Quantum Electron. 34, 292-299 (1998).
[CrossRef]

M. I. Demchuk, N. V. Kuleshov, and V. P. Mikhailov, "Saturable absorbers based on impurity and defect centers in crystals," IEEE J. Quantum Electron. 30, 2120-2126 (1994).
[CrossRef]

Izv. Akad. Nauk SSSR Ser. Fiz. (1)

N. I. Borodin, V. A. Zhitnyuk, A. G. Okhrimchuk, and A. V. Shestakov, "Oscillation of a Y3Al5O12:Cr4+ laser in wave length region of 1.34-1.6 mm," Izv. Akad. Nauk SSSR Ser. Fiz. 54, 1500-1506 (1990).

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

Opt. Eng. (1)

A. Sennaroglu, A. Kurt, and S. Buhours, "Analysis and optimization of diode end-pumped solid-state lasers: Application to Nd3+:YVO4 lasers at 1064 and 1342 nm," Opt. Eng. 44, 054202 (2005).
[CrossRef]

Opt. Laser Technol. (2)

J. Chen, H.-F. Yau, H.-P. Liu, T.-C. Chen, C.-C. Cheng, and F.-M. Liu, "Passive Q-switch and mode-locking modulators for Nd:hosted lasers," Opt. Laser Technol. 32, 215-219 (2000).
[CrossRef]

T. Dascalu, G. Philipps, and H. Weber, "Investigation of a Cr4+:YAG passive Q-switch in cw pumped Nd: YAG lasers," Opt. Laser Technol. 29, 145-149 (1997).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. B (1)

A. G. Okhrimchuk and A. V. Shestakov, "Absorption saturation mechanism for YAG:Cr4+ crystals," Phys. Rev. B 61, 988-995 (2000).
[CrossRef]

Prog. Quantum Electron. (2)

A. Sennaroglu, "Broadly tunable Cr4+-doped solid-state lasers in the near infrared and visible," Prog. Quantum Electron. 26, 287-352 (2002).
[CrossRef]

Y. Kalisky, "Cr4+-doped crystals: their use as lasers and passive Q switches," Prog. Quantum Electron. 28, 249-303 (2004).
[CrossRef]

Other (5)

H. R. Verdun and L. Merkle, "Evidence of excited-state absorption of pump radiation in the Cr:forsterite laser," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

V. G. Baryshevski, M. V. Korzhik, M. G. Livshitz, A. A. Tarasov, A. E. Kimaev, I. I. Mishkel, M. L. Meilman, B. J. Minkov, and A. P. Shkadarevich, "Properties of forsterite and the performance of forsterite lasers with lasers and flashlamp pumping," in Digest of Advanced Solid-State Lasers (Optical Society of America, 1991).

Y. Kalisky, R. Moncorge, Y. Guyot, and M. Kokta, "Laser operation and Q-switching properties of (Cr4+,Mg2+):YAG crystal," in Advanced Solid-State Lasers, Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1998).

S. Kück, K. Petermann, and G. Huber, "Spectroscopic investigation of the Cr4+-center in YAG," in Advanced Solid-State Lasers (Optical Society of America, 1991).

S. Naumov, E. Sorokin, and I. T. Sorokina, "Measurement of the excited state absorption cross-section in Cr4+:YAG using relaxation oscillations study," in Advanced Solid-State Photonics, Vol. 98 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2005).

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Figures (7)

Fig. 1
Fig. 1

Energy-level diagram of a saturable absorber exhibiting excited-state absorption. Zig-zagged lines indicate nonradiative decay processes.

Fig. 2
Fig. 2

Sketch of the experimental setup ( λ 2 , half-wave plate at 1064 nm ).

Fig. 3
Fig. 3

Measured and fit variations of the spot-size function ω p ( z ) as a function of position z. The best-fit values of the beam waist and the M 2 factor were determined to be 25 μ m and 1.04, respectively.

Fig. 4
Fig. 4

Calculated variation of the transmission for a hypothetical absorber as a function of (a) incident power (cw case) and (b) incident pulse energy (pulsed case) for different amounts of excited-state absorption. (Absorber parameters: σ a = 25 × 10 19 cm 2 , τ f = 5 μ s , α p 0 = 1.5 cm 1 , λ p = 1064 nm , L 0 = 20 mm , n 0 = 1.635 , z fp = L 0 2 , ω p 0 = 25 μ m ).

Fig. 5
Fig. 5

Calculated variation of the transmission for a hypothetical absorber as a function of the beam-waist location for the (a) cw and (b) pulsed cases for different levels of excited-state absorption. (Absorber parameters: σ a = 25 × 10 19 cm 2 , τ f = 5 μ s , α p 0 = 1.5 cm 1 , λ p = 1064 nm , L 0 = 20 mm , n 0 = 1.635 , and ω .p 0 = 25 μ m .)

Fig. 6
Fig. 6

Measured and fit variations of the transmission as a function of the (a) incident power (cw case) and (b) incident pulse energy (pulsed case) for the three Cr 4 + :forsterite crystals.

Fig. 7
Fig. 7

Measured and fit variation of the transmission as a function of the (a) incident power (cw case) and (b) incident pulse energy (pulsed case) for the Cr 4 + :YAG crystals.

Tables (9)

Tables Icon

Table 1 Length and Small-Signal Absorption Coefficient α p 0 of Each Sample Used in the Saturation Measurements a

Tables Icon

Table 2 Best-Fit Values of α p 0 , f p , and σ a Obtained by Analyzing the cw and Pulsed Transmission Data of the Cr 4 + :Forsterite Samples Separately

Tables Icon

Table 3 Best-Fit Values of α p 0 , f p , and σ a for Cr 4 + :Forsterite Samples Obtained by Using the Iterative Analysis Scheme a

Tables Icon

Table 4 Previously Reported σ a and f p Values for Cr 4 + :Forsterite in the Literature a

Tables Icon

Table 5 Best-Fit Values of α p 0 , f p , and σ a Obtained by Analyzing the cw and Pulsed Transmission Data of the Cr 4 + :YAG Samples Separately a

Tables Icon

Table 6 Best-Fit Values of α p 0 , f p , and σ a for Cr 4 + :YAG Samples Obtained by Using the Iterative Analysis Scheme a

Tables Icon

Table 7 Previously Reported σ a and f p Values for Cr 4 + :YAG in the Literature a

Tables Icon

Table 8 Best-Fit Values of f p , q 0 , P sa , and σ ̱ a ̱ for the cw Transmission Data of Cr 4 + :YAG and Cr 4 + :Forsterite Samples Obtained with the Lumped Models

Tables Icon

Table 9 Best-Fit Values of f p , q 0 , P s , and σ a for the Pulsed Transmission Data of Cr 4 + :YAG and Cr 4 + :Forsterite Samples Obtained with the Lumped Models

Equations (22)

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N 2 ( r , z ) t = N g ( r , z ) t = σ a λ p I p ( r , z ) h c N g ( r , z ) N 2 ( r , z ) τ f ,
A d z u p t = [ I p ( z ) I p ( z + d z ) ] A ( N g σ a I p + N 2 σ e s a I p ) A d z ,
I p z + 1 v g I p t = σ a I p ( N g + f p N 2 ) .
f p = σ esa ( λ p ) σ a ( λ p ) .
N 2 = N T I p I sa 1 + I p I sa .
I p z = α p 0 I p ( 1 + f p I p I sa 1 + I p I sa ) .
I p ( r , z ) = P p ( z ) Φ p ( r , z ) ,
Φ P = 2 π ω p 2 exp ( 2 r 2 ω p 2 ) .
d P p d z = α p 0 P p 0 d r 2 π r Φ p ( 1 + f p P p Φ p I sa 1 + P p Φ p I sa ) .
τ d t I p ( t ) = E ¯ p ,
I p z + 1 v g I p t = ( 1 f p ) h c λ p N g t f p α p 0 I p .
N g = N T exp ( E ¯ p E sa ) ,
E ¯ p z = ( 1 f p ) α p 0 E sa [ 1 exp ( E ¯ p E sa ) ] f p α p 0 E ¯ p .
E ¯ p = E p Φ p ,
E p z = ( 1 f p ) α p 0 E sa 0 d r 2 π r [ 1 exp ( E p Φ p E sa ) ] f p α p 0 E p .
ω p ( z ) = ω p 0 [ 1 + ( z z f p z R p ) 2 ] 1 2 ,
T max = exp ( f p α p 0 L 0 ) .
1 q ( z ) 2 + d d z ( 1 q ( z ) ) + β ( z ) 2 = 0 ,
β ( z ) = [ n T h 0 ( z ) 2 κ n 0 ] 1 2 .
h 0 ( z ) = α p 0 1 + ( I p I sa ) η h I p .
T cw = 1 q 0 1 + f p ( P p P sa ) 1 + ( P p P sa ) ,
T pulsed = 1 q 0 ( 1 f p ) E p E A [ 1 exp ( E p E A ) ] q 0 f p .

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