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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 4 — Feb. 14, 2011
  • pp: 2904–2909
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Ultrashort pulse generation from diode pumped mode-locked Yb3+:sesquioxide single crystal lasers

M. Tokurakawa, A. Shirakawa, K. Ueda, R. Peters, S. T. Fredrich-Thornton, K. Petermann, and G. Huber  »View Author Affiliations


Optics Express, Vol. 19, Issue 4, pp. 2904-2909 (2011)
http://dx.doi.org/10.1364/OE.19.002904


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Abstract

We present diode pumped SESAM supported Kerr-lens mode locked laser operation based on Yb3+:Sc2O3 and Yb3+:Lu2O3 single crystals. Pulses as short as 71 fs with an average power of 1.09 W were obtained from an Yb3+:Lu2O3 single crystal. Yb3+:Sc2O3 delivered pulses as short as 81 fs with an average power of 840 mW. The mode locked laser operation was stable for longer than 2 hours.

© 2011 OSA

1. Introduction

Yb3+-doped materials have several advantages as gain media for high-power femtosecond laser operation. Their absorption bands and broad emission bands enable femtosecond laser operation with direct laser diode (LD) pumping. The simple energy-level scheme of the Yb3+ ion (2 F 5/22 F 7/2 inter-manifold transition) leads to a very small quantum defect and avoids undesirable processes such as excited-state absorption, cross relaxation, and concentration quenching [1

1. W. F. Krupke, “Ytterbium solid-state lasers-the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000). [CrossRef]

] so that highly efficient high power laser operation with small heat load can be realized unless the Yb3+-doping concentration and the inversion exceeds some critical value [2

2. R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Influence of the Yb-Doping Concentration on the Efficiency of Lu2O3Thin Disk Lasers,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper MF2.

]. Since the spectroscopic, thermal, and mechanical properties of Yb3+-doped materials strongly depend on the host material, femtosecond lasers based on various kinds of Yb3+-doped crystalline materials have been reported in the past decade [3

3. J. Saikawa, Y. Sato, T. Taira, and A. Ikesue, “Passive mode locking of a mixed garnet Yb:Y3ScAl4O12 ceramic laser,” Appl. Phys. Lett. 85(24), 5845 (2004). [CrossRef]

11

11. P. Klopp, V. Petrov, U. Griebner, K. Petermann, V. Peters, and G. Erbert, “Highly efficient mode-locked Yb:Sc2O3 laser,” Opt. Lett. 29(4), 391–393 (2004). [CrossRef] [PubMed]

]. By adequate choice of the host material and good thermal management, Yb3+-doped gain media can be pumped by high-brightness, high-power LDs. Sub-100 fs mode-locked oscillators with average powers above 1 W have been obtained with high-intensity pump LDs [6

6. A. A. Lagatsky, V. E. Kisel, F. Baina, C. T. A. Browna, N. V. Kuleshovb, and W. Sibbetta, “Advances in femtosecond lasers having enhanced efficiencies,” Proc. SPIE 6731, 673103 (2007).

,12

12. M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, M. Noriyuki, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped ultrashort-pulse generation based on Yb(3+):Sc(2)O(3) and Yb(3+):Y(2)O(3) ceramic multi-gain-media oscillator,” Opt. Express 17(5), 3353–3361 (2009). [CrossRef] [PubMed]

]. Mode-locked oscillators with average powers of up to 80 W and pulse energies beyond the 20 µJ level have been reported based on Yb:YAG thin-disk laser [13

13. F. Brunner, E. Innerhofer, S. V. Marchese, T. Südmeyer, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, G. Arisholm, and U. Keller, “Powerful red-green-blue laser source pumped with a mode-locked thin disk laser,” Opt. Lett. 29(16), 1921–1923 (2004). [CrossRef] [PubMed]

,14

14. J. Neuhaus, D. Bauer, J. Zhang, A. Killi, J. Kleinbauer, M. Kumkar, S. Weiler, M. Guina, D. H. Sutter, and T. Dekorsy, “Subpicosecond thin-disk laser oscillator with pulse energies of up to 25.9 microjoules by use of an active multipass geometry,” Opt. Express 16(25), 20530–20539 (2008). [CrossRef] [PubMed]

]. An amplifier system with multi-mJ pulse energy and sub-200 fs pulse duration at high repetition rate based on cryogenic cooling has also been reported [15

15. A. Pugžlys, G. Andriukaitis, A. Baltuška, L. Su, J. Xu, H. Li, R. Li, W. J. Lai, P. B. Phua, A. Marcinkevičius, M. E. Fermann, L. Giniūnas, R. Danielius, and S. Ališauskas, “Multi-mJ, 200-fs, cw-pumped, cryogenically cooled, Yb,Na:CaF2 amplifier,” Opt. Lett. 34(13), 2075–2077 (2009). [CrossRef] [PubMed]

].

Among the Yb3+-doped materials, the isotropic sesquioxides Yb3+:RE2O3 (RE = Y, Sc or Lu) are very attractive as gain media for high-power femtosecond laser operation, because they have high thermal conductivities, broader fluorescence spectra than Yb:YAG [10

10. U. Griebner, V. Petrov, K. Petermann, and V. Peters, “Passively mode-locked Yb:Lu(2)O(3) laser,” Opt. Express 12(14), 3125–3130 (2004). [CrossRef] [PubMed]

], and their isotropic structures avoid anisotropy-problems. Recently 141-W average power mode-locked laser operation with 738 fs pulse duration based on an Yb3+:Lu2O3 single crystal thin-disk laser has been reported [16

16. C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett. 35(13), 2302–2304 (2010). [CrossRef] [PubMed]

]. Sub-100 fs pulses generation based on Kerr lens mode-locked (KLM) Yb3+-doped sesquioxide ceramic and mixed sesquioxide single crystal lasers have also been reported [12

12. M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, M. Noriyuki, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped ultrashort-pulse generation based on Yb(3+):Sc(2)O(3) and Yb(3+):Y(2)O(3) ceramic multi-gain-media oscillator,” Opt. Express 17(5), 3353–3361 (2009). [CrossRef] [PubMed]

,17

17. M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped sub-100 fs Kerr-lens mode-locked Yb3+:Sc2O3 ceramic laser,” Opt. Lett. 32(23), 3382–3384 (2007). [CrossRef] [PubMed]

20

20. A. Schmidt, V. Petrov, U. Griebner, R. Peters, K. Petermann, G. Huber, C. Fiebig, K. Paschke, and G. Erbert, “Diode-pumped mode-locked Yb:LuScO(3) single crystal laser with 74 fs pulse duration,” Opt. Lett. 35(4), 511–513 (2010). [CrossRef] [PubMed]

]. In this paper we report on high-power broad-stripe LD pumped sub-100 fs KLM laser operation with around 1-W average powers based on Yb3+:Sc2O3 and Yb3+:Lu2O3 single crystals.

2. Experimental setup

3. Results

4. Conclusion

Acknowledgement

This research was partly supported by Grant-in-Aid for Scientific Research and the Photon Frontier Network Program of Ministry of Education, Culture, Sports, Science and Technology.

References and links

1.

W. F. Krupke, “Ytterbium solid-state lasers-the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000). [CrossRef]

2.

R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Influence of the Yb-Doping Concentration on the Efficiency of Lu2O3Thin Disk Lasers,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper MF2.

3.

J. Saikawa, Y. Sato, T. Taira, and A. Ikesue, “Passive mode locking of a mixed garnet Yb:Y3ScAl4O12 ceramic laser,” Appl. Phys. Lett. 85(24), 5845 (2004). [CrossRef]

4.

H. Liu, J. Nees, and G. Mourou, “Diode-pumped Kerr-lens mode-locked Yb:KY(WO(4))(2) laser,” Opt. Lett. 26(21), 1723–1725 (2001). [CrossRef]

5.

F. Druon, D. N. Papadopoulos, J. Boudeile, M. Hanna, P. Georges, A. Benayad, P. Camy, J. L. Doualan, V. Ménard, and R. Moncorgé, “Mode-locked operation of a diode-pumped femtosecond Yb:SrF2 laser,” Opt. Lett. 34(15), 2354–2356 (2009). [CrossRef] [PubMed]

6.

A. A. Lagatsky, V. E. Kisel, F. Baina, C. T. A. Browna, N. V. Kuleshovb, and W. Sibbetta, “Advances in femtosecond lasers having enhanced efficiencies,” Proc. SPIE 6731, 673103 (2007).

7.

S. Rivier, A. Schmidt, C. Kränkel, R. Peters, K. Petermann, G. Huber, M. Zorn, M. Weyers, A. Klehr, G. Erbert, V. Petrov, and U. Griebner, “Ultrashort pulse Yb:LaSc(3)(BO(3))(4) mode-locked oscillator,” Opt. Express 15(23), 15539–15544 (2007). [CrossRef] [PubMed]

8.

F. Thibault, D. Pelenc, F. Druon, Y. Zaouter, M. Jacquemet, and P. Georges, “Efficient diode-pumped Yb3+:Y2SiO5 and Yb3+:Lu2SiO5 high-power femtosecond laser operation,” Opt. Lett. 31(10), 1555–1557 (2006). [CrossRef] [PubMed]

9.

Y. Zaouter, J. Didierjean, F. Balembois, G. L Leclin, F. Druon, P. Georges, J. Petit, P. Goldner, and B. Viana, “47-fs diode-pumped Yb3+:CaGdAlO4 laser,” Opt. Lett. 31(1), 119–121 (2006). [CrossRef] [PubMed]

10.

U. Griebner, V. Petrov, K. Petermann, and V. Peters, “Passively mode-locked Yb:Lu(2)O(3) laser,” Opt. Express 12(14), 3125–3130 (2004). [CrossRef] [PubMed]

11.

P. Klopp, V. Petrov, U. Griebner, K. Petermann, V. Peters, and G. Erbert, “Highly efficient mode-locked Yb:Sc2O3 laser,” Opt. Lett. 29(4), 391–393 (2004). [CrossRef] [PubMed]

12.

M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, M. Noriyuki, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped ultrashort-pulse generation based on Yb(3+):Sc(2)O(3) and Yb(3+):Y(2)O(3) ceramic multi-gain-media oscillator,” Opt. Express 17(5), 3353–3361 (2009). [CrossRef] [PubMed]

13.

F. Brunner, E. Innerhofer, S. V. Marchese, T. Südmeyer, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, G. Arisholm, and U. Keller, “Powerful red-green-blue laser source pumped with a mode-locked thin disk laser,” Opt. Lett. 29(16), 1921–1923 (2004). [CrossRef] [PubMed]

14.

J. Neuhaus, D. Bauer, J. Zhang, A. Killi, J. Kleinbauer, M. Kumkar, S. Weiler, M. Guina, D. H. Sutter, and T. Dekorsy, “Subpicosecond thin-disk laser oscillator with pulse energies of up to 25.9 microjoules by use of an active multipass geometry,” Opt. Express 16(25), 20530–20539 (2008). [CrossRef] [PubMed]

15.

A. Pugžlys, G. Andriukaitis, A. Baltuška, L. Su, J. Xu, H. Li, R. Li, W. J. Lai, P. B. Phua, A. Marcinkevičius, M. E. Fermann, L. Giniūnas, R. Danielius, and S. Ališauskas, “Multi-mJ, 200-fs, cw-pumped, cryogenically cooled, Yb,Na:CaF2 amplifier,” Opt. Lett. 34(13), 2075–2077 (2009). [CrossRef] [PubMed]

16.

C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett. 35(13), 2302–2304 (2010). [CrossRef] [PubMed]

17.

M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped sub-100 fs Kerr-lens mode-locked Yb3+:Sc2O3 ceramic laser,” Opt. Lett. 32(23), 3382–3384 (2007). [CrossRef] [PubMed]

18.

M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, S. Hosokawa, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped 65 fs Kerr-lens mode-locked Yb(3+):Lu(2)O(3) and nondoped Y(2)O(3) combined ceramic laser,” Opt. Lett. 33(12), 1380–1382 (2008). [CrossRef] [PubMed]

19.

M. Tokurakawa, H. Kurokawa, A. Shirakawa, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Continuous-wave and mode-locked lasers on the base of partially disordered crystalline Yb3+:YGd2[Sc2](Al2Ga)O12 ceramics,” Opt. Express 18(5), 4390–4395 (2010). [CrossRef] [PubMed]

20.

A. Schmidt, V. Petrov, U. Griebner, R. Peters, K. Petermann, G. Huber, C. Fiebig, K. Paschke, and G. Erbert, “Diode-pumped mode-locked Yb:LuScO(3) single crystal laser with 74 fs pulse duration,” Opt. Lett. 35(4), 511–513 (2010). [CrossRef] [PubMed]

21.

T. Brabec, Ch. Spielmann, P. F. Curley, and F. Krausz, “Kerr lens mode locking,” Opt. Lett. 17(18), 1292–1294 (1992). [CrossRef] [PubMed]

22.

M. Piché and F. Salin, “Self-mode locking of solid-state lasers without apertures,” Opt. Lett. 18(13), 1041–1043 (1993). [CrossRef] [PubMed]

23.

M. Tokurakawa, A. Shirakawa, and K. Ueda, “Estimation of Gain Bandwidth Limitation of Short Pulse Duration Based on Competition of Gain Saturation,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper AMB16.

24.

F. X. Kärtner, J. A. Au, and U. Keller, “Mode-Locking with Slow and Fast Saturable. Absorbers-What's the Difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 159–168 (1998). [CrossRef]

25.

M. J. Lederer, B. Luther-Davies, H. H. Tan, C. Jagadish, N. N. Akhmediev, and J. M. Soto-Crespo, “Multipulse operation of a Ti:sapphire laser mode locked by an ion-implanted semiconductor saturable-absorber mirror,” J. Opt. Soc. Am. B 16(6), 895–904 (1999). [CrossRef]

OCIS Codes
(140.3480) Lasers and laser optics : Lasers, diode-pumped
(140.3580) Lasers and laser optics : Lasers, solid-state
(140.4050) Lasers and laser optics : Mode-locked lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: December 21, 2010
Revised Manuscript: January 24, 2011
Manuscript Accepted: January 27, 2011
Published: January 31, 2011

Citation
M. Tokurakawa, A. Shirakawa, K. Ueda, R. Peters, S. T. Fredrich-Thornton, K. Petermann, and G. Huber, "Ultrashort pulse generation from diode pumped mode-locked Yb3+:sesquioxide single crystal lasers," Opt. Express 19, 2904-2909 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-2904


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References

  1. W. F. Krupke, “Ytterbium solid-state lasers-the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000). [CrossRef]
  2. R. Peters, C. Kränkel, K. Petermann, and G. Huber, “Influence of the Yb-Doping Concentration on the Efficiency of Lu2O3Thin Disk Lasers,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper MF2.
  3. J. Saikawa, Y. Sato, T. Taira, and A. Ikesue, “Passive mode locking of a mixed garnet Yb:Y3ScAl4O12 ceramic laser,” Appl. Phys. Lett. 85(24), 5845 (2004). [CrossRef]
  4. H. Liu, J. Nees, and G. Mourou, “Diode-pumped Kerr-lens mode-locked Yb:KY(WO(4))(2) laser,” Opt. Lett. 26(21), 1723–1725 (2001). [CrossRef]
  5. F. Druon, D. N. Papadopoulos, J. Boudeile, M. Hanna, P. Georges, A. Benayad, P. Camy, J. L. Doualan, V. Ménard, and R. Moncorgé, “Mode-locked operation of a diode-pumped femtosecond Yb:SrF2 laser,” Opt. Lett. 34(15), 2354–2356 (2009). [CrossRef] [PubMed]
  6. A. A. Lagatsky, V. E. Kisel, F. Baina, C. T. A. Browna, N. V. Kuleshovb, and W. Sibbetta, “Advances in femtosecond lasers having enhanced efficiencies,” Proc. SPIE 6731, 673103 (2007).
  7. S. Rivier, A. Schmidt, C. Kränkel, R. Peters, K. Petermann, G. Huber, M. Zorn, M. Weyers, A. Klehr, G. Erbert, V. Petrov, and U. Griebner, “Ultrashort pulse Yb:LaSc(3)(BO(3))(4) mode-locked oscillator,” Opt. Express 15(23), 15539–15544 (2007). [CrossRef] [PubMed]
  8. F. Thibault, D. Pelenc, F. Druon, Y. Zaouter, M. Jacquemet, and P. Georges, “Efficient diode-pumped Yb3+:Y2SiO5 and Yb3+:Lu2SiO5 high-power femtosecond laser operation,” Opt. Lett. 31(10), 1555–1557 (2006). [CrossRef] [PubMed]
  9. Y. Zaouter, J. Didierjean, F. Balembois, G. L Leclin, F. Druon, P. Georges, J. Petit, P. Goldner, and B. Viana, “47-fs diode-pumped Yb3+:CaGdAlO4 laser,” Opt. Lett. 31(1), 119–121 (2006). [CrossRef] [PubMed]
  10. U. Griebner, V. Petrov, K. Petermann, and V. Peters, “Passively mode-locked Yb:Lu(2)O(3) laser,” Opt. Express 12(14), 3125–3130 (2004). [CrossRef] [PubMed]
  11. P. Klopp, V. Petrov, U. Griebner, K. Petermann, V. Peters, and G. Erbert, “Highly efficient mode-locked Yb:Sc2O3 laser,” Opt. Lett. 29(4), 391–393 (2004). [CrossRef] [PubMed]
  12. M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, M. Noriyuki, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped ultrashort-pulse generation based on Yb(3+):Sc(2)O(3) and Yb(3+):Y(2)O(3) ceramic multi-gain-media oscillator,” Opt. Express 17(5), 3353–3361 (2009). [CrossRef] [PubMed]
  13. F. Brunner, E. Innerhofer, S. V. Marchese, T. Südmeyer, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, G. Arisholm, and U. Keller, “Powerful red-green-blue laser source pumped with a mode-locked thin disk laser,” Opt. Lett. 29(16), 1921–1923 (2004). [CrossRef] [PubMed]
  14. J. Neuhaus, D. Bauer, J. Zhang, A. Killi, J. Kleinbauer, M. Kumkar, S. Weiler, M. Guina, D. H. Sutter, and T. Dekorsy, “Subpicosecond thin-disk laser oscillator with pulse energies of up to 25.9 microjoules by use of an active multipass geometry,” Opt. Express 16(25), 20530–20539 (2008). [CrossRef] [PubMed]
  15. A. Pugžlys, G. Andriukaitis, A. Baltuška, L. Su, J. Xu, H. Li, R. Li, W. J. Lai, P. B. Phua, A. Marcinkevičius, M. E. Fermann, L. Giniūnas, R. Danielius, and S. Ališauskas, “Multi-mJ, 200-fs, cw-pumped, cryogenically cooled, Yb,Na:CaF2 amplifier,” Opt. Lett. 34(13), 2075–2077 (2009). [CrossRef] [PubMed]
  16. C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett. 35(13), 2302–2304 (2010). [CrossRef] [PubMed]
  17. M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped sub-100 fs Kerr-lens mode-locked Yb3+:Sc2O3 ceramic laser,” Opt. Lett. 32(23), 3382–3384 (2007). [CrossRef] [PubMed]
  18. M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, S. Hosokawa, T. Yanagitani, and A. A. Kaminskii, “Diode-pumped 65 fs Kerr-lens mode-locked Yb(3+):Lu(2)O(3) and nondoped Y(2)O(3) combined ceramic laser,” Opt. Lett. 33(12), 1380–1382 (2008). [CrossRef] [PubMed]
  19. M. Tokurakawa, H. Kurokawa, A. Shirakawa, K. Ueda, H. Yagi, T. Yanagitani, and A. A. Kaminskii, “Continuous-wave and mode-locked lasers on the base of partially disordered crystalline Yb3+:YGd2[Sc2](Al2Ga)O12 ceramics,” Opt. Express 18(5), 4390–4395 (2010). [CrossRef] [PubMed]
  20. A. Schmidt, V. Petrov, U. Griebner, R. Peters, K. Petermann, G. Huber, C. Fiebig, K. Paschke, and G. Erbert, “Diode-pumped mode-locked Yb:LuScO(3) single crystal laser with 74 fs pulse duration,” Opt. Lett. 35(4), 511–513 (2010). [CrossRef] [PubMed]
  21. T. Brabec, Ch. Spielmann, P. F. Curley, and F. Krausz, “Kerr lens mode locking,” Opt. Lett. 17(18), 1292–1294 (1992). [CrossRef] [PubMed]
  22. M. Piché and F. Salin, “Self-mode locking of solid-state lasers without apertures,” Opt. Lett. 18(13), 1041–1043 (1993). [CrossRef] [PubMed]
  23. M. Tokurakawa, A. Shirakawa, and K. Ueda, “Estimation of Gain Bandwidth Limitation of Short Pulse Duration Based on Competition of Gain Saturation,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper AMB16.
  24. F. X. Kärtner, J. A. Au, and U. Keller, “Mode-Locking with Slow and Fast Saturable. Absorbers-What's the Difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 159–168 (1998). [CrossRef]
  25. M. J. Lederer, B. Luther-Davies, H. H. Tan, C. Jagadish, N. N. Akhmediev, and J. M. Soto-Crespo, “Multipulse operation of a Ti:sapphire laser mode locked by an ion-implanted semiconductor saturable-absorber mirror,” J. Opt. Soc. Am. B 16(6), 895–904 (1999). [CrossRef]

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