Abstract

The all solid-state combination of a saturable Bragg mirror for amplitude modulation and a cascaded χ(2)(2) nonlinearity (phase-mismatched second harmonic crystal) as an axial-mode phase locker for continuous-wave mode locking of large mode area lasers is investigated. The dual-passive mode-locking technique generates extremely stable sub-10ps sech2 pulses at 76MHz from a ∼6W, TEM00-mode, diode-pumped, thermal-lens-shaped, Brewster Nd:GdVO4 laser.

© 2006 Optical Society of America

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2005 (1)

2004 (3)

2003 (2)

2001 (3)

Y. F. Chen, S. W. Tsai, and S. C. Wang, "High-power diode-pumped nonlinear mirror mode-locked Nd:YVO4 laser with periodically-poled KTP," Appl. Phys. B 72, 395-397 (2001).
[CrossRef]

Y. F. Chen, S. W. Tsai, Y. P. Lan, S. C. Wang, and K. F. Huang, "Diode-end-pumped passively mode-locked high-power Nd:YVO4 laser with a relaxed saturable Bragg reflector," Opt. Lett. 26, 199-201 (2001).
[CrossRef]

R. Paschotta and U. Keller, "Passive mode locking with slow saturable absorbers," Appl. Phys. B 73, 653-662 (2001).
[CrossRef]

2000 (3)

G. J. Spühler, T. Südmeyer, R. Paschotta, M. Moser, K. J. Weingarten, and U. Keller, "Passively mode-locked high-power Nd:YAG lasers with multiple laser heads," Appl. Phys. B 71, 19-25 (2000).
[CrossRef]

D. Burns, M. Hetterich, A. I. Ferguson, E. Bente, M. D. Dawson, J. I. Davis, and S. W. Bland, "High-average-power (>20W) Nd:YVO4 lasers mode locked by strain-compensated saturable Bragg reflectors," J. Opt. Soc. Am. B 17, 919-926 (2000).
[CrossRef]

T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, "Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption," Appl. Phys. B 70, S41-S49 (2000).
[CrossRef]

1999 (3)

S.H. Cho, B.E. Bouma, E.P. Ippen, and J.G. Fujimoto, "Low-repetition-rate high-peak-power Kerr-lens mode-locked Ti:Al2O3 laser with a multiple-pass cavity," Opt. Lett,  24, 417-419 (1999).
[CrossRef]

L.J. Qian, X. Liu, and F.W. Wise, "Femtosecond Kerr-lens mode locking with negative nonlinear phase shifts," Opt. Lett. 24, 166-168 (1999).
[CrossRef]

H. Hellwig, J. Liebertz, and L. Bohaty, "Exceptional large nonlinear optical coefficients in the monoclinic bismuth borate BiB3O6 (BIBO)," Solid State Commun. 109, 249-251 (1999).
[CrossRef]

1998 (1)

1995 (2)

G. Cerullo, S. De Silvestri, A. Monguzzi, D. Segala, and V. Magni, "Self-starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities," Opt. Lett. 20, 746-748 (1995).
[CrossRef] [PubMed]

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

1994 (4)

T. Jensen, V.G. Ostroumov, J.-P. Meyn, G. Huber, A.I. Zagumennyi, and I.A. Shcherbakov, "Spectroscopic characterization and laser performance of diode-laser-pumped Nd:GdVO4," Appl. Phys. B 58, 373-379 (1994).
[CrossRef]

G. Cerullo, M.B. Danailov, S. De Silvestri, P. Laporta, D. Gegala, and S. Taccheo, "A diode-pumped nonlinear mirror mode-locked Nd:YAG laser," Appl. Phys. Lett. 65,2392-2394 (1994).
[CrossRef]

M.B. Danailov, G. Cerullo, V. Magni, D. Segala, and S. De Silvestri, "Nonlinear mirror mode locking of a cw Nd:YLF laser," Opt. Lett. 19, 792-794 (1994).
[CrossRef] [PubMed]

K. Kato, "Temperature-tuned 90° phase-matching properties of LiB3O5," IEEE J. Quantum Electron. 30, 2950-2952 (1994).
[CrossRef]

1992 (1)

1991 (2)

1990 (1)

1975 (1)

H. Haus, "Theory of mode locking with a fast saturable absorber," J. Appl. Phys. 46, 3049-3058 (1975).
[CrossRef]

Agnesi, A.

Aschwanden, A.

Bente, E.

Bland, S. W.

Bohaty, L.

H. Hellwig, J. Liebertz, and L. Bohaty, "Exceptional large nonlinear optical coefficients in the monoclinic bismuth borate BiB3O6 (BIBO)," Solid State Commun. 109, 249-251 (1999).
[CrossRef]

Bouma, B.E.

S.H. Cho, B.E. Bouma, E.P. Ippen, and J.G. Fujimoto, "Low-repetition-rate high-peak-power Kerr-lens mode-locked Ti:Al2O3 laser with a multiple-pass cavity," Opt. Lett,  24, 417-419 (1999).
[CrossRef]

Brickeen, B.K.

Brovelli, L. R.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Brunner, F.

Burns, D.

Calasso, I.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Carruthers, T. F.

Cerullo, G.

Chekhlov, O. V.

Chen, Y. F.

Y. F. Chen, S. W. Tsai, Y. P. Lan, S. C. Wang, and K. F. Huang, "Diode-end-pumped passively mode-locked high-power Nd:YVO4 laser with a relaxed saturable Bragg reflector," Opt. Lett. 26, 199-201 (2001).
[CrossRef]

Y. F. Chen, S. W. Tsai, and S. C. Wang, "High-power diode-pumped nonlinear mirror mode-locked Nd:YVO4 laser with periodically-poled KTP," Appl. Phys. B 72, 395-397 (2001).
[CrossRef]

Cho, S.H.

S.H. Cho, B.E. Bouma, E.P. Ippen, and J.G. Fujimoto, "Low-repetition-rate high-peak-power Kerr-lens mode-locked Ti:Al2O3 laser with a multiple-pass cavity," Opt. Lett,  24, 417-419 (1999).
[CrossRef]

Danailov, M.B.

G. Cerullo, M.B. Danailov, S. De Silvestri, P. Laporta, D. Gegala, and S. Taccheo, "A diode-pumped nonlinear mirror mode-locked Nd:YAG laser," Appl. Phys. Lett. 65,2392-2394 (1994).
[CrossRef]

M.B. Danailov, G. Cerullo, V. Magni, D. Segala, and S. De Silvestri, "Nonlinear mirror mode locking of a cw Nd:YLF laser," Opt. Lett. 19, 792-794 (1994).
[CrossRef] [PubMed]

Davis, J. I.

Dawson, M. D.

De Silvestri, S.

DeSalvo, R.

Duling, I. N.

Ebrahim-Zadeh, M.

Ferguson, A. I.

Fujimoto, J.G.

S.H. Cho, B.E. Bouma, E.P. Ippen, and J.G. Fujimoto, "Low-repetition-rate high-peak-power Kerr-lens mode-locked Ti:Al2O3 laser with a multiple-pass cavity," Opt. Lett,  24, 417-419 (1999).
[CrossRef]

Gegala, D.

G. Cerullo, M.B. Danailov, S. De Silvestri, P. Laporta, D. Gegala, and S. Taccheo, "A diode-pumped nonlinear mirror mode-locked Nd:YAG laser," Appl. Phys. Lett. 65,2392-2394 (1994).
[CrossRef]

Ghotbi, M.

Guandalini, A.

Hagan, D. J.

Häring, R.

Haus, H.

H. Haus, "Theory of mode locking with a fast saturable absorber," J. Appl. Phys. 46, 3049-3058 (1975).
[CrossRef]

He, J.-L.

Hellwig, H.

H. Hellwig, J. Liebertz, and L. Bohaty, "Exceptional large nonlinear optical coefficients in the monoclinic bismuth borate BiB3O6 (BIBO)," Solid State Commun. 109, 249-251 (1999).
[CrossRef]

Hetterich, M.

Holmgren, S. J.

Hönninger, C.

Huang, J. Y. J.

Huang, K. F.

Huang, K.-F.

Huber, G.

T. Jensen, V.G. Ostroumov, J.-P. Meyn, G. Huber, A.I. Zagumennyi, and I.A. Shcherbakov, "Spectroscopic characterization and laser performance of diode-laser-pumped Nd:GdVO4," Appl. Phys. B 58, 373-379 (1994).
[CrossRef]

Innerhofer, E.

Ippen, E. P.

T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, "Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption," Appl. Phys. B 70, S41-S49 (2000).
[CrossRef]

Ippen, E.P.

S.H. Cho, B.E. Bouma, E.P. Ippen, and J.G. Fujimoto, "Low-repetition-rate high-peak-power Kerr-lens mode-locked Ti:Al2O3 laser with a multiple-pass cavity," Opt. Lett,  24, 417-419 (1999).
[CrossRef]

Jensen, T.

T. Jensen, V.G. Ostroumov, J.-P. Meyn, G. Huber, A.I. Zagumennyi, and I.A. Shcherbakov, "Spectroscopic characterization and laser performance of diode-laser-pumped Nd:GdVO4," Appl. Phys. B 58, 373-379 (1994).
[CrossRef]

Kamp, M.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Kärtner, F. X.

T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, "Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption," Appl. Phys. B 70, S41-S49 (2000).
[CrossRef]

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Kato, K.

K. Kato, "Temperature-tuned 90° phase-matching properties of LiB3O5," IEEE J. Quantum Electron. 30, 2950-2952 (1994).
[CrossRef]

Keller, U.

E. Innerhofer, T. Südmeyer, F. Brunner, R. Häring, A. Aschwanden, R. Paschotta, C. Hönninger, M. Kumkar, and U. Keller, "60-W average power in 810-fs pulses from a thin-disk Yb:YAG laser," Opt. Lett. 28, 367-369 (2003).
[CrossRef] [PubMed]

R. Paschotta and U. Keller, "Passive mode locking with slow saturable absorbers," Appl. Phys. B 73, 653-662 (2001).
[CrossRef]

G. J. Spühler, T. Südmeyer, R. Paschotta, M. Moser, K. J. Weingarten, and U. Keller, "Passively mode-locked high-power Nd:YAG lasers with multiple laser heads," Appl. Phys. B 71, 19-25 (2000).
[CrossRef]

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Kopf, D.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Kumkar, M.

Lan, Y. P.

Laporta, P.

G. Cerullo, M.B. Danailov, S. De Silvestri, P. Laporta, D. Gegala, and S. Taccheo, "A diode-pumped nonlinear mirror mode-locked Nd:YAG laser," Appl. Phys. Lett. 65,2392-2394 (1994).
[CrossRef]

Laurel, F.

Lee, C.-K.

Liebertz, J.

H. Hellwig, J. Liebertz, and L. Bohaty, "Exceptional large nonlinear optical coefficients in the monoclinic bismuth borate BiB3O6 (BIBO)," Solid State Commun. 109, 249-251 (1999).
[CrossRef]

Liu, X.

Magni, V.

Meyn, J.-P.

T. Jensen, V.G. Ostroumov, J.-P. Meyn, G. Huber, A.I. Zagumennyi, and I.A. Shcherbakov, "Spectroscopic characterization and laser performance of diode-laser-pumped Nd:GdVO4," Appl. Phys. B 58, 373-379 (1994).
[CrossRef]

Mirkov, M.G.

Monguzzi, A.

Moser, M.

G. J. Spühler, T. Südmeyer, R. Paschotta, M. Moser, K. J. Weingarten, and U. Keller, "Passively mode-locked high-power Nd:YAG lasers with multiple laser heads," Appl. Phys. B 71, 19-25 (2000).
[CrossRef]

Ostroumov, V.G.

T. Jensen, V.G. Ostroumov, J.-P. Meyn, G. Huber, A.I. Zagumennyi, and I.A. Shcherbakov, "Spectroscopic characterization and laser performance of diode-laser-pumped Nd:GdVO4," Appl. Phys. B 58, 373-379 (1994).
[CrossRef]

Pan, C.-L.

Paschotta, R.

E. Innerhofer, T. Südmeyer, F. Brunner, R. Häring, A. Aschwanden, R. Paschotta, C. Hönninger, M. Kumkar, and U. Keller, "60-W average power in 810-fs pulses from a thin-disk Yb:YAG laser," Opt. Lett. 28, 367-369 (2003).
[CrossRef] [PubMed]

R. Paschotta and U. Keller, "Passive mode locking with slow saturable absorbers," Appl. Phys. B 73, 653-662 (2001).
[CrossRef]

G. J. Spühler, T. Südmeyer, R. Paschotta, M. Moser, K. J. Weingarten, and U. Keller, "Passively mode-locked high-power Nd:YAG lasers with multiple laser heads," Appl. Phys. B 71, 19-25 (2000).
[CrossRef]

Pasiskevicius, V.

Qian, L.J.

Rimington, N.W.

Sani, E.

Schibli, T. R.

T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, "Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption," Appl. Phys. B 70, S41-S49 (2000).
[CrossRef]

Schieffer, S.L.

Schroeder, W.A.

Segala, D.

Shcherbakov, I.A.

T. Jensen, V.G. Ostroumov, J.-P. Meyn, G. Huber, A.I. Zagumennyi, and I.A. Shcherbakov, "Spectroscopic characterization and laser performance of diode-laser-pumped Nd:GdVO4," Appl. Phys. B 58, 373-379 (1994).
[CrossRef]

Sheik-Bahae, M.

Spühler, G. J.

G. J. Spühler, T. Südmeyer, R. Paschotta, M. Moser, K. J. Weingarten, and U. Keller, "Passively mode-locked high-power Nd:YAG lasers with multiple laser heads," Appl. Phys. B 71, 19-25 (2000).
[CrossRef]

Stankov, K.A.

Stegeman, G.

Südmeyer, T.

E. Innerhofer, T. Südmeyer, F. Brunner, R. Häring, A. Aschwanden, R. Paschotta, C. Hönninger, M. Kumkar, and U. Keller, "60-W average power in 810-fs pulses from a thin-disk Yb:YAG laser," Opt. Lett. 28, 367-369 (2003).
[CrossRef] [PubMed]

G. J. Spühler, T. Südmeyer, R. Paschotta, M. Moser, K. J. Weingarten, and U. Keller, "Passively mode-locked high-power Nd:YAG lasers with multiple laser heads," Appl. Phys. B 71, 19-25 (2000).
[CrossRef]

Taccheo, S.

G. Cerullo, M.B. Danailov, S. De Silvestri, P. Laporta, D. Gegala, and S. Taccheo, "A diode-pumped nonlinear mirror mode-locked Nd:YAG laser," Appl. Phys. Lett. 65,2392-2394 (1994).
[CrossRef]

Thoen, E. R.

T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, "Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption," Appl. Phys. B 70, S41-S49 (2000).
[CrossRef]

Tnocelli, A.

Tomaselli, A.

Tonelli, M.

Tsai, S. W.

Y. F. Chen, S. W. Tsai, and S. C. Wang, "High-power diode-pumped nonlinear mirror mode-locked Nd:YVO4 laser with periodically-poled KTP," Appl. Phys. B 72, 395-397 (2001).
[CrossRef]

Y. F. Chen, S. W. Tsai, Y. P. Lan, S. C. Wang, and K. F. Huang, "Diode-end-pumped passively mode-locked high-power Nd:YVO4 laser with a relaxed saturable Bragg reflector," Opt. Lett. 26, 199-201 (2001).
[CrossRef]

Tzolov, V.P.

Van Stryland, E. W.

Vanherzeele, H.

Wang, S. C.

Y. F. Chen, S. W. Tsai, and S. C. Wang, "High-power diode-pumped nonlinear mirror mode-locked Nd:YVO4 laser with periodically-poled KTP," Appl. Phys. B 72, 395-397 (2001).
[CrossRef]

Y. F. Chen, S. W. Tsai, Y. P. Lan, S. C. Wang, and K. F. Huang, "Diode-end-pumped passively mode-locked high-power Nd:YVO4 laser with a relaxed saturable Bragg reflector," Opt. Lett. 26, 199-201 (2001).
[CrossRef]

Wang, S.-C.

Weingarten, K. J.

G. J. Spühler, T. Südmeyer, R. Paschotta, M. Moser, K. J. Weingarten, and U. Keller, "Passively mode-locked high-power Nd:YAG lasers with multiple laser heads," Appl. Phys. B 71, 19-25 (2000).
[CrossRef]

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[CrossRef]

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Appl. Opt. (1)

Appl. Phys. B (5)

Y. F. Chen, S. W. Tsai, and S. C. Wang, "High-power diode-pumped nonlinear mirror mode-locked Nd:YVO4 laser with periodically-poled KTP," Appl. Phys. B 72, 395-397 (2001).
[CrossRef]

G. J. Spühler, T. Südmeyer, R. Paschotta, M. Moser, K. J. Weingarten, and U. Keller, "Passively mode-locked high-power Nd:YAG lasers with multiple laser heads," Appl. Phys. B 71, 19-25 (2000).
[CrossRef]

T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, "Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption," Appl. Phys. B 70, S41-S49 (2000).
[CrossRef]

T. Jensen, V.G. Ostroumov, J.-P. Meyn, G. Huber, A.I. Zagumennyi, and I.A. Shcherbakov, "Spectroscopic characterization and laser performance of diode-laser-pumped Nd:GdVO4," Appl. Phys. B 58, 373-379 (1994).
[CrossRef]

R. Paschotta and U. Keller, "Passive mode locking with slow saturable absorbers," Appl. Phys. B 73, 653-662 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

G. Cerullo, M.B. Danailov, S. De Silvestri, P. Laporta, D. Gegala, and S. Taccheo, "A diode-pumped nonlinear mirror mode-locked Nd:YAG laser," Appl. Phys. Lett. 65,2392-2394 (1994).
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Opt. Eng. (1)

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
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Opt. Express (3)

Opt. Lett (1)

S.H. Cho, B.E. Bouma, E.P. Ippen, and J.G. Fujimoto, "Low-repetition-rate high-peak-power Kerr-lens mode-locked Ti:Al2O3 laser with a multiple-pass cavity," Opt. Lett,  24, 417-419 (1999).
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M.B. Danailov, G. Cerullo, V. Magni, D. Segala, and S. De Silvestri, "Nonlinear mirror mode locking of a cw Nd:YLF laser," Opt. Lett. 19, 792-794 (1994).
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G. Cerullo, S. De Silvestri, A. Monguzzi, D. Segala, and V. Magni, "Self-starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities," Opt. Lett. 20, 746-748 (1995).
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Y. F. Chen, S. W. Tsai, Y. P. Lan, S. C. Wang, and K. F. Huang, "Diode-end-pumped passively mode-locked high-power Nd:YVO4 laser with a relaxed saturable Bragg reflector," Opt. Lett. 26, 199-201 (2001).
[CrossRef]

E. Innerhofer, T. Südmeyer, F. Brunner, R. Häring, A. Aschwanden, R. Paschotta, C. Hönninger, M. Kumkar, and U. Keller, "60-W average power in 810-fs pulses from a thin-disk Yb:YAG laser," Opt. Lett. 28, 367-369 (2003).
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Solid State Commun. (1)

H. Hellwig, J. Liebertz, and L. Bohaty, "Exceptional large nonlinear optical coefficients in the monoclinic bismuth borate BiB3O6 (BIBO)," Solid State Commun. 109, 249-251 (1999).
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U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the extended-cavity, mode-locked, thermal-lens-shaped (focal length f T), Brewster Nd:GdVO4 oscillator: LD = 40W laser diode, SBR = saturable Bragg reflector, OC = output coupler, and the Bismuth triborate (BiBO), β-Barium borate (BBO), and Lithium triborate (LBO) second harmonic crystals are positioned a distance d from the OC. The cavity is extended from the plane-plane auxiliary cavity (dashed mirrors M1 and M2) on one end using two mirrors with radii of curvature R 1 and R 2 arranged for unity ray transformation on a round trip. The mirror M1 is replaced by the SBR, which is moved forward by Δz ≈ 3cm to match the thermally-induced bowing of the SBR to the intracavity TEM00-mode.

Fig. 2.
Fig. 2.

Shortest measured pulse duration as a function of the CW mode-locked output power for the TLS Nd:GdVO4 resonator with M = 2, a 1% modulation depth SBR, a 5.0mm BiBO crystal, and a 13% output coupler; 1/2Δk.L ≈ -π (open circles) and 1/2Δk.L ≈ -2π (filled squares). The horizontal dashed line indicates the 15ps pulse duration obtained at 8W of output power without an intracavity SHG crystal.

Fig. 3.
Fig. 3.

Measured second-harmonic autocorrelations (data points) of the shortest pulses produced by the dual-passive mode-locked TLS Nd:GdVO4 laser under different operation conditions; intracavity telescope magnification (M), β-Barium borate (BBO) and Lithium triborate (LBO) doubling crystals, phase mismatch (1/2Δk.L), and saturable Bragg reflector modulation depth (ΔRSBR ). The data is fit to the autocorrelation function of a sech2 pulse (lines).

Fig. 4.
Fig. 4.

Dependence of the extra-cavity second-harmonic generation signal (data points) as a function of phase-mismatch (i.e., crystal temperature) in the region of stable 6W CW ML operation between 1/2Δk.L ≈ -6.5π and 1/2Δk.L ≈ -3.5π for the 1cm-long NCPM Lithium triborate (LBO) doubling crystal with cavity parameters M = 1 and ΔR SBR = 2%. Also shown are the SHG (solid line) and SPM (dashed line) contributions for the cascaded χ(2)(2) process from equation (3).

Equations (4)

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

E c = E A E L Δ R ,
E c = E A Δ R 2 β ˜ + 1 E L
β ˜ = 4 π 2 Z 0 ( d eff L ) 2 3 n 3 λ ω 2 A SHG τ .
E ω ( L ) { 1 ξ 2 sin c 2 ( Δ k L 2 ) i ξ 2 Δ k L [ 1 sin c ( Δ k L ) ] 2 } E ω ( 0 ) ,

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