Abstract

We have studied Kerr-lens mode-locking efficiency in a Ti-sapphire laser both experimentally and theoretically. The criterion of mode-locking efficiency based on the spatiotemporal model of a self-consistent laser field was proposed. We investigated ultrashort-pulse stability, taking into account the gain saturation and group-velocity dispersion. A stable regime of double pulse collision at the active medium has been observed and analyzed theoretically.

© 1997 Optical Society of America

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  1. D. E. Spence, P. N. Kean, and W. Sibbet, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 42 (1991).
    [CrossRef] [PubMed]
  2. C. Huang, M. T. Asaki, S. Backus, M. M. Murnane, and H. C. Kapteyn, “17-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1289 (1992).
    [CrossRef] [PubMed]
  3. G. P. A. Malcolm and A. I. Ferguson, “Self-mode locking of a diode-pumped Nd-YLF laser,” Opt. Lett. 16, 1967 (1991).
    [CrossRef] [PubMed]
  4. M. Ramaswamy, A. S. Gouveia-Neto, D. K. Negus, J. A. Izatt, and J. G. Fujimoto, “2.3-ps pulses from a Kerr-lens mode-locked lamp-pumped Nd:YLF laserwith a microdot mirror,” Opt. Lett. 18, 1825 (1993).
    [CrossRef] [PubMed]
  5. K. X. Liu, C. J. Flood, D. R. Walker, and H. M. van Driel, “Kerr lens mode locking a diode-pumped ND:YAG laser,” Opt. Lett. 19, 1361 (1992).
    [CrossRef]
  6. A. Sennarogly, C. R. Pollock, and H. Nathel, “Continuous-wave self-mode-locked operation of a femtosecond Cr4+:YAG laser,” Opt. Lett. 19, 390 (1994).
  7. Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168 (1993).
    [CrossRef] [PubMed]
  8. J. M. Evans, D. E. Spence, W. Sibbett, B. H. T. Chai, and A. Meller, “50-fs pulse generation from a self-mode-locked Cr:LiSrAlF6 laser,” Opt. Lett. 17, 1447 (1992).
    [CrossRef]
  9. P. M. W. French, R. Mellish, J. R. Teylor, P. J. Delfyett, and L. T. Florez, “Mode-locked all-solid state diode-pumped Cr:LiSAF laser,” Opt. Lett. 18, 1934 (1993).
    [CrossRef] [PubMed]
  10. J. R. Lincoln, M. J. P. Dymott, and A. J. Ferguson, “Femtosecond pulses from an all-solid-state Kerr-lens mode-locked Cr:LiSAFlaser,” Opt. Lett. 19, 1210 (1994).
    [CrossRef] [PubMed]
  11. P. LiKamWa, B. H. T. Chai, and A. Miller, “Self-mode-locked Cr3+:LiCaAlF6 laser,” Opt. Lett. 17, 1438 (1992).
    [CrossRef]
  12. C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphireself-modelocked laser,” Opt. Commun. 102, 464 (1993).
    [CrossRef]
  13. M. Piche, “Beam reshaping and self-mode-locking in nonlinear laser resonators,” Opt. Commun. 86, 156 (1991).
    [CrossRef]
  14. A. Penzkofer, M. Wittmann, M. Lorenz, E. Siegert, and S. Macnamara, “Kerr lens effects in a folded-cavity four-mirror linear resonator,” Opt. Quantum Electron. 28, 423 (1996).
    [CrossRef]
  15. H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytical theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
    [CrossRef]
  16. T. Brabec, P. F. Curley, Ch. Spielmann, E. Winter, and A. J. Schmidt, “Hard-aperture Kerr-lens mode-locking,” J. Opt. Soc. Am. B 10, 1029 (1993).
    [CrossRef]
  17. V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of Gaussianbeams through Kerr media,” Opt. Commun. 96, 348 (1993).
    [CrossRef]
  18. V. Magni, G. Cerullo, and S. De Silvestri, “Close form Gaussian beam analysis of resonators containing a Kerr mediumfor femtosecond lasers,” Opt. Commun. 101, 365 (1993).
    [CrossRef]
  19. G. Cerullo, S. De Silvestri, V. Magni, and L. Pallaro, “Resonators for Kerr-lens mode-locked femtosecond Ti:sapphire lasers,” Opt. Lett. 19, 807 (1994).
    [CrossRef] [PubMed]
  20. G. Cerullo, S. De Silvestri, and V. Magni, “Self-starting Kerr-lens mode-locking of a Ti:sapphire laser,” Opt. Lett. 19, 1040 (1994).
    [CrossRef] [PubMed]
  21. G. Cerullo, S. De Silvestri, and V. Magni, “Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lensmode locking,” J. Opt. Soc. Am. B 12, 476 (1995).
    [CrossRef]
  22. J. Herrmann, “Theory of Kerr-lens mode locking: role of self-focusing and radiallyvarying gain,” J. Opt. Soc. Am. B 11, 498 (1994).
    [CrossRef]
  23. V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
    [CrossRef]
  24. D. Kopf, F. X. Kartner, K. J. Weingarten, and U. Keller, “Pulse shortening in a Nd:glass laser by gain reshaping and solitonformation,” Opt. Lett. 19, 2146 (1994).
    [CrossRef] [PubMed]
  25. H. A. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049 (1975).
    [CrossRef]
  26. V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, I. G. Poloyko, and M. I. Demchuk, “Passive mode-locking features of a cw wide-band solid-state lasers,” Quantum Electron. 23, 129 (1993).
    [CrossRef]
  27. A. R. Bishop, in Solitons in Action, K. Lonngen and A. Scott, eds. (Academic, New York, 1978), Chap. 4.
  28. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992), Chap. 2, p. 85.

1996 (1)

A. Penzkofer, M. Wittmann, M. Lorenz, E. Siegert, and S. Macnamara, “Kerr lens effects in a folded-cavity four-mirror linear resonator,” Opt. Quantum Electron. 28, 423 (1996).
[CrossRef]

1995 (2)

1994 (6)

1993 (8)

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphireself-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of Gaussianbeams through Kerr media,” Opt. Commun. 96, 348 (1993).
[CrossRef]

V. Magni, G. Cerullo, and S. De Silvestri, “Close form Gaussian beam analysis of resonators containing a Kerr mediumfor femtosecond lasers,” Opt. Commun. 101, 365 (1993).
[CrossRef]

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, I. G. Poloyko, and M. I. Demchuk, “Passive mode-locking features of a cw wide-band solid-state lasers,” Quantum Electron. 23, 129 (1993).
[CrossRef]

T. Brabec, P. F. Curley, Ch. Spielmann, E. Winter, and A. J. Schmidt, “Hard-aperture Kerr-lens mode-locking,” J. Opt. Soc. Am. B 10, 1029 (1993).
[CrossRef]

Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168 (1993).
[CrossRef] [PubMed]

M. Ramaswamy, A. S. Gouveia-Neto, D. K. Negus, J. A. Izatt, and J. G. Fujimoto, “2.3-ps pulses from a Kerr-lens mode-locked lamp-pumped Nd:YLF laserwith a microdot mirror,” Opt. Lett. 18, 1825 (1993).
[CrossRef] [PubMed]

P. M. W. French, R. Mellish, J. R. Teylor, P. J. Delfyett, and L. T. Florez, “Mode-locked all-solid state diode-pumped Cr:LiSAF laser,” Opt. Lett. 18, 1934 (1993).
[CrossRef] [PubMed]

1992 (5)

1991 (3)

1975 (1)

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

Asaki, M. T.

Backus, S.

Brabec, T.

Cerullo, G.

Chai, B. H. T.

Curley, P. F.

De Silvestri, S.

Delfyett, P. J.

Demchuk, M. I.

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, I. G. Poloyko, and M. I. Demchuk, “Passive mode-locking features of a cw wide-band solid-state lasers,” Quantum Electron. 23, 129 (1993).
[CrossRef]

Dymott, M. J. P.

Evans, J. M.

Ferguson, A. I.

Ferguson, A. J.

Flood, C. J.

Florez, L. T.

French, P. M. W.

Fujimoto, J. G.

Gouveia-Neto, A. S.

Haus, H.

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytical theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

Haus, H. A.

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

Herrmann, J.

Huang, C.

Ippen, E. P.

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytical theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

Izatt, J. A.

Kalashnikov, V. L.

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
[CrossRef]

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, I. G. Poloyko, and M. I. Demchuk, “Passive mode-locking features of a cw wide-band solid-state lasers,” Quantum Electron. 23, 129 (1993).
[CrossRef]

Kalosha, V. P.

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
[CrossRef]

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, I. G. Poloyko, and M. I. Demchuk, “Passive mode-locking features of a cw wide-band solid-state lasers,” Quantum Electron. 23, 129 (1993).
[CrossRef]

Kapteyn, H. C.

Kartner, F. X.

Kean, P. N.

Keller, U.

Kopf, D.

Krasinski, J. S.

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphireself-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

LiKamWa, P.

Lincoln, J. R.

Liu, K. X.

Lorenz, M.

A. Penzkofer, M. Wittmann, M. Lorenz, E. Siegert, and S. Macnamara, “Kerr lens effects in a folded-cavity four-mirror linear resonator,” Opt. Quantum Electron. 28, 423 (1996).
[CrossRef]

Macnamara, S.

A. Penzkofer, M. Wittmann, M. Lorenz, E. Siegert, and S. Macnamara, “Kerr lens effects in a folded-cavity four-mirror linear resonator,” Opt. Quantum Electron. 28, 423 (1996).
[CrossRef]

Magni, V.

Malcolm, G. P. A.

Meller, A.

Mellish, R.

Mikhailov, V. P.

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
[CrossRef]

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, I. G. Poloyko, and M. I. Demchuk, “Passive mode-locking features of a cw wide-band solid-state lasers,” Quantum Electron. 23, 129 (1993).
[CrossRef]

Miller, A.

Minkov, B. I.

Murnane, M. M.

Nathel, H.

Negus, D. K.

Pallaro, L.

Pang, Y.

Pearson, C. W.

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphireself-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

Penzkofer, A.

A. Penzkofer, M. Wittmann, M. Lorenz, E. Siegert, and S. Macnamara, “Kerr lens effects in a folded-cavity four-mirror linear resonator,” Opt. Quantum Electron. 28, 423 (1996).
[CrossRef]

Piche, M.

M. Piche, “Beam reshaping and self-mode-locking in nonlinear laser resonators,” Opt. Commun. 86, 156 (1991).
[CrossRef]

Pollock, C. R.

Poloyko, I. G.

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
[CrossRef]

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, I. G. Poloyko, and M. I. Demchuk, “Passive mode-locking features of a cw wide-band solid-state lasers,” Quantum Electron. 23, 129 (1993).
[CrossRef]

Radzewicz, C.

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphireself-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

Ramaswamy, M.

Schmidt, A. J.

Sennarogly, A.

Sibbet, W.

Sibbett, W.

Siegert, E.

A. Penzkofer, M. Wittmann, M. Lorenz, E. Siegert, and S. Macnamara, “Kerr lens effects in a folded-cavity four-mirror linear resonator,” Opt. Quantum Electron. 28, 423 (1996).
[CrossRef]

Spence, D. E.

Spielmann, Ch.

Teylor, J. R.

van Driel, H. M.

Walker, D. R.

Weingarten, K. J.

Winter, E.

Wise, F.

Wittmann, M.

A. Penzkofer, M. Wittmann, M. Lorenz, E. Siegert, and S. Macnamara, “Kerr lens effects in a folded-cavity four-mirror linear resonator,” Opt. Quantum Electron. 28, 423 (1996).
[CrossRef]

Yanovsky, V.

IEEE J. Quantum Electron. (1)

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytical theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

J. Appl. Phys. (1)

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

J. Opt. Soc. Am. B (4)

Opt. Commun. (4)

V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of Gaussianbeams through Kerr media,” Opt. Commun. 96, 348 (1993).
[CrossRef]

V. Magni, G. Cerullo, and S. De Silvestri, “Close form Gaussian beam analysis of resonators containing a Kerr mediumfor femtosecond lasers,” Opt. Commun. 101, 365 (1993).
[CrossRef]

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphireself-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

M. Piche, “Beam reshaping and self-mode-locking in nonlinear laser resonators,” Opt. Commun. 86, 156 (1991).
[CrossRef]

Opt. Lett. (14)

D. E. Spence, P. N. Kean, and W. Sibbet, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 42 (1991).
[CrossRef] [PubMed]

G. P. A. Malcolm and A. I. Ferguson, “Self-mode locking of a diode-pumped Nd-YLF laser,” Opt. Lett. 16, 1967 (1991).
[CrossRef] [PubMed]

C. Huang, M. T. Asaki, S. Backus, M. M. Murnane, and H. C. Kapteyn, “17-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1289 (1992).
[CrossRef] [PubMed]

P. LiKamWa, B. H. T. Chai, and A. Miller, “Self-mode-locked Cr3+:LiCaAlF6 laser,” Opt. Lett. 17, 1438 (1992).
[CrossRef]

J. M. Evans, D. E. Spence, W. Sibbett, B. H. T. Chai, and A. Meller, “50-fs pulse generation from a self-mode-locked Cr:LiSrAlF6 laser,” Opt. Lett. 17, 1447 (1992).
[CrossRef]

Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168 (1993).
[CrossRef] [PubMed]

M. Ramaswamy, A. S. Gouveia-Neto, D. K. Negus, J. A. Izatt, and J. G. Fujimoto, “2.3-ps pulses from a Kerr-lens mode-locked lamp-pumped Nd:YLF laserwith a microdot mirror,” Opt. Lett. 18, 1825 (1993).
[CrossRef] [PubMed]

P. M. W. French, R. Mellish, J. R. Teylor, P. J. Delfyett, and L. T. Florez, “Mode-locked all-solid state diode-pumped Cr:LiSAF laser,” Opt. Lett. 18, 1934 (1993).
[CrossRef] [PubMed]

A. Sennarogly, C. R. Pollock, and H. Nathel, “Continuous-wave self-mode-locked operation of a femtosecond Cr4+:YAG laser,” Opt. Lett. 19, 390 (1994).

G. Cerullo, S. De Silvestri, V. Magni, and L. Pallaro, “Resonators for Kerr-lens mode-locked femtosecond Ti:sapphire lasers,” Opt. Lett. 19, 807 (1994).
[CrossRef] [PubMed]

G. Cerullo, S. De Silvestri, and V. Magni, “Self-starting Kerr-lens mode-locking of a Ti:sapphire laser,” Opt. Lett. 19, 1040 (1994).
[CrossRef] [PubMed]

J. R. Lincoln, M. J. P. Dymott, and A. J. Ferguson, “Femtosecond pulses from an all-solid-state Kerr-lens mode-locked Cr:LiSAFlaser,” Opt. Lett. 19, 1210 (1994).
[CrossRef] [PubMed]

K. X. Liu, C. J. Flood, D. R. Walker, and H. M. van Driel, “Kerr lens mode locking a diode-pumped ND:YAG laser,” Opt. Lett. 19, 1361 (1992).
[CrossRef]

D. Kopf, F. X. Kartner, K. J. Weingarten, and U. Keller, “Pulse shortening in a Nd:glass laser by gain reshaping and solitonformation,” Opt. Lett. 19, 2146 (1994).
[CrossRef] [PubMed]

Opt. Quantum Electron. (1)

A. Penzkofer, M. Wittmann, M. Lorenz, E. Siegert, and S. Macnamara, “Kerr lens effects in a folded-cavity four-mirror linear resonator,” Opt. Quantum Electron. 28, 423 (1996).
[CrossRef]

Quantum Electron. (1)

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, I. G. Poloyko, and M. I. Demchuk, “Passive mode-locking features of a cw wide-band solid-state lasers,” Quantum Electron. 23, 129 (1993).
[CrossRef]

Other (2)

A. R. Bishop, in Solitons in Action, K. Lonngen and A. Scott, eds. (Academic, New York, 1978), Chap. 4.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992), Chap. 2, p. 85.

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Figures (4)

Fig. 1
Fig. 1

Experimentally determined normalized cw (1) and pulse (2) transmission and transmission coefficient Σ (3) (the maximum of curve 3 corresponds to 1.026×10-6 W-1); analytical cw (4) and pulse (5) transmission and nonlinear transmission coefficient (6) versus slit size d. Dotted curve 7 is the theoretical limit for the minimal negative amount of net GVD |k2| providing for stable ultrashort-pulse generation.

Fig. 2
Fig. 2

Pulse duration versus net GVD (experiment). The arrow denotes the stability boundary for ultrashort-pulse generation. The pump power is 1.9 W.

Fig. 3
Fig. 3

Generation spectrum for a, single- and b, double-pulse regimes. The noise suppression is clearly seen. The pump power is 2.1 W, and the slit size d is 2.6 mm.

Fig. 4
Fig. 4

a, Evolution of a single pulse (dashed curve) and double pulses colliding at an active medium (solid curve) in the presence of self-phase modulation and GVD. b, The same as in a, but for the case of only Kerr-lensing in an active medium.

Equations (10)

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

a(z, t)z=G+(1+ik2) 2t2+1-iσ|a(z, t)|2a(z, t),
ϕ=2ψ+k2-ψ2k2tp2,
tp=2ψk2+ψ2-1G1/2,
ψ=-3k2G+2k2a02+[G2(8+9k22)+12G(a02+k22a02)+4a02(1+k02)]1/22(G+a02).
a041s2+2k2s-8k22-9+a02G3k2s-24k22-27
-18G2(1+k22)=0.
-(1+ik2) d2dt2+q(t)ς(t)=Eς(t),
-d2dt2+q(t)ς(t)=Eς(t),
q(t)=-[1-k2/s-i(k2+1/s)]a02×sech2(t/tp)/(1+k22)
E=G-λ+k2ϕ+i(ϕ-k2G+k2λ)1+k22.

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