Abstract

A spatiotemporal model for the evolution process of the pulse and beam shapes in femtosecond Kerr-lens mode-locked solid-state lasers is presented. For different cavity configurations we comprehensively studied the dependence of the pulse and beam parameters on laser-control parameters such as pump rate, linear phase dispersion up to fourth order, self-phase modulation, and self-amplitude modulation owing to nonlinear resonator transmission. We determine the conditions for the ultimate shortest pulse duration. The influence of third- and fourth-order dispersion results in spectral sidebands, which are phase matched with the peak of the principal spectrum. Excessive fourth-order dispersion yields a steady-state multipulse operating regime with constant peak separation.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode locked Ti:sapphire laser,” Opt. Lett. 16, 42–44 (1991).
    [CrossRef] [PubMed]
  2. D. K. Negus, L. Spinelli, N. Goldblatt, and G. Feugnet, “Sub-100-fs pulse generation by Kerr lens mode locking in Ti:Al2O3,” in Advanced Solid State Lasers, G. Dubé and L. Chase, eds., Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), postdeadline paper PDP4, pp. 120–124.
  3. N. Sarukura, Y. Ishida, and N. Nakano, “Generation of 50-fsec pulses from a pulse-compressed, cw, passively mode-locked Ti:sapphire laser,” Opt. Lett. 16, 153–155 (1991).
    [PubMed]
  4. U. Keller, G. W. tHooft, W. H. Knox, and J. E. Cunningham, “Femtosecond pulses from a continuously self-starting passively mode-locked Ti:sapphire laser,” Opt. Lett. 16, 1022–1024 (1991).
    [CrossRef] [PubMed]
  5. G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, E. P. Ippen, and J. G. Fujimoto, “Femtosecond pulse generation of Ti:Al2O3 using a microdot mirror mode locker,” Opt. Lett. 16, 1756–1758 (1991).
    [CrossRef] [PubMed]
  6. Ch. Spielmann, P. F. Curley, T. Brabec, E. Wintner, and F. Krausz, “Generation of sub-20 fs mode locked pulses from a Ti:sapphire laser,” Electron. Lett. 28, 1532–1533 (1992).
    [CrossRef]
  7. M. T. Asaki, C. P. Huang, D. Harvey, J. Zhou, H. Nathel, H. C. Kapteyn, and M. M. Murnane, “11 femtosecond pulses from a modelocked Ti:sapphire laser,” Opt. Photonics News 5, 12 (65;1992).
  8. J. Zhou, G. Taft, C. P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Pulse evolution in a broad-bandwidth Ti:sapphire laser,” Opt. Lett. 19, 1149–1151 (1994).
    [CrossRef] [PubMed]
  9. Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroad-band femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
    [CrossRef]
  10. A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, “Generation of 11-fs pulses from a Ti:sapphire laser without the use of prisms,” Opt. Lett. 19, 204–206 (1994).
    [CrossRef] [PubMed]
  11. A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, and R. Szipöcs, “Sub-10-fs mirror-dispersion-controlled Ti:sapphire laser,” Opt. Lett. 20, 602–604 (1995).
    [CrossRef] [PubMed]
  12. A. Kasper and K. J. Witte, “10-fs pulse generation from a unidirectional Kerr-lens mode locked Ti:sapphire laser,” Opt. Lett. 21, 360–362 (1996).
    [CrossRef] [PubMed]
  13. L. Xu, Ch. Spielmann, and F. Krausz, “Ultrabroadband ring oscillator for sub-10-fs pulse generation,” Opt. Lett. 21, 1250–1252 (1996).
    [CrossRef]
  14. G. P. A. Malcom and A. I. Ferguson, “Self-mode locking of a diode-pumped Nd:YLF laser,” Opt. Lett. 16, 1967–1969 (1991).
    [CrossRef]
  15. J. R. Lincoln and A. I. Ferguson, “All-solid-state self-mode locking of a Nd:YLF laser,” Opt. Lett. 19, 2119–2121 (1994).
    [CrossRef] [PubMed]
  16. N. H. Rizvi, P. M. W. French, and J. R. Taylor, “Generation of 33-fs pulses from a passively mode-locked Cr3+:LiSrAlF6 laser,” Opt. Lett. 17, 1605–1607 (1992).
    [CrossRef] [PubMed]
  17. V. Yanovsky, Y. Pang, F. Wise, and B. I. Minkov, “Generation of 25-fs pulses from a self-mode-locked Cr:forsterite laser with optimized group-delay dispersion,” Opt. Lett. 18, 1541–1543 (1993).
    [CrossRef] [PubMed]
  18. P. J. Conlon, Y. P. Tong, P. M. W. French, and J. R. Taylor, “Passive mode locking and dispersion measurement of a sub-100-fs Cr4+:YAG laser,” Opt. Lett. 19, 1468–1470 (1994).
    [CrossRef] [PubMed]
  19. J. M. Sutherland, P. M. W. French, J. R. Taylor, and B. H. T. Chai, “Visible continuous-wave laser transitions in Pr3+:YLF and femtosecond pulse generation,” Opt. Lett. 20, 1041–1043 (1995).
    [CrossRef]
  20. I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Prismless passively mode-locked femtosecond Cr:LiSGaF lasers,” Opt. Lett. 21, 1165–1168 (1996).
    [CrossRef] [PubMed]
  21. V. Petrov, U. Griebner, D. Ehrt, and W. Seeber, “Femtosecond self-mode locking of Yb:fluoride phosphate glass laser,” Opt. Lett. 22, 408–410 (1997).
    [CrossRef] [PubMed]
  22. K. Lamb, D. E. Spence, J. Hong, C. Yelland, and W. Sibbett, “All-solid-state self-mode-locked Ti:sapphire laser,” Opt. Lett. 19, 1864–1866 (1994).
    [CrossRef] [PubMed]
  23. K. Read, F. Blonigen, N. Ricelli, M. Murnane, and H. Kapteyn, “Low threshold operation of an ultrashort-pulse mode-locked Ti:sapphire laser,” Opt. Lett. 21, 489–491 (1996).
    [CrossRef] [PubMed]
  24. M. Piche, “Beam reshaping and self-mode-locking in nonlinear laser resonators,” Opt. Commun. 86, 156–160 (1991).
    [CrossRef]
  25. F. Salin, J. Squier, and M. Piche, “Mode-locking of Ti:Al2O3 lasers and self-focusing: a Gaussian approximation,” Opt. Lett. 16, 1674–1676 (1991).
    [CrossRef] [PubMed]
  26. D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens modelocked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
    [CrossRef]
  27. Th. Brabec, Ch. Spielmann, P. F. Curley, and F. Krausz, “Kerr lens mode locking,” Opt. Lett. 17, 1292–1294 (1992).
    [CrossRef] [PubMed]
  28. D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, and J. G. Fujimoto, “Self-focusing-induced saturable loss for laser mode locking,” Opt. Lett. 17, 511–513 (1992).
    [CrossRef] [PubMed]
  29. M. Piche and F. Salin, “Self-mode locking of solid-state lasers without apertures,” Opt. Lett. 18, 1041–1043 (1993).
    [CrossRef] [PubMed]
  30. J. Herrmann, “Theory of Kerr-lens mode locking: role of self-focusing and radially varying gain,” J. Opt. Soc. Am. B 11, 498–512 (1994).
    [CrossRef]
  31. S. Gatz and J. Herrmann, “Geometrical threshold zones and Gaussian modes in lasers with radially varying gain,” Opt. Lett. 19, 1696–1699 (1994).
    [CrossRef] [PubMed]
  32. R. E. Bridges, R. W. Boyd, and G. V. Agrawal, “Effect of beam ellipticity on self-mode locking in lasers,” Opt. Lett. 18, 2026–2028 (1993).
    [CrossRef] [PubMed]
  33. V. Magni, G. Cerullo, S. de Silvestri, and A. Monguzzi, “Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lens mode locking,” J. Opt. Soc. Am. B 12, 476–485 (1995).
    [CrossRef]
  34. S. Gatz and J. Herrmann, “Astigmatism and gain guiding in Kerr-lens mode locked lasers,” Opt. Lett. 20, 825–827 (1995).
    [CrossRef] [PubMed]
  35. K. H. Lin and W. F. Hsieh, “Analytical design of symmetrical Kerr-lens mode-locking laser cavities,” J. Opt. Soc. Am. B 11, 737–741 (1994).
    [CrossRef]
  36. V. I. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerr self-focusing,” J. Opt. Soc. Am. B 13, 462–467 (1995).
    [CrossRef]
  37. K. H. Lin, Y. Lai, and W. F. Hsieh, “Simple analytical method of cavity design for astigmatism-compensated Kerr-lens mode-locked ring lasers and its applications,” J. Opt. Soc. Am. B 12, 468–475 (1995).
    [CrossRef]
  38. Y. C. Chen, X. Y. Zheng, T. S. Lai, X. S. Xu, D. Mo, and W. Z. Lin, “Resonators for self-mode-locking Ti:sapphire lasers without apertures,” Opt. Lett. 21, 1469–1471 (1996).
    [CrossRef] [PubMed]
  39. V. Magni, “Perturbation theory of nonlinear resonators with an application to Kerr-lens mode locking,” J. Opt. Soc. Am. B 13, 2498–2507 (1996).
    [CrossRef]
  40. G. Cerullo, S. De Silvestri, and V. Magni, “Self-starting Kerr-lens mode-locking of a Ti:sapphire laser,” Opt. Lett. 19, 1040–1042 (1994).
    [CrossRef] [PubMed]
  41. P. G. Kryukov and V. S. Lethokov, “Fluctuation mechanism of ultrashort pulse generation by lasers with saturable absorber,” IEEE J. Quantum Electron. QE-8, 766–782 (1972).
    [CrossRef]
  42. J. Herrmann, F. Weidner, and B. Wilhelmi, “Influence of the inversion depletion in the active medium on the evolution of ultrashort pulses in a passively mode locked solid-state laser,” Appl. Phys. 20, 237–245 (1979).
    [CrossRef]
  43. J. Herrmann, “Starting dynamic, self-starting condition and mode-locking threshold in passive, coupled cavity or Kerr-lens mode-locked lasers,” Opt. Commun. 98, 111–116 (1993).
    [CrossRef]
  44. H. A. Haus and E. P. Ippen, “Self-starting of passively mode-locked lasers,” Opt. Lett. 16, 1331–1333 (1991).
    [CrossRef] [PubMed]
  45. K. Tamura, J. Jacobson, E. P. Ippen, H. A. Haus, and J. G. Fujimoto, “Unidirectional ring resonators for self-starting passively mode-locked lasers,” Opt. Lett. 18, 220–222 (1993).
    [CrossRef] [PubMed]
  46. F. Krausz and Th. Brabec, “Passive mode locking in standing-wave laser resonators,” Opt. Lett. 18, 888–890 (1993).
    [CrossRef] [PubMed]
  47. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8, 2068–2076 (1991).
    [CrossRef]
  48. P. A. Belanger, “Coupled-cavity mode locking: a nonlinear model,” J. Opt. Soc. Am. B 8, 2077–2081 (1991).
    [CrossRef]
  49. V. Petrov, D. Georgiev, J. Herrmann, and U. Stamm, “Theory of cw passive mode-locking with addition of nonlinear index and group velocity dispersion,” Opt. Commun. 91, 123–130 (1992).
    [CrossRef]
  50. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
    [CrossRef]
  51. J. D. Moores, “On the Ginzburg-Landau laser mode locking model with fifth-order saturable absorber term,” Opt. Commun. 96, 65–70 (1992).
    [CrossRef]
  52. F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114, 447–452 (1995).
    [CrossRef]
  53. J. Herrmann and M. Müller, “Theory of coupled-cavity mode locking,” J. Opt. Soc. Am. B 13, 1542–1558 (1996).
    [CrossRef]
  54. Th. Brabec, Ch. Spielmann, and F. Krausz, “Mode locking in solitary lasers,” Opt. Lett. 16, 1961–1963 (1991).
    [CrossRef] [PubMed]
  55. Th. Brabec, Ch. Spielmann, and F. Krausz, “Limits of pulse shortening in solitary lasers,” Opt. Lett. 17, 748–750 (1992).
    [CrossRef] [PubMed]
  56. Th. Brabec and S. M. J. Kelly, “Third order dispersion as a limiting factor to mode locking in femtosecond solitary lasers,” Opt. Lett. 18, 2002–2004 (1993).
    [CrossRef]
  57. H. A. Haus, J. D. Moores, and L. E. Nelson, “Effect of third order dispersion on passive mode locking,” Opt. Lett. 18, 51–53 (1993).
    [CrossRef] [PubMed]
  58. J. Herrmann, V. P. Kalosha, and M. Müller, “Higher order phase dispersion in Kerr-lens mode-locked solid-state lasers: sideband generation and pulse splitting,” Opt. Lett. 22, 236–238 (1997).
    [CrossRef] [PubMed]
  59. M. Santagiustina, “Third-order dispersion in solid-state solitary lasers,” J. Opt. Soc. Am. B 14, 1484–1495 (1997).
    [CrossRef]
  60. I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and C. P. Huang, “Fourth-order dispersion-limited solitary pulses,” Opt. Lett. 19, 1465–1467 (1994).
    [CrossRef] [PubMed]
  61. O. E. Martinez and J. L. A. Chilla, “Self-mode-locking of Ti:sapphire lasers: a matrix formalism,” Opt. Lett. 17, 1210–1212 (1992).
    [CrossRef] [PubMed]
  62. J. L. A. Chilla and O. E. Martinez, “Spatio-temporal analysis of the self-mode-locked Ti:sapphire laser,” J. Opt. Soc. Am. B 10, 638–643 (1993).
    [CrossRef]
  63. A. A. Hnilo, “Self-mode-locking Ti:sapphire laser description with an iterative map,” J. Opt. Soc. Am. B 12, 718–725 (1995).
    [CrossRef]
  64. I. P. Christov, V. D. Stoev, M. M. Murnane, and H. C. Kapteyn, “Mode locking with compensated space-time astigmatism,” Opt. Lett. 20, 2111–2113 (1995).
    [CrossRef] [PubMed]
  65. I. P. Christov, V. D. Stoev, M. M. Murnane, and H. C. Kapteyn, “Sub-10-fs operation of Kerr-lens mode locked lasers,” Opt. Lett. 21, 1493–1495 (1996).
    [CrossRef] [PubMed]
  66. F. J. Duarte, ed., Tunable Lasers, 1st ed. (Academic, New York, 1995).
  67. A. E. Siegmann, Lasers (University Science, Mill Valley, Calif., 1986).
  68. M. Karlsson, D. Anderson, M. Desiax, and M. Lisak, “Dynamic effects of Kerr nonlinearity and spatial diffraction on self-phase modulation of optical pulses,” Opt. Lett. 16, 1373–1375 (1991).
    [CrossRef] [PubMed]
  69. R. E. Bridges, R. W. Boyd, and G. P. Agrawal, “Multidimensional coupling owing to optical nonlinearities. I. General formulation,” J. Opt. Soc. Am. B 13, 553–559 (1996); “Multidimensional coupling owing to optical nonlinearities. II. Results,” J. Opt. Soc. Am. B 13, 560–569 (1996).
    [CrossRef]
  70. S. T. Cundiff, W. H. Knox, E. P. Ippen, and H. A. Haus, “Frequency-dependent mode size in broadband Kerr-lens mode locking,” Opt. Lett. 21, 662–664 (1996).
    [CrossRef] [PubMed]
  71. B. E. Bouma and J. G. Fujimoto, “Compact Kerr-lens mode-locked resonator,” Opt. Lett. 21, 134–136 (1996).
    [CrossRef] [PubMed]
  72. V. I. Kalashnikov, V. P. Kalosha, I. G. Poloyko, and V. P. Mikhailov, “Optimal resonators for self-mode locking of continuous-wave solid-state lasers,” J. Opt. Soc. Am. B 14, 964–969 (1997).
    [CrossRef]
  73. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [CrossRef]
  74. B. Proctor, E. Westwig, and F. Wise, “Characterization of a Kerr-lens mode locked Ti:sapphire laser with positive group-velocity dispersion,” Opt. Lett. 18, 1654–1656 (1993).
    [CrossRef] [PubMed]
  75. Th. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
    [CrossRef]
  76. A. Kasper and K. J. Witte, “Contrast and phase characterization of ultrashort laser pulses emitted from mirror-dispersion-controlled Ti:sapphire ring and Fabry–Perot resonators,” Opt. Lett. (to be published).
  77. I. N. Duling III, ed., Compact Sources of Ultrashort Pulses, 1st ed. (Cambridge University, Cambridge, England, 1995), Chap. 4.2.3., p. 157.
  78. C. P. J. Barty, T. Guo, C. Le Blanc, F. Raksi, C. Rose-Petruck, J. Squier, K. R. Wilson, V. V. Yakovlev, and K. Yamakawa, “Generation of 18-fs multiterawatt pulses by regenerative pulse shape and chirped-pulse amplification,” Opt. Lett. 21, 668–670 (1996).
    [CrossRef] [PubMed]
  79. A. Braun, J. V. Rudd, H. Cheng, G. Mourou, D. Kopf, I. D. Jung, K. J. Weingarten, and U. Keller, “Characterization of short-pulse oscillators by means of a high-dynamic-range autocorrelation measurement,” Opt. Lett. 20, 1889–1891 (1995).
    [CrossRef] [PubMed]
  80. G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, and I. P. Christov, “Ultrashort optical waveform measurements using frequency-resolved optical gating,” Opt. Lett. 20, 743–745 (1995).
    [CrossRef] [PubMed]
  81. J. N. Elgin, “Soliton propagation in an optical fiber with third-order dispersion,” Opt. Lett. 17, 1409–1411 (1992).
    [CrossRef] [PubMed]
  82. C. Wang, W. Zhang, K. F. Lee, and K. M. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
    [CrossRef]

1997 (6)

1996 (11)

B. E. Bouma and J. G. Fujimoto, “Compact Kerr-lens mode-locked resonator,” Opt. Lett. 21, 134–136 (1996).
[CrossRef] [PubMed]

A. Kasper and K. J. Witte, “10-fs pulse generation from a unidirectional Kerr-lens mode locked Ti:sapphire laser,” Opt. Lett. 21, 360–362 (1996).
[CrossRef] [PubMed]

K. Read, F. Blonigen, N. Ricelli, M. Murnane, and H. Kapteyn, “Low threshold operation of an ultrashort-pulse mode-locked Ti:sapphire laser,” Opt. Lett. 21, 489–491 (1996).
[CrossRef] [PubMed]

S. T. Cundiff, W. H. Knox, E. P. Ippen, and H. A. Haus, “Frequency-dependent mode size in broadband Kerr-lens mode locking,” Opt. Lett. 21, 662–664 (1996).
[CrossRef] [PubMed]

C. P. J. Barty, T. Guo, C. Le Blanc, F. Raksi, C. Rose-Petruck, J. Squier, K. R. Wilson, V. V. Yakovlev, and K. Yamakawa, “Generation of 18-fs multiterawatt pulses by regenerative pulse shape and chirped-pulse amplification,” Opt. Lett. 21, 668–670 (1996).
[CrossRef] [PubMed]

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Prismless passively mode-locked femtosecond Cr:LiSGaF lasers,” Opt. Lett. 21, 1165–1168 (1996).
[CrossRef] [PubMed]

L. Xu, Ch. Spielmann, and F. Krausz, “Ultrabroadband ring oscillator for sub-10-fs pulse generation,” Opt. Lett. 21, 1250–1252 (1996).
[CrossRef]

Y. C. Chen, X. Y. Zheng, T. S. Lai, X. S. Xu, D. Mo, and W. Z. Lin, “Resonators for self-mode-locking Ti:sapphire lasers without apertures,” Opt. Lett. 21, 1469–1471 (1996).
[CrossRef] [PubMed]

I. P. Christov, V. D. Stoev, M. M. Murnane, and H. C. Kapteyn, “Sub-10-fs operation of Kerr-lens mode locked lasers,” Opt. Lett. 21, 1493–1495 (1996).
[CrossRef] [PubMed]

J. Herrmann and M. Müller, “Theory of coupled-cavity mode locking,” J. Opt. Soc. Am. B 13, 1542–1558 (1996).
[CrossRef]

V. Magni, “Perturbation theory of nonlinear resonators with an application to Kerr-lens mode locking,” J. Opt. Soc. Am. B 13, 2498–2507 (1996).
[CrossRef]

1995 (11)

A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, and R. Szipöcs, “Sub-10-fs mirror-dispersion-controlled Ti:sapphire laser,” Opt. Lett. 20, 602–604 (1995).
[CrossRef] [PubMed]

G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, and I. P. Christov, “Ultrashort optical waveform measurements using frequency-resolved optical gating,” Opt. Lett. 20, 743–745 (1995).
[CrossRef] [PubMed]

S. Gatz and J. Herrmann, “Astigmatism and gain guiding in Kerr-lens mode locked lasers,” Opt. Lett. 20, 825–827 (1995).
[CrossRef] [PubMed]

J. M. Sutherland, P. M. W. French, J. R. Taylor, and B. H. T. Chai, “Visible continuous-wave laser transitions in Pr3+:YLF and femtosecond pulse generation,” Opt. Lett. 20, 1041–1043 (1995).
[CrossRef]

A. Braun, J. V. Rudd, H. Cheng, G. Mourou, D. Kopf, I. D. Jung, K. J. Weingarten, and U. Keller, “Characterization of short-pulse oscillators by means of a high-dynamic-range autocorrelation measurement,” Opt. Lett. 20, 1889–1891 (1995).
[CrossRef] [PubMed]

I. P. Christov, V. D. Stoev, M. M. Murnane, and H. C. Kapteyn, “Mode locking with compensated space-time astigmatism,” Opt. Lett. 20, 2111–2113 (1995).
[CrossRef] [PubMed]

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114, 447–452 (1995).
[CrossRef]

V. I. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerr self-focusing,” J. Opt. Soc. Am. B 13, 462–467 (1995).
[CrossRef]

K. H. Lin, Y. Lai, and W. F. Hsieh, “Simple analytical method of cavity design for astigmatism-compensated Kerr-lens mode-locked ring lasers and its applications,” J. Opt. Soc. Am. B 12, 468–475 (1995).
[CrossRef]

V. Magni, G. Cerullo, S. de Silvestri, and A. Monguzzi, “Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lens mode locking,” J. Opt. Soc. Am. B 12, 476–485 (1995).
[CrossRef]

A. A. Hnilo, “Self-mode-locking Ti:sapphire laser description with an iterative map,” J. Opt. Soc. Am. B 12, 718–725 (1995).
[CrossRef]

1994 (11)

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroad-band femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

J. Herrmann, “Theory of Kerr-lens mode locking: role of self-focusing and radially varying gain,” J. Opt. Soc. Am. B 11, 498–512 (1994).
[CrossRef]

K. H. Lin and W. F. Hsieh, “Analytical design of symmetrical Kerr-lens mode-locking laser cavities,” J. Opt. Soc. Am. B 11, 737–741 (1994).
[CrossRef]

A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, “Generation of 11-fs pulses from a Ti:sapphire laser without the use of prisms,” Opt. Lett. 19, 204–206 (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, 1040–1042 (1994).
[CrossRef] [PubMed]

J. Zhou, G. Taft, C. P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Pulse evolution in a broad-bandwidth Ti:sapphire laser,” Opt. Lett. 19, 1149–1151 (1994).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and C. P. Huang, “Fourth-order dispersion-limited solitary pulses,” Opt. Lett. 19, 1465–1467 (1994).
[CrossRef] [PubMed]

P. J. Conlon, Y. P. Tong, P. M. W. French, and J. R. Taylor, “Passive mode locking and dispersion measurement of a sub-100-fs Cr4+:YAG laser,” Opt. Lett. 19, 1468–1470 (1994).
[CrossRef] [PubMed]

S. Gatz and J. Herrmann, “Geometrical threshold zones and Gaussian modes in lasers with radially varying gain,” Opt. Lett. 19, 1696–1699 (1994).
[CrossRef] [PubMed]

K. Lamb, D. E. Spence, J. Hong, C. Yelland, and W. Sibbett, “All-solid-state self-mode-locked Ti:sapphire laser,” Opt. Lett. 19, 1864–1866 (1994).
[CrossRef] [PubMed]

J. R. Lincoln and A. I. Ferguson, “All-solid-state self-mode locking of a Nd:YLF laser,” Opt. Lett. 19, 2119–2121 (1994).
[CrossRef] [PubMed]

1993 (10)

J. L. A. Chilla and O. E. Martinez, “Spatio-temporal analysis of the self-mode-locked Ti:sapphire laser,” J. Opt. Soc. Am. B 10, 638–643 (1993).
[CrossRef]

H. A. Haus, J. D. Moores, and L. E. Nelson, “Effect of third order dispersion on passive mode locking,” Opt. Lett. 18, 51–53 (1993).
[CrossRef] [PubMed]

K. Tamura, J. Jacobson, E. P. Ippen, H. A. Haus, and J. G. Fujimoto, “Unidirectional ring resonators for self-starting passively mode-locked lasers,” Opt. Lett. 18, 220–222 (1993).
[CrossRef] [PubMed]

F. Krausz and Th. Brabec, “Passive mode locking in standing-wave laser resonators,” Opt. Lett. 18, 888–890 (1993).
[CrossRef] [PubMed]

V. Yanovsky, Y. Pang, F. Wise, and B. I. Minkov, “Generation of 25-fs pulses from a self-mode-locked Cr:forsterite laser with optimized group-delay dispersion,” Opt. Lett. 18, 1541–1543 (1993).
[CrossRef] [PubMed]

B. Proctor, E. Westwig, and F. Wise, “Characterization of a Kerr-lens mode locked Ti:sapphire laser with positive group-velocity dispersion,” Opt. Lett. 18, 1654–1656 (1993).
[CrossRef] [PubMed]

Th. Brabec and S. M. J. Kelly, “Third order dispersion as a limiting factor to mode locking in femtosecond solitary lasers,” Opt. Lett. 18, 2002–2004 (1993).
[CrossRef]

R. E. Bridges, R. W. Boyd, and G. V. Agrawal, “Effect of beam ellipticity on self-mode locking in lasers,” Opt. Lett. 18, 2026–2028 (1993).
[CrossRef] [PubMed]

J. Herrmann, “Starting dynamic, self-starting condition and mode-locking threshold in passive, coupled cavity or Kerr-lens mode-locked lasers,” Opt. Commun. 98, 111–116 (1993).
[CrossRef]

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

1992 (12)

O. E. Martinez and J. L. A. Chilla, “Self-mode-locking of Ti:sapphire lasers: a matrix formalism,” Opt. Lett. 17, 1210–1212 (1992).
[CrossRef] [PubMed]

V. Petrov, D. Georgiev, J. Herrmann, and U. Stamm, “Theory of cw passive mode-locking with addition of nonlinear index and group velocity dispersion,” Opt. Commun. 91, 123–130 (1992).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

J. D. Moores, “On the Ginzburg-Landau laser mode locking model with fifth-order saturable absorber term,” Opt. Commun. 96, 65–70 (1992).
[CrossRef]

Ch. Spielmann, P. F. Curley, T. Brabec, E. Wintner, and F. Krausz, “Generation of sub-20 fs mode locked pulses from a Ti:sapphire laser,” Electron. Lett. 28, 1532–1533 (1992).
[CrossRef]

M. T. Asaki, C. P. Huang, D. Harvey, J. Zhou, H. Nathel, H. C. Kapteyn, and M. M. Murnane, “11 femtosecond pulses from a modelocked Ti:sapphire laser,” Opt. Photonics News 5, 12 (65;1992).

D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens modelocked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, and J. G. Fujimoto, “Self-focusing-induced saturable loss for laser mode locking,” Opt. Lett. 17, 511–513 (1992).
[CrossRef] [PubMed]

Th. Brabec, Ch. Spielmann, and F. Krausz, “Limits of pulse shortening in solitary lasers,” Opt. Lett. 17, 748–750 (1992).
[CrossRef] [PubMed]

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

J. N. Elgin, “Soliton propagation in an optical fiber with third-order dispersion,” Opt. Lett. 17, 1409–1411 (1992).
[CrossRef] [PubMed]

N. H. Rizvi, P. M. W. French, and J. R. Taylor, “Generation of 33-fs pulses from a passively mode-locked Cr3+:LiSrAlF6 laser,” Opt. Lett. 17, 1605–1607 (1992).
[CrossRef] [PubMed]

1991 (12)

D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode locked Ti:sapphire laser,” Opt. Lett. 16, 42–44 (1991).
[CrossRef] [PubMed]

N. Sarukura, Y. Ishida, and N. Nakano, “Generation of 50-fsec pulses from a pulse-compressed, cw, passively mode-locked Ti:sapphire laser,” Opt. Lett. 16, 153–155 (1991).
[PubMed]

U. Keller, G. W. tHooft, W. H. Knox, and J. E. Cunningham, “Femtosecond pulses from a continuously self-starting passively mode-locked Ti:sapphire laser,” Opt. Lett. 16, 1022–1024 (1991).
[CrossRef] [PubMed]

H. A. Haus and E. P. Ippen, “Self-starting of passively mode-locked lasers,” Opt. Lett. 16, 1331–1333 (1991).
[CrossRef] [PubMed]

M. Karlsson, D. Anderson, M. Desiax, and M. Lisak, “Dynamic effects of Kerr nonlinearity and spatial diffraction on self-phase modulation of optical pulses,” Opt. Lett. 16, 1373–1375 (1991).
[CrossRef] [PubMed]

G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, E. P. Ippen, and J. G. Fujimoto, “Femtosecond pulse generation of Ti:Al2O3 using a microdot mirror mode locker,” Opt. Lett. 16, 1756–1758 (1991).
[CrossRef] [PubMed]

Th. Brabec, Ch. Spielmann, and F. Krausz, “Mode locking in solitary lasers,” Opt. Lett. 16, 1961–1963 (1991).
[CrossRef] [PubMed]

G. P. A. Malcom and A. I. Ferguson, “Self-mode locking of a diode-pumped Nd:YLF laser,” Opt. Lett. 16, 1967–1969 (1991).
[CrossRef]

M. Piche, “Beam reshaping and self-mode-locking in nonlinear laser resonators,” Opt. Commun. 86, 156–160 (1991).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8, 2068–2076 (1991).
[CrossRef]

P. A. Belanger, “Coupled-cavity mode locking: a nonlinear model,” J. Opt. Soc. Am. B 8, 2077–2081 (1991).
[CrossRef]

F. Salin, J. Squier, and M. Piche, “Mode-locking of Ti:Al2O3 lasers and self-focusing: a Gaussian approximation,” Opt. Lett. 16, 1674–1676 (1991).
[CrossRef] [PubMed]

1989 (1)

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

1979 (1)

J. Herrmann, F. Weidner, and B. Wilhelmi, “Influence of the inversion depletion in the active medium on the evolution of ultrashort pulses in a passively mode locked solid-state laser,” Appl. Phys. 20, 237–245 (1979).
[CrossRef]

1972 (1)

P. G. Kryukov and V. S. Lethokov, “Fluctuation mechanism of ultrashort pulse generation by lasers with saturable absorber,” IEEE J. Quantum Electron. QE-8, 766–782 (1972).
[CrossRef]

Acioli, L. H.

Agrawal, G. V.

Anderson, D.

Asaki, M. T.

M. T. Asaki, C. P. Huang, D. Harvey, J. Zhou, H. Nathel, H. C. Kapteyn, and M. M. Murnane, “11 femtosecond pulses from a modelocked Ti:sapphire laser,” Opt. Photonics News 5, 12 (65;1992).

Barty, C. P. J.

Belanger, P. A.

Blonigen, F.

Blow, K. J.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Bouma, B. E.

Boyd, R. W.

Brabec, T.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroad-band femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

Ch. Spielmann, P. F. Curley, T. Brabec, E. Wintner, and F. Krausz, “Generation of sub-20 fs mode locked pulses from a Ti:sapphire laser,” Electron. Lett. 28, 1532–1533 (1992).
[CrossRef]

Brabec, Th.

Braun, A.

Bridges, R. E.

Cassanho, A.

Cerullo, G.

Chai, B. H. T.

Chen, Y. C.

Cheng, H.

Chilla, J. L. A.

Christov, I. P.

Conlon, P. J.

Cundiff, S. T.

Cunningham, J. E.

Curley, P. F.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroad-band femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

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

Ch. Spielmann, P. F. Curley, T. Brabec, E. Wintner, and F. Krausz, “Generation of sub-20 fs mode locked pulses from a Ti:sapphire laser,” Electron. Lett. 28, 1532–1533 (1992).
[CrossRef]

de Silvestri, S.

DeLong, K. W.

Desiax, M.

Ehrt, D.

Elgin, J. N.

Ferguson, A. I.

French, P. M. W.

Fujimoto, J. G.

Gabetta, G.

Gatz, S.

Georgiev, D.

D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens modelocked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

V. Petrov, D. Georgiev, J. Herrmann, and U. Stamm, “Theory of cw passive mode-locking with addition of nonlinear index and group velocity dispersion,” Opt. Commun. 91, 123–130 (1992).
[CrossRef]

Griebner, U.

Guo, T.

Harvey, D.

M. T. Asaki, C. P. Huang, D. Harvey, J. Zhou, H. Nathel, H. C. Kapteyn, and M. M. Murnane, “11 femtosecond pulses from a modelocked Ti:sapphire laser,” Opt. Photonics News 5, 12 (65;1992).

Haus, H. A.

Herrmann, J.

J. Herrmann, V. P. Kalosha, and M. Müller, “Higher order phase dispersion in Kerr-lens mode-locked solid-state lasers: sideband generation and pulse splitting,” Opt. Lett. 22, 236–238 (1997).
[CrossRef] [PubMed]

J. Herrmann and M. Müller, “Theory of coupled-cavity mode locking,” J. Opt. Soc. Am. B 13, 1542–1558 (1996).
[CrossRef]

S. Gatz and J. Herrmann, “Astigmatism and gain guiding in Kerr-lens mode locked lasers,” Opt. Lett. 20, 825–827 (1995).
[CrossRef] [PubMed]

S. Gatz and J. Herrmann, “Geometrical threshold zones and Gaussian modes in lasers with radially varying gain,” Opt. Lett. 19, 1696–1699 (1994).
[CrossRef] [PubMed]

J. Herrmann, “Theory of Kerr-lens mode locking: role of self-focusing and radially varying gain,” J. Opt. Soc. Am. B 11, 498–512 (1994).
[CrossRef]

J. Herrmann, “Starting dynamic, self-starting condition and mode-locking threshold in passive, coupled cavity or Kerr-lens mode-locked lasers,” Opt. Commun. 98, 111–116 (1993).
[CrossRef]

V. Petrov, D. Georgiev, J. Herrmann, and U. Stamm, “Theory of cw passive mode-locking with addition of nonlinear index and group velocity dispersion,” Opt. Commun. 91, 123–130 (1992).
[CrossRef]

D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens modelocked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

J. Herrmann, F. Weidner, and B. Wilhelmi, “Influence of the inversion depletion in the active medium on the evolution of ultrashort pulses in a passively mode locked solid-state laser,” Appl. Phys. 20, 237–245 (1979).
[CrossRef]

Hnilo, A. A.

Hong, J.

Hsieh, W. F.

Huang, C. P.

Huang, D.

Ippen, E. P.

Ishida, Y.

Jacobson, J.

Jenssen, H. P.

Jung, I. D.

Kalashnikov, V. I.

V. I. Kalashnikov, V. P. Kalosha, I. G. Poloyko, and V. P. Mikhailov, “Optimal resonators for self-mode locking of continuous-wave solid-state lasers,” J. Opt. Soc. Am. B 14, 964–969 (1997).
[CrossRef]

V. I. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerr self-focusing,” J. Opt. Soc. Am. B 13, 462–467 (1995).
[CrossRef]

Kalosha, V. P.

Kapteyn, H.

Kapteyn, H. C.

Karlsson, M.

Kasper, A.

Kean, P. N.

Keller, U.

Kelly, S. M. J.

Khatri, F. I.

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114, 447–452 (1995).
[CrossRef]

Knox, W. H.

Kopf, D.

Krausz, F.

Th. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

L. Xu, Ch. Spielmann, and F. Krausz, “Ultrabroadband ring oscillator for sub-10-fs pulse generation,” Opt. Lett. 21, 1250–1252 (1996).
[CrossRef]

A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, and R. Szipöcs, “Sub-10-fs mirror-dispersion-controlled Ti:sapphire laser,” Opt. Lett. 20, 602–604 (1995).
[CrossRef] [PubMed]

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroad-band femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, “Generation of 11-fs pulses from a Ti:sapphire laser without the use of prisms,” Opt. Lett. 19, 204–206 (1994).
[CrossRef] [PubMed]

F. Krausz and Th. Brabec, “Passive mode locking in standing-wave laser resonators,” Opt. Lett. 18, 888–890 (1993).
[CrossRef] [PubMed]

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

Th. Brabec, Ch. Spielmann, and F. Krausz, “Limits of pulse shortening in solitary lasers,” Opt. Lett. 17, 748–750 (1992).
[CrossRef] [PubMed]

Ch. Spielmann, P. F. Curley, T. Brabec, E. Wintner, and F. Krausz, “Generation of sub-20 fs mode locked pulses from a Ti:sapphire laser,” Electron. Lett. 28, 1532–1533 (1992).
[CrossRef]

Th. Brabec, Ch. Spielmann, and F. Krausz, “Mode locking in solitary lasers,” Opt. Lett. 16, 1961–1963 (1991).
[CrossRef] [PubMed]

Kryukov, P. G.

P. G. Kryukov and V. S. Lethokov, “Fluctuation mechanism of ultrashort pulse generation by lasers with saturable absorber,” IEEE J. Quantum Electron. QE-8, 766–782 (1972).
[CrossRef]

Lai, T. S.

Lai, Y.

Lamb, K.

Le Blanc, C.

Lee, K. F.

C. Wang, W. Zhang, K. F. Lee, and K. M. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

Lenz, G.

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114, 447–452 (1995).
[CrossRef]

Lenzner, M.

Lethokov, V. S.

P. G. Kryukov and V. S. Lethokov, “Fluctuation mechanism of ultrashort pulse generation by lasers with saturable absorber,” IEEE J. Quantum Electron. QE-8, 766–782 (1972).
[CrossRef]

Lin, K. H.

Lin, W. Z.

Lincoln, J. R.

Lisak, M.

Magni, V.

Malcom, G. P. A.

Martinez, O. E.

Mikhailov, V. P.

V. I. Kalashnikov, V. P. Kalosha, I. G. Poloyko, and V. P. Mikhailov, “Optimal resonators for self-mode locking of continuous-wave solid-state lasers,” J. Opt. Soc. Am. B 14, 964–969 (1997).
[CrossRef]

V. I. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerr self-focusing,” J. Opt. Soc. Am. B 13, 462–467 (1995).
[CrossRef]

Minkov, B. I.

Mo, D.

Monguzzi, A.

Moores, J. D.

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114, 447–452 (1995).
[CrossRef]

H. A. Haus, J. D. Moores, and L. E. Nelson, “Effect of third order dispersion on passive mode locking,” Opt. Lett. 18, 51–53 (1993).
[CrossRef] [PubMed]

J. D. Moores, “On the Ginzburg-Landau laser mode locking model with fifth-order saturable absorber term,” Opt. Commun. 96, 65–70 (1992).
[CrossRef]

Mourou, G.

Müller, M.

Murnane, M.

Murnane, M. M.

Nakano, N.

Nathel, H.

M. T. Asaki, C. P. Huang, D. Harvey, J. Zhou, H. Nathel, H. C. Kapteyn, and M. M. Murnane, “11 femtosecond pulses from a modelocked Ti:sapphire laser,” Opt. Photonics News 5, 12 (65;1992).

Nelson, L. E.

Pang, Y.

Petrov, V.

V. Petrov, U. Griebner, D. Ehrt, and W. Seeber, “Femtosecond self-mode locking of Yb:fluoride phosphate glass laser,” Opt. Lett. 22, 408–410 (1997).
[CrossRef] [PubMed]

V. Petrov, D. Georgiev, J. Herrmann, and U. Stamm, “Theory of cw passive mode-locking with addition of nonlinear index and group velocity dispersion,” Opt. Commun. 91, 123–130 (1992).
[CrossRef]

Piche, M.

Poloyko, I. G.

V. I. Kalashnikov, V. P. Kalosha, I. G. Poloyko, and V. P. Mikhailov, “Optimal resonators for self-mode locking of continuous-wave solid-state lasers,” J. Opt. Soc. Am. B 14, 964–969 (1997).
[CrossRef]

V. I. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerr self-focusing,” J. Opt. Soc. Am. B 13, 462–467 (1995).
[CrossRef]

Proctor, B.

Raksi, F.

Ramaswamy, M.

Read, K.

Ricelli, N.

Rizvi, N. H.

Rose-Petruck, C.

Rudd, J. V.

Rundquist, A.

Salin, F.

Santagiustina, M.

Sarukura, N.

Seeber, W.

Sibbett, W.

Sorokin, E.

Sorokina, I. T.

Spence, D. E.

Spielmann, Ch.

Squier, J.

Stamm, U.

D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens modelocked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

V. Petrov, D. Georgiev, J. Herrmann, and U. Stamm, “Theory of cw passive mode-locking with addition of nonlinear index and group velocity dispersion,” Opt. Commun. 91, 123–130 (1992).
[CrossRef]

Stingl, A.

Stoev, V. D.

Sutherland, J. M.

Szipöcs, R.

Taft, G.

Tamura, K.

Taylor, J. R.

tHooft, G. W.

Tong, Y. P.

Trebino, R.

Ulman, M.

Wang, C.

C. Wang, W. Zhang, K. F. Lee, and K. M. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

Weidner, F.

J. Herrmann, F. Weidner, and B. Wilhelmi, “Influence of the inversion depletion in the active medium on the evolution of ultrashort pulses in a passively mode locked solid-state laser,” Appl. Phys. 20, 237–245 (1979).
[CrossRef]

Weingarten, K. J.

Westwig, E.

Wilhelmi, B.

J. Herrmann, F. Weidner, and B. Wilhelmi, “Influence of the inversion depletion in the active medium on the evolution of ultrashort pulses in a passively mode locked solid-state laser,” Appl. Phys. 20, 237–245 (1979).
[CrossRef]

Wilson, K. R.

Wintner, E.

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Prismless passively mode-locked femtosecond Cr:LiSGaF lasers,” Opt. Lett. 21, 1165–1168 (1996).
[CrossRef] [PubMed]

Ch. Spielmann, P. F. Curley, T. Brabec, E. Wintner, and F. Krausz, “Generation of sub-20 fs mode locked pulses from a Ti:sapphire laser,” Electron. Lett. 28, 1532–1533 (1992).
[CrossRef]

Wise, F.

Witte, K. J.

Wood, D.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Xu, L.

Xu, X. S.

Yakovlev, V. V.

Yamakawa, K.

Yanovsky, V.

Yelland, C.

Yoo, K. M.

C. Wang, W. Zhang, K. F. Lee, and K. M. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

Zhang, W.

C. Wang, W. Zhang, K. F. Lee, and K. M. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

Zheng, X. Y.

Zhou, J.

Appl. Phys. (1)

J. Herrmann, F. Weidner, and B. Wilhelmi, “Influence of the inversion depletion in the active medium on the evolution of ultrashort pulses in a passively mode locked solid-state laser,” Appl. Phys. 20, 237–245 (1979).
[CrossRef]

Electron. Lett. (1)

Ch. Spielmann, P. F. Curley, T. Brabec, E. Wintner, and F. Krausz, “Generation of sub-20 fs mode locked pulses from a Ti:sapphire laser,” Electron. Lett. 28, 1532–1533 (1992).
[CrossRef]

IEEE J. Quantum Electron. (4)

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroad-band femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

P. G. Kryukov and V. S. Lethokov, “Fluctuation mechanism of ultrashort pulse generation by lasers with saturable absorber,” IEEE J. Quantum Electron. QE-8, 766–782 (1972).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

J. Opt. Soc. Am. B (13)

J. L. A. Chilla and O. E. Martinez, “Spatio-temporal analysis of the self-mode-locked Ti:sapphire laser,” J. Opt. Soc. Am. B 10, 638–643 (1993).
[CrossRef]

P. A. Belanger, “Coupled-cavity mode locking: a nonlinear model,” J. Opt. Soc. Am. B 8, 2077–2081 (1991).
[CrossRef]

K. H. Lin, Y. Lai, and W. F. Hsieh, “Simple analytical method of cavity design for astigmatism-compensated Kerr-lens mode-locked ring lasers and its applications,” J. Opt. Soc. Am. B 12, 468–475 (1995).
[CrossRef]

V. Magni, G. Cerullo, S. de Silvestri, and A. Monguzzi, “Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lens mode locking,” J. Opt. Soc. Am. B 12, 476–485 (1995).
[CrossRef]

A. A. Hnilo, “Self-mode-locking Ti:sapphire laser description with an iterative map,” J. Opt. Soc. Am. B 12, 718–725 (1995).
[CrossRef]

J. Herrmann and M. Müller, “Theory of coupled-cavity mode locking,” J. Opt. Soc. Am. B 13, 1542–1558 (1996).
[CrossRef]

V. Magni, “Perturbation theory of nonlinear resonators with an application to Kerr-lens mode locking,” J. Opt. Soc. Am. B 13, 2498–2507 (1996).
[CrossRef]

V. I. Kalashnikov, V. P. Kalosha, I. G. Poloyko, and V. P. Mikhailov, “Optimal resonators for self-mode locking of continuous-wave solid-state lasers,” J. Opt. Soc. Am. B 14, 964–969 (1997).
[CrossRef]

M. Santagiustina, “Third-order dispersion in solid-state solitary lasers,” J. Opt. Soc. Am. B 14, 1484–1495 (1997).
[CrossRef]

V. I. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerr self-focusing,” J. Opt. Soc. Am. B 13, 462–467 (1995).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8, 2068–2076 (1991).
[CrossRef]

J. Herrmann, “Theory of Kerr-lens mode locking: role of self-focusing and radially varying gain,” J. Opt. Soc. Am. B 11, 498–512 (1994).
[CrossRef]

K. H. Lin and W. F. Hsieh, “Analytical design of symmetrical Kerr-lens mode-locking laser cavities,” J. Opt. Soc. Am. B 11, 737–741 (1994).
[CrossRef]

Opt. Commun. (7)

M. Piche, “Beam reshaping and self-mode-locking in nonlinear laser resonators,” Opt. Commun. 86, 156–160 (1991).
[CrossRef]

D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens modelocked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

J. D. Moores, “On the Ginzburg-Landau laser mode locking model with fifth-order saturable absorber term,” Opt. Commun. 96, 65–70 (1992).
[CrossRef]

F. I. Khatri, J. D. Moores, G. Lenz, and H. A. Haus, “Models for self-limited additive pulse mode-locking,” Opt. Commun. 114, 447–452 (1995).
[CrossRef]

J. Herrmann, “Starting dynamic, self-starting condition and mode-locking threshold in passive, coupled cavity or Kerr-lens mode-locked lasers,” Opt. Commun. 98, 111–116 (1993).
[CrossRef]

V. Petrov, D. Georgiev, J. Herrmann, and U. Stamm, “Theory of cw passive mode-locking with addition of nonlinear index and group velocity dispersion,” Opt. Commun. 91, 123–130 (1992).
[CrossRef]

C. Wang, W. Zhang, K. F. Lee, and K. M. Yoo, “Pulse splitting in a self-mode-locked Ti:sapphire laser,” Opt. Commun. 137, 89–92 (1997).
[CrossRef]

Opt. Lett. (48)

F. Salin, J. Squier, and M. Piche, “Mode-locking of Ti:Al2O3 lasers and self-focusing: a Gaussian approximation,” Opt. Lett. 16, 1674–1676 (1991).
[CrossRef] [PubMed]

O. E. Martinez and J. L. A. Chilla, “Self-mode-locking of Ti:sapphire lasers: a matrix formalism,” Opt. Lett. 17, 1210–1212 (1992).
[CrossRef] [PubMed]

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

J. Herrmann, V. P. Kalosha, and M. Müller, “Higher order phase dispersion in Kerr-lens mode-locked solid-state lasers: sideband generation and pulse splitting,” Opt. Lett. 22, 236–238 (1997).
[CrossRef] [PubMed]

V. Petrov, U. Griebner, D. Ehrt, and W. Seeber, “Femtosecond self-mode locking of Yb:fluoride phosphate glass laser,” Opt. Lett. 22, 408–410 (1997).
[CrossRef] [PubMed]

B. E. Bouma and J. G. Fujimoto, “Compact Kerr-lens mode-locked resonator,” Opt. Lett. 21, 134–136 (1996).
[CrossRef] [PubMed]

A. Kasper and K. J. Witte, “10-fs pulse generation from a unidirectional Kerr-lens mode locked Ti:sapphire laser,” Opt. Lett. 21, 360–362 (1996).
[CrossRef] [PubMed]

K. Read, F. Blonigen, N. Ricelli, M. Murnane, and H. Kapteyn, “Low threshold operation of an ultrashort-pulse mode-locked Ti:sapphire laser,” Opt. Lett. 21, 489–491 (1996).
[CrossRef] [PubMed]

S. T. Cundiff, W. H. Knox, E. P. Ippen, and H. A. Haus, “Frequency-dependent mode size in broadband Kerr-lens mode locking,” Opt. Lett. 21, 662–664 (1996).
[CrossRef] [PubMed]

C. P. J. Barty, T. Guo, C. Le Blanc, F. Raksi, C. Rose-Petruck, J. Squier, K. R. Wilson, V. V. Yakovlev, and K. Yamakawa, “Generation of 18-fs multiterawatt pulses by regenerative pulse shape and chirped-pulse amplification,” Opt. Lett. 21, 668–670 (1996).
[CrossRef] [PubMed]

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Prismless passively mode-locked femtosecond Cr:LiSGaF lasers,” Opt. Lett. 21, 1165–1168 (1996).
[CrossRef] [PubMed]

L. Xu, Ch. Spielmann, and F. Krausz, “Ultrabroadband ring oscillator for sub-10-fs pulse generation,” Opt. Lett. 21, 1250–1252 (1996).
[CrossRef]

Y. C. Chen, X. Y. Zheng, T. S. Lai, X. S. Xu, D. Mo, and W. Z. Lin, “Resonators for self-mode-locking Ti:sapphire lasers without apertures,” Opt. Lett. 21, 1469–1471 (1996).
[CrossRef] [PubMed]

I. P. Christov, V. D. Stoev, M. M. Murnane, and H. C. Kapteyn, “Sub-10-fs operation of Kerr-lens mode locked lasers,” Opt. Lett. 21, 1493–1495 (1996).
[CrossRef] [PubMed]

A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, and R. Szipöcs, “Sub-10-fs mirror-dispersion-controlled Ti:sapphire laser,” Opt. Lett. 20, 602–604 (1995).
[CrossRef] [PubMed]

G. Taft, A. Rundquist, M. M. Murnane, H. C. Kapteyn, K. W. DeLong, R. Trebino, and I. P. Christov, “Ultrashort optical waveform measurements using frequency-resolved optical gating,” Opt. Lett. 20, 743–745 (1995).
[CrossRef] [PubMed]

S. Gatz and J. Herrmann, “Astigmatism and gain guiding in Kerr-lens mode locked lasers,” Opt. Lett. 20, 825–827 (1995).
[CrossRef] [PubMed]

J. M. Sutherland, P. M. W. French, J. R. Taylor, and B. H. T. Chai, “Visible continuous-wave laser transitions in Pr3+:YLF and femtosecond pulse generation,” Opt. Lett. 20, 1041–1043 (1995).
[CrossRef]

A. Braun, J. V. Rudd, H. Cheng, G. Mourou, D. Kopf, I. D. Jung, K. J. Weingarten, and U. Keller, “Characterization of short-pulse oscillators by means of a high-dynamic-range autocorrelation measurement,” Opt. Lett. 20, 1889–1891 (1995).
[CrossRef] [PubMed]

I. P. Christov, V. D. Stoev, M. M. Murnane, and H. C. Kapteyn, “Mode locking with compensated space-time astigmatism,” Opt. Lett. 20, 2111–2113 (1995).
[CrossRef] [PubMed]

D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode locked Ti:sapphire laser,” Opt. Lett. 16, 42–44 (1991).
[CrossRef] [PubMed]

N. Sarukura, Y. Ishida, and N. Nakano, “Generation of 50-fsec pulses from a pulse-compressed, cw, passively mode-locked Ti:sapphire laser,” Opt. Lett. 16, 153–155 (1991).
[PubMed]

U. Keller, G. W. tHooft, W. H. Knox, and J. E. Cunningham, “Femtosecond pulses from a continuously self-starting passively mode-locked Ti:sapphire laser,” Opt. Lett. 16, 1022–1024 (1991).
[CrossRef] [PubMed]

H. A. Haus and E. P. Ippen, “Self-starting of passively mode-locked lasers,” Opt. Lett. 16, 1331–1333 (1991).
[CrossRef] [PubMed]

M. Karlsson, D. Anderson, M. Desiax, and M. Lisak, “Dynamic effects of Kerr nonlinearity and spatial diffraction on self-phase modulation of optical pulses,” Opt. Lett. 16, 1373–1375 (1991).
[CrossRef] [PubMed]

G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, E. P. Ippen, and J. G. Fujimoto, “Femtosecond pulse generation of Ti:Al2O3 using a microdot mirror mode locker,” Opt. Lett. 16, 1756–1758 (1991).
[CrossRef] [PubMed]

Th. Brabec, Ch. Spielmann, and F. Krausz, “Mode locking in solitary lasers,” Opt. Lett. 16, 1961–1963 (1991).
[CrossRef] [PubMed]

G. P. A. Malcom and A. I. Ferguson, “Self-mode locking of a diode-pumped Nd:YLF laser,” Opt. Lett. 16, 1967–1969 (1991).
[CrossRef]

D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, and J. G. Fujimoto, “Self-focusing-induced saturable loss for laser mode locking,” Opt. Lett. 17, 511–513 (1992).
[CrossRef] [PubMed]

Th. Brabec, Ch. Spielmann, and F. Krausz, “Limits of pulse shortening in solitary lasers,” Opt. Lett. 17, 748–750 (1992).
[CrossRef] [PubMed]

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

J. N. Elgin, “Soliton propagation in an optical fiber with third-order dispersion,” Opt. Lett. 17, 1409–1411 (1992).
[CrossRef] [PubMed]

N. H. Rizvi, P. M. W. French, and J. R. Taylor, “Generation of 33-fs pulses from a passively mode-locked Cr3+:LiSrAlF6 laser,” Opt. Lett. 17, 1605–1607 (1992).
[CrossRef] [PubMed]

H. A. Haus, J. D. Moores, and L. E. Nelson, “Effect of third order dispersion on passive mode locking,” Opt. Lett. 18, 51–53 (1993).
[CrossRef] [PubMed]

K. Tamura, J. Jacobson, E. P. Ippen, H. A. Haus, and J. G. Fujimoto, “Unidirectional ring resonators for self-starting passively mode-locked lasers,” Opt. Lett. 18, 220–222 (1993).
[CrossRef] [PubMed]

F. Krausz and Th. Brabec, “Passive mode locking in standing-wave laser resonators,” Opt. Lett. 18, 888–890 (1993).
[CrossRef] [PubMed]

V. Yanovsky, Y. Pang, F. Wise, and B. I. Minkov, “Generation of 25-fs pulses from a self-mode-locked Cr:forsterite laser with optimized group-delay dispersion,” Opt. Lett. 18, 1541–1543 (1993).
[CrossRef] [PubMed]

B. Proctor, E. Westwig, and F. Wise, “Characterization of a Kerr-lens mode locked Ti:sapphire laser with positive group-velocity dispersion,” Opt. Lett. 18, 1654–1656 (1993).
[CrossRef] [PubMed]

Th. Brabec and S. M. J. Kelly, “Third order dispersion as a limiting factor to mode locking in femtosecond solitary lasers,” Opt. Lett. 18, 2002–2004 (1993).
[CrossRef]

R. E. Bridges, R. W. Boyd, and G. V. Agrawal, “Effect of beam ellipticity on self-mode locking in lasers,” Opt. Lett. 18, 2026–2028 (1993).
[CrossRef] [PubMed]

A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, “Generation of 11-fs pulses from a Ti:sapphire laser without the use of prisms,” Opt. Lett. 19, 204–206 (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, 1040–1042 (1994).
[CrossRef] [PubMed]

J. Zhou, G. Taft, C. P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Pulse evolution in a broad-bandwidth Ti:sapphire laser,” Opt. Lett. 19, 1149–1151 (1994).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and C. P. Huang, “Fourth-order dispersion-limited solitary pulses,” Opt. Lett. 19, 1465–1467 (1994).
[CrossRef] [PubMed]

P. J. Conlon, Y. P. Tong, P. M. W. French, and J. R. Taylor, “Passive mode locking and dispersion measurement of a sub-100-fs Cr4+:YAG laser,” Opt. Lett. 19, 1468–1470 (1994).
[CrossRef] [PubMed]

S. Gatz and J. Herrmann, “Geometrical threshold zones and Gaussian modes in lasers with radially varying gain,” Opt. Lett. 19, 1696–1699 (1994).
[CrossRef] [PubMed]

K. Lamb, D. E. Spence, J. Hong, C. Yelland, and W. Sibbett, “All-solid-state self-mode-locked Ti:sapphire laser,” Opt. Lett. 19, 1864–1866 (1994).
[CrossRef] [PubMed]

J. R. Lincoln and A. I. Ferguson, “All-solid-state self-mode locking of a Nd:YLF laser,” Opt. Lett. 19, 2119–2121 (1994).
[CrossRef] [PubMed]

Opt. Photonics News (1)

M. T. Asaki, C. P. Huang, D. Harvey, J. Zhou, H. Nathel, H. C. Kapteyn, and M. M. Murnane, “11 femtosecond pulses from a modelocked Ti:sapphire laser,” Opt. Photonics News 5, 12 (65;1992).

Phys. Rev. Lett. (1)

Th. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[CrossRef]

Other (6)

A. Kasper and K. J. Witte, “Contrast and phase characterization of ultrashort laser pulses emitted from mirror-dispersion-controlled Ti:sapphire ring and Fabry–Perot resonators,” Opt. Lett. (to be published).

I. N. Duling III, ed., Compact Sources of Ultrashort Pulses, 1st ed. (Cambridge University, Cambridge, England, 1995), Chap. 4.2.3., p. 157.

F. J. Duarte, ed., Tunable Lasers, 1st ed. (Academic, New York, 1995).

A. E. Siegmann, Lasers (University Science, Mill Valley, Calif., 1986).

R. E. Bridges, R. W. Boyd, and G. P. Agrawal, “Multidimensional coupling owing to optical nonlinearities. I. General formulation,” J. Opt. Soc. Am. B 13, 553–559 (1996); “Multidimensional coupling owing to optical nonlinearities. II. Results,” J. Opt. Soc. Am. B 13, 560–569 (1996).
[CrossRef]

D. K. Negus, L. Spinelli, N. Goldblatt, and G. Feugnet, “Sub-100-fs pulse generation by Kerr lens mode locking in Ti:Al2O3,” in Advanced Solid State Lasers, G. Dubé and L. Chase, eds., Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991), postdeadline paper PDP4, pp. 120–124.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

KLM resonator configuration with the arm lengths c,d; folding distance a+b; crystal position b; focal length f; tilting angle Θ; output coupler r; and an additional aperture.

Fig. 2
Fig. 2

Kerr-lens sensitivity γ with aperture in dependence on the KLM resonator configuration [folding distance (a+b)/f and crystal position b/f]; (a) symmetrical cavity, (b) asymmetrical cavity. Saturable-aperture-loss parameter in the tangential plane γxa; pump-beam waist 75 μm.

Fig. 3
Fig. 3

Kerr-lens sensitivity γ without aperture in dependence on the KLM resonator configuration [folding distance (a+b)/f and crystal position b/f]; (a) symmetrical cavity, (b) asymmetrical cavity. Saturable-aperture-loss parameter in the tangential plane γxa. Pump-beam waist 30 μm.

Fig. 4
Fig. 4

Power dependence of aperture transmission Ta(P) according to Eq. (16). (a) Cavity configuration with weak SAM [(a+b)/f=2.074, b/f=1.02 in Fig. 2(a)] and different linear aperture losses: (1) Γ=1%, (2) Γ=5%, (3) Γ=10%, (4) Γ =15% (solid curves); beam waist in the aperture plane w(P) (dashed curve). (b) Cavity configuration with strong SAM [(a +b)/f=2.075, b/f=1.06 in Fig. 2(a)] and different linear-aperture losses: (1) Γ=0.5%, (2) Γ=1%, (3) Γ=2%, (4) Γ =5% (solid curves); beam waist in the aperture plane w(P) (dashed curve).

Fig. 5
Fig. 5

Pulse duration over pump rate for weak SAM (solid curve) and strong SAM (dashed curve) with different linear-aperture losses according to Fig. 4. Laser parameters: T2 =2.5 fs, λ21=790 nm, UR=10 nJ, Δ=0, r=0.98.

Fig. 6
Fig. 6

(a) Pulse duration over net GVD for weak SAM, μ=2, Γ=5%, D2gLg=62.5 fs2; and different SPM (1) κLg=0, (2) κLg=10-8 W-1, (3) κLg=5×10-8 W-1, (4) κLg=10-7 W-1, (5) κLg=1.5×10-7 W-1, (6) κLg=2×10-7 W-1. (b) Pulse duration over net GVD for strong SAM, μ=0.1, Γ=2%; and different SPM (1) κLg=10-7 W-1, (2) κLg=5×10-7 W-1, (3) κLg=10-6 W-1, (4) κLg=2.5×10-7 W-1. (c) Pulse duration over net GVD for weak SAM, Γ=5% for different pump rates, (1) μ=1; (2) μ=2; (3) μ =3 for κLg=10-7 W-1 (solid curves) and κLg=10-8 W-1 (dashed curve). Laser parameters are as in Fig. 5, and D2gLg =62.5 fs2. Note the logarithmically scaled y axis.

Fig. 7
Fig. 7

(a) Shortest pulse shape (solid curves) and instantaneous frequency shift (dashed curves) for (1) weak SAM: Γ =5%, μ=2, κLg=10-7 W-1; net GVD 0.025 fs2, τp=7.1 fs; and (2) strong SAM: Γ=2%, μ=0.1, κLg=5×10-6 W-1, net GVD 0.125 fs2, τp=3.9 fs. (b) Corresponding spectrum (solid curves) and spectral gain line (dashed curve). Laser parameters are as in Fig. 6.

Fig. 8
Fig. 8

Pulse duration over net GVD for weak SAM: Γ =5%, μ=2, κLg=10-7 W-1, and different TOD (1) D3=0, (2) D3=1.6 fs3; (3) D3=4.7 fs3; (4) D3=15.6 fs3; (5) D3 =31.2 fs3; (6) D3=49.9 fs3, (7) D3=78.1 fs3. Laser parameters are as in Fig. 6.

Fig. 9
Fig. 9

(a) Spectral pulse shape (solid curves) and phase (dashed curves) versus wavelength. (b) Temporal pulse shape (solid curve) and instantaneous frequency shift (dashed curve) versus local time. Laser parameters for weak SAM: D2gLg=62.5 fs2, T2=2.5 fs, λ21=790 nm, UR=10 nJ, κLg=10-7 W-1, Γ=7%, Δ=0, μ=2, net GVD -0.94 fs2, FOD D4=19.5 fs4, and different TOD as (1) D3=1.6 fs3, (2) D3, =3.1 fs3, (3) D3=4.7 fs3, (4) D3=7.8 fs3, (5) D3=15.6 fs3, (6) D3=23.4 fs3, (7) D3=31.3 fs3.

Fig. 10
Fig. 10

(a) Spectral pulse shape (solid curves) and phase (dashed curves) versus wavelength. (b) Temporal pulse shape (solid curves) and instantaneous frequency shift (dashed curves) versus local time. Laser parameters are as Fig. 6. μ=2, net GVD -1.6 fs2, TOD D4=7.8 fs3 and different FOD, (1) D4=0, (2) D4=19.5 fs4, (3) D4=39.1 fs4, (4) D4=58.6 fs4, (5) D4 =78.1 fs4, (6) D4=97.7 fs4, (7) D4=117.2 fs4.

Fig. 11
Fig. 11

(a) Temporal pulse shape and (b) steady-state spectrum in the double-pulse regime. Laser parameters are as in Fig. 6. μ=2, κLg=10-7 W-1, net GVD -1.6 fs2, D3=1.6 fs3, D4 =105.5 fs4.

Fig. 12
Fig. 12

Evolution of a double-pulse regime of up to 25 000 round trips for the laser parameters of Fig. 11.

Fig. 13
Fig. 13

Evolution of a triple-pulse regime of up to 25 000 round trips for the laser parameter of Fig. 14.

Fig. 14
Fig. 14

(a) Temporal pulse shape and (b) steady-state spectrum in the triple-pulse regime. Laser parameters are as in Fig. 11 but with increased FOD D4=109.4 fs4.

Equations (47)

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

EL(z, x, t)=12 EL(z, x, t)exp[i(ωLt-KLz)]+c.c.,
z EL(z, x, η)+i2K0 2x2+2y2EL(z, x, η)
=-i n2ωL1nL2c |EL(z, x, η)|2EL(z, x, η)
+iD2g 2η2 EL(z, x, η)+1T221×-ηexp -(1+iΔL) η-ηT221×g(z, x, η)EL(z, x, η)dη,
gk(z, x)=g0(z, x)+gk-1(z, x)×exp-- |EL(z, x, η)|2UL dη-g0(z, x) exp-1T1+P0(x)TR.
EL(z, x, η)=ψ(z, η)αx(z, η)αy(z, η)×exp {i[Qx(z, η)x2+Qy(z, η)y2]},
Qx/y(z, η)=-KL2 1Rx/y(z, η)-iλπwx/y2(z, η),
z αx/y(z, η)=Qx/y(z, η)KL αx/y(z, η).
z ψ(z, η)=-i34 κ|ψ(z, η)|2ψ(z, η)+iD2g2η2 ψ(z, η)+F1[Qx/y]+ILP2T221 g-η exp -η-ηLLT221×ψ(z, η)dη,
zQx/y(z, η)-2KL Qx/y2(z, η)
=Hx/y(z, η)=12 κ|ψ(z, η)|2Qx/y(z, η)
+D2g2η2Qx/y(z, η)+F2[Qx/y]+2iIggwp,x/y2 gS,
Qx/y+(z, η)=Dx/y+(z, η)Qx/y+(0, η)-KL2 Cx/y+(z, η)Ax/y+(z, η)-2KL Bx/y+(z, η)Qx/y+(0, η),
z Ax/y+(z, η)=1nL Cx/y+(z, η),
z Bx/y+(z, η)=1nL Dx/y+(z, η),
z Cx/y+(z, η)=-2KL Hx/y+(z, η)Ax/y+(z, η),
z Dx/y+(z, η)=-2KL Hx/y+(z, η)Bx/y+(z, η).
αx/y+(z, η)
=Ax/y+(z, η)-2KL Bx/y+(z, η)Qx/y+(0, η)-1/2.
Qx/y=KL4B^x/y [A^x/y-D^x/y±(A^x/y+D^x/y)2-4],
αx/y-1=12 [A^x/y+D^x/y±(A^x/y+D^x/y)2-4].
Tx/ya(P)=1-erf-2 w0wx/y(P),
Tgg(P)= |αx(P)αy(P)|2 exp[2G(P)],
Dˆ(ω)=exp[-i(D2ω2+D3ω3+D4ω4)],
EL,P(z, x, t)=12 EL,P(z, x, t)×exp[i(ωL,Pt-KL,Pz)]+c.c.,
PL,P=Ndxρ˜x,
ρx=12 ρ˜xexp[i(ωL,Pt-KL,Pz)],x[12,03],
t ρ˜12+1T221+i(ωL-ω21)ρ˜12=i d12 (ρ22-ρ11)EL,
t ρ22+ρ22T121=-1 Im[d21ρ˜12EL*]+ρ33T132,
t ρ˜03+1T230+i(ωP-ω30)ρ˜03=i d03 (ρ33-ρ00)EP,
t ρ33+ρ33T132=-1 Im[d30ρ˜03EP*],
t+1T121g(z, x, t)=-Re-t exp-t-tLLT221g(z, x, t)×EL(z, x, t)UL dtEL*(z, x, t)+|EP(0, x)|2UP [σLN-g(z, x, t)]
×expRe(LP)σ30Nz-σ30σ21 0zg(z, x, t)dz,
Θ()=|d21| -|EL(t)|dtπ,
gk(z, x)=g0(z, x)+gk-1(z, x)exp-- |EL(z, x, η)|2UL dη-g0(z, x)exp-1T1+P0(x)TR,
P0(x)=|EP,0|2UP exp-2x2wP,x2+y2wP,y2,
g0(z, x)=gmax[1-Re(LP)gmax z]P0(x)T1+g0(z)exp-2x2wP,x2+y2wP,y2,
g(z, x)=g0(z)1+T1TR - |EL(z, x, η)|2UL dη×exp-2x2wP,x2+y2wP,y2.
z ψ(z, η)=-i 34 κ|ψ(z, η)|2ψ(z, η)+iD2g2g2 ψ(z, η)+F1[Qx/y]+ILP2T221 g-η exp-η-ηLLT221×ψ(z, η)dη,
z Qx/y(z, η)-2K0 Qx/y2(z, η)
=12 κ|ψ(z, η)|2Qx/y(z, η)+D2g2η2 Qx/y(z, η)+F2[Qx/y]+2iIggwp,x/y2 gS.
F1[Qx/y]=116 η Qx(z, η)Qx(z, η)2+η Qy(z, η)Qy(z, η)2-η Qx(z, η) η Qy(z, η)Qx(z, η)Qy(z, η),
F2[Qx/y]=2iη ψ(z, η)ψ(z, η) η Qx/y(z, η)-23 η Qx/y(z, η)2Qx/y(z, η)-12 η Qx(z, η) η Qy(z, η)Qy/x(z, η).
ILP=12 QxQywp,xwp,y(1+Qxwp,x2)(1+Qywp,y2)×2+Qxwp,x21+Qxwp,x2+2+Qywp,y21+Qywp,y2,
Igg=Qx/y(z, η)wp,x/y21+Qx/y(z, η)wp,x/y22.
S=12T2ψ(z, η)×-η exp-η-ηLLT221ψ(z, η)dη,
g=g0(z)1+U/UR,

Metrics