Abstract

The effect of third-order dispersion on solitonlike operation of the L-fold cavity Cr4+:YAG laser is studied. Dispersion equations are derived to the fourth order for an L-fold cavity, and dispersion values for a Cr4+:YAG laser are calculated. Third-order dispersion is found to be comparable with the second-order dispersion in a 60-fs-class Cr4+:YAG laser, and fourth-order dispersion is negligible. The temporal and spectral phases of a 60-fs pulse are calculated from the dispersion properties of the cavity. The spectral phase is constant, despite considerable third-order dispersion. A second-harmonic generation (SHG) frequency-resolved optical gating (FROG) trace is calculated for the simulated pulse. The SHG spectrum has a tail to the short-wavelength side at zero delay, consistent with experimental results. The calculated phase and the FROG trace should be recognized as characteristic of the third-order-dispersion effect on solitonlike lasers.

© 2001 Optical Society of America

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References

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  1. R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multiplayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19, 201–203 (1994).
    [Crossref]
  2. G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics,” Science 286, 1507–1512 (1999), and references therein.
    [Crossref] [PubMed]
  3. 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]
  4. P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, and A. J. Schmidt, “Operation of a femtosecond Ti: sapphire solitary laser in the vicinity of zero group-delay dispersion,” Opt. Lett. 18, 54–56 (1993).
    [Crossref] [PubMed]
  5. T. 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] [PubMed]
  6. 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]
  7. C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
    [Crossref]
  8. Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
    [Crossref]
  9. J. Herrmann, V. P. Kalosha, and M. Müller, “Higher-order phase dispersion in femtosecond Kerr-lens mode-locked solid-state lasers: sideband generation and pulse splitting,” Opt. Lett. 22, 236–238 (1997).
    [Crossref] [PubMed]
  10. V. P. Kalosha, M. Müller, J. Herrmann, and S. Gatz, “Spatiotemporal model of femtosecond pulse generation in Kerr-lens mode-locked solid-state lasers,” J. Opt. Soc. Am. B 15, 535–550 (1998).
    [Crossref]
  11. Z. E. Penman, T. Schittkowski, W. Sleat, D. T. Reid, and W. Sibbett, “Experimental comparison of conventional pulse characterization techniques and second-harmonic generation frequency-resolved optical gating,” Opt. Commun. 155, 297–300 (1998).
    [Crossref]
  12. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
    [Crossref]
  13. T. Tomaru and H. Petek, “Femtosecond Cr4+:YAG laser with an L-fold cavity operating at a 1.2-GHz repetition rate,” Opt. Lett. 25, 584–586 (2000).
    [Crossref]
  14. M. Ramaswamy-Paye and J. G. Fujimoto, “Compact dispersion-compensating geometry for Kerr-lens mode-locked femtosecond lasers,” Opt. Lett. 19, 1756–1758 (1994).
    [Crossref] [PubMed]
  15. Z. Zhang, T. Nakagawa, K. Torizuka, T. Sugaya, and K. Kobayashi, “Self-starting mode-locked Cr4+:YAG laser with a low-loss broadband semiconductor saturable-absorber mirror,” Opt. Lett. 24, 1768–1770 (1999).
    [Crossref]
  16. B. E. Lemoff and C. P. J. Barty, “Cubic-phase-free dispersion compensation in solid-state ultrashort-pulse lasers,” Opt. Lett. 18, 57–59 (1993).
    [Crossref] [PubMed]
  17. A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
    [Crossref]
  18. O. E. Martinez, J. P. Gordon, and R. L. Fork, “Negative group-velocity dispersion using refraction,” J. Opt. Soc. Am. A 1, 1003–1006 (1984).
    [Crossref]
  19. R. L. Fork, C. H. B. Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compression,” Opt. Lett. 12, 483–485 (1987).
    [Crossref] [PubMed]
  20. J. P. Gordon and R. L. Fork, “Optical resonator with negative dispersion,” Opt. Lett. 9, 153–155 (1984).
    [Crossref] [PubMed]
  21. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
    [Crossref]
  22. W. I. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
    [Crossref]
  23. Y. Ishida, K. Naganuma, and H. Kamada, “Multi-sideband generation in a femtosecond Cr4+:YAG laser,” Opt. Rev. 6, 37–41 (1999).
    [Crossref]
  24. D. J. Kane, G. Rodriguez, A. J. Taylor, and T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. B 14, 935–943 (1997).
    [Crossref]
  25. J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).
    [Crossref]
  26. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
  27. The coefficients of Sellmeier’s equation are given in a diskette-type Schott 1996 catalog of optical glass (version 1.1e) (Schott Glass, 1998).
  28. Calculated by use of refractive indices of ZnSe for 0.54–10.6-µm wavelengths from the optics catalog of II–VI, Inc., and evaluated by fitting of np(λ) to the expression np2=B0+B1/(λ2+C1)+B2λ2, where B0=5.92833,B1=0.24165,B2=-0.00139, and C1=-0.09441 in units of micrometers.

2000 (1)

1999 (3)

Z. Zhang, T. Nakagawa, K. Torizuka, T. Sugaya, and K. Kobayashi, “Self-starting mode-locked Cr4+:YAG laser with a low-loss broadband semiconductor saturable-absorber mirror,” Opt. Lett. 24, 1768–1770 (1999).
[Crossref]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics,” Science 286, 1507–1512 (1999), and references therein.
[Crossref] [PubMed]

Y. Ishida, K. Naganuma, and H. Kamada, “Multi-sideband generation in a femtosecond Cr4+:YAG laser,” Opt. Rev. 6, 37–41 (1999).
[Crossref]

1998 (3)

Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
[Crossref]

V. P. Kalosha, M. Müller, J. Herrmann, and S. Gatz, “Spatiotemporal model of femtosecond pulse generation in Kerr-lens mode-locked solid-state lasers,” J. Opt. Soc. Am. B 15, 535–550 (1998).
[Crossref]

Z. E. Penman, T. Schittkowski, W. Sleat, D. T. Reid, and W. Sibbett, “Experimental comparison of conventional pulse characterization techniques and second-harmonic generation frequency-resolved optical gating,” Opt. Commun. 155, 297–300 (1998).
[Crossref]

1997 (4)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

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

D. J. Kane, G. Rodriguez, A. J. Taylor, and T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. B 14, 935–943 (1997).
[Crossref]

1994 (4)

1993 (4)

1992 (1)

1987 (1)

1984 (2)

1965 (2)

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
[Crossref]

W. I. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

Backus, S.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

Barty, C. P. J.

Becker, P. C.

Bond, W. I.

W. I. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[Crossref]

Brabec, T.

Chang, Z.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

Christov, I.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

Christov, I. P.

Clement, T. S.

Cruz, C. H. B.

Curley, P. F.

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

Durfee, C.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

Ferencz, K.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

Fork, R. L.

Fujimoto, J. G.

Gallmann, L.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics,” Science 286, 1507–1512 (1999), and references therein.
[Crossref] [PubMed]

Gatz, S.

Gordon, J. P.

Haus, H. A.

Herrmann, J.

Huang, C.-P.

Ishida, Y.

Y. Ishida, K. Naganuma, and H. Kamada, “Multi-sideband generation in a femtosecond Cr4+:YAG laser,” Opt. Rev. 6, 37–41 (1999).
[Crossref]

Kalosha, V. P.

Kamada, H.

Y. Ishida, K. Naganuma, and H. Kamada, “Multi-sideband generation in a femtosecond Cr4+:YAG laser,” Opt. Rev. 6, 37–41 (1999).
[Crossref]

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

D. J. Kane, G. Rodriguez, A. J. Taylor, and T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. B 14, 935–943 (1997).
[Crossref]

Kapteyn, H. C.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

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]

Keller, U.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics,” Science 286, 1507–1512 (1999), and references therein.
[Crossref] [PubMed]

Kelly, S. M. J.

Kobayashi, K.

Krausz, F.

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

Lemoff, B. E.

Lin, Q.

Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
[Crossref]

Malitson, I. H.

Martinez, O. E.

Matuschek, N.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics,” Science 286, 1507–1512 (1999), and references therein.
[Crossref] [PubMed]

Moores, J. D.

Müller, M.

Murnane, M. M.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

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]

Naganuma, K.

Y. Ishida, K. Naganuma, and H. Kamada, “Multi-sideband generation in a femtosecond Cr4+:YAG laser,” Opt. Rev. 6, 37–41 (1999).
[Crossref]

Nakagawa, T.

Nelson, L. E.

Penman, Z. E.

Z. E. Penman, T. Schittkowski, W. Sleat, D. T. Reid, and W. Sibbett, “Experimental comparison of conventional pulse characterization techniques and second-harmonic generation frequency-resolved optical gating,” Opt. Commun. 155, 297–300 (1998).
[Crossref]

Petek, H.

Ramaswamy-Paye, M.

Reid, D. T.

Z. E. Penman, T. Schittkowski, W. Sleat, D. T. Reid, and W. Sibbett, “Experimental comparison of conventional pulse characterization techniques and second-harmonic generation frequency-resolved optical gating,” Opt. Commun. 155, 297–300 (1998).
[Crossref]

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

Rodriguez, G.

Rundquist, A.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

Schittkowski, T.

Z. E. Penman, T. Schittkowski, W. Sleat, D. T. Reid, and W. Sibbett, “Experimental comparison of conventional pulse characterization techniques and second-harmonic generation frequency-resolved optical gating,” Opt. Commun. 155, 297–300 (1998).
[Crossref]

Schmidt, A. J.

Shank, C. V.

Sibbett, W.

Z. E. Penman, T. Schittkowski, W. Sleat, D. T. Reid, and W. Sibbett, “Experimental comparison of conventional pulse characterization techniques and second-harmonic generation frequency-resolved optical gating,” Opt. Commun. 155, 297–300 (1998).
[Crossref]

Sleat, W.

Z. E. Penman, T. Schittkowski, W. Sleat, D. T. Reid, and W. Sibbett, “Experimental comparison of conventional pulse characterization techniques and second-harmonic generation frequency-resolved optical gating,” Opt. Commun. 155, 297–300 (1998).
[Crossref]

Sorokina, I.

Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
[Crossref]

Spielmann, C.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[Crossref]

R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multiplayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19, 201–203 (1994).
[Crossref]

Spielmann, Ch.

Steinmeyer, G.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics,” Science 286, 1507–1512 (1999), and references therein.
[Crossref] [PubMed]

Stoev, V.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

Sugaya, T.

Sutter, D. H.

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics,” Science 286, 1507–1512 (1999), and references therein.
[Crossref] [PubMed]

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

Szipöcs, R.

Taft, G.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

Taylor, A. J.

Tomaru, T.

Torizuka, K.

Trebino, R.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

Wintner, E.

Zeek, E.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

Zhang, Z.

Zhou, J.

Appl. Phys. B (1)

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, “Ultrafast laser and amplifier sources,” Appl. Phys. B 65, 161–174 (1997).
[Crossref]

IEEE J. Quantum Electron. (1)

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[Crossref]

J. Appl. Phys. (1)

W. I. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

Z. E. Penman, T. Schittkowski, W. Sleat, D. T. Reid, and W. Sibbett, “Experimental comparison of conventional pulse characterization techniques and second-harmonic generation frequency-resolved optical gating,” Opt. Commun. 155, 297–300 (1998).
[Crossref]

Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
[Crossref]

Opt. Lett. (12)

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

R. Szipöcs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multiplayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19, 201–203 (1994).
[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]

P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, and A. J. Schmidt, “Operation of a femtosecond Ti: sapphire solitary laser in the vicinity of zero group-delay dispersion,” Opt. Lett. 18, 54–56 (1993).
[Crossref] [PubMed]

T. 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] [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]

R. L. Fork, C. H. B. Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compression,” Opt. Lett. 12, 483–485 (1987).
[Crossref] [PubMed]

J. P. Gordon and R. L. Fork, “Optical resonator with negative dispersion,” Opt. Lett. 9, 153–155 (1984).
[Crossref] [PubMed]

T. Tomaru and H. Petek, “Femtosecond Cr4+:YAG laser with an L-fold cavity operating at a 1.2-GHz repetition rate,” Opt. Lett. 25, 584–586 (2000).
[Crossref]

M. Ramaswamy-Paye and J. G. Fujimoto, “Compact dispersion-compensating geometry for Kerr-lens mode-locked femtosecond lasers,” Opt. Lett. 19, 1756–1758 (1994).
[Crossref] [PubMed]

Z. Zhang, T. Nakagawa, K. Torizuka, T. Sugaya, and K. Kobayashi, “Self-starting mode-locked Cr4+:YAG laser with a low-loss broadband semiconductor saturable-absorber mirror,” Opt. Lett. 24, 1768–1770 (1999).
[Crossref]

B. E. Lemoff and C. P. J. Barty, “Cubic-phase-free dispersion compensation in solid-state ultrashort-pulse lasers,” Opt. Lett. 18, 57–59 (1993).
[Crossref] [PubMed]

Opt. Rev. (1)

Y. Ishida, K. Naganuma, and H. Kamada, “Multi-sideband generation in a femtosecond Cr4+:YAG laser,” Opt. Rev. 6, 37–41 (1999).
[Crossref]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

Science (1)

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, “Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics,” Science 286, 1507–1512 (1999), and references therein.
[Crossref] [PubMed]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

The coefficients of Sellmeier’s equation are given in a diskette-type Schott 1996 catalog of optical glass (version 1.1e) (Schott Glass, 1998).

Calculated by use of refractive indices of ZnSe for 0.54–10.6-µm wavelengths from the optics catalog of II–VI, Inc., and evaluated by fitting of np(λ) to the expression np2=B0+B1/(λ2+C1)+B2λ2, where B0=5.92833,B1=0.24165,B2=-0.00139, and C1=-0.09441 in units of micrometers.

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Figures (3)

Fig. 1
Fig. 1

(a) Equivalent L-fold cavity with a folding curved mirror replaced by a biconvex lens. The cavity is divided into two parts for the calculation of dispersion. (b) Magnification of Part 2 of (a).

Fig. 2
Fig. 2

(a1) Temporal phase of the soliton pulse with TOD simulated (sim.) from Eq. (20). The pulse envelope’s shape is assumed to be sech2(t/τ). The sign of phase is defined such that a positive second derivative with respect to time implies positive dispersion. Intensity is normalized to unity, indicated as “Norm.” (a2) The Fourier transform of (a1) gives a flat phase, but the spectral intensity has a tail at the short-wavelength side. (a3) The calculated FROG trace from the pulse in (a1). The spectrum at zero delay is elongated to the short-wavelength side. (b1) Pulse envelope and phase in the time domain retrieved from experimental (Exp.) FROG data for the optimized L-fold-cavity Cr4+:YAG laser. The qualitative shape of the phase curve is the same as in (a1). Phase behavior outside of -150–150-fs delay has no significance because of low intensity. (b2) Fourier transform of (b1). The phase is almost flat, and the intensity curve has a tail at the short-wavelength side as in (a2). The extra peaks at 1575 and 1610 nm are discussed by Ishida et al.23 The phase behavior for large delays has no significance, as in (b1). (b3) The measured FROG trace to produce (b1) and (b2). The elongated spectrum to the short-wavelength side at zero delay is similar to that in (a3).

Fig. 3
Fig. 3

Relative group delay φ/ω-ϕ=ϕΔω(+ϕΔω2/2) plotted with respect to wavelength. Negative dispersion causes an advance for the short-wavelength components of a pulse and a delay for the long-wavelength components. The front part of a pulse is redshifted by SPM, and the back part is blueshifted. In the presence of GDD only, the red and blue shifts are balanced, but the addition of TOD breaks the balance, resulting in a tail at the short-wavelength side of the spectrum.

Tables (1)

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Table 1 Cavity Round-Trip Dispersiona

Equations (22)

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d2ϕdω2=λ32πc2 d2Pdλ2,
d3ϕdω3=-λ44π2c3 λ d3Pdλ3+3 d2Pdλ2,
d4ϕdω4=λ58π3c4 λ2 d4Pdλ4+8λ d3Pdλ3+12 d2Pdλ2,
1/f=-1/CO+1/CO,
CO=f (tan θp/tan θg-1),
CO=f (1-tan θg/tan θp).
limλλc θpθg=limλλc dnθp/dλndnθg/dλn,
limλλc dn(θp/θg)dλn=0,
limλλc dn COdλn=limλλc dnCOdλn=0
POC1=OD1+np D1C1=l cos β,
dPOC1(λc)dλ=dPOC1(λc)dβ dβ(λc)dnp dnp(λc)dλ.
dPOC1(λc)dβ=-d3POC1(λc)dβ3=-l sin β(λc)=-D0C0 cos φp(λc)sin α,
d2POC1(λc)dβ2=-d4POC1(λc)dβ 3=-l cos β(λc)=-(OD0+npD0C0)
-dβdnp=dθdnp=[(sin α)-2-np2]1/2,
-d2βdnp2=d2θdnp2=npdθdnp3,
-d3βdnp3=d3θdnp3=dθdnp3+3np2dθdnp5,
-d4βdnp4=d4θdnp4=9npdθdnp5+15np3dθdnp7
d2POC1(λc)dλ2=d2npdλ2C0D0-dnpdλ2OD0,
d3POC1(λc)dλ3=d3n pdλ3C0D0-3npdnpdλ3+dnpdλ d2npdλ2OD0,
d4POC1(λc)dλ4=d4npdλ4C0D0-3(1+5np2)dnpdλ4+6npdnpdλ2 d2npdλ2+d2npdλ22+43 dnpdλ d3npdλ3OD0.
-ϕτ2τ dφd t+ϕ3!τ 3 1-6 sech2tτ+ΔTτ=0,
φ=ϕ6ϕτ2 t-6τ tanhtτ.

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