Abstract

The performances of a tunable femtosecond dye laser are analyzed using accurate correlation techniques. The source is a passively mode-locked dye laser, of which both the frequency and frequency modulation are controlled by one or two intracavity prisms. Interferometric second-order autocorrelations, with a peak-to-background ratio of 8 to 1, are used simultaneously with the conventional intensity autocorrelation and the pulse spectrum to determine the pulse shape. The main advantages of the interferometric autocorrelations are that they provide phase information otherwise not available, and they are more sensitive to the pulse shape than the intensity autocorrelation. The phase sensitivity is demonstrated in an analysis of the Gaussian pulses with a linear frequency modulation. Analytical expressions for the envelopes of the interferometric autocorrelations of typical pulse shapes are provided for quick pulse shape identification. A numerical method is used to analyze the more complex pulse shapes and chirps that can be produced by the laser. A series of examples demonstrates the control of this laser over various pulse shapes and frequency modulations. Pulse broadening or compression by propagation through glass is calculated for the pulse shapes determined from the fittings. Comparisons of autocorrelations and cross correlations calculated for the dispersed pulses, with the actual measurements, demonstrate the accuracy of the fitting procedure. The method of pulse shape determination demonstrated here requires a train of identical pulses. Indeed, it is shown that, for example, a train of unchirped pulses randomly distributed in frequency can have the same interferometric autocorrelation than a single chirped pulse. In the case of the present source, a comparison of the pulse spectrum, with that of the second harmonic, gives an additional proof that pulse-to-pulse fluctuations are negligible.

© 1985 Optical Society of America

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References

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  1. R. L. Fork, B. I. Green, C. V. Shank, “Generation of Optical Pulses Shorter than 0.1 ps by Colliding Pulse Mode-Locking,” Appl. Phys. Lett. 38, 671 (1981).
    [CrossRef]
  2. W. Dietel, E. Dopel, D. Kühlke, B. Wilhelmi, “Pulses in the Femtosecond Range from a cw Dye Ring Laser in the Colliding Pulse Mode-Locking Regime with Downchirp,” Opt. Commun. 43, 433 (1982).
    [CrossRef]
  3. W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity Pulse Compression with Glass: A New Method of Generating Pulses Shorter than 60 fsec.” Opt. Lett. 8, 4 (1983).
    [CrossRef] [PubMed]
  4. J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a Mode-Locked Ring Laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
    [CrossRef]
  5. J.-C. Diels, E. W. Van Stryland, D. Gold, “Investigation of the Parameters Affecting Subpicosecond Pulse Duration of Passively Mode-Locked Dye Laser,” in Proceedings, First International Conference on Picosecond Phenomena (Springer, New York, 1978), p. 117.
    [CrossRef]
  6. J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase Sensitive Measurements of fs Laser Pulses from a Ring Cavity,” in Lasers 83, San Francisco (Dec. 1983).
  7. B. Nikolaus, D. Grischowsky, “12× Pulse Compression Using Optical Fibers,” Appl. Phys. Lett. 42, 1 (1983).
    [CrossRef]
  8. D. Kuhlke, W. Rudolph, B. Wilhelmi, “Calculation of the Colliding Pulse Mode Locking in cw Dye Ring Lasers,” IEEE J. Quantum Electron. QE-19, 526 (1984).
  9. W. Dietel, “Transient Absorber Gratings Shorten the Pulses of a Passively Mode-Locked cw Dye Laser,” Opt. Commun. 43, 69 (1982).
    [CrossRef]
  10. J.-C. Diels, I. C. McMichael, J. J. Fontaine, C. Y. Wang, “Subpicosecond Pulse Shape Measurement and Modeling of Passively Mode Locked Dye Lasers Including Saturation and Spatial Hole Burning,” in Proceedings, Third International Conference on Picosecond Phenomena (Springer, Berlin, 1982), p. 116.
    [CrossRef]
  11. W. Rudolph, B. Wilhelmi, “Calculation of Light Pulses with Chirp in Passively Mode Locked Lasers Taking into Account the Phase Memory of Absorber and Amplifier,” Appl. Phys. B 34, 274 (1984).
  12. J.-C. Diels et al. “Control of Profile and Chirp of fs Light Pulses by Propagating Them Through Resonant and Nonresonant Optical Media,” IQEC 84, Anaheim (June1984), paper MDD3.
  13. J.-C. Diels et al. “Colliding Pulse Femtosecond Lasers and Applications to the Measurement of Optical Parameters,” in Ultrafast Phenomena IV (Springer, Berlin, 1984), pp. 30–34.
    [CrossRef]
  14. J.-C. Diels et al.Kvantovaya Elektron 10, 2398 (1983);“Experimental and Theoretical Study of a Femtosecond Laser,” Sov. J. Quantum Electron. 13, 1562 (1983).
  15. W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer Dielectric Mirrors Generate Chirp in fs Dye Ring Lasers,” Opt. Commun. 50, 179 (1984).
    [CrossRef]
  16. J. P. Gordon, R. L. Fork, “Optical Resonator with Negative dispersion,” Opt. Lett. 9, 153 (1984).
    [CrossRef] [PubMed]
  17. J.-C. Diels, J. J. Fontaine, W. Dietel, W. Rudolph, B. Wilhelmi, “Analysis of a Mode Locked Ring Laser: Chirped Solitary Pulse Solutions,” J. Opt. Soc. Am. B 2, 680 (1985).
    [CrossRef]
  18. J.-C. Diels, H. Vanherzeele, R. Torti, “Femtosecond Pulse Generation in a Linear Cavity Terminated by an Antiresonant Ring,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper WC5.
  19. H. P. Weber, H. G. Danielmeyer, “Multimode Effects in Intensity Correlation Measurements,” Phys. Rev. A 2, 2074 (1970).
    [CrossRef]
  20. K. L. Sala, G. A. Kenny-Walace, G. E. Hall, “CW Autocorrelation Measurements of Picosecond Laser Pulses,” IEEE J. Quantum Electron. QE-16, 990 (1980).
    [CrossRef]
  21. E. P. Ippen, C. V. Shank, “Techniques for Measurements,” in Ultrashort Light Pulses, S. L. Shapiro, Ed. (Springer, New York, 1977), pp. 313–345.
  22. E. P. Ippen, C. V. Shank, “Dynamic Spectroscopy and Subpicosecond Pulse Compression,” Appl. Phys. Lett. 27, 488 (1975).
    [CrossRef]
  23. D. J. Bradley, G. H. C. New, “Ultrashort Pulse Measurements,” Proc. IEEE 62, 313 (1974).
    [CrossRef]
  24. E. W. Van Stryland, “The Effect of Pulse to Pulse Variation on Ultrashort Pulsewidth Measurements,” Opt. Commun. 31, 93 (1979).
    [CrossRef]
  25. J. M. Catherall, G. H. C. New, “Theoretical Studies of Active, Synchronous, and Hybrid Mode-Locking,” in Ultrafast Phenomena IV (Springer, Berlin, 1984), pp. 75–77.
    [CrossRef]
  26. G. Arfkin, Mathematical Methods for Physicists (Academic, New York, 1970).
  27. T. Anderson, S. T. Eng. “Determination of the Pulse Response from Intensity Autocorrelation Measurements of Ultrashort Laser Pulses,” Opt. Commun. 47, 288 (1983).
    [CrossRef]
  28. W. Dietel, W. Rudolph, B. Wilhelmi, J.-C. Diels, J. J. Fontaine, “Formation of Solitary Femtosecond Light Pulses with Chirp in Passively Mode Locked Lasers,” in Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480 (1984).
  29. I. C. McMichael, J.-C. Diels, “Degenerate Four Wave Mixing of Femtosecond Pulses in the Saturable Absorber of a Ring Dye Laser,” XIIIth Int. in Proceedings, Thirteenth International Quantum Electronics Conference (June 1984), paper MDD2.
  30. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), pp. 212–215.
  31. “Optical Glass,” Schott Catalog No. 3111.

1985 (1)

1984 (5)

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer Dielectric Mirrors Generate Chirp in fs Dye Ring Lasers,” Opt. Commun. 50, 179 (1984).
[CrossRef]

J. P. Gordon, R. L. Fork, “Optical Resonator with Negative dispersion,” Opt. Lett. 9, 153 (1984).
[CrossRef] [PubMed]

D. Kuhlke, W. Rudolph, B. Wilhelmi, “Calculation of the Colliding Pulse Mode Locking in cw Dye Ring Lasers,” IEEE J. Quantum Electron. QE-19, 526 (1984).

W. Rudolph, B. Wilhelmi, “Calculation of Light Pulses with Chirp in Passively Mode Locked Lasers Taking into Account the Phase Memory of Absorber and Amplifier,” Appl. Phys. B 34, 274 (1984).

J.-C. Diels et al. “Control of Profile and Chirp of fs Light Pulses by Propagating Them Through Resonant and Nonresonant Optical Media,” IQEC 84, Anaheim (June1984), paper MDD3.

1983 (5)

J.-C. Diels et al.Kvantovaya Elektron 10, 2398 (1983);“Experimental and Theoretical Study of a Femtosecond Laser,” Sov. J. Quantum Electron. 13, 1562 (1983).

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity Pulse Compression with Glass: A New Method of Generating Pulses Shorter than 60 fsec.” Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a Mode-Locked Ring Laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

B. Nikolaus, D. Grischowsky, “12× Pulse Compression Using Optical Fibers,” Appl. Phys. Lett. 42, 1 (1983).
[CrossRef]

T. Anderson, S. T. Eng. “Determination of the Pulse Response from Intensity Autocorrelation Measurements of Ultrashort Laser Pulses,” Opt. Commun. 47, 288 (1983).
[CrossRef]

1982 (2)

W. Dietel, E. Dopel, D. Kühlke, B. Wilhelmi, “Pulses in the Femtosecond Range from a cw Dye Ring Laser in the Colliding Pulse Mode-Locking Regime with Downchirp,” Opt. Commun. 43, 433 (1982).
[CrossRef]

W. Dietel, “Transient Absorber Gratings Shorten the Pulses of a Passively Mode-Locked cw Dye Laser,” Opt. Commun. 43, 69 (1982).
[CrossRef]

1981 (1)

R. L. Fork, B. I. Green, C. V. Shank, “Generation of Optical Pulses Shorter than 0.1 ps by Colliding Pulse Mode-Locking,” Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

1980 (1)

K. L. Sala, G. A. Kenny-Walace, G. E. Hall, “CW Autocorrelation Measurements of Picosecond Laser Pulses,” IEEE J. Quantum Electron. QE-16, 990 (1980).
[CrossRef]

1979 (1)

E. W. Van Stryland, “The Effect of Pulse to Pulse Variation on Ultrashort Pulsewidth Measurements,” Opt. Commun. 31, 93 (1979).
[CrossRef]

1975 (1)

E. P. Ippen, C. V. Shank, “Dynamic Spectroscopy and Subpicosecond Pulse Compression,” Appl. Phys. Lett. 27, 488 (1975).
[CrossRef]

1974 (1)

D. J. Bradley, G. H. C. New, “Ultrashort Pulse Measurements,” Proc. IEEE 62, 313 (1974).
[CrossRef]

1970 (1)

H. P. Weber, H. G. Danielmeyer, “Multimode Effects in Intensity Correlation Measurements,” Phys. Rev. A 2, 2074 (1970).
[CrossRef]

Anderson, T.

T. Anderson, S. T. Eng. “Determination of the Pulse Response from Intensity Autocorrelation Measurements of Ultrashort Laser Pulses,” Opt. Commun. 47, 288 (1983).
[CrossRef]

Arfkin, G.

G. Arfkin, Mathematical Methods for Physicists (Academic, New York, 1970).

Bradley, D. J.

D. J. Bradley, G. H. C. New, “Ultrashort Pulse Measurements,” Proc. IEEE 62, 313 (1974).
[CrossRef]

Catherall, J. M.

J. M. Catherall, G. H. C. New, “Theoretical Studies of Active, Synchronous, and Hybrid Mode-Locking,” in Ultrafast Phenomena IV (Springer, Berlin, 1984), pp. 75–77.
[CrossRef]

Danielmeyer, H. G.

H. P. Weber, H. G. Danielmeyer, “Multimode Effects in Intensity Correlation Measurements,” Phys. Rev. A 2, 2074 (1970).
[CrossRef]

Diels, J.-C.

J.-C. Diels, J. J. Fontaine, W. Dietel, W. Rudolph, B. Wilhelmi, “Analysis of a Mode Locked Ring Laser: Chirped Solitary Pulse Solutions,” J. Opt. Soc. Am. B 2, 680 (1985).
[CrossRef]

J.-C. Diels et al. “Control of Profile and Chirp of fs Light Pulses by Propagating Them Through Resonant and Nonresonant Optical Media,” IQEC 84, Anaheim (June1984), paper MDD3.

J.-C. Diels et al.Kvantovaya Elektron 10, 2398 (1983);“Experimental and Theoretical Study of a Femtosecond Laser,” Sov. J. Quantum Electron. 13, 1562 (1983).

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a Mode-Locked Ring Laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity Pulse Compression with Glass: A New Method of Generating Pulses Shorter than 60 fsec.” Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

W. Dietel, W. Rudolph, B. Wilhelmi, J.-C. Diels, J. J. Fontaine, “Formation of Solitary Femtosecond Light Pulses with Chirp in Passively Mode Locked Lasers,” in Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480 (1984).

I. C. McMichael, J.-C. Diels, “Degenerate Four Wave Mixing of Femtosecond Pulses in the Saturable Absorber of a Ring Dye Laser,” XIIIth Int. in Proceedings, Thirteenth International Quantum Electronics Conference (June 1984), paper MDD2.

J.-C. Diels, E. W. Van Stryland, D. Gold, “Investigation of the Parameters Affecting Subpicosecond Pulse Duration of Passively Mode-Locked Dye Laser,” in Proceedings, First International Conference on Picosecond Phenomena (Springer, New York, 1978), p. 117.
[CrossRef]

J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase Sensitive Measurements of fs Laser Pulses from a Ring Cavity,” in Lasers 83, San Francisco (Dec. 1983).

J.-C. Diels, I. C. McMichael, J. J. Fontaine, C. Y. Wang, “Subpicosecond Pulse Shape Measurement and Modeling of Passively Mode Locked Dye Lasers Including Saturation and Spatial Hole Burning,” in Proceedings, Third International Conference on Picosecond Phenomena (Springer, Berlin, 1982), p. 116.
[CrossRef]

J.-C. Diels et al. “Colliding Pulse Femtosecond Lasers and Applications to the Measurement of Optical Parameters,” in Ultrafast Phenomena IV (Springer, Berlin, 1984), pp. 30–34.
[CrossRef]

J.-C. Diels, H. Vanherzeele, R. Torti, “Femtosecond Pulse Generation in a Linear Cavity Terminated by an Antiresonant Ring,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper WC5.

Dietel, W.

J.-C. Diels, J. J. Fontaine, W. Dietel, W. Rudolph, B. Wilhelmi, “Analysis of a Mode Locked Ring Laser: Chirped Solitary Pulse Solutions,” J. Opt. Soc. Am. B 2, 680 (1985).
[CrossRef]

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer Dielectric Mirrors Generate Chirp in fs Dye Ring Lasers,” Opt. Commun. 50, 179 (1984).
[CrossRef]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a Mode-Locked Ring Laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity Pulse Compression with Glass: A New Method of Generating Pulses Shorter than 60 fsec.” Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

W. Dietel, E. Dopel, D. Kühlke, B. Wilhelmi, “Pulses in the Femtosecond Range from a cw Dye Ring Laser in the Colliding Pulse Mode-Locking Regime with Downchirp,” Opt. Commun. 43, 433 (1982).
[CrossRef]

W. Dietel, “Transient Absorber Gratings Shorten the Pulses of a Passively Mode-Locked cw Dye Laser,” Opt. Commun. 43, 69 (1982).
[CrossRef]

W. Dietel, W. Rudolph, B. Wilhelmi, J.-C. Diels, J. J. Fontaine, “Formation of Solitary Femtosecond Light Pulses with Chirp in Passively Mode Locked Lasers,” in Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480 (1984).

Dopel, E.

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer Dielectric Mirrors Generate Chirp in fs Dye Ring Lasers,” Opt. Commun. 50, 179 (1984).
[CrossRef]

W. Dietel, E. Dopel, D. Kühlke, B. Wilhelmi, “Pulses in the Femtosecond Range from a cw Dye Ring Laser in the Colliding Pulse Mode-Locking Regime with Downchirp,” Opt. Commun. 43, 433 (1982).
[CrossRef]

Eng, S. T.

T. Anderson, S. T. Eng. “Determination of the Pulse Response from Intensity Autocorrelation Measurements of Ultrashort Laser Pulses,” Opt. Commun. 47, 288 (1983).
[CrossRef]

Fontaine, J. J.

J.-C. Diels, J. J. Fontaine, W. Dietel, W. Rudolph, B. Wilhelmi, “Analysis of a Mode Locked Ring Laser: Chirped Solitary Pulse Solutions,” J. Opt. Soc. Am. B 2, 680 (1985).
[CrossRef]

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity Pulse Compression with Glass: A New Method of Generating Pulses Shorter than 60 fsec.” Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a Mode-Locked Ring Laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase Sensitive Measurements of fs Laser Pulses from a Ring Cavity,” in Lasers 83, San Francisco (Dec. 1983).

J.-C. Diels, I. C. McMichael, J. J. Fontaine, C. Y. Wang, “Subpicosecond Pulse Shape Measurement and Modeling of Passively Mode Locked Dye Lasers Including Saturation and Spatial Hole Burning,” in Proceedings, Third International Conference on Picosecond Phenomena (Springer, Berlin, 1982), p. 116.
[CrossRef]

W. Dietel, W. Rudolph, B. Wilhelmi, J.-C. Diels, J. J. Fontaine, “Formation of Solitary Femtosecond Light Pulses with Chirp in Passively Mode Locked Lasers,” in Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480 (1984).

Fork, R. L.

J. P. Gordon, R. L. Fork, “Optical Resonator with Negative dispersion,” Opt. Lett. 9, 153 (1984).
[CrossRef] [PubMed]

R. L. Fork, B. I. Green, C. V. Shank, “Generation of Optical Pulses Shorter than 0.1 ps by Colliding Pulse Mode-Locking,” Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Gold, D.

J.-C. Diels, E. W. Van Stryland, D. Gold, “Investigation of the Parameters Affecting Subpicosecond Pulse Duration of Passively Mode-Locked Dye Laser,” in Proceedings, First International Conference on Picosecond Phenomena (Springer, New York, 1978), p. 117.
[CrossRef]

Gordon, J. P.

Green, B. I.

R. L. Fork, B. I. Green, C. V. Shank, “Generation of Optical Pulses Shorter than 0.1 ps by Colliding Pulse Mode-Locking,” Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Grischowsky, D.

B. Nikolaus, D. Grischowsky, “12× Pulse Compression Using Optical Fibers,” Appl. Phys. Lett. 42, 1 (1983).
[CrossRef]

Hall, G. E.

K. L. Sala, G. A. Kenny-Walace, G. E. Hall, “CW Autocorrelation Measurements of Picosecond Laser Pulses,” IEEE J. Quantum Electron. QE-16, 990 (1980).
[CrossRef]

Hehl, K.

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer Dielectric Mirrors Generate Chirp in fs Dye Ring Lasers,” Opt. Commun. 50, 179 (1984).
[CrossRef]

Ippen, E. P.

E. P. Ippen, C. V. Shank, “Dynamic Spectroscopy and Subpicosecond Pulse Compression,” Appl. Phys. Lett. 27, 488 (1975).
[CrossRef]

E. P. Ippen, C. V. Shank, “Techniques for Measurements,” in Ultrashort Light Pulses, S. L. Shapiro, Ed. (Springer, New York, 1977), pp. 313–345.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), pp. 212–215.

Kenny-Walace, G. A.

K. L. Sala, G. A. Kenny-Walace, G. E. Hall, “CW Autocorrelation Measurements of Picosecond Laser Pulses,” IEEE J. Quantum Electron. QE-16, 990 (1980).
[CrossRef]

Kuhlke, D.

D. Kuhlke, W. Rudolph, B. Wilhelmi, “Calculation of the Colliding Pulse Mode Locking in cw Dye Ring Lasers,” IEEE J. Quantum Electron. QE-19, 526 (1984).

Kühlke, D.

W. Dietel, E. Dopel, D. Kühlke, B. Wilhelmi, “Pulses in the Femtosecond Range from a cw Dye Ring Laser in the Colliding Pulse Mode-Locking Regime with Downchirp,” Opt. Commun. 43, 433 (1982).
[CrossRef]

McMichael, I. C.

I. C. McMichael, J.-C. Diels, “Degenerate Four Wave Mixing of Femtosecond Pulses in the Saturable Absorber of a Ring Dye Laser,” XIIIth Int. in Proceedings, Thirteenth International Quantum Electronics Conference (June 1984), paper MDD2.

J.-C. Diels, I. C. McMichael, J. J. Fontaine, C. Y. Wang, “Subpicosecond Pulse Shape Measurement and Modeling of Passively Mode Locked Dye Lasers Including Saturation and Spatial Hole Burning,” in Proceedings, Third International Conference on Picosecond Phenomena (Springer, Berlin, 1982), p. 116.
[CrossRef]

New, G. H. C.

D. J. Bradley, G. H. C. New, “Ultrashort Pulse Measurements,” Proc. IEEE 62, 313 (1974).
[CrossRef]

J. M. Catherall, G. H. C. New, “Theoretical Studies of Active, Synchronous, and Hybrid Mode-Locking,” in Ultrafast Phenomena IV (Springer, Berlin, 1984), pp. 75–77.
[CrossRef]

Nikolaus, B.

B. Nikolaus, D. Grischowsky, “12× Pulse Compression Using Optical Fibers,” Appl. Phys. Lett. 42, 1 (1983).
[CrossRef]

Rudolph, W.

J.-C. Diels, J. J. Fontaine, W. Dietel, W. Rudolph, B. Wilhelmi, “Analysis of a Mode Locked Ring Laser: Chirped Solitary Pulse Solutions,” J. Opt. Soc. Am. B 2, 680 (1985).
[CrossRef]

D. Kuhlke, W. Rudolph, B. Wilhelmi, “Calculation of the Colliding Pulse Mode Locking in cw Dye Ring Lasers,” IEEE J. Quantum Electron. QE-19, 526 (1984).

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer Dielectric Mirrors Generate Chirp in fs Dye Ring Lasers,” Opt. Commun. 50, 179 (1984).
[CrossRef]

W. Rudolph, B. Wilhelmi, “Calculation of Light Pulses with Chirp in Passively Mode Locked Lasers Taking into Account the Phase Memory of Absorber and Amplifier,” Appl. Phys. B 34, 274 (1984).

W. Dietel, W. Rudolph, B. Wilhelmi, J.-C. Diels, J. J. Fontaine, “Formation of Solitary Femtosecond Light Pulses with Chirp in Passively Mode Locked Lasers,” in Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480 (1984).

Sala, K. L.

K. L. Sala, G. A. Kenny-Walace, G. E. Hall, “CW Autocorrelation Measurements of Picosecond Laser Pulses,” IEEE J. Quantum Electron. QE-16, 990 (1980).
[CrossRef]

Schmidt, E.

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer Dielectric Mirrors Generate Chirp in fs Dye Ring Lasers,” Opt. Commun. 50, 179 (1984).
[CrossRef]

Shank, C. V.

R. L. Fork, B. I. Green, C. V. Shank, “Generation of Optical Pulses Shorter than 0.1 ps by Colliding Pulse Mode-Locking,” Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

E. P. Ippen, C. V. Shank, “Dynamic Spectroscopy and Subpicosecond Pulse Compression,” Appl. Phys. Lett. 27, 488 (1975).
[CrossRef]

E. P. Ippen, C. V. Shank, “Techniques for Measurements,” in Ultrashort Light Pulses, S. L. Shapiro, Ed. (Springer, New York, 1977), pp. 313–345.

Simoni, F.

J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase Sensitive Measurements of fs Laser Pulses from a Ring Cavity,” in Lasers 83, San Francisco (Dec. 1983).

Torti, R.

J.-C. Diels, H. Vanherzeele, R. Torti, “Femtosecond Pulse Generation in a Linear Cavity Terminated by an Antiresonant Ring,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper WC5.

Van Stryland, E. W.

E. W. Van Stryland, “The Effect of Pulse to Pulse Variation on Ultrashort Pulsewidth Measurements,” Opt. Commun. 31, 93 (1979).
[CrossRef]

J.-C. Diels, E. W. Van Stryland, D. Gold, “Investigation of the Parameters Affecting Subpicosecond Pulse Duration of Passively Mode-Locked Dye Laser,” in Proceedings, First International Conference on Picosecond Phenomena (Springer, New York, 1978), p. 117.
[CrossRef]

Vanherzeele, H.

J.-C. Diels, H. Vanherzeele, R. Torti, “Femtosecond Pulse Generation in a Linear Cavity Terminated by an Antiresonant Ring,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper WC5.

Wang, C. Y.

J.-C. Diels, I. C. McMichael, J. J. Fontaine, C. Y. Wang, “Subpicosecond Pulse Shape Measurement and Modeling of Passively Mode Locked Dye Lasers Including Saturation and Spatial Hole Burning,” in Proceedings, Third International Conference on Picosecond Phenomena (Springer, Berlin, 1982), p. 116.
[CrossRef]

Weber, H. P.

H. P. Weber, H. G. Danielmeyer, “Multimode Effects in Intensity Correlation Measurements,” Phys. Rev. A 2, 2074 (1970).
[CrossRef]

Wilhelmi, B.

J.-C. Diels, J. J. Fontaine, W. Dietel, W. Rudolph, B. Wilhelmi, “Analysis of a Mode Locked Ring Laser: Chirped Solitary Pulse Solutions,” J. Opt. Soc. Am. B 2, 680 (1985).
[CrossRef]

W. Rudolph, B. Wilhelmi, “Calculation of Light Pulses with Chirp in Passively Mode Locked Lasers Taking into Account the Phase Memory of Absorber and Amplifier,” Appl. Phys. B 34, 274 (1984).

D. Kuhlke, W. Rudolph, B. Wilhelmi, “Calculation of the Colliding Pulse Mode Locking in cw Dye Ring Lasers,” IEEE J. Quantum Electron. QE-19, 526 (1984).

W. Dietel, E. Dopel, D. Kühlke, B. Wilhelmi, “Pulses in the Femtosecond Range from a cw Dye Ring Laser in the Colliding Pulse Mode-Locking Regime with Downchirp,” Opt. Commun. 43, 433 (1982).
[CrossRef]

W. Dietel, W. Rudolph, B. Wilhelmi, J.-C. Diels, J. J. Fontaine, “Formation of Solitary Femtosecond Light Pulses with Chirp in Passively Mode Locked Lasers,” in Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480 (1984).

Appl. Phys. B (1)

W. Rudolph, B. Wilhelmi, “Calculation of Light Pulses with Chirp in Passively Mode Locked Lasers Taking into Account the Phase Memory of Absorber and Amplifier,” Appl. Phys. B 34, 274 (1984).

Appl. Phys. Lett. (3)

R. L. Fork, B. I. Green, C. V. Shank, “Generation of Optical Pulses Shorter than 0.1 ps by Colliding Pulse Mode-Locking,” Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

B. Nikolaus, D. Grischowsky, “12× Pulse Compression Using Optical Fibers,” Appl. Phys. Lett. 42, 1 (1983).
[CrossRef]

E. P. Ippen, C. V. Shank, “Dynamic Spectroscopy and Subpicosecond Pulse Compression,” Appl. Phys. Lett. 27, 488 (1975).
[CrossRef]

IEEE J. Quantum Electron. (3)

D. Kuhlke, W. Rudolph, B. Wilhelmi, “Calculation of the Colliding Pulse Mode Locking in cw Dye Ring Lasers,” IEEE J. Quantum Electron. QE-19, 526 (1984).

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in a Mode-Locked Ring Laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

K. L. Sala, G. A. Kenny-Walace, G. E. Hall, “CW Autocorrelation Measurements of Picosecond Laser Pulses,” IEEE J. Quantum Electron. QE-16, 990 (1980).
[CrossRef]

IQEC 84, Anaheim (1)

J.-C. Diels et al. “Control of Profile and Chirp of fs Light Pulses by Propagating Them Through Resonant and Nonresonant Optical Media,” IQEC 84, Anaheim (June1984), paper MDD3.

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

Kvantovaya Elektron (1)

J.-C. Diels et al.Kvantovaya Elektron 10, 2398 (1983);“Experimental and Theoretical Study of a Femtosecond Laser,” Sov. J. Quantum Electron. 13, 1562 (1983).

Opt. Commun. (5)

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer Dielectric Mirrors Generate Chirp in fs Dye Ring Lasers,” Opt. Commun. 50, 179 (1984).
[CrossRef]

W. Dietel, E. Dopel, D. Kühlke, B. Wilhelmi, “Pulses in the Femtosecond Range from a cw Dye Ring Laser in the Colliding Pulse Mode-Locking Regime with Downchirp,” Opt. Commun. 43, 433 (1982).
[CrossRef]

W. Dietel, “Transient Absorber Gratings Shorten the Pulses of a Passively Mode-Locked cw Dye Laser,” Opt. Commun. 43, 69 (1982).
[CrossRef]

E. W. Van Stryland, “The Effect of Pulse to Pulse Variation on Ultrashort Pulsewidth Measurements,” Opt. Commun. 31, 93 (1979).
[CrossRef]

T. Anderson, S. T. Eng. “Determination of the Pulse Response from Intensity Autocorrelation Measurements of Ultrashort Laser Pulses,” Opt. Commun. 47, 288 (1983).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

H. P. Weber, H. G. Danielmeyer, “Multimode Effects in Intensity Correlation Measurements,” Phys. Rev. A 2, 2074 (1970).
[CrossRef]

Proc. IEEE (1)

D. J. Bradley, G. H. C. New, “Ultrashort Pulse Measurements,” Proc. IEEE 62, 313 (1974).
[CrossRef]

Other (12)

J. M. Catherall, G. H. C. New, “Theoretical Studies of Active, Synchronous, and Hybrid Mode-Locking,” in Ultrafast Phenomena IV (Springer, Berlin, 1984), pp. 75–77.
[CrossRef]

G. Arfkin, Mathematical Methods for Physicists (Academic, New York, 1970).

W. Dietel, W. Rudolph, B. Wilhelmi, J.-C. Diels, J. J. Fontaine, “Formation of Solitary Femtosecond Light Pulses with Chirp in Passively Mode Locked Lasers,” in Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480 (1984).

I. C. McMichael, J.-C. Diels, “Degenerate Four Wave Mixing of Femtosecond Pulses in the Saturable Absorber of a Ring Dye Laser,” XIIIth Int. in Proceedings, Thirteenth International Quantum Electronics Conference (June 1984), paper MDD2.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), pp. 212–215.

“Optical Glass,” Schott Catalog No. 3111.

J.-C. Diels et al. “Colliding Pulse Femtosecond Lasers and Applications to the Measurement of Optical Parameters,” in Ultrafast Phenomena IV (Springer, Berlin, 1984), pp. 30–34.
[CrossRef]

J.-C. Diels, H. Vanherzeele, R. Torti, “Femtosecond Pulse Generation in a Linear Cavity Terminated by an Antiresonant Ring,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1984), paper WC5.

E. P. Ippen, C. V. Shank, “Techniques for Measurements,” in Ultrashort Light Pulses, S. L. Shapiro, Ed. (Springer, New York, 1977), pp. 313–345.

J.-C. Diels, E. W. Van Stryland, D. Gold, “Investigation of the Parameters Affecting Subpicosecond Pulse Duration of Passively Mode-Locked Dye Laser,” in Proceedings, First International Conference on Picosecond Phenomena (Springer, New York, 1978), p. 117.
[CrossRef]

J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase Sensitive Measurements of fs Laser Pulses from a Ring Cavity,” in Lasers 83, San Francisco (Dec. 1983).

J.-C. Diels, I. C. McMichael, J. J. Fontaine, C. Y. Wang, “Subpicosecond Pulse Shape Measurement and Modeling of Passively Mode Locked Dye Lasers Including Saturation and Spatial Hole Burning,” in Proceedings, Third International Conference on Picosecond Phenomena (Springer, Berlin, 1982), p. 116.
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Sketch of the laser cavity. Mirrors of 5-cm radius of curvature were used around the amplifier dye jet (M0, M1, and M2), and 3-cm curvature around the saturable absorber jet (M3 and M4). The mirror M5 has a radius of curvature of 1 m. Transmission factors ranging from 2% to 10% were used for the output coupler M6. To adjust the amount of intracavity glass, the prism P is mounted on a translation stage oriented along the bisector of the angle made by the beams leaving the prism.

Fig. 2
Fig. 2

Successive intensity autocorrelations taken for increasing amounts of intracavity glass.

Fig. 3
Fig. 3

Sketch of a second-order autocorrelation measurement. Optical delay lines are used to split the original laser pulse in a sequence of two pulses of relative phase ϕ and delay τ. The second harmonic of that pulse sequence, generated in a KDP crystal, is detected through the color filers F (to eliminate the fundamental radiation) by the photomultiplier tube PM.

Fig. 4
Fig. 4

Interferometric autocorrelation.

Fig. 5
Fig. 5

Locus of the maxima of the lower envelope of the interferometric autocorrelations of linearly chirped Gaussian pulses as a function of chirp parameter A. The locus of the corresponding value of the upper envelope is also plotted. The locus of the lower envelope is only slightly below (of the upper envelope slightly above) the intensity autocorrelation (dashed line). The loci are graduated in values of chirp parameter A. The particular interferometric autocorrelation corresponding to A = 2 is also shown.

Fig. 6
Fig. 6

Pulse spectra taken for increasing amounts of intracavity glass.

Fig. 7
Fig. 7

Three successive spectra and corresponding interferometric autocorrelations taken for successive increments of intracavity glass (indicated in the figure).

Fig. 8
Fig. 8

Recording of an interferometric autocorrelation (used in the pulse shape fitting of Fig. 9).

Fig. 9
Fig. 9

Example of pulse shape determination through fitting of the intensity autocorrelation (a), the pulse spectrum (b), and the interferometric autocorrelation (c). The crosses are the experimental data points. The solid lines are the corresponding functions calculated for the trial test function indicated in the figure.

Fig. 10
Fig. 10

Interferometric autocorrelation of a pulse that propagated through 10 cm of SF5 glass. The solid line is a calculated autocorrelation using published data on SF5 to calculate the distortion of the initial pulse shape. The latter (detailed in the text) was determined by simultaneous fitting of the autocorrelations and spectrum.

Fig. 11
Fig. 11

Extracavity chirp compensation. The laser is undercompensated by 1 mm (above) or 2.2 mm (below) of fused silica. The pulse duration is measured after transmission through various thicknesses of BK7 glass.

Fig. 12
Fig. 12

Sketch of the cross correlator for downchirped pulses. A block of glass (5 cm of BK7) is inserted in one arm of the interferometer. As the delay in that arm is varied, the cross correlation of the original pulse with the pulse compressed through the glass will be measured.

Fig. 13
Fig. 13

Above: intensity and interferometric autocorrelations of the laser pulse. These measurements, together with the pulse spectrum, were used to determine the pulse shape and chirp. The dashed line is the result of the fitting procedure for the pulse electric field envelope indicated in the text. Middle: intensity and interferometric autocorrelations of the pulse after propagation through 10 cm of BK7 glass. The dashed lines are obtained by calculating successively the propagation and autocorrelations of the laser pulse determined from the previous fitting. Below: intensity and interferometric correlations after insertion of 5-cm BK7 glass in one arm of the interferometer of Fig. 12. The dashed lines are calculated correlations using the laser pulse shape determination of the upper figure.

Fig. 14
Fig. 14

Comparison of the pulse spectrum with that of the second harmonic.

Tables (1)

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Table I Diagnostic Functions Corresponding to Various Pulse Shapes

Equations (48)

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Ic 1 = 1 + 2 { I ( t ) I ( t τ ) dt } / { I 2 dt } ,
I c = I ( t ) I ( t τ ) dt / I 2 dt
I t = | { ( t ) exp i ( ω t + ϕ ) + ( t τ ) exp i [ ω ( t τ ) + ϕ ( t τ ) ] } 2 | 2 dt .
I t ( 0 ) = 2 4 4 ( t ) dt .
E ( t ) = exp { ( t w ) 2 ( 1 + iA ) } .
I t = { 1 + 2 exp ( τ 2 ) + 4 exp ( A 2 + 3 τ 2 4 ) cos A τ 2 2 cos ω τ + exp [ ( 1 + A 2 ) τ 2 ] cos 2 ω τ } .
I t = { 1 + 2 exp ( τ ) 2 ) + 4 exp ( 3 / 4 τ 2 ) cos ω τ + exp ( τ ) 2 cos 2 ω τ } F ( Δ ω ) .
F ( Δ ω ) = 2 A exp ( Δ ω 2 A 2 ) .
g 1 ( τ ) = | E ( t ) + E ( t τ ) | 2 dt / 2 | E ( t ) | 2 dt .
g 2 ( τ ) = | { E ( t ) + E ( t τ ) } 2 | 2 dt / 2 | E 2 ( t ) | 2 dt .
G 2 ( τ ) = | E 2 ( t ) E 2 ( t τ ) | dt / | E 2 ( t ) | 2 dt .
( t ) = 1 exp ( t / τ F ) + exp ( t / τ R ) ,
( t ) = exp [ 0.15 i ( t / τ ) 2 ] / { exp [ t / 0.75 τ ] + exp [ t / 1.25 τ ] } .
τ 2 = τ 1 1 + k 0 2 ,
A = k 0 .
k 0 = 2 d 2 ϕ d ( ω τ 1 ) 2 = 2 τ 1 2 · d 2 k d ω 2 ,
d 2 k d ω 2 = 2 c 0 dn d ω + ω c 0 d 2 n d ω 2 .
n SF 5 = 1.6691 + 0.1792 × 10 3 Δ ω + 0.3743 × 10 6 Δ ω 2 + 0.38 × 10 8 Δ ω 3 ,
k ( Δ ω ) = 0.9735 × 10 2 Δ ω 2 + 0.5124 × 10 4 Δ ω 3 .
n BK 7 = 1.5153 + 0.7326 × 10 4 Δ ω + 0.8772 × 10 7 Δ ω 2 + 0.16 × 10 8 Δ ω 3 ,
k ( Δ ω ) = 0.3323 × 10 2 Δ ω 2 + 0.1907 × 10 4 Δ ω 3 .
E ( t ) = exp [ iA ( t / τ ) 2 ] exp [ t / τ ( 1 + a ) ] + exp [ t / τ ( 1 a ) ] ,
E ( t ) = exp [ i ϕ ( t ) ] exp [ t / τ ( 1 a ] + exp [ t / τ ( 1 + a ) ] ,
ϕ = 2 Bdt / τ exp ( t R ) + exp ( t F ) + A ( t / τ ) 2 .
t R = 2 ( t t c ) / τ ( 1 a ) , t F = 2 ( t t c ) / τ ( 1 + a ) .
E 2 ω = η ( ω ) E 1 E 2 .
E 2 ω ( τ ) = dt d t η ( t ) E 1 ( t t ) E 2 ( t τ ) dt .
1 + e τ 2 4
e τ 2 2
1 + 3 G 2 ( τ ) ± 4 e 3 8 τ 2
sech 2 π ω 2
1 ± τ sinh τ
3 ( τ cosh τ sinh τ ) sinh 3 τ
1 + 3 G 2 ( τ ) ± 3 ( sinh 2 τ 2 τ ) sinh 3 τ
1 + 1 / 2 cosh 15 π 16 ω + 1 / 2
1 ± 4 sinh 1 3 τ sinh 4 3 τ
1 cosh 3 8 15 τ
1 + 3 G 2 ( τ ) ± 4 cosh 3 4 15 τ cosh 3 8 15 τ
sech 3 π 4 ω
1 ± 2 sinh τ sinh 2 τ
3 sinh 8 3 τ 8 τ 4 sinh 3 4 3 τ
1 + 3 G 2 ( τ ) ± 4 τ cosh 2 τ 3 2 cosh 2 2 3 τ sinh 2 3 τ ( 2 cosh 4 3 τ ) sinh 3 4 3 τ
1 1 / 2 cosh 7 π 16 ω 1 / 2
1 ± 4 3 sinh 3 τ sinh 4 τ
2 cosh 16 7 τ + 3 5 cosh 3 8 7 τ
1 + 3 G 2 ( τ ) ± 4 cosh 3 4 7 τ ( 6 cosh 8 7 τ 1 ) 5 cosh 3 8 7 τ
1 ( e t + e rt ) 2
1 ± r + 1 r 1 sinh ( r 1 2 τ ) sinh ( r + 1 2 τ )

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