Abstract

We present measurements on mode-locked ring dye lasers that demonstrate the role of self-phase modulation in the saturable absorber dye. The resulting bandwidth increase plays an essential role in ultrashort pulse generation, because it leads to intracavity pulse compression in the presence of normally dispersive components. The role of various intracavity components (glass, coatings) in intracavity compression is analyzed. As opposed to extracavity compression, measurements of pulse amplitude and phase show that the nonlinear phase modulation can be completely compensated. The interaction of the light pulse with the absorber is analyzed using Maxwell–Bloch equations. Next, we find the steady-state solution for the problem of pulse propagation through an infinite periodic medium containing all the essential intracavity elements (bandwidth-limiting filter, amplifier, absorber, dispersive component). The condition that the solitary pulses be unchirped enables us to determine the optimum intracavity dispersion, which, in agreement with the experimental data, leads to the shortest pulses.

© 1985 Optical Society of America

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  1. H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736–746 (1975).
    [CrossRef]
  2. J. Herrman, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982).
    [CrossRef]
  3. J. Herrman, B. Wilhelmi, in Laser für Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984), pp. 181–185.
  4. J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in mode-locked ring lasers,” IEEE J. Quantum Electron. QE-19, 1467–1469 (1983).
    [CrossRef]
  5. W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, “Pulses in the femtosecond range from a cw dye ring laser in the colliding pulse mode-locking (CPM) regime with down-chirp,” Opt. Commun. 43, 433–436 (1982).
    [CrossRef]
  6. 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,” presented at 3rd Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480–491 (1984).
  7. W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass—a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4–8 (1982).
    [CrossRef]
  8. J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).
  9. 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 35, 37–44 (1984).
    [CrossRef]
  10. J. P. Gordon, R. L. Fork, “Optical resonators with negative dispersion,” Opt. Lett. 9, 153–157 (1984).
    [CrossRef] [PubMed]
  11. De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode locked lasers,” IEEE J. Quantum Electron. QE-20, 533–539 (1984).
    [CrossRef]
  12. 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. 36, 671–672 (1981).
    [CrossRef]
  13. J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.
  14. W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer dielectric mirrors generate chirp in fs dye ring lasers,” Opt. Commun. 50, 179–183 (1984).
    [CrossRef]
  15. J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase sensitive measurements of femtosecond laser pulses from a ring cavity,” in Proceedings of International Conference on Lasers 83 (STS, McLean, Va., 1985), pp. 348–355.
  16. J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
    [CrossRef]
  17. J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. (to be published).
  18. I. C. McMichael, J.-C. Diels, “Degenerate four wave mixing of femtosecond pulses in the saturable absorber of a ring dye laser,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD2.
  19. J. A. Armstrong, E. Courtens, “Exact solution of a π pulse problem,” IEEE J. Quantum Electron. QE-5, 411–419 (1968).
    [CrossRef]
  20. H. Haken, H. Ohno, “Theory of ultrashort pulses,” Opt. Commun. 16, 205–209 (1976).
    [CrossRef]
  21. J.-C. Diels, E. L. Hahn, “Carrier frequency distance dependence of a pulse propagating in a two level system,” Phys. Rev. A 8, 1084–1110 (1973).
    [CrossRef]
  22. J.-C. Diels, E. L. Hahn, “Pulse propagation stability in absorbing and amplifying media,” IEEE J. Quantum Electron. QE-12, 411–416 (1976).
    [CrossRef]

1984 (4)

De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode locked lasers,” IEEE J. Quantum Electron. QE-20, 533–539 (1984).
[CrossRef]

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer dielectric mirrors generate chirp in fs dye ring lasers,” Opt. Commun. 50, 179–183 (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 35, 37–44 (1984).
[CrossRef]

J. P. Gordon, R. L. Fork, “Optical resonators with negative dispersion,” Opt. Lett. 9, 153–157 (1984).
[CrossRef] [PubMed]

1983 (2)

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in mode-locked ring lasers,” IEEE J. Quantum Electron. QE-19, 1467–1469 (1983).
[CrossRef]

1982 (3)

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, “Pulses in the femtosecond range from a cw dye ring laser in the colliding pulse mode-locking (CPM) regime with down-chirp,” Opt. Commun. 43, 433–436 (1982).
[CrossRef]

J. Herrman, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982).
[CrossRef]

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass—a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4–8 (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. 36, 671–672 (1981).
[CrossRef]

1976 (2)

J.-C. Diels, E. L. Hahn, “Pulse propagation stability in absorbing and amplifying media,” IEEE J. Quantum Electron. QE-12, 411–416 (1976).
[CrossRef]

H. Haken, H. Ohno, “Theory of ultrashort pulses,” Opt. Commun. 16, 205–209 (1976).
[CrossRef]

1975 (1)

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736–746 (1975).
[CrossRef]

1973 (1)

J.-C. Diels, E. L. Hahn, “Carrier frequency distance dependence of a pulse propagating in a two level system,” Phys. Rev. A 8, 1084–1110 (1973).
[CrossRef]

1968 (1)

J. A. Armstrong, E. Courtens, “Exact solution of a π pulse problem,” IEEE J. Quantum Electron. QE-5, 411–419 (1968).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, E. Courtens, “Exact solution of a π pulse problem,” IEEE J. Quantum Electron. QE-5, 411–419 (1968).
[CrossRef]

Courtens, E.

J. A. Armstrong, E. Courtens, “Exact solution of a π pulse problem,” IEEE J. Quantum Electron. QE-5, 411–419 (1968).
[CrossRef]

De Silvestri,

De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode locked lasers,” IEEE J. Quantum Electron. QE-20, 533–539 (1984).
[CrossRef]

Diels, J.-C.

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in mode-locked ring lasers,” IEEE J. Quantum Electron. QE-19, 1467–1469 (1983).
[CrossRef]

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass—a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4–8 (1982).
[CrossRef]

J.-C. Diels, E. L. Hahn, “Pulse propagation stability in absorbing and amplifying media,” IEEE J. Quantum Electron. QE-12, 411–416 (1976).
[CrossRef]

J.-C. Diels, E. L. Hahn, “Carrier frequency distance dependence of a pulse propagating in a two level system,” Phys. Rev. A 8, 1084–1110 (1973).
[CrossRef]

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.

I. C. McMichael, J.-C. Diels, “Degenerate four wave mixing of femtosecond pulses in the saturable absorber of a ring dye laser,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD2.

J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. (to be published).

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[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,” presented at 3rd Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480–491 (1984).

J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase sensitive measurements of femtosecond laser pulses from a ring cavity,” in Proceedings of International Conference on Lasers 83 (STS, McLean, Va., 1985), pp. 348–355.

Dietel, W.

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer dielectric mirrors generate chirp in fs dye ring lasers,” Opt. Commun. 50, 179–183 (1984).
[CrossRef]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in mode-locked ring lasers,” IEEE J. Quantum Electron. QE-19, 1467–1469 (1983).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass—a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4–8 (1982).
[CrossRef]

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, “Pulses in the femtosecond range from a cw dye ring laser in the colliding pulse mode-locking (CPM) regime with down-chirp,” Opt. Commun. 43, 433–436 (1982).
[CrossRef]

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.

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,” presented at 3rd Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480–491 (1984).

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

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, 179–183 (1984).
[CrossRef]

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, “Pulses in the femtosecond range from a cw dye ring laser in the colliding pulse mode-locking (CPM) regime with down-chirp,” Opt. Commun. 43, 433–436 (1982).
[CrossRef]

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

Fontaine, J. J.

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in mode-locked ring lasers,” IEEE J. Quantum Electron. QE-19, 1467–1469 (1983).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).

W. Dietel, J. J. Fontaine, J.-C. Diels, “Intracavity pulse compression with glass—a new method of generating pulses shorter than 60 femtoseconds,” Opt. Lett. 8, 4–8 (1982).
[CrossRef]

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[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,” presented at 3rd Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480–491 (1984).

J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase sensitive measurements of femtosecond laser pulses from a ring cavity,” in Proceedings of International Conference on Lasers 83 (STS, McLean, Va., 1985), pp. 348–355.

J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. (to be published).

Fork, R. L.

J. P. Gordon, R. L. Fork, “Optical resonators with negative dispersion,” Opt. Lett. 9, 153–157 (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. 36, 671–672 (1981).
[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. 36, 671–672 (1981).
[CrossRef]

Hahn, E. L.

J.-C. Diels, E. L. Hahn, “Pulse propagation stability in absorbing and amplifying media,” IEEE J. Quantum Electron. QE-12, 411–416 (1976).
[CrossRef]

J.-C. Diels, E. L. Hahn, “Carrier frequency distance dependence of a pulse propagating in a two level system,” Phys. Rev. A 8, 1084–1110 (1973).
[CrossRef]

Haken, H.

H. Haken, H. Ohno, “Theory of ultrashort pulses,” Opt. Commun. 16, 205–209 (1976).
[CrossRef]

Haus, H. A.

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736–746 (1975).
[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, 179–183 (1984).
[CrossRef]

Herrman, J.

J. Herrman, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982).
[CrossRef]

J. Herrman, B. Wilhelmi, in Laser für Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984), pp. 181–185.

Kuhlke, D.

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, “Pulses in the femtosecond range from a cw dye ring laser in the colliding pulse mode-locking (CPM) regime with down-chirp,” Opt. Commun. 43, 433–436 (1982).
[CrossRef]

Laporta, P.

De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode locked lasers,” IEEE J. Quantum Electron. QE-20, 533–539 (1984).
[CrossRef]

McMichael, I. C.

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.

J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. (to be published).

I. C. McMichael, J.-C. Diels, “Degenerate four wave mixing of femtosecond pulses in the saturable absorber of a ring dye laser,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD2.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

Ohno, H.

H. Haken, H. Ohno, “Theory of ultrashort pulses,” Opt. Commun. 16, 205–209 (1976).
[CrossRef]

Rudolph, W.

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 35, 37–44 (1984).
[CrossRef]

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer dielectric mirrors generate chirp in fs dye ring lasers,” Opt. Commun. 50, 179–183 (1984).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[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,” presented at 3rd Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480–491 (1984).

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, 179–183 (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. 36, 671–672 (1981).
[CrossRef]

Simoni, F.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.

J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. (to be published).

J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase sensitive measurements of femtosecond laser pulses from a ring cavity,” in Proceedings of International Conference on Lasers 83 (STS, McLean, Va., 1985), pp. 348–355.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

Svelto, O.

De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode locked lasers,” IEEE J. Quantum Electron. QE-20, 533–539 (1984).
[CrossRef]

Torti, R.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

Vanherzeele, H.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

Weidner, F.

J. Herrman, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982).
[CrossRef]

Wilhelmi, B.

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 35, 37–44 (1984).
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, “Pulses in the femtosecond range from a cw dye ring laser in the colliding pulse mode-locking (CPM) regime with down-chirp,” Opt. Commun. 43, 433–436 (1982).
[CrossRef]

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.

J. Herrman, B. Wilhelmi, in Laser für Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984), pp. 181–185.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[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,” presented at 3rd Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480–491 (1984).

Appl. Phys. B (2)

J. Herrman, F. Weidner, “Theory of passively mode-locked cw dye lasers,” Appl. Phys. B 27, 105–113 (1982).
[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 35, 37–44 (1984).
[CrossRef]

Appl. Phys. Lett. (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. 36, 671–672 (1981).
[CrossRef]

IEEE J. Quantum Electron. (5)

J. A. Armstrong, E. Courtens, “Exact solution of a π pulse problem,” IEEE J. Quantum Electron. QE-5, 411–419 (1968).
[CrossRef]

J.-C. Diels, E. L. Hahn, “Pulse propagation stability in absorbing and amplifying media,” IEEE J. Quantum Electron. QE-12, 411–416 (1976).
[CrossRef]

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736–746 (1975).
[CrossRef]

J. J. Fontaine, W. Dietel, J.-C. Diels, “Chirp in mode-locked ring lasers,” IEEE J. Quantum Electron. QE-19, 1467–1469 (1983).
[CrossRef]

De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode locked lasers,” IEEE J. Quantum Electron. QE-20, 533–539 (1984).
[CrossRef]

Kvantovaya Elektron. (1)

J.-C. Diels, J. J. Fontaine, I. C. McMichael, B. Wilhelmi, W. Dietel, D. Kuhlke, W. Rudolph, “Experimental and theoretical study of a femtosecond laser,” Kvantovaya Elektron. 10, 2398–2410 (1983);translation in Sov. J. Quantum Electron. 13, 1562–1569 (1983).

Opt. Commun. (3)

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, “Pulses in the femtosecond range from a cw dye ring laser in the colliding pulse mode-locking (CPM) regime with down-chirp,” Opt. Commun. 43, 433–436 (1982).
[CrossRef]

H. Haken, H. Ohno, “Theory of ultrashort pulses,” Opt. Commun. 16, 205–209 (1976).
[CrossRef]

W. Dietel, E. Dopel, K. Hehl, W. Rudolph, E. Schmidt, “Multilayer dielectric mirrors generate chirp in fs dye ring lasers,” Opt. Commun. 50, 179–183 (1984).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

J.-C. Diels, E. L. Hahn, “Carrier frequency distance dependence of a pulse propagating in a two level system,” Phys. Rev. A 8, 1084–1110 (1973).
[CrossRef]

Other (7)

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, B. Wilhelmi, “Control of profile and chirp of fs light pulses by propagating them through resonant and nonresonant optical media,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD3.

J.-C. Diels, J. J. Fontaine, F. Simoni, “Phase sensitive measurements of femtosecond laser pulses from a ring cavity,” in Proceedings of International Conference on Lasers 83 (STS, McLean, Va., 1985), pp. 348–355.

J.-C. Diels, W. Dietel, E. Dopel, J. J. Fontaine, I. C. McMichael, W. Rudolph, F. Simoni, R. Torti, H. Vanherzeele, B. Wilhelmi, “Colliding pulse femtosecond lasers and applications to the measurement of optical parameters,” in Ultrafast Phenomena IV, D. H. Auston, K. B. Eisenthal, eds. (Springer-Verlag, Berlin, 1984), pp. 30–34.
[CrossRef]

J.-C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. (to be published).

I. C. McMichael, J.-C. Diels, “Degenerate four wave mixing of femtosecond pulses in the saturable absorber of a ring dye laser,” in Digest of XIIIth International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1984), paper MDD2.

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,” presented at 3rd Conference on Ultrafast Phenomena in Spectroscopy, Minsk (1983);Izv. Akad. Nauk SSSR Ser. Fiz. 48, 480–491 (1984).

J. Herrman, B. Wilhelmi, in Laser für Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984), pp. 181–185.

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Figures (8)

Fig. 1
Fig. 1

Laser cavity. The focusing mirrors at the amplifier jet and at the absorber jet have radii of curvature of 5 cm (M1, M2) and 3 cm (M4, M5), respectively.

Fig. 2
Fig. 2

Variation of downchirp with intensity in the absorber jet. The variation in thickness of the intracavity compensating glass is taken as a measure of downchirp (squares). The intensity (in the absorber) is varied by moving the jet away from the focal spot. The pulse bandwidth is also indicated (circles).

Fig. 3
Fig. 3

Mirror dispersion. Above: The reflection coefficient [R(ω) = |r(ω)|2 and phase shift φ(ω) On reflection are plotted against normalized wavelength for a 19-λ/4 (solid line) and for a 18-λ/4 + λ/2 (dotted line) mirror structure. Below: Compensating glass thickness for the two sets of mirrors. The curves are calculated. The eight experimental data points are obtained by intracavity compensation.

Fig. 4
Fig. 4

Interferometric autocorrelation of a pulse with a nonlinear chirp. The thickness of intracavity glass is 7.7 mm, which is 1.3 mm less than the amount required for exact chirp compensation in this particular cavity alignment. The pulse duration is 150 fsec (FWHM), and its bandwidth is 3.2 nm (center wavelength: 619 nm). The far-extending region of interferences in the wings of the autocorrelation indicates that the pulse front and the pulse tail are coherent with each other.

Fig. 5
Fig. 5

Fitting of a downchirped pulse, through its interferometric autocorrelation (a) and spectrum (b). The best fit corresponds to an asymmetric downchirped pulse (solid line) of which the electric-field envelope is indicated in the figure. The best fit for a pulse envelope E(t) = sech t/τ is also indicated (dashed line). A change of 10% in any of the pulse parameters results in a noticeable modification of the interferometric autocorrelation. Both indicated pulse shapes provide an excellent fit for the intensity autocorrelation.

Fig. 6
Fig. 6

Instantaneous frequency versus time for a single passage through the absorber.

Fig. 7
Fig. 7

Calculated detuning versus optical thickness of the absorber.

Fig. 8
Fig. 8

Optimum dispersion calculated as a function of the optical thickness of the absorber.

Equations (18)

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E ( t ) = exp { [ 0.2 i ( t / τ ) ] 2 } / { exp [ 0.7 ( t / τ ) ] + exp [ 1.3 ( t / τ ) ] } ,
[ ( t + 1 T 2 + i ( ω ω 0 ) ] σ 12 = i μ 2 γ W E ,
W t = 2 i ( μ 12 σ 21 μ 21 σ 12 ) E W W e T 1 ,
σ 12 = i μ 12 2 γ T 2 { n = 0 ( T 2 ) n d n d t n [ E W ] } .
= 1 1 + i Δ ω T 2 ,
W t = β r W | E | 2 + β Re { E * [ n = 1 ( T 2 ) n n t n × ( W E ) ] } W W e T 1 ,
β = 1 2 | μ 12 | 2 T 2 .
E ( t ) = E 0 ( t ) α 2 [ 1 + 1 2 2 + T 2 d d t + β T 2 t d t Re ( 2 E 0 * E 0 t ) ] E 0 ( t ) + α T 2 2 t [ ( 1 ) T 2 t ] E 0 ( t ) .
( t ) = β r t d t | E 0 ( t ) | 2 ;
α = | μ 12 | 2 T 2 ω μ 0 W e × Δ z ,
θ = μ 12 2 d t E ( t ) < 1 .
m = q m 0 r b r a ,
H ( ω ω d ) = [ 1 + 2 i ( ω ω d ) Δ ] 1 .
( u d d t + υ d 2 d t 2 )
1 2 i r d 2 d t 2 .
r = 4 π 2 c L ω 3 d 2 n d λ 2 .
{ g ( t ) [ u + h + α a 2 T 2 a a ( 1 a ) α b T 2 b b 2 ( 1 m a ) ] d d t + [ υ 1 2 h 2 1 2 i r + α a ( a T 2 a ) 2 2 α b ( b T 2 b ) 2 2 ] } E ( t ) = 0 ,
g ( t ) = 1 2 ( α a α b γ ) + 1 2 a ( m α b α a ) 1 4 a 2 m 2 α b 1 2 α b T 2 b b d b d t α a T 2 a a d a d t 1 2 α b β b T 2 b t d t Re ( b 2 E * E t ) + 1 2 α a β a T 2 a t d t Re a 2 E * E t .

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