Abstract

Measurements of intracavity dispersion in operating tunable, passively mode-locked, femtosecond lasers have been performed by use of a new frequency-domain dispersion (FDD) technique. The basis for these measurements is more fully developed, and the meaning of intracavity dispersion in an operating nonlinear system is discussed. We conclude that nonlinearity, although critically important in the mode-locking dynamics, contributes little to FDD measurements; therefore FDD is essentially a linear technique.

© 1993 Optical Society of America

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  1. G. W. ’tHooft, Philips Laboratory, Eindhoven, The Netherlands (personal communication, 1992).
  2. W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, “Interferometric measurements of femtosecond group delay in optical components,” Opt. Lett. 13, 574 (1988); K. D. Li, W. H. Knox, N. M. Pearson, “Broadband cubic-phase compensation with resonant Gires–Tournois interferometers,” Opt. Lett. 14, 450 (1989).
    [CrossRef] [PubMed]
  3. M. Beck, I. A. Walmsley, “Measurement of group delay with high temporal and spectral resolution,” Opt. Lett. 15, 492 (1990); M. Beck, I. A. Walmsley, J. D. Kafka, “Group delay measurements of optical components near 800 nm,” IEEE J. Quantum Electron. 27, 2074 (1991).
    [CrossRef] [PubMed]
  4. K. Naganuma, K. Mogi, H. Yamada, “Group-delay measurements using the Fourier transform of an interferometric cross-correlation generated by white light,” Opt. Lett. 15, 393 (1990).
    [CrossRef] [PubMed]
  5. W. H. Knox, “In situ measurement of complete intracavity dispersion in an operating Ti:sapphire femtosecond laser,” Opt. Lett. 27, 1 (1992).
  6. D. E. Spence, P. N. Kean, W. Sibbett, “60-fs pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 42 (1991).
    [CrossRef] [PubMed]
  7. N. Sarukura, Y. Ishida, N. Nakano, “Generation of 50-fs pulses from a pulse-compressed cw passively mode-locked Ti:sapphire laser,” Opt. Lett. 16, 153 (1991).
    [PubMed]
  8. H. A. Haus, J. G. Fujimoto, E. P. Ippen, “Structures for additive pulse modelocking,” J. Opt. Soc. Am. B 8, 2068 (1991); H. A. Haus, J. D. Moores, L. E. Nelson, “Effect of third-order dispersion on passive mode locking,” Opt. Lett. 18, 51 (1993).
    [CrossRef] [PubMed]
  9. C.-P. Huang, H. C. Kapteyn, J. W. MacIntosh, M. Murnane, “Generation of transform-limited 32-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 139 (1992); B. E. Lemoff, C. P. J. Barty, “Generation of high-peak-power 20-fs pulses from a regeneratively initiated, self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1367 (1992).
    [CrossRef] [PubMed]
  10. F. Krausz, C. Spielmann, T. Brabec, E. Wintner, A. J. Schmidt, “Generation of 33-fs optical pulses from a solid-state laser,” Opt. Lett. 17, 204 (1992); F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, Ch. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097 (1992).
    [CrossRef] [PubMed]
  11. J. M. Jacobsen, K. Naganuma, H. A. Haus, J. G. Fujimoto, A. G. Jacobsen, “Femtosecond pulse generation in a Ti:sapphire laser by using second- and third-order intracavity dispersion,” Opt. Lett. 17, 1608 (1992).
    [CrossRef]
  12. R. Proctor, F. Wise, “Quartz prism sequence for reduction of cubic phase in a mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1295 (1992).
    [CrossRef] [PubMed]
  13. M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. Nathel, H. C. Kapteyn, M. Murnane, “11 fs pulses from a modelocked Ti:sapphire laser,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), postdeadline paper PD-17.
  14. M. Born, E. Wolf, Principles of Optics (Pergamon Press, New York, 1975).
  15. J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrodinger equation,” J. Opt. Soc. Am. B 9, 91 (1992).
    [CrossRef]
  16. M. R. X. de Barros, R. S. Miranda, C. H. Brito-Cruz, “Third-order group velocity dispersion in a colliding-pulse mode-locked dye laser,” Opt. Lett. 15, 127 (1990).
    [CrossRef]
  17. J. Jacobsen, Massachusetts Institute of Technology, Cambridge, Mass. (personal communication, 1992).
  18. I. N. Duling, U.S. Naval Research Laboratory, Washington, D.C. (personal communication, 1992); Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C.1992), paper wu1.
  19. W. H. Knox, “The revolution in femtosecond near-infrared pulse generation,” Opt. Photon. News 3(5), 10 (1992).
    [CrossRef]

1992

W. H. Knox, “In situ measurement of complete intracavity dispersion in an operating Ti:sapphire femtosecond laser,” Opt. Lett. 27, 1 (1992).

W. H. Knox, “The revolution in femtosecond near-infrared pulse generation,” Opt. Photon. News 3(5), 10 (1992).
[CrossRef]

J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrodinger equation,” J. Opt. Soc. Am. B 9, 91 (1992).
[CrossRef]

C.-P. Huang, H. C. Kapteyn, J. W. MacIntosh, M. Murnane, “Generation of transform-limited 32-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 139 (1992); B. E. Lemoff, C. P. J. Barty, “Generation of high-peak-power 20-fs pulses from a regeneratively initiated, self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1367 (1992).
[CrossRef] [PubMed]

F. Krausz, C. Spielmann, T. Brabec, E. Wintner, A. J. Schmidt, “Generation of 33-fs optical pulses from a solid-state laser,” Opt. Lett. 17, 204 (1992); F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, Ch. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097 (1992).
[CrossRef] [PubMed]

R. Proctor, F. Wise, “Quartz prism sequence for reduction of cubic phase in a mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1295 (1992).
[CrossRef] [PubMed]

J. M. Jacobsen, K. Naganuma, H. A. Haus, J. G. Fujimoto, A. G. Jacobsen, “Femtosecond pulse generation in a Ti:sapphire laser by using second- and third-order intracavity dispersion,” Opt. Lett. 17, 1608 (1992).
[CrossRef]

1991

1990

1988

’tHooft, G. W.

G. W. ’tHooft, Philips Laboratory, Eindhoven, The Netherlands (personal communication, 1992).

Asaki, M. T.

M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. Nathel, H. C. Kapteyn, M. Murnane, “11 fs pulses from a modelocked Ti:sapphire laser,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), postdeadline paper PD-17.

Beck, M.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, New York, 1975).

Brabec, T.

Brito-Cruz, C. H.

de Barros, M. R. X.

Duling, I. N.

I. N. Duling, U.S. Naval Research Laboratory, Washington, D.C. (personal communication, 1992); Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C.1992), paper wu1.

Fujimoto, J. G.

Garvey, D.

M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. Nathel, H. C. Kapteyn, M. Murnane, “11 fs pulses from a modelocked Ti:sapphire laser,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), postdeadline paper PD-17.

Gordon, J. P.

Haus, H. A.

Hirlimann, C. A.

Huang, C.-P.

C.-P. Huang, H. C. Kapteyn, J. W. MacIntosh, M. Murnane, “Generation of transform-limited 32-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 139 (1992); B. E. Lemoff, C. P. J. Barty, “Generation of high-peak-power 20-fs pulses from a regeneratively initiated, self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1367 (1992).
[CrossRef] [PubMed]

M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. Nathel, H. C. Kapteyn, M. Murnane, “11 fs pulses from a modelocked Ti:sapphire laser,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), postdeadline paper PD-17.

Ippen, E. P.

Ishida, Y.

Jacobsen, A. G.

Jacobsen, J.

J. Jacobsen, Massachusetts Institute of Technology, Cambridge, Mass. (personal communication, 1992).

Jacobsen, J. M.

Kapteyn, H. C.

C.-P. Huang, H. C. Kapteyn, J. W. MacIntosh, M. Murnane, “Generation of transform-limited 32-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 139 (1992); B. E. Lemoff, C. P. J. Barty, “Generation of high-peak-power 20-fs pulses from a regeneratively initiated, self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1367 (1992).
[CrossRef] [PubMed]

M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. Nathel, H. C. Kapteyn, M. Murnane, “11 fs pulses from a modelocked Ti:sapphire laser,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), postdeadline paper PD-17.

Kean, P. N.

Knox, W. H.

W. H. Knox, “The revolution in femtosecond near-infrared pulse generation,” Opt. Photon. News 3(5), 10 (1992).
[CrossRef]

W. H. Knox, “In situ measurement of complete intracavity dispersion in an operating Ti:sapphire femtosecond laser,” Opt. Lett. 27, 1 (1992).

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, “Interferometric measurements of femtosecond group delay in optical components,” Opt. Lett. 13, 574 (1988); K. D. Li, W. H. Knox, N. M. Pearson, “Broadband cubic-phase compensation with resonant Gires–Tournois interferometers,” Opt. Lett. 14, 450 (1989).
[CrossRef] [PubMed]

Krausz, F.

Li, K. D.

MacIntosh, J. W.

Miranda, R. S.

Mogi, K.

Murnane, M.

C.-P. Huang, H. C. Kapteyn, J. W. MacIntosh, M. Murnane, “Generation of transform-limited 32-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 139 (1992); B. E. Lemoff, C. P. J. Barty, “Generation of high-peak-power 20-fs pulses from a regeneratively initiated, self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1367 (1992).
[CrossRef] [PubMed]

M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. Nathel, H. C. Kapteyn, M. Murnane, “11 fs pulses from a modelocked Ti:sapphire laser,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), postdeadline paper PD-17.

Naganuma, K.

Nakano, N.

Nathel, H.

M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. Nathel, H. C. Kapteyn, M. Murnane, “11 fs pulses from a modelocked Ti:sapphire laser,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), postdeadline paper PD-17.

Pearson, N. M.

Proctor, R.

Sarukura, N.

Schmidt, A. J.

Sibbett, W.

Spence, D. E.

Spielmann, C.

Walmsley, I. A.

Wintner, E.

Wise, F.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, New York, 1975).

Yamada, H.

Zhou, J.

M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. Nathel, H. C. Kapteyn, M. Murnane, “11 fs pulses from a modelocked Ti:sapphire laser,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), postdeadline paper PD-17.

J. Opt. Soc. Am. B

Opt. Lett.

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, “Interferometric measurements of femtosecond group delay in optical components,” Opt. Lett. 13, 574 (1988); K. D. Li, W. H. Knox, N. M. Pearson, “Broadband cubic-phase compensation with resonant Gires–Tournois interferometers,” Opt. Lett. 14, 450 (1989).
[CrossRef] [PubMed]

M. R. X. de Barros, R. S. Miranda, C. H. Brito-Cruz, “Third-order group velocity dispersion in a colliding-pulse mode-locked dye laser,” Opt. Lett. 15, 127 (1990).
[CrossRef]

K. Naganuma, K. Mogi, H. Yamada, “Group-delay measurements using the Fourier transform of an interferometric cross-correlation generated by white light,” Opt. Lett. 15, 393 (1990).
[CrossRef] [PubMed]

M. Beck, I. A. Walmsley, “Measurement of group delay with high temporal and spectral resolution,” Opt. Lett. 15, 492 (1990); M. Beck, I. A. Walmsley, J. D. Kafka, “Group delay measurements of optical components near 800 nm,” IEEE J. Quantum Electron. 27, 2074 (1991).
[CrossRef] [PubMed]

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

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

C.-P. Huang, H. C. Kapteyn, J. W. MacIntosh, M. Murnane, “Generation of transform-limited 32-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 139 (1992); B. E. Lemoff, C. P. J. Barty, “Generation of high-peak-power 20-fs pulses from a regeneratively initiated, self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1367 (1992).
[CrossRef] [PubMed]

F. Krausz, C. Spielmann, T. Brabec, E. Wintner, A. J. Schmidt, “Generation of 33-fs optical pulses from a solid-state laser,” Opt. Lett. 17, 204 (1992); F. Krausz, M. E. Fermann, T. Brabec, P. F. Curley, M. Hofer, M. H. Ober, Ch. Spielmann, E. Wintner, A. J. Schmidt, “Femtosecond solid state lasers,” IEEE J. Quantum Electron. 28, 2097 (1992).
[CrossRef] [PubMed]

R. Proctor, F. Wise, “Quartz prism sequence for reduction of cubic phase in a mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1295 (1992).
[CrossRef] [PubMed]

J. M. Jacobsen, K. Naganuma, H. A. Haus, J. G. Fujimoto, A. G. Jacobsen, “Femtosecond pulse generation in a Ti:sapphire laser by using second- and third-order intracavity dispersion,” Opt. Lett. 17, 1608 (1992).
[CrossRef]

W. H. Knox, “In situ measurement of complete intracavity dispersion in an operating Ti:sapphire femtosecond laser,” Opt. Lett. 27, 1 (1992).

Opt. Photon. News

W. H. Knox, “The revolution in femtosecond near-infrared pulse generation,” Opt. Photon. News 3(5), 10 (1992).
[CrossRef]

Other

G. W. ’tHooft, Philips Laboratory, Eindhoven, The Netherlands (personal communication, 1992).

M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. Nathel, H. C. Kapteyn, M. Murnane, “11 fs pulses from a modelocked Ti:sapphire laser,” in Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), postdeadline paper PD-17.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, New York, 1975).

J. Jacobsen, Massachusetts Institute of Technology, Cambridge, Mass. (personal communication, 1992).

I. N. Duling, U.S. Naval Research Laboratory, Washington, D.C. (personal communication, 1992); Annual Meeting, Vol. 23 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C.1992), paper wu1.

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Figures (12)

Fig. 1
Fig. 1

(a) Simple cavity consisting of two ideal parallel mirrors; (b) cavity containing a block of dispersive material; (c) approximation to a passively mode-locked laser system; (d) approximation to (c), containing a linear (intensity-dependent) dispersive medium and with an intensity-dependent refractive index.

Fig. 2
Fig. 2

Experimental setup for FDD measurements. A cw-pumped passive mode-locked Ti:sapphire laser is tuned by translating a slit by a stepper motor. The repetition rate is analyzed with a photodiode and a frequency counter, and the output spectrum is analyzed with a spectrometer/multichannel analyzer (OMA): GPIB, Computer interface bus.

Fig. 3
Fig. 3

(a) Raw frequency change data; (b) conversion to change in round-trip time.

Fig. 4
Fig. 4

(a) Measured group delay characteristic under typical conditions; (b) typical spectrum of laser operating at 825 nm; (c) the repetition rates of the individual spectral components (shifted down for clarity). Inset, the laser spectrum is dispersed with a diffraction grating, and individual frequency components are analyzed for repetition rate.

Fig. 5
Fig. 5

(a) Group delay for Coherent MIRA laser (laser B) with second-order least-squares polynomial fit; (b) individual components in the wavelength picture. In (c) the same data are plotted in the frequency picture, and (d) shows the two components in the frequency-domain picture.

Fig. 6
Fig. 6

(a) Cavity repetition rate changes for aperture open and slightly closed conditions. Inset shows the reduction of lasing bandwidth that corresponds to pulse lengthening on insertion of loss. (b) Time-domain version of the data, showing that round-trip time is effectively independent of intensity or pulse width over this range.

Fig. 7
Fig. 7

Linear propagation of a 100-fs pulse in a group delay characteristic similar to that of Fig. 5(a). After only two round trips, significant pulse broadening is observed. After 10 round trips, the pulse is tripled in width. The ringing is a result of the cubic phase contribution. In mode-locked operation, this broadening is counteracted by the nonlinearity.

Fig. 8
Fig. 8

(a) System dispersion for laser A for two prism positions. The upper and the lower dispersion limits of stability are shown. (b) Mode-locking stability diagram adapted from master equation model8 showing the appearance of a minimum negative dispersion required for mode locking but no maximum limit.

Fig. 9
Fig. 9

(a) Group delay in negative dispersion regime generating 100-fs pulses and after translating both prisms to introduce ~2 cm of additional SF-10 glass into the laser. A stable mode-locked pulse train is maintained, and the positive disper sion is shown. (b) Calculation for SF-10 prisms alone for similar conditions.

Fig. 10
Fig. 10

Intracavity spectroscopy of mirror (a) group delay of reference cavity and (b) group delay scan of the cavity with New port BD.2 mirror inserted; (c) difference.

Fig. 11
Fig. 11

Mean group delay for pulse as a function of pulse width in system containing cubic phase error for data in Fig. 5(a).

Fig. 12
Fig. 12

Thermal effects arising from change in pump power.

Equations (14)

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Φ ( ω ) = ( 2 ω / c ) { L + [ n ( ω ) 1 ] l } .
T = Φ ω = 2 c ( L l ) + 2 l ω [ n ( ω ) ω / c ] .
1 V g ω [ n ( ω ) ω c ] ,
T = 2 c ( L l ) + 2 l V g ,
D = ( / λ ) V g 1 ,
T λ = 2 l D .
T λ = 2 i l i D i .
Φ ( ω ) = T ( ω ) d ω .
Φ ( ω ) = α ( ω ω 0 ) 2 + β ( ω ω 0 ) 3 + .
T RT = T ( ω ) I ( ω ) d ω I ( ω ) d ω
n = n 0 + n 2 I ,
Φ nl = ( 2 ω / c ) ( n 2 I L ) .
Δ T nl = Φ nl ω = 2 c ( n 2 I L ) .
Δ T nl = 2 c λ 2 = 1 ν = 2.7 fs .

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