Abstract

It is shown that the fiber and grating-pair pulse-compression technique is limited by higher-order terms in the response of the grating-pair compressor and that these terms also limit the usefulness of the compressor for canceling the effects of group-velocity dispersion on the propagation of ultrashort optical pulses. Numerical evaluations of these limits are in good agreement with the minimum experimentally observed compressed pulse width of 8 fsec. Approaches for achieving shorter pulses are discussed.

© 1987 Optical Society of America

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References

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  1. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
    [CrossRef]
  2. W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. B 1, 139–149 (1984).
    [CrossRef]
  3. J. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 44, 832–834 (1984).
    [CrossRef]
  4. J.-M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
    [CrossRef]
  5. W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
    [CrossRef]
  6. A preliminary report on this work was presented at the 1985 Annual Meeting of the Optical Society of America: W. H. Knox, R. H. Stolen, and W. J. Tomlinson, “Optics with pulses of a few cycles duration,” J. Opt. Soc. Am. A 2(13), P43 (1985).
  7. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
    [CrossRef] [PubMed]
  8. D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
    [CrossRef]
  9. J. P. Heritage, R. N. Thurston, W. J. Tomlinson, and A. M. Weiner, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
    [CrossRef]
  10. E. Bourkoff, R. I. Joseph, W. Zhao, and D. N. Christodoulides, “Analysis of femtosecond pulse compression,” J. Opt. Soc. Am. A 3(13), P90 (1986).
  11. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
    [CrossRef]
  12. I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
    [CrossRef]
  13. S. D. Brorson and H. A. Haus, “Geometrical limitations in grating pair pulse compression,” J. Opt. Soc. Am. B (to be published).
  14. R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150–152 (1984).
    [CrossRef] [PubMed]
  15. A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond time-resolved reflectometry measurements of multiple-layer dielectric mirrors,” Opt. Lett. 10, 71–73 (1985).
    [CrossRef] [PubMed]
  16. J. Kuhl and J. Heppner, “Compression of femtosecond optical pulses with dielectric multilayer interferometers,” IEEE J. Quantum Electron. QE-22, 182–185 (1986).
    [CrossRef]
  17. D. N. Christodoulides, E. Bourkoff, R. I. Joseph, and T. Simos, “Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors—analysis,” IEEE J. Quantum Electron. QE-22, 186–191 (1986).
    [CrossRef]
  18. A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:yttrium aluminum garnet laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
    [CrossRef]
  19. W. H. Knox, M. C. Downer, R. L. Fork, and C. V. Shank, “Amplified femtosecond optical pulses and continuum generation at 5-kHz repetition rate,” Opt. Lett. 9, 552–554 (1984).
    [CrossRef] [PubMed]
  20. Since the submission of this paper, compressed pulses with widths of 6 fsec have been obtained by using prisms in the compressor to compensate for the cubic term in the grating response: R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to 6 fs using cubic phase competition,” Opt. Lett. 12, 483 (1987)
    [CrossRef] [PubMed]

1987 (1)

1986 (4)

E. Bourkoff, R. I. Joseph, W. Zhao, and D. N. Christodoulides, “Analysis of femtosecond pulse compression,” J. Opt. Soc. Am. A 3(13), P90 (1986).

I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[CrossRef]

J. Kuhl and J. Heppner, “Compression of femtosecond optical pulses with dielectric multilayer interferometers,” IEEE J. Quantum Electron. QE-22, 182–185 (1986).
[CrossRef]

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, and T. Simos, “Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors—analysis,” IEEE J. Quantum Electron. QE-22, 186–191 (1986).
[CrossRef]

1985 (5)

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

A preliminary report on this work was presented at the 1985 Annual Meeting of the Optical Society of America: W. H. Knox, R. H. Stolen, and W. J. Tomlinson, “Optics with pulses of a few cycles duration,” J. Opt. Soc. Am. A 2(13), P43 (1985).

W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
[CrossRef] [PubMed]

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, and A. M. Weiner, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[CrossRef]

A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond time-resolved reflectometry measurements of multiple-layer dielectric mirrors,” Opt. Lett. 10, 71–73 (1985).
[CrossRef] [PubMed]

1984 (6)

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. B 1, 139–149 (1984).
[CrossRef]

J. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

J.-M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:yttrium aluminum garnet laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

W. H. Knox, M. C. Downer, R. L. Fork, and C. V. Shank, “Amplified femtosecond optical pulses and continuum generation at 5-kHz repetition rate,” Opt. Lett. 9, 552–554 (1984).
[CrossRef] [PubMed]

R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150–152 (1984).
[CrossRef] [PubMed]

1982 (2)

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

1969 (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Balant, A. C.

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

Becker, P. C.

Bourkoff, E.

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, and T. Simos, “Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors—analysis,” IEEE J. Quantum Electron. QE-22, 186–191 (1986).
[CrossRef]

E. Bourkoff, R. I. Joseph, W. Zhao, and D. N. Christodoulides, “Analysis of femtosecond pulse compression,” J. Opt. Soc. Am. A 3(13), P90 (1986).

Brito-Cruz, C. H.

Brorson, S. D.

S. D. Brorson and H. A. Haus, “Geometrical limitations in grating pair pulse compression,” J. Opt. Soc. Am. B (to be published).

Christodoulides, D. N.

E. Bourkoff, R. I. Joseph, W. Zhao, and D. N. Christodoulides, “Analysis of femtosecond pulse compression,” J. Opt. Soc. Am. A 3(13), P90 (1986).

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, and T. Simos, “Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors—analysis,” IEEE J. Quantum Electron. QE-22, 186–191 (1986).
[CrossRef]

Christov, I. P.

I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[CrossRef]

Downer, M. C.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

W. H. Knox, M. C. Downer, R. L. Fork, and C. V. Shank, “Amplified femtosecond optical pulses and continuum generation at 5-kHz repetition rate,” Opt. Lett. 9, 552–554 (1984).
[CrossRef] [PubMed]

Fork, R. L.

Fujimoto, J. G.

A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond time-resolved reflectometry measurements of multiple-layer dielectric mirrors,” Opt. Lett. 10, 71–73 (1985).
[CrossRef] [PubMed]

J. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

Gordon, J. P.

Grischkowsky, D.

J.-M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

Halbout, J.-M.

J.-M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

Haus, H. A.

S. D. Brorson and H. A. Haus, “Geometrical limitations in grating pair pulse compression,” J. Opt. Soc. Am. B (to be published).

Heppner, J.

J. Kuhl and J. Heppner, “Compression of femtosecond optical pulses with dielectric multilayer interferometers,” IEEE J. Quantum Electron. QE-22, 182–185 (1986).
[CrossRef]

Heritage, J. P.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, and A. M. Weiner, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[CrossRef]

Ippen, E. P.

A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond time-resolved reflectometry measurements of multiple-layer dielectric mirrors,” Opt. Lett. 10, 71–73 (1985).
[CrossRef] [PubMed]

J. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

Johnson, A. M.

W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
[CrossRef] [PubMed]

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:yttrium aluminum garnet laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

Joseph, R. I.

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, and T. Simos, “Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors—analysis,” IEEE J. Quantum Electron. QE-22, 186–191 (1986).
[CrossRef]

E. Bourkoff, R. I. Joseph, W. Zhao, and D. N. Christodoulides, “Analysis of femtosecond pulse compression,” J. Opt. Soc. Am. A 3(13), P90 (1986).

Knox, W. H.

A preliminary report on this work was presented at the 1985 Annual Meeting of the Optical Society of America: W. H. Knox, R. H. Stolen, and W. J. Tomlinson, “Optics with pulses of a few cycles duration,” J. Opt. Soc. Am. A 2(13), P43 (1985).

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

W. H. Knox, M. C. Downer, R. L. Fork, and C. V. Shank, “Amplified femtosecond optical pulses and continuum generation at 5-kHz repetition rate,” Opt. Lett. 9, 552–554 (1984).
[CrossRef] [PubMed]

Kuhl, J.

J. Kuhl and J. Heppner, “Compression of femtosecond optical pulses with dielectric multilayer interferometers,” IEEE J. Quantum Electron. QE-22, 182–185 (1986).
[CrossRef]

Martinez, O. E.

Shank, C. V.

Since the submission of this paper, compressed pulses with widths of 6 fsec have been obtained by using prisms in the compressor to compensate for the cubic term in the grating response: R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to 6 fs using cubic phase competition,” Opt. Lett. 12, 483 (1987)
[CrossRef] [PubMed]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. B 1, 139–149 (1984).
[CrossRef]

W. H. Knox, M. C. Downer, R. L. Fork, and C. V. Shank, “Amplified femtosecond optical pulses and continuum generation at 5-kHz repetition rate,” Opt. Lett. 9, 552–554 (1984).
[CrossRef] [PubMed]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Simos, T.

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, and T. Simos, “Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors—analysis,” IEEE J. Quantum Electron. QE-22, 186–191 (1986).
[CrossRef]

Simpson, W. M.

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:yttrium aluminum garnet laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

Stolen, R. H.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
[CrossRef] [PubMed]

A preliminary report on this work was presented at the 1985 Annual Meeting of the Optical Society of America: W. H. Knox, R. H. Stolen, and W. J. Tomlinson, “Optics with pulses of a few cycles duration,” J. Opt. Soc. Am. A 2(13), P43 (1985).

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. B 1, 139–149 (1984).
[CrossRef]

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:yttrium aluminum garnet laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Thurston, R. N.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, and A. M. Weiner, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[CrossRef]

Tomlinson, W. J.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, and A. M. Weiner, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[CrossRef]

A preliminary report on this work was presented at the 1985 Annual Meeting of the Optical Society of America: W. H. Knox, R. H. Stolen, and W. J. Tomlinson, “Optics with pulses of a few cycles duration,” J. Opt. Soc. Am. A 2(13), P43 (1985).

W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
[CrossRef] [PubMed]

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. B 1, 139–149 (1984).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Tomov, I. V.

I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[CrossRef]

Treacy, E. B.

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Valdmanis, J. A.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

Weiner, A. M.

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, and A. M. Weiner, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[CrossRef]

A. M. Weiner, J. G. Fujimoto, and E. P. Ippen, “Femtosecond time-resolved reflectometry measurements of multiple-layer dielectric mirrors,” Opt. Lett. 10, 71–73 (1985).
[CrossRef] [PubMed]

J. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

Yen, R.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Zhao, W.

E. Bourkoff, R. I. Joseph, W. Zhao, and D. N. Christodoulides, “Analysis of femtosecond pulse compression,” J. Opt. Soc. Am. A 3(13), P90 (1986).

Appl. Phys. Lett. (7)

J. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 44, 832–834 (1984).
[CrossRef]

J.-M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

J. P. Heritage, R. N. Thurston, W. J. Tomlinson, and A. M. Weiner, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87–89 (1985).
[CrossRef]

A. M. Johnson, R. H. Stolen, and W. M. Simpson, “80× single-stage compression of frequency doubled Nd:yttrium aluminum garnet laser pulses,” Appl. Phys. Lett. 44, 729–731 (1984).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. Kuhl and J. Heppner, “Compression of femtosecond optical pulses with dielectric multilayer interferometers,” IEEE J. Quantum Electron. QE-22, 182–185 (1986).
[CrossRef]

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, and T. Simos, “Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors—analysis,” IEEE J. Quantum Electron. QE-22, 186–191 (1986).
[CrossRef]

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

J. Opt. Soc. Am. A (2)

E. Bourkoff, R. I. Joseph, W. Zhao, and D. N. Christodoulides, “Analysis of femtosecond pulse compression,” J. Opt. Soc. Am. A 3(13), P90 (1986).

A preliminary report on this work was presented at the 1985 Annual Meeting of the Optical Society of America: W. H. Knox, R. H. Stolen, and W. J. Tomlinson, “Optics with pulses of a few cycles duration,” J. Opt. Soc. Am. A 2(13), P43 (1985).

J. Opt. Soc. B (1)

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. B 1, 139–149 (1984).
[CrossRef]

Opt. Commun. (1)

I. P. Christov and I. V. Tomov, “Large bandwidth pulse compression with diffraction gratings,” Opt. Commun. 58, 338–342 (1986).
[CrossRef]

Opt. Lett. (5)

Other (1)

S. D. Brorson and H. A. Haus, “Geometrical limitations in grating pair pulse compression,” J. Opt. Soc. Am. B (to be published).

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Figures (5)

Fig. 1
Fig. 1

(a) Calculated spectra for normalized input-pulse amplitudes of A = 3, 5, 7, 10. The other parameters, chosen to match the experiments described in Ref. 5, were a fiber length of z/z0 = 0.5, an input-pulse-width parameter t0 = 40/1.76 fsec, and a center wavelength of 620 nm. (b) Experimental spectrum, from Ref. 5, for the conditions that gave an 8-fsec compressed pulse.

Fig. 2
Fig. 2

(a) Calculated uncompressed temporal pulse shape for a normalized input-pulse amplitude A = 7 and a fiber length z/z0 = 0.5. (b) Instantaneous frequency as a function of time for the pulse in (a). (For consistency with earlier publications,2,7 the negative of the instantaneous frequency is plotted.)

Fig. 3
Fig. 3

Calculated compressed pulses and their autocorrelations for an input-pulse amplitude A = 7 and a fiber length z/z0 = 0.5 for various compressors. The top of the figure gives the actual temporal shapes of the pulses, and the bottom shows their autocorrelations. The intensity variable is |u/A|2, and the autocorrelations are all normalized to a peak intensity of unity.

Fig. 4
Fig. 4

Calculated compressed-pulse autocorrelation widths, as a function of the amplitude of the input pulse, for various compressors. The data are for a fiber length of z/z0 = 0.5.

Fig. 5
Fig. 5

Calculated and experimental autocorrelations of compressed pulses. a, b, Calculated results for a real compressor (β0 = 2) for A = 7 and A = 10, respectively. c, Experimental result from Ref. 5. d, Experimental result for the same conditions as for c, except that the amplitude of the input pulse was about a factor of 1.4 higher (an intensity a factor of 2 higher).

Tables (1)

Tables Icon

Table 1 Results of Calculations for Various Input Pulse Amplitudes and Compressorsa

Equations (11)

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u ( z / z 0 ) = + i π 4 [ 2 u ( t / t 0 ) 2 - 2 u 2 u ] ,
ψ c ( ω ) = - a c ( ω - ω 0 ) 2 .
ψ c ( ω ) = - a c ( ω - ω 0 ) 2 [ 1 - β c ( ω - ω 0 ) ω 0 ] .
β c = [ 1 - sin ( γ ) sin ( γ ) ] / cos 2 ( γ ) ,
ψ m ( ω ) = + a m ( ω - ω 0 ) 2 [ 1 + β m ( ω - ω 0 ) ω 0 ] ,
ψ c ( ω ) = - a 0 ( ω - ω 0 ) 2 [ 1 - β 0 ( ω - ω 0 ) ω 0 ] ,
β 0 = ( 1 + a m / a 0 ) β c + ( a m / a 0 ) β m .
z 0 = 0.322 π 2 c 2 τ 0 2 D ( λ ) λ
A = P / P 1 ,
P 1 = n c λ A eff 16 π z 0 n 2 × 10 - 7 W ,
a c = b λ 3 4 π c 2 d 2 cos 2 γ .

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