Abstract

The synthesis of arbitrarily shaped femtosecond pulses by spectral filtering in a temporally nondispersive grating apparatus is demonstrated. Spectral filtering is accomplished by utilizing spatially patterned masks to modify the amplitude and the phase of the optical frequency components that are spatially dispersed within the apparatus. We are able to pattern spectra over a large dynamic range (approaching 104) and with unprecedented resolution. We illustrate the power of this technique by synthesizing a number of femtosecond waveforms, including femtosecond tone bursts with terahertz repetition rates, picosecond square pulses with 100-fsec rise times, and highly complex pseudonoise bursts produced by spectral phase encoding.

© 1988 Optical Society of America

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  1. R. Skaug, J. F. Hjelmstad, Spread Spectrum in Communications (Peregrinus, London, 1985).
  2. J. Desbois, F. Gires, P. Tournois, “A new approach to picosecond laser pulse analysis, shaping and coding,” IEEE J. Quantum Electron. QE-9, 213 (1973).
    [CrossRef]
  3. J. Agostinelli, G. Harvey, T. Stone, C. Gabel, “Optical pulse shaping with a grating pair,” Appl. Opt. 18, 2500 (1979).
    [CrossRef] [PubMed]
  4. C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.
  5. J. P. Heritage, R. N. Thurston, W. J. Tomlinson, A. M. Weiner, R. H. Stolen, “Spectral windowing of frequency-modulated optical pulses in a grating compressor,” Appl. Phys. Lett. 47, 87 (1985).
    [CrossRef]
  6. J. P. Heritage, A. M. Weiner, R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609 (1985).
    [CrossRef] [PubMed]
  7. A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase coherent, picosecond optical square pulses,” Opt. Lett. 11, 153 (1986).
    [CrossRef]
  8. R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682 (1986).
    [CrossRef]
  9. M. Haner, W. S. Warren, “Generation of programmable, picosecond-resolution-shaped laser pulses by fiber-grating pulse compression,” Opt. Lett. 12, 398 (1987).
    [CrossRef] [PubMed]
  10. R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671 (1981).
    [CrossRef]
  11. J. A. Valdmanis, R. L. Fork, J. P. Gordon, “Generation of optical pulses as short as 27 femtoseconds directly from a laser balancing self-phase modulation, group-velocity dispersion, saturable absorption, and saturable gain,” Opt. Lett. 10, 131 (1985).
    [CrossRef] [PubMed]
  12. A. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619 (1987).
    [CrossRef]
  13. A. M. Weiner, J. P. Heritage, J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13, 300 (1988).
    [CrossRef] [PubMed]
  14. E. B. Treacy, “Optical pulse compression with diffracton gratings,” IEEE J. Quantum Electron. QE-5, 454 (1969).
    [CrossRef]
  15. A. M. Johnson, R. H. Stolen, W. M. Simpson, “80X single-stage compression of frequency doubled Nd:yttrium aluminum garnet laser pulses,” Appl. Phys. Lett. 44, 729 (1984).
    [CrossRef]
  16. O. E. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in 1.3–1.6μm region,” IEEE J. Quantum Electron. QE-23, 59 (1987).
    [CrossRef]
  17. J. P. Heritage, A. M. Weiner, O. E. Martinez, “Stabilized subpicosecond pulse compression due to multiple-order stimulated Raman scattering,” J. Opt. Soc. Am A 4(13), P69 (1987).
  18. M. Pessot, P. Maine, G. Mourou, “1000 times expansion/ compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419 (1987).
    [CrossRef]
  19. K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49, 236 (1986).
    [CrossRef]
  20. J. P. Heritage, A. M. Weiner, R. N. Thurston, “Fourier transform picosecond pulse shaping and spectral phase measurement in a grating pulse-compressor,” in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), pp. 33–37.
  21. J. E. Rothenberg, D. Grischkowsky, A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
    [CrossRef]
  22. A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  23. P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62, 374 (1987).
    [CrossRef]
  24. D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, “Dark pulse propagation in optical fibers,” Phys. Rev. Lett. 60, 29 (1988).
    [CrossRef]
  25. M. R. Schroeder, Number Theory in Science and Communication (Springer-Verlag, Berlin, 1986).
  26. Y.-X. Yan, E. B. Gamble, K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391 (1985).
    [CrossRef]
  27. K. A. Nelson, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (personal communication).
  28. The relations Bδt≃ 0.44 and δfT≃ 0.44 are derived assuming Gaussian line shapes for the power spectrum and for the finest achievable spectral feature, with B, δf, T,and δt all referring to FWHM intensity widths. If, instead, the power spectrum is rectangular, then Bδt≃ 0.886, and we obtain T/δt≃ 0.5B/δf= 0.5η.
  29. In Ref. 8 a slightly different complexity measure m was introduced, defined in terms of spatial factors, such as the laser spot size at the mask, and the physical width of the spatially dispersed spectrum. The complexity measure used here, η,is defined in Eq. (4) in terms of spectral features. The relationship is η= m/(ln 2)1/2.
  30. In the present setup, encoding and decoding masks are placed adjacent to each other; in a real CDMA system the two masks would be located apart from each other at separate pulse-shaping stations. As a result, the contrast between correctly and incorrectly addressed information will be somewhat different in a real system than in the present data. The difference arises because of scattering from the edges of individual pixels on the phase masks. In a real system, frequency components impinging upon the edges of pixels will be attenuated by scattering, and decoded pulses will have narrow holes in their frequency spectra. The primary effect of these holes is to diminish the intensity of decoded pulses. When an encoding and a matching decoding mask are adjacent, however, much of the scattering is eliminated. Under the present circumstances, with length 127 M sequences and with a resolving power η= 250, we calculate that the intensity of decoded pulses would be diminished by ≃50% in a real system. The contrast in second-harmonic intensity generated by correctly and incorrectly decoded pulses would be ≃67:1, as opposed to the ratio of ≃130:1 evident in Fig. 12. For the case of high resolving power (η/P≫ 1), the distinction discussed above disappears.
  31. E. P. Ippen, C. V. Shank, “Techniques for measurement,” in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, Berlin, 1977), pp. 85–88.

1988 (2)

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, “Dark pulse propagation in optical fibers,” Phys. Rev. Lett. 60, 29 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13, 300 (1988).
[CrossRef] [PubMed]

1987 (6)

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62, 374 (1987).
[CrossRef]

A. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619 (1987).
[CrossRef]

M. Haner, W. S. Warren, “Generation of programmable, picosecond-resolution-shaped laser pulses by fiber-grating pulse compression,” Opt. Lett. 12, 398 (1987).
[CrossRef] [PubMed]

O. E. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in 1.3–1.6μm region,” IEEE J. Quantum Electron. QE-23, 59 (1987).
[CrossRef]

J. P. Heritage, A. M. Weiner, O. E. Martinez, “Stabilized subpicosecond pulse compression due to multiple-order stimulated Raman scattering,” J. Opt. Soc. Am A 4(13), P69 (1987).

M. Pessot, P. Maine, G. Mourou, “1000 times expansion/ compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419 (1987).
[CrossRef]

1986 (3)

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase coherent, picosecond optical square pulses,” Opt. Lett. 11, 153 (1986).
[CrossRef]

1985 (4)

J. A. Valdmanis, R. L. Fork, J. P. Gordon, “Generation of optical pulses as short as 27 femtoseconds directly from a laser balancing self-phase modulation, group-velocity dispersion, saturable absorption, and saturable gain,” Opt. Lett. 10, 131 (1985).
[CrossRef] [PubMed]

J. P. Heritage, A. M. Weiner, R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609 (1985).
[CrossRef] [PubMed]

Y.-X. Yan, E. B. Gamble, K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391 (1985).
[CrossRef]

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

1984 (2)

J. E. Rothenberg, D. Grischkowsky, A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

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

1981 (1)

R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

1979 (1)

1973 (2)

J. Desbois, F. Gires, P. Tournois, “A new approach to picosecond laser pulse analysis, shaping and coding,” IEEE J. Quantum Electron. QE-9, 213 (1973).
[CrossRef]

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

1969 (1)

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

Agostinelli, J.

Balant, A. C.

J. E. Rothenberg, D. Grischkowsky, A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

Barthelemy, A.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62, 374 (1987).
[CrossRef]

Colombeau, B.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

Desbois, J.

J. Desbois, F. Gires, P. Tournois, “A new approach to picosecond laser pulse analysis, shaping and coding,” IEEE J. Quantum Electron. QE-9, 213 (1973).
[CrossRef]

Emplit, P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62, 374 (1987).
[CrossRef]

Fork, R. L.

Froehly, C.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62, 374 (1987).
[CrossRef]

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

Gabel, C.

Gamble, E. B.

Y.-X. Yan, E. B. Gamble, K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391 (1985).
[CrossRef]

Gires, F.

J. Desbois, F. Gires, P. Tournois, “A new approach to picosecond laser pulse analysis, shaping and coding,” IEEE J. Quantum Electron. QE-9, 213 (1973).
[CrossRef]

Giuliani, G.

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, “Dark pulse propagation in optical fibers,” Phys. Rev. Lett. 60, 29 (1988).
[CrossRef]

Gordon, J. P.

Greene, B. I.

R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Grischkowsky, D.

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, “Dark pulse propagation in optical fibers,” Phys. Rev. Lett. 60, 29 (1988).
[CrossRef]

J. E. Rothenberg, D. Grischkowsky, A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

Halas, N. J.

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, “Dark pulse propagation in optical fibers,” Phys. Rev. Lett. 60, 29 (1988).
[CrossRef]

Hamaide, J. P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62, 374 (1987).
[CrossRef]

Haner, M.

Harvey, G.

Hasegawa, A.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Heritage, J. P.

A. M. Weiner, J. P. Heritage, J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13, 300 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619 (1987).
[CrossRef]

J. P. Heritage, A. M. Weiner, O. E. Martinez, “Stabilized subpicosecond pulse compression due to multiple-order stimulated Raman scattering,” J. Opt. Soc. Am A 4(13), P69 (1987).

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase coherent, picosecond optical square pulses,” Opt. Lett. 11, 153 (1986).
[CrossRef]

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

J. P. Heritage, A. M. Weiner, R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609 (1985).
[CrossRef] [PubMed]

J. P. Heritage, A. M. Weiner, R. N. Thurston, “Fourier transform picosecond pulse shaping and spectral phase measurement in a grating pulse-compressor,” in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), pp. 33–37.

Hjelmstad, J. F.

R. Skaug, J. F. Hjelmstad, Spread Spectrum in Communications (Peregrinus, London, 1985).

Ippen, E. P.

E. P. Ippen, C. V. Shank, “Techniques for measurement,” in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, Berlin, 1977), pp. 85–88.

Jewell, J. L.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Johnson, A. M.

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

Krokel, D.

D. Krokel, N. J. Halas, G. Giuliani, D. Grischkowsky, “Dark pulse propagation in optical fibers,” Phys. Rev. Lett. 60, 29 (1988).
[CrossRef]

Maine, P.

M. Pessot, P. Maine, G. Mourou, “1000 times expansion/ compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419 (1987).
[CrossRef]

Martinez, O. E.

O. E. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in 1.3–1.6μm region,” IEEE J. Quantum Electron. QE-23, 59 (1987).
[CrossRef]

J. P. Heritage, A. M. Weiner, O. E. Martinez, “Stabilized subpicosecond pulse compression due to multiple-order stimulated Raman scattering,” J. Opt. Soc. Am A 4(13), P69 (1987).

Mourou, G.

M. Pessot, P. Maine, G. Mourou, “1000 times expansion/ compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419 (1987).
[CrossRef]

Nelson, K. A.

Y.-X. Yan, E. B. Gamble, K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391 (1985).
[CrossRef]

K. A. Nelson, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (personal communication).

Pessot, M.

M. Pessot, P. Maine, G. Mourou, “1000 times expansion/ compression of optical pulses for chirped pulse amplification,” Opt. Commun. 62, 419 (1987).
[CrossRef]

Reynaud, F.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62, 374 (1987).
[CrossRef]

Rothenberg, J. E.

J. E. Rothenberg, D. Grischkowsky, A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

Salehi, J. A.

Schroeder, M. R.

M. R. Schroeder, Number Theory in Science and Communication (Springer-Verlag, Berlin, 1986).

Shank, C. V.

R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

E. P. Ippen, C. V. Shank, “Techniques for measurement,” in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, Berlin, 1977), pp. 85–88.

Simpson, W. M.

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

Skaug, R.

R. Skaug, J. F. Hjelmstad, Spread Spectrum in Communications (Peregrinus, London, 1985).

Stolen, R. H.

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

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

Stone, T.

Tai, K.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Tappert, F.

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Thurston, R. N.

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase coherent, picosecond optical square pulses,” Opt. Lett. 11, 153 (1986).
[CrossRef]

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

J. P. Heritage, A. M. Weiner, R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609 (1985).
[CrossRef] [PubMed]

J. P. Heritage, A. M. Weiner, R. N. Thurston, “Fourier transform picosecond pulse shaping and spectral phase measurement in a grating pulse-compressor,” in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), pp. 33–37.

Tomita, A.

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Tomlinson, W. J.

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

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

Tournois, P.

J. Desbois, F. Gires, P. Tournois, “A new approach to picosecond laser pulse analysis, shaping and coding,” IEEE J. Quantum Electron. QE-9, 213 (1973).
[CrossRef]

Treacy, E. B.

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

Valdmanis, J. A.

Vampouille, M.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

Warren, W. S.

Weiner, A. M.

A. M. Weiner, J. P. Heritage, J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13, 300 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619 (1987).
[CrossRef]

J. P. Heritage, A. M. Weiner, O. E. Martinez, “Stabilized subpicosecond pulse compression due to multiple-order stimulated Raman scattering,” J. Opt. Soc. Am A 4(13), P69 (1987).

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase coherent, picosecond optical square pulses,” Opt. Lett. 11, 153 (1986).
[CrossRef]

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

J. P. Heritage, A. M. Weiner, R. N. Thurston, “Picosecond pulse shaping by spectral phase and amplitude manipulation,” Opt. Lett. 10, 609 (1985).
[CrossRef] [PubMed]

J. P. Heritage, A. M. Weiner, R. N. Thurston, “Fourier transform picosecond pulse shaping and spectral phase measurement in a grating pulse-compressor,” in Ultrafast Phenomena V, G. R. Fleming, A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), pp. 33–37.

Yan, Y.-X.

Y.-X. Yan, E. B. Gamble, K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391 (1985).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

R. L. Fork, B. I. Greene, C. V. Shank, “Generation of optical pulses shorter than 0.1 psec by colliding pulse mode-locking,” Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

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

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

K. Tai, A. Tomita, J. L. Jewell, A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

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The relations Bδt≃ 0.44 and δfT≃ 0.44 are derived assuming Gaussian line shapes for the power spectrum and for the finest achievable spectral feature, with B, δf, T,and δt all referring to FWHM intensity widths. If, instead, the power spectrum is rectangular, then Bδt≃ 0.886, and we obtain T/δt≃ 0.5B/δf= 0.5η.

In Ref. 8 a slightly different complexity measure m was introduced, defined in terms of spatial factors, such as the laser spot size at the mask, and the physical width of the spatially dispersed spectrum. The complexity measure used here, η,is defined in Eq. (4) in terms of spectral features. The relationship is η= m/(ln 2)1/2.

In the present setup, encoding and decoding masks are placed adjacent to each other; in a real CDMA system the two masks would be located apart from each other at separate pulse-shaping stations. As a result, the contrast between correctly and incorrectly addressed information will be somewhat different in a real system than in the present data. The difference arises because of scattering from the edges of individual pixels on the phase masks. In a real system, frequency components impinging upon the edges of pixels will be attenuated by scattering, and decoded pulses will have narrow holes in their frequency spectra. The primary effect of these holes is to diminish the intensity of decoded pulses. When an encoding and a matching decoding mask are adjacent, however, much of the scattering is eliminated. Under the present circumstances, with length 127 M sequences and with a resolving power η= 250, we calculate that the intensity of decoded pulses would be diminished by ≃50% in a real system. The contrast in second-harmonic intensity generated by correctly and incorrectly decoded pulses would be ≃67:1, as opposed to the ratio of ≃130:1 evident in Fig. 12. For the case of high resolving power (η/P≫ 1), the distinction discussed above disappears.

E. P. Ippen, C. V. Shank, “Techniques for measurement,” in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, Berlin, 1977), pp. 85–88.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

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