Abstract

We measured the space–time profile of ultrashort optical pulses shaped with a Fourier pulse shaper. Spatial chirp, which originated in the space–time coupling at the pulse shaper, was observed directly with two-dimensional spatial spectral interferometry. By analyzing the two-dimensional fringe pattern, we successfully obtained a spatial and a temporal distribution in both amplitude and phase for shaped pulses. Numerically predicted spatiotemporal patterns were compared with experimental results.

© 2002 Optical Society of America

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  1. A. M. Weiner, J. P. Heritage, and J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13, 300–302 (1988).
    [CrossRef] [PubMed]
  2. A. H. Zewail, “Femtochemistry: recent progress in studies of dynamics and control of reactions and their transition states,” J. Phys. Chem. 100, 12701–12724 (1996).
    [CrossRef]
  3. D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
    [CrossRef]
  4. C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
    [CrossRef]
  5. C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).
  6. J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, “Nouvelle méthode de mesure de la résponse impulsionnelle des fibres optiques,” Appl. Opt. 19, 3749–3755 (1980).
    [CrossRef] [PubMed]
  7. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based to-mography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  8. G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1–9 (2000).
    [CrossRef]
  9. D. Meshulach, D. Yelin, and Y. Silberberg, “Real-time spatial–spectral interference measurements of ultrashort optical pulses,” J. Opt. Soc. Am. B 14, 2095–2098 (1997).
    [CrossRef]
  10. T. Tanabe, N. Takei, H. Tanabe, and F. Kannari, “Simultaneous two-dimensional space and time measurement of ultrashort optical pulses based on spatial-spectral interferometry,” in Ultrafast Phenomena 2000, Vol. 43 of OSA Trend in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 188–190.
  11. T. Tanabe, N. Takei, H. Tanabe, Y. Teramura, and F. Kannari, “Measurement of Space and Time Profile of Shaped Ultrafast Optical Pulses using Spatial-Spectral Interfernce,” in Proceedings of 2000 CLEO Europe Nice, conference digest (Institute of Electrical and Electronics Engineers, New York, 2000), p. 137.
  12. L. Gallmann, G. Steinmeyer, D. H. Sutter, T. Rupp, C. Iaconis, A. Walmsley, and U. Keller, “Spatially resolved amplitude and phase characterization of femtosecond optical pulses,” Opt. Lett. 26, 96–98 (2001).
    [CrossRef]
  13. Y. Teramura and F. Kannari, “Spatial phase information transmission through an optical fiber by coherence function synthesis,” Appl. Opt. 40, 6466–6473 (2001).
    [CrossRef]
  14. A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
    [CrossRef]
  15. M. M. Wefers and K. A. Nelson, “Analysis of programmable ultrashort waveform generation using liquid-crystal spatial light modulators,” J. Opt. Soc. Am. B 12, 1343–1362 (1995).
    [CrossRef]
  16. L. Wang and A. M. Weiner, “Programmable spectral phase coding of an amplified spontaneous emission light source,” Opt. Commun. 167, 211–224 (1999).
    [CrossRef]
  17. H. Wang, Z. Zheng, D. E. Leaird, A. M. Weiner, T. A. Dorschner, J. J. Fijol, L. J. Friedman, H. Q. Nguyen, and L. A. Palmaccio, “20-fs pulse shaping with a 512-element phase-only liquid-crystal modulator,” in Ultrafast Phenomena 2000, Vol. 43 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 161–163.
  18. M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
    [CrossRef]
  19. H. Tanabe, K. Takasago, and F. Kannari, “The space-time coupling of Fourier synthesized femtosecond pulses and their applications,” in Proceedings of the Eleventh Annual Meeting LEOS (Institute of Electrical and Electronics Engineers, New York, 1998), Vol. 1, pp. 63–64.
  20. Y. Yasuno, Y. Suto, M. Mori, M. Itoh, and T. Yatagai, “Analysis of spatio-temporally coupled pulse-shaper by Wigner distribution function,” IEICE Trans. Electron. E83-C, 318–324 (2000).
  21. Y. Teramura, M. Suekuni, and F. Kannari, “Two-dimensional optical coherence tomography using spectral domain interferometry,” Pure Appl. Opt. 2, 21–26 (2000).
    [CrossRef]

2001 (2)

2000 (3)

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1–9 (2000).
[CrossRef]

Y. Yasuno, Y. Suto, M. Mori, M. Itoh, and T. Yatagai, “Analysis of spatio-temporally coupled pulse-shaper by Wigner distribution function,” IEICE Trans. Electron. E83-C, 318–324 (2000).

Y. Teramura, M. Suekuni, and F. Kannari, “Two-dimensional optical coherence tomography using spectral domain interferometry,” Pure Appl. Opt. 2, 21–26 (2000).
[CrossRef]

1999 (2)

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

L. Wang and A. M. Weiner, “Programmable spectral phase coding of an amplified spontaneous emission light source,” Opt. Commun. 167, 211–224 (1999).
[CrossRef]

1997 (1)

1996 (2)

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

A. H. Zewail, “Femtochemistry: recent progress in studies of dynamics and control of reactions and their transition states,” J. Phys. Chem. 100, 12701–12724 (1996).
[CrossRef]

1995 (1)

1993 (1)

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

1988 (2)

1982 (1)

1980 (1)

1973 (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

Arnaud, J. A.

Colombeau, B.

Froehly, C.

J. Piasecki, B. Colombeau, M. Vampouille, C. Froehly, and J. A. Arnaud, “Nouvelle méthode de mesure de la résponse impulsionnelle des fibres optiques,” Appl. Opt. 19, 3749–3755 (1980).
[CrossRef] [PubMed]

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

Gallmann, L.

Heritage, J. P.

Iaconis, C.

L. Gallmann, G. Steinmeyer, D. H. Sutter, T. Rupp, C. Iaconis, A. Walmsley, and U. Keller, “Spatially resolved amplitude and phase characterization of femtosecond optical pulses,” Opt. Lett. 26, 96–98 (2001).
[CrossRef]

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

Ina, H.

Itoh, M.

Y. Yasuno, Y. Suto, M. Mori, M. Itoh, and T. Yatagai, “Analysis of spatio-temporally coupled pulse-shaper by Wigner distribution function,” IEICE Trans. Electron. E83-C, 318–324 (2000).

Kane, D. J.

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

Kannari, F.

Y. Teramura and F. Kannari, “Spatial phase information transmission through an optical fiber by coherence function synthesis,” Appl. Opt. 40, 6466–6473 (2001).
[CrossRef]

Y. Teramura, M. Suekuni, and F. Kannari, “Two-dimensional optical coherence tomography using spectral domain interferometry,” Pure Appl. Opt. 2, 21–26 (2000).
[CrossRef]

Kasper, A.

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1–9 (2000).
[CrossRef]

Keller, U.

Kirschner, E. M.

Kobayashi, S.

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

Meshulach, D.

Mori, M.

Y. Yasuno, Y. Suto, M. Mori, M. Itoh, and T. Yatagai, “Analysis of spatio-temporally coupled pulse-shaper by Wigner distribution function,” IEICE Trans. Electron. E83-C, 318–324 (2000).

Nelson, K. A.

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

M. M. Wefers and K. A. Nelson, “Analysis of programmable ultrashort waveform generation using liquid-crystal spatial light modulators,” J. Opt. Soc. Am. B 12, 1343–1362 (1995).
[CrossRef]

Piasecki, J.

Pretzler, G.

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1–9 (2000).
[CrossRef]

Rupp, T.

Salehi, J. A.

Silberberg, Y.

Steinmeyer, G.

Suekuni, M.

Y. Teramura, M. Suekuni, and F. Kannari, “Two-dimensional optical coherence tomography using spectral domain interferometry,” Pure Appl. Opt. 2, 21–26 (2000).
[CrossRef]

Suto, Y.

Y. Yasuno, Y. Suto, M. Mori, M. Itoh, and T. Yatagai, “Analysis of spatio-temporally coupled pulse-shaper by Wigner distribution function,” IEICE Trans. Electron. E83-C, 318–324 (2000).

Sutter, D. H.

Takeda, M.

Teramura, Y.

Y. Teramura and F. Kannari, “Spatial phase information transmission through an optical fiber by coherence function synthesis,” Appl. Opt. 40, 6466–6473 (2001).
[CrossRef]

Y. Teramura, M. Suekuni, and F. Kannari, “Two-dimensional optical coherence tomography using spectral domain interferometry,” Pure Appl. Opt. 2, 21–26 (2000).
[CrossRef]

Trebino, R.

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

Vampouille, M.

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

Walmsley, A.

Walmsley, I. A.

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

Wang, L.

L. Wang and A. M. Weiner, “Programmable spectral phase coding of an amplified spontaneous emission light source,” Opt. Commun. 167, 211–224 (1999).
[CrossRef]

Wefers, M. M.

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

M. M. Wefers and K. A. Nelson, “Analysis of programmable ultrashort waveform generation using liquid-crystal spatial light modulators,” J. Opt. Soc. Am. B 12, 1343–1362 (1995).
[CrossRef]

Weiner, A. M.

Witte, K. J.

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1–9 (2000).
[CrossRef]

Yasuno, Y.

Y. Yasuno, Y. Suto, M. Mori, M. Itoh, and T. Yatagai, “Analysis of spatio-temporally coupled pulse-shaper by Wigner distribution function,” IEICE Trans. Electron. E83-C, 318–324 (2000).

Yatagai, T.

Y. Yasuno, Y. Suto, M. Mori, M. Itoh, and T. Yatagai, “Analysis of spatio-temporally coupled pulse-shaper by Wigner distribution function,” IEICE Trans. Electron. E83-C, 318–324 (2000).

Yelin, D.

Zewail, A. H.

A. H. Zewail, “Femtochemistry: recent progress in studies of dynamics and control of reactions and their transition states,” J. Phys. Chem. 100, 12701–12724 (1996).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

G. Pretzler, A. Kasper, and K. J. Witte, “Angular chirp and tilted light pulses in CPA lasers,” Appl. Phys. B 70, 1–9 (2000).
[CrossRef]

IEEE J. Quantum Electron. (3)

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

D. J. Kane and R. Trebino, “Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating,” IEEE J. Quantum Electron. 29, 571–579 (1993).
[CrossRef]

C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999).
[CrossRef]

IEICE Trans. Electron. (1)

Y. Yasuno, Y. Suto, M. Mori, M. Itoh, and T. Yatagai, “Analysis of spatio-temporally coupled pulse-shaper by Wigner distribution function,” IEICE Trans. Electron. E83-C, 318–324 (2000).

J. Opt. (Paris) (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils: experimental confirmations and applications,” J. Opt. (Paris) 4, 183–196 (1973).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (3)

J. Phys. Chem. (1)

A. H. Zewail, “Femtochemistry: recent progress in studies of dynamics and control of reactions and their transition states,” J. Phys. Chem. 100, 12701–12724 (1996).
[CrossRef]

Opt. Commun. (1)

L. Wang and A. M. Weiner, “Programmable spectral phase coding of an amplified spontaneous emission light source,” Opt. Commun. 167, 211–224 (1999).
[CrossRef]

Opt. Lett. (2)

Pure Appl. Opt. (1)

Y. Teramura, M. Suekuni, and F. Kannari, “Two-dimensional optical coherence tomography using spectral domain interferometry,” Pure Appl. Opt. 2, 21–26 (2000).
[CrossRef]

Other (4)

H. Wang, Z. Zheng, D. E. Leaird, A. M. Weiner, T. A. Dorschner, J. J. Fijol, L. J. Friedman, H. Q. Nguyen, and L. A. Palmaccio, “20-fs pulse shaping with a 512-element phase-only liquid-crystal modulator,” in Ultrafast Phenomena 2000, Vol. 43 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 161–163.

H. Tanabe, K. Takasago, and F. Kannari, “The space-time coupling of Fourier synthesized femtosecond pulses and their applications,” in Proceedings of the Eleventh Annual Meeting LEOS (Institute of Electrical and Electronics Engineers, New York, 1998), Vol. 1, pp. 63–64.

T. Tanabe, N. Takei, H. Tanabe, and F. Kannari, “Simultaneous two-dimensional space and time measurement of ultrashort optical pulses based on spatial-spectral interferometry,” in Ultrafast Phenomena 2000, Vol. 43 of OSA Trend in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 188–190.

T. Tanabe, N. Takei, H. Tanabe, Y. Teramura, and F. Kannari, “Measurement of Space and Time Profile of Shaped Ultrafast Optical Pulses using Spatial-Spectral Interfernce,” in Proceedings of 2000 CLEO Europe Nice, conference digest (Institute of Electrical and Electronics Engineers, New York, 2000), p. 137.

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Figures (8)

Fig. 1
Fig. 1

Experimental setup consisting of two parts: a pulse shaper and SSI apparatus.

Fig. 2
Fig. 2

Axis of coordinates and the arrangement of components in a 4f pulse shaper. The variables are described in the text.

Fig. 3
Fig. 3

Measured SSI fringe pattern of the pulse shaper with (a) no modulation, (b) discrete phase change of π at pixel 64, (c) second-order chirp, (d) third-order chirp added in the LC-SLM.

Fig. 4
Fig. 4

(a) Calculated spatiotemporal intensity distribution of a pulse shaped with an alternating phase-only mask. The measured spatiotemporal intensity distributions of the pulse shaped with the 4f pulse shaper is shown in (b) and (c). The shaping mask is an alternating phase-only mask. The (b) horizontal space–time xt distribution and the (c) vertical space–time yt distribution are measured, where x is the identical direction of the spectral dispersion at the grating in the pulse shaper and y is perpendicular to x.

Fig. 5
Fig. 5

Measured two-dimensional phase distribution of the alternating phase-only mask. The abrupt change in phase is successfully reconstructed as (0, π, 0, π, …).

Fig. 6
Fig. 6

(a) Calculated and (b) measured spatiotemporal intensity distributions of the pulse shaped with the 4f pulse shaper. The shaping mask is an M sequence mask with a symbol code length of seven (π, π, π, 0, π, 0, 0).

Fig. 7
Fig. 7

(a) Calculated spatiotemporal intensity distribution of a pulse shaped with the 4f pulse shaper, where the angle of the output grating differs slightly by 1° from that at the input. The shaping mask is an alternating phase-only mask. (b) The corresponding experimental result.

Fig. 8
Fig. 8

(a) Measured spatiotemporal intensity when the output grating differs slightly in its position. The alternating phase mask is used at the pulse shaper. (b) Spectral-phase distribution of the output pulse (x=0) from the pulse shaper at the grating position corresponding to that of (a). The dotted curve indicates the spectral phase with the ideal 4f setting. The null phase mask is used at the pulse shaper. (c) The measured spatiotemporal intensity when the output lens differs slightly in its position. The alternating phase mask is used at the pulse shaper. (d) Spatial phase distribution of the output pulse (t=0) at the lens positions corresponding to those of (c). The dotted curve indicates the spatial phase with the ideal 4f setting. The null phase mask is used at the pulse shaper.

Equations (22)

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x(ω)=f tanarcsin2πcdω-sin θi-θd(ω0).
E˜out(k, ω)=E˜in(-k, Ω)m-λ0f(γΩ+βk)2π,
γβ=λ0cd cos θi
E˜j(k, ω)=E˜i(k, ω)exp-i Lxλ0k24π.
Ej(x, ω)=1β Eixβ, ωexpi γβΩx.
E˜j(k, ω)=βE˜i(γΩ+βk, ω),
Ej(x, ω)=2πλ0f1/2E˜i2πxλ0f, ω.
E˜j(k, ω)=λ0f2π1/2Ei-λ0f2πk, ω.
E˜4(k, ω)=1β E˜in-kβ+γβΩ, Ωm-λ0f2πk.
E˜out(k, ω)=ββ E˜in-ββk+γβ-γβΩ, Ω×m-λ0f2π(γΩ+βk).
E˜2Δ(k, ω)=1βE˜inkβ+γβΩ, Ωexpi L1λ0k24π.
E3(x, ω)=2πβλ0f1/2E˜in2πβλ0fx+γβΩ, Ω×expi πx2L1λ0f2m(x).
E˜4(k, ω)=λ0f2πβ1/2E˜in-kβ+γβΩ, Ω×exp-i λ0(-L1+L4)4πk2m-λ0f2πk.
E˜out(k, ω)=E˜in(-k, Ω)m-λ0f(γΩ+βk)2π×exp-i λ0(-L1+L4)4π(γΩ+βk)2,
E3Δ(x, ω)=2πβλ0f1/2E˜in2πxβλ0f+γβΩ, Ω,
E˜3(k, ω)=βλ0f2π1/2Ein-βλ0f2πk, Ω×exp-iλ0fγΩ2πk-λL24πk2M(k),
Eout(x, ω)=Ein(-x, Ω)exp-iγβΩx-πL2β2λ0f2x2M2πβλ0fx×expiγβΩx-πL3β2λ0f2x2.
eout(x, t)=exp(iω0t)ein-(x-x), t+γβxexpi πL2β2λ0f2(x-x)2×M2πβλ0fxdxexp-i πL3β2λ0f2x2.
uref(r, t)=Eref(r)exp[i(kref·r+ϕref(r)-ωt)],
usig(r, t)=Esig(r)exp[i(ksig·r+ϕsig(r)-ωt)],
I(x, y)=|uref(x, y, t)+usig(x, y, t)|2=Eref2(xω, y)+Esig2(xω, y)+2Eref(xω, y)Esig(xω, y)cos{2ky sin θ+[ϕref(xω, y)-ϕsig(xω, y)]},
Δx=λ0f2πβΔξ,

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