Abstract

A new spectral shearing interferometry technique for ultra-short pulse characterization is demonstrated. The method makes use of a spectral shear that varies across the test pulse beam profile to generate a two-dimensional interferogram that allows simultaneous reference phase measurement and pulse-field reconstruction from a single data set. The method uses a new configuration for upconversion of a single (non-spatially chirped) test pulse with two spatially chirped ancillary pulses in a medium with a highly asymmetric phase matching function. This technique is particularly suited for spectral regions where second harmonic is much easier detectable that the fundamental wavelength, such as telecom band around 1.5 μm, since all the data are available from the measurement at the upconverted wavelength. The high degree of redundancy in the two-dimensional interferogram provides a built-in check of the consistency of the reconstruction.

© 2007 Optical Society of America

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  1. C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort pulses," Opt. Lett. 23, 792 (1998).
    [CrossRef]
  2. R. Trebino and D. J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating," J. Opt. Soc. Am. A 10, 1101 (1993).
    [CrossRef]
  3. V. Wong and I. A. Walmsley, "Analysis of ultrashort pulse-shape measurement using linear interferometers," Opt. Lett.,  19, 287 (1994).
    [CrossRef] [PubMed]
  4. C. Iaconis, V. Wong, and I. A. Walmsley, "Direct interferometric techniques for characterizing ultrashort optical pulses," IEEE J. Select. Topics Quantum Electron.,  4, 1 (1998).
    [CrossRef]
  5. C. Dorrer and I. A. Walmsley, "Concept for the temporal characterization of short optical pulses," J. App. Sig. Proc. 10, 1541-1553 (2005).
  6. P. Kockaert,M. Haelterman, Ph. Emplit, and C. Froehly, "Complete characterisation of (ultra)short optical pulses using fast linear detectors," IEEE J. Select. Topics Quantum Electron. 10, 206-212 (2004).
    [CrossRef]
  7. M. Lelek, F. Louradour, A. Barthelemy, and C. Froehly, "Time resolved spectral interferometry for single shot femtosecond characterization," Opt. Commun. 261, 124-129 (2006).
    [CrossRef]
  8. I. Kang, C. Dorrer, and F. Quochi, "Implementation of electro-optic spectral shearing interferometry for ultrashort pulse characterization," Opt. Lett. 28, 2264-2266 (2003).
    [CrossRef] [PubMed]
  9. E.M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, "Interferometric technique for measuring broadband ultrashort pulses at the sampling limit," Opt. Lett. 30, 326-328 (2005).
    [CrossRef] [PubMed]
  10. A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, "Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 31, 1914 (2006).
    [CrossRef] [PubMed]
  11. J. R. Birge, R. Ell, and F. X. K artner, "Two-dimensional spectral shearing interferometry for few-cycle pulse characterization," Opt. Lett. 31, 2063 (2006).
    [CrossRef] [PubMed]
  12. C. Iaconis and I. A. Walmsley, "Self-referencing spectral interferometry for measuring ultrashort optical pulses," IEEE J. Quantum Electron. 35, 501-509 (1999).
    [CrossRef]
  13. P. Baum, S. Lochbrunner, and E. Riedle, "Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses," Opt. Lett. 29, 210 (2004).
    [CrossRef] [PubMed]
  14. C. Dorrer, P. Londero, and I. A. Walmsley, "Homodyne detection in spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 26, 1510 (2001).
    [CrossRef]
  15. C. Dorrer and I. A. Walmsley, "Accuracy criterion for ultrashort pulse charcterization techniques: application to spectral phase interferometry for direct electric field reconstruction," J. Opt. Soc. Am. B 19, 1019 (2002).
    [CrossRef]
  16. A. S. Radunsky, E. M. Kosik, I. A. Walmsley, P. Wasylczyk, W. Wasilewski, A. B. U’Ren, and M. E. Anderson, "Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal," Opt. Lett. 31, 1008 (2006).
    [CrossRef] [PubMed]
  17. A. S. Radunsky, I. A. Walmsley, S.-P. Gorza, and P. Wasylczyk, "Compact spectral shearing interferometer for ultrashort pulse characterization," Opt. Lett. 32, 181-183 (2007).
    [CrossRef]
  18. S.-P. Gorza, A. S. Radunsky, P. Wasylczyk, and I. A. Walmsley, "Tailoring the phase-matching function for ultrashort pulse characterization by spectral shearing interferometry," J. Opt. Soc. Am. B. 24, 2064 (2007).
    [CrossRef]

2007

S.-P. Gorza, A. S. Radunsky, P. Wasylczyk, and I. A. Walmsley, "Tailoring the phase-matching function for ultrashort pulse characterization by spectral shearing interferometry," J. Opt. Soc. Am. B. 24, 2064 (2007).
[CrossRef]

A. S. Radunsky, I. A. Walmsley, S.-P. Gorza, and P. Wasylczyk, "Compact spectral shearing interferometer for ultrashort pulse characterization," Opt. Lett. 32, 181-183 (2007).
[CrossRef]

2006

2005

E.M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, "Interferometric technique for measuring broadband ultrashort pulses at the sampling limit," Opt. Lett. 30, 326-328 (2005).
[CrossRef] [PubMed]

C. Dorrer and I. A. Walmsley, "Concept for the temporal characterization of short optical pulses," J. App. Sig. Proc. 10, 1541-1553 (2005).

2004

P. Kockaert,M. Haelterman, Ph. Emplit, and C. Froehly, "Complete characterisation of (ultra)short optical pulses using fast linear detectors," IEEE J. Select. Topics Quantum Electron. 10, 206-212 (2004).
[CrossRef]

P. Baum, S. Lochbrunner, and E. Riedle, "Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses," Opt. Lett. 29, 210 (2004).
[CrossRef] [PubMed]

2003

2002

2001

1999

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

1998

C. Iaconis, V. Wong, and I. A. Walmsley, "Direct interferometric techniques for characterizing ultrashort optical pulses," IEEE J. Select. Topics Quantum Electron.,  4, 1 (1998).
[CrossRef]

C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort pulses," Opt. Lett. 23, 792 (1998).
[CrossRef]

1994

1993

Barthelemy, A.

M. Lelek, F. Louradour, A. Barthelemy, and C. Froehly, "Time resolved spectral interferometry for single shot femtosecond characterization," Opt. Commun. 261, 124-129 (2006).
[CrossRef]

Baum, P.

Birge, J. R.

Dorrer, C.

Ell, R.

Emplit, Ph.

P. Kockaert,M. Haelterman, Ph. Emplit, and C. Froehly, "Complete characterisation of (ultra)short optical pulses using fast linear detectors," IEEE J. Select. Topics Quantum Electron. 10, 206-212 (2004).
[CrossRef]

Froehly, C.

M. Lelek, F. Louradour, A. Barthelemy, and C. Froehly, "Time resolved spectral interferometry for single shot femtosecond characterization," Opt. Commun. 261, 124-129 (2006).
[CrossRef]

P. Kockaert,M. Haelterman, Ph. Emplit, and C. Froehly, "Complete characterisation of (ultra)short optical pulses using fast linear detectors," IEEE J. Select. Topics Quantum Electron. 10, 206-212 (2004).
[CrossRef]

Gorza, S.-P.

S.-P. Gorza, A. S. Radunsky, P. Wasylczyk, and I. A. Walmsley, "Tailoring the phase-matching function for ultrashort pulse characterization by spectral shearing interferometry," J. Opt. Soc. Am. B. 24, 2064 (2007).
[CrossRef]

A. S. Radunsky, I. A. Walmsley, S.-P. Gorza, and P. Wasylczyk, "Compact spectral shearing interferometer for ultrashort pulse characterization," Opt. Lett. 32, 181-183 (2007).
[CrossRef]

Haelterman, M.

P. Kockaert,M. Haelterman, Ph. Emplit, and C. Froehly, "Complete characterisation of (ultra)short optical pulses using fast linear detectors," IEEE J. Select. Topics Quantum Electron. 10, 206-212 (2004).
[CrossRef]

Iaconis, C.

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

C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort pulses," Opt. Lett. 23, 792 (1998).
[CrossRef]

C. Iaconis, V. Wong, and I. A. Walmsley, "Direct interferometric techniques for characterizing ultrashort optical pulses," IEEE J. Select. Topics Quantum Electron.,  4, 1 (1998).
[CrossRef]

Kane, D. J.

Kang, I.

Kockaert, P.

P. Kockaert,M. Haelterman, Ph. Emplit, and C. Froehly, "Complete characterisation of (ultra)short optical pulses using fast linear detectors," IEEE J. Select. Topics Quantum Electron. 10, 206-212 (2004).
[CrossRef]

Kosik, E. M.

Kosik, E.M.

Lelek, M.

M. Lelek, F. Louradour, A. Barthelemy, and C. Froehly, "Time resolved spectral interferometry for single shot femtosecond characterization," Opt. Commun. 261, 124-129 (2006).
[CrossRef]

Lochbrunner, S.

Londero, P.

Louradour, F.

M. Lelek, F. Louradour, A. Barthelemy, and C. Froehly, "Time resolved spectral interferometry for single shot femtosecond characterization," Opt. Commun. 261, 124-129 (2006).
[CrossRef]

Quochi, F.

Radunsky, A. S.

Riedle, E.

Steinmeyer, G.

Stibenz, G.

Trebino, R.

Walmsley, I. A.

A. S. Radunsky, I. A. Walmsley, S.-P. Gorza, and P. Wasylczyk, "Compact spectral shearing interferometer for ultrashort pulse characterization," Opt. Lett. 32, 181-183 (2007).
[CrossRef]

S.-P. Gorza, A. S. Radunsky, P. Wasylczyk, and I. A. Walmsley, "Tailoring the phase-matching function for ultrashort pulse characterization by spectral shearing interferometry," J. Opt. Soc. Am. B. 24, 2064 (2007).
[CrossRef]

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, "Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 31, 1914 (2006).
[CrossRef] [PubMed]

A. S. Radunsky, E. M. Kosik, I. A. Walmsley, P. Wasylczyk, W. Wasilewski, A. B. U’Ren, and M. E. Anderson, "Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal," Opt. Lett. 31, 1008 (2006).
[CrossRef] [PubMed]

C. Dorrer and I. A. Walmsley, "Concept for the temporal characterization of short optical pulses," J. App. Sig. Proc. 10, 1541-1553 (2005).

E.M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, "Interferometric technique for measuring broadband ultrashort pulses at the sampling limit," Opt. Lett. 30, 326-328 (2005).
[CrossRef] [PubMed]

C. Dorrer and I. A. Walmsley, "Accuracy criterion for ultrashort pulse charcterization techniques: application to spectral phase interferometry for direct electric field reconstruction," J. Opt. Soc. Am. B 19, 1019 (2002).
[CrossRef]

C. Dorrer, P. Londero, and I. A. Walmsley, "Homodyne detection in spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 26, 1510 (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]

C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort pulses," Opt. Lett. 23, 792 (1998).
[CrossRef]

C. Iaconis, V. Wong, and I. A. Walmsley, "Direct interferometric techniques for characterizing ultrashort optical pulses," IEEE J. Select. Topics Quantum Electron.,  4, 1 (1998).
[CrossRef]

V. Wong and I. A. Walmsley, "Analysis of ultrashort pulse-shape measurement using linear interferometers," Opt. Lett.,  19, 287 (1994).
[CrossRef] [PubMed]

Wasilewski, W.

Wasylczyk, P.

Wong, V.

C. Iaconis, V. Wong, and I. A. Walmsley, "Direct interferometric techniques for characterizing ultrashort optical pulses," IEEE J. Select. Topics Quantum Electron.,  4, 1 (1998).
[CrossRef]

V. Wong and I. A. Walmsley, "Analysis of ultrashort pulse-shape measurement using linear interferometers," Opt. Lett.,  19, 287 (1994).
[CrossRef] [PubMed]

Wyatt, A. S.

IEEE J. Quantum Electron.

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

IEEE J. Select. Topics Quantum Electron.

C. Iaconis, V. Wong, and I. A. Walmsley, "Direct interferometric techniques for characterizing ultrashort optical pulses," IEEE J. Select. Topics Quantum Electron.,  4, 1 (1998).
[CrossRef]

P. Kockaert,M. Haelterman, Ph. Emplit, and C. Froehly, "Complete characterisation of (ultra)short optical pulses using fast linear detectors," IEEE J. Select. Topics Quantum Electron. 10, 206-212 (2004).
[CrossRef]

J. App. Sig. Proc.

C. Dorrer and I. A. Walmsley, "Concept for the temporal characterization of short optical pulses," J. App. Sig. Proc. 10, 1541-1553 (2005).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Opt. Soc. Am. B.

S.-P. Gorza, A. S. Radunsky, P. Wasylczyk, and I. A. Walmsley, "Tailoring the phase-matching function for ultrashort pulse characterization by spectral shearing interferometry," J. Opt. Soc. Am. B. 24, 2064 (2007).
[CrossRef]

Opt. Commun.

M. Lelek, F. Louradour, A. Barthelemy, and C. Froehly, "Time resolved spectral interferometry for single shot femtosecond characterization," Opt. Commun. 261, 124-129 (2006).
[CrossRef]

Opt. Lett.

V. Wong and I. A. Walmsley, "Analysis of ultrashort pulse-shape measurement using linear interferometers," Opt. Lett.,  19, 287 (1994).
[CrossRef] [PubMed]

C. Iaconis and I. A. Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort pulses," Opt. Lett. 23, 792 (1998).
[CrossRef]

C. Dorrer, P. Londero, and I. A. Walmsley, "Homodyne detection in spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 26, 1510 (2001).
[CrossRef]

I. Kang, C. Dorrer, and F. Quochi, "Implementation of electro-optic spectral shearing interferometry for ultrashort pulse characterization," Opt. Lett. 28, 2264-2266 (2003).
[CrossRef] [PubMed]

P. Baum, S. Lochbrunner, and E. Riedle, "Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses," Opt. Lett. 29, 210 (2004).
[CrossRef] [PubMed]

E.M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, "Interferometric technique for measuring broadband ultrashort pulses at the sampling limit," Opt. Lett. 30, 326-328 (2005).
[CrossRef] [PubMed]

A. S. Radunsky, E. M. Kosik, I. A. Walmsley, P. Wasylczyk, W. Wasilewski, A. B. U’Ren, and M. E. Anderson, "Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal," Opt. Lett. 31, 1008 (2006).
[CrossRef] [PubMed]

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, "Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 31, 1914 (2006).
[CrossRef] [PubMed]

J. R. Birge, R. Ell, and F. X. K artner, "Two-dimensional spectral shearing interferometry for few-cycle pulse characterization," Opt. Lett. 31, 2063 (2006).
[CrossRef] [PubMed]

A. S. Radunsky, I. A. Walmsley, S.-P. Gorza, and P. Wasylczyk, "Compact spectral shearing interferometer for ultrashort pulse characterization," Opt. Lett. 32, 181-183 (2007).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Principle of the Chirped ARrangement for SPIDER (CAR-SPIDER) – spatially chirped replica of the pulse to be measured is generated by mixing with a spatially chirped ancillary beam. Two copies of the replica, of which one is laterally inverted, interfere in an imaging spectrometer. Insets show the beam profiles at different positions in x (lateral position)-ω (frequency) coordinates.

Fig. 2.
Fig. 2.

(a) Density plot of (x,ω) with τ ≠ 0 and ρ = 0. The input pulse quadratic phase manifests itself by a linear variation of the fringe spacing across the beam. (b) 2D Fourier transform of the intensity distribution plotted in (a). FFT : fast Fourier transform.

Fig. 3.
Fig. 3.

Experimental setup for the CAR-SPIDER with a type II nonlinear crystal. HP, half-wave plate; QP, predelay quartz plate; L1, focusing lens; KDP, nonlinear crystal; BF, blue filter; L2, imaging lens; τ, delay. Pulse polarization in the crystal is presented by dashed (ordinary) and solid (extraordinary) lines. Arrows indicate the spatial chirp. A lateral inversion of this spatial chirp takes place in one arm of the interferometer. The entrance slit of the 2D imaging spectrometer is oriented in the drawing plane.

Fig. 4.
Fig. 4.

(a-b) Measured density plots of the 2D spectra of the two chirped replicas (black stands for high intensity value). (c) Measured spectral shear versus position (cross) and linear fit (solid line). The reverse spatial chirp between the two replicas enables the spectral shear to vary from positive to negative values. The calibration slice is at x = 197 in which the shear is zero. (d) CAR-SPIDER interferogram of a chirped pulse with ρ = 0 and τ = 1.8 ps.

Fig. 5.
Fig. 5.

(a) Extracted spectral intensity as well as reconstructed spectral phase for five different values of the shear (4, 5, 6, 7, and 8 mrad/fs) corresponding to five different positions in the interferogram. (b) Measured (dashed line) and calculated (solid line) spectral phase introduced by a 10 cm block of BK7 glass.

Equations (3)

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S ˜ x ω = I ˜ ( ω αx ) A ( x ) 2 + I ˜ ( ω + αx ) A ( x ) 2
+ 2 I ˜ ( ω αx ) I ˜ ( ω + αx ) A ( x ) A ( x )
× cos [ ϕ ˜ ( ω + αx ) ϕ ˜ ( ω αx ) + ρx + ωτ + φ ( x ) ] .

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