Abstract

We report a new version of spectral phase interferometry for direct electric field reconstruction (SPIDER), in which two spatially chirped ancilla fields are used to generate a spatially encoded SPIDER interferogram. We dub this new technique Spatially Encoded Arrangement for Chirped ARrangement for SPIDER (SEA-CAR-SPIDER). The single shot interferogram contains multiple shears, the spectral amplitude of the test pulse, and the reference phase, which is accurate for broadband pulses. The technique enables consistency checking through the simultaneous acquisition of multiple shears and offers a simple and precise calibration method. All calibration parameters — the shears, and the upconversion-frequency— can be accurately obtained from a single calibration trace.

© 2009 Optical Society of America

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References

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  1. I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
    [Crossref]
  2. P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort-pulse measurement,” Opt. Lett. 26, 932–934 (2001).
    [Crossref]
  3. 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]
  4. C. Dorrer, “Influence of the calibration of the detector on spectral interferometry,” J. Opt. Soc. Am. B 16, 1160–1168 (1999).
    [Crossref]
  5. C. Dorrer and I. Walmsley, “Precision and consistency criteria in spectral phase interferometry for direct electric-field reconstruction,” J. Opt. Soc. Am. B 19, 1030–1038 (2002).
    [Crossref]
  6. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, 2002).
    [Crossref]
  7. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794(1998).
    [Crossref]
  8. E. Kosik, A. Radunsky, I. Walmsley, and C. Dorrer, “Interferometric technique for measuring broadband ultrashort pulses at the sampling limit,” Opt. Lett. 30, 326–328(2005).
    [Crossref] [PubMed]
  9. J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31, 2063–2065 (2006).
    [Crossref] [PubMed]
  10. T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34, 881–883 (2009).
    [Crossref] [PubMed]
  11. A. Monmayrant, M. Joffre, T. Oksenhendler, R. Herzog, D. Kaplan, and P. Tournois, “Time-domain interferometry for direct electric-field reconstruction by use of an acousto-optic programmable filter and a two-photon detector,” Opt. Lett. 28, 278–280 (2003).
    [Crossref] [PubMed]
  12. P. Baum, S. Lochbrunner, and E. Riedle, “Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses,” Opt. Lett. 29, 210–212 (2004).
    [Crossref] [PubMed]
  13. 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]
  14. S.-P. Gorza, P. Wasylczyk, and I. A. Walmsley, “Spectral shearing interferometry with spatially chirped replicas for measuring ultrashort pulses,” Opt. Express 15, 15168–15174 (2007).
    [Crossref] [PubMed]
  15. J. Wemans, G. Figueira, N. Lopes, and L. Cardoso, “Self-referencing spectral phase interferometry for direct electric-field reconstruction with chirped pulses,” Opt. Lett. 31, 2217–2219 (2006).
    [Crossref] [PubMed]
  16. D. R. Austin, T. Witting, and I. A. Walmsley, “Broadband astigmatism-free Czerny-Turner imaging spectrometer using spherical mirrors,” Appl. Opt. 48, 3846–3853 (2009).
    [Crossref] [PubMed]
  17. R. W. Boyd, Nonlinear optics (Academic Press, 2003).
  18. D. Keusters, H.-S. Tan, P. O’Shea, E. Zeek, R. Trebino, and W. S. Warren, “Relative-phase ambiguities in measurements of ultrashort pulses with well-separated multiple frequency components,” J. Opt. Soc. Am. B 20, 2226–2237 (2003).
    [Crossref]
  19. D. R. Austin, T. Witting, and I. A. Walmsley, “High precision self-referenced phase retrieval of complex pulses with multiple-shearing spectral interferometry,” J. Opt. Soc. Am. B 26, 1818–1830 (2009).
    [Crossref]
  20. C. Dorrer and I. A. Walmsley, “Accuracy criterion for ultrashort pulse characterization techniques: application to spectral phase interferometry for direct electric field reconstruction,” J. Opt. Soc. Am. B 19, 1019–1029 (2002).
    [Crossref]

2009 (4)

2007 (2)

2006 (3)

2005 (1)

2004 (1)

2003 (2)

2002 (2)

2001 (1)

1999 (1)

1998 (1)

Austin, D. R.

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.

Boyd, R. W.

R. W. Boyd, Nonlinear optics (Academic Press, 2003).

Cardoso, L.

Dorrer, C.

Ell, R.

Figueira, G.

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]

Gorza, S.-P.

Gu, X.

Herzog, R.

Iaconis, C.

Joffre, M.

Kaplan, D.

Kärtner, F. X.

Keusters, D.

Kimmel, M.

Kosik, E.

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.

Lopes, N.

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]

Monmayrant, A.

O’Shea, P.

Oksenhendler, T.

Radunsky, A.

Radunsky, A. S.

Riedle, E.

Tan, H.-S.

Tournois, P.

Trebino, R.

Walmsley, I.

Walmsley, I. A.

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photon. 1, 308–437 (2009).
[Crossref]

T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34, 881–883 (2009).
[Crossref] [PubMed]

D. R. Austin, T. Witting, and I. A. Walmsley, “High precision self-referenced phase retrieval of complex pulses with multiple-shearing spectral interferometry,” J. Opt. Soc. Am. B 26, 1818–1830 (2009).
[Crossref]

D. R. Austin, T. Witting, and I. A. Walmsley, “Broadband astigmatism-free Czerny-Turner imaging spectrometer using spherical mirrors,” Appl. Opt. 48, 3846–3853 (2009).
[Crossref] [PubMed]

S.-P. Gorza, P. Wasylczyk, and I. A. Walmsley, “Spectral shearing interferometry with spatially chirped replicas for measuring ultrashort pulses,” Opt. Express 15, 15168–15174 (2007).
[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]

C. Dorrer and I. A. Walmsley, “Accuracy criterion for ultrashort pulse characterization techniques: application to spectral phase interferometry for direct electric field reconstruction,” J. Opt. Soc. Am. B 19, 1019–1029 (2002).
[Crossref]

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794(1998).
[Crossref]

Warren, W. S.

Wasylczyk, P.

Wemans, J.

Witting, T.

Zeek, E.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

J. Opt. Soc. Am. B (5)

Opt. Commun. (1)

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. Express (1)

Opt. Lett. (9)

J. Wemans, G. Figueira, N. Lopes, and L. Cardoso, “Self-referencing spectral phase interferometry for direct electric-field reconstruction with chirped pulses,” Opt. Lett. 31, 2217–2219 (2006).
[Crossref] [PubMed]

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort-pulse measurement,” Opt. Lett. 26, 932–934 (2001).
[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]

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794(1998).
[Crossref]

E. Kosik, A. Radunsky, I. Walmsley, and C. Dorrer, “Interferometric technique for measuring broadband ultrashort pulses at the sampling limit,” Opt. Lett. 30, 326–328(2005).
[Crossref] [PubMed]

J. R. Birge, R. Ell, and F. X. Kärtner, “Two-dimensional spectral shearing interferometry for few-cycle pulse characterization,” Opt. Lett. 31, 2063–2065 (2006).
[Crossref] [PubMed]

T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34, 881–883 (2009).
[Crossref] [PubMed]

A. Monmayrant, M. Joffre, T. Oksenhendler, R. Herzog, D. Kaplan, and P. Tournois, “Time-domain interferometry for direct electric-field reconstruction by use of an acousto-optic programmable filter and a two-photon detector,” Opt. Lett. 28, 278–280 (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, 210–212 (2004).
[Crossref] [PubMed]

Other (2)

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, 2002).
[Crossref]

R. W. Boyd, Nonlinear optics (Academic Press, 2003).

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Figures (8)

Fig. 1.
Fig. 1.

SEA-CAR-SPIDER concept: test pulse (TP), spatially chirped ancillae A and B with local frequencies ω A and ω B increasing along the arrows, and sum-frequency beams TP+A and TP+B. The coordinate system used in the text is shown. The entrance slit of the imaging spectrometer is parallel to the x-axis. The spatial fringes along x are used to encode the phase.

Fig. 2.
Fig. 2.

Example SEA-CAR-SPIDER traces calculated for pulses with different order polynomial spectral phases. (a) Transform-limited pulse; (b) quadratic spectral phase; (c) cubic spectral phase; (d) quartic spectral phase. The fringes map out the phase gradient scaled by the shear.

Fig. 3.
Fig. 3.

SEA-CAR-SPIDER experimental setup. For detailed explanation refer to text. The inset shows the spatio-spectral structure of the test pulse and the ancillae beams in the crystal plane. The test pulse upconverts with different ancilla frequencies from the two oppositely spatially chirped ancilla beams in each spatial position across the crystal resulting in a varying shear across x.

Fig. 4.
Fig. 4.

SEA-CAR-SPIDER calibration: (a) Spatially resolved spectrum of the upconversion from the two ancilla pulses yields calibration of upconversion frequency and shear. 20 dB color scale. The black dashed lines are linear fits. (b) Fitting the shear using the sum-frequency signal. Central frequencies of individual spectral slices (black dots) obtained from cross-correlation, linear fit (black line). (c) Residuals of fits of the ancilla as in (a) in red circles, residuals of fit (b) in black dots.

Fig. 5.
Fig. 5.

Evaluation of the stability of the calibration parameters. We recorded 50 single-shot calibration traces and performed the fitting routines on each. (a) Shear slope α. (b) Position of x-origin (zero shear row) determined from the crossing point. (c) Upconversion frequency ω up.

Fig. 6.
Fig. 6.

(a) Typical single-shot SEA-CAR-SPIDER interferogram for a 54 fs pulse. (b) Spatial lineout at center wavelength showing the spatial carrier fringes. (c) 2D-DFT of the interferogram (80 dB scale). The black rectangle indicates the sideband filter; the green rectangle indicates the signal-free region used to determine the noise amplitude. (d) Γ(ω,x) after filtering (2π scale). The spatial carrier has been removed for clarity.

Fig. 7.
Fig. 7.

Example reconstructions for different shears Ω=12.07,13.27, and 18.08mrad=fs. (a) Spectral domain with amplitude extracted from the trace at x=0 and the 3 phases corresponding to each shear. (b) Temporal domain: intensities and phases for each shear.

Fig. 8.
Fig. 8.

Reconstruction of a 59 fs pulse for shears from 8.4 to 14.4 mrad/fs. (a) Spectral domain: intensity (red, left axis) and mean phase (dark blue line, right axis) and ±1 standard deviation (light blue region) across the shears. (b) Temporal domain: mean intensity (red) and ±1 standard deviation interval (light red region) across the shears. (c) RMS phase variations magnified: over all shots at a single shear (black dash-dotted), over all 12 shears (blue, solid), and expected variation in the reconstructed phase resulting from fluctuations in the upconversion frequency (green dashed).

Equations (9)

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S (ω+ωup,x)=I(ω+αx)+I(ωαx)+D(ω,x)+D*(ω,x)
D (ω,x) = I(ω+αx)I(ωαx) exp [iΓ(ω,x)]
Γ (ω,x)=ϕ(ω+αx)ϕ(ωαx)+kxx+C(ω)
C (ω)=12unwrap[Arg0D(ω,x)D(ω,x)dx]
dΓ[ω,xcon(ω)]dω=Γ[ω,xcon(ω)]ω+Γ[ω,xcon(ω)]xxcon(ω)ω=0
Γ (ω,x)ϕ(ω)ω2αx+kxx.
Γ(ω,x)x = ϕ(ω)ω 2 α + kx .
xcon(ω)ω = 2αxcon(ω)kx 2ϕω2 .
γ2 = {Δ[ϕ(ωm)ϕ(ωn)]}2=k=nm1ηΓ(ωk+Ω2,x)2.

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