Abstract

We analyze the characterization of strongly chirped pulses by spectral phase interferometry for direct electric-field reconstruction (SPIDER). We show how to extend the working range of this technique for these relevant cases and derive correction factors for typical operating parameters. The results are straightforward to implement in the calculation algorithms. We demonstrate the validity of this technique by characterizing numerically and experimentally pulses with a known spectral phase profile.

© 2006 Optical Society of America

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  1. C. Iaconis and I. A. Walmsley, Opt. Lett. 23, 792 (1998).
    [CrossRef]
  2. C. Iaconis and I. A. Walmsley, IEEE J. Quantum Electron. 35, 501 (1999).
    [CrossRef]
  3. M. Takeda, H. Ina, and S. Kobayashi, in Proc. SPIE 72, 156 (1982).
  4. C. Dorrer, Opt. Lett. 24, 15321534 (1999).
  5. T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, and I. A. Walmsley, Opt. Express 5, 134143 (1999).
    [CrossRef]
  6. C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
    [CrossRef]
  7. E. M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, Opt. Lett. 30, 326 (2005).
    [CrossRef] [PubMed]
  8. C. Dorrer, E. M. Kosik, and I. A. Walmsley, Appl. Phys. B: Lasers Opt. 74, S209 (2002).
    [CrossRef]
  9. C. Dorrer, P. Londero, and I. A. Walmsley, Opt. Lett. 26, 1510 (2001).
    [CrossRef]
  10. N. K. Berger, B. Levit, V. Smulakovsky, and B. Fischer, Appl. Opt. 44, 7862 (2005).
    [CrossRef] [PubMed]
  11. G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
    [CrossRef]

2005 (3)

2002 (1)

C. Dorrer, E. M. Kosik, and I. A. Walmsley, Appl. Phys. B: Lasers Opt. 74, S209 (2002).
[CrossRef]

2001 (1)

2000 (1)

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

1999 (3)

C. Iaconis and I. A. Walmsley, IEEE J. Quantum Electron. 35, 501 (1999).
[CrossRef]

C. Dorrer, Opt. Lett. 24, 15321534 (1999).

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, and I. A. Walmsley, Opt. Express 5, 134143 (1999).
[CrossRef]

1998 (1)

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, in Proc. SPIE 72, 156 (1982).

Anderson, M. E.

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, and I. A. Walmsley, Opt. Express 5, 134143 (1999).
[CrossRef]

Berger, N. K.

Bromage, J.

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, and I. A. Walmsley, Opt. Express 5, 134143 (1999).
[CrossRef]

Cardoso, L.

G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
[CrossRef]

Chambaret, J.-P.

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

de Beauvoir, B.

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

Dias, J. M.

G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
[CrossRef]

Dorrer, C.

E. M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, Opt. Lett. 30, 326 (2005).
[CrossRef] [PubMed]

C. Dorrer, E. M. Kosik, and I. A. Walmsley, Appl. Phys. B: Lasers Opt. 74, S209 (2002).
[CrossRef]

C. Dorrer, P. Londero, and I. A. Walmsley, Opt. Lett. 26, 1510 (2001).
[CrossRef]

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

C. Dorrer, Opt. Lett. 24, 15321534 (1999).

Fajardo, M.

G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
[CrossRef]

Figueira, G.

G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
[CrossRef]

Fischer, B.

Iaconis, C.

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, and I. A. Walmsley, Opt. Express 5, 134143 (1999).
[CrossRef]

C. Iaconis and I. A. Walmsley, IEEE J. Quantum Electron. 35, 501 (1999).
[CrossRef]

C. Iaconis and I. A. Walmsley, Opt. Lett. 23, 792 (1998).
[CrossRef]

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, in Proc. SPIE 72, 156 (1982).

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, in Proc. SPIE 72, 156 (1982).

Kosik, E. M.

E. M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, Opt. Lett. 30, 326 (2005).
[CrossRef] [PubMed]

C. Dorrer, E. M. Kosik, and I. A. Walmsley, Appl. Phys. B: Lasers Opt. 74, S209 (2002).
[CrossRef]

Le Blanc, C.

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

Leitão, C.

G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
[CrossRef]

Levit, B.

Londero, P.

Lopes, N.

G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
[CrossRef]

Mendonça, J. T.

G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
[CrossRef]

Radunsky, A. S.

Ranc, S.

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

Rousseau, J.-P.

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

Rousseau, P.

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

Salin, F.

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

Shuman, T. M.

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, and I. A. Walmsley, Opt. Express 5, 134143 (1999).
[CrossRef]

Smulakovsky, V.

Takeda, M.

M. Takeda, H. Ina, and S. Kobayashi, in Proc. SPIE 72, 156 (1982).

Walmsley, I. A.

E. M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, Opt. Lett. 30, 326 (2005).
[CrossRef] [PubMed]

C. Dorrer, E. M. Kosik, and I. A. Walmsley, Appl. Phys. B: Lasers Opt. 74, S209 (2002).
[CrossRef]

C. Dorrer, P. Londero, and I. A. Walmsley, Opt. Lett. 26, 1510 (2001).
[CrossRef]

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, and I. A. Walmsley, Opt. Express 5, 134143 (1999).
[CrossRef]

C. Iaconis and I. A. Walmsley, IEEE J. Quantum Electron. 35, 501 (1999).
[CrossRef]

C. Iaconis and I. A. Walmsley, Opt. Lett. 23, 792 (1998).
[CrossRef]

Waxer, L.

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, and I. A. Walmsley, Opt. Express 5, 134143 (1999).
[CrossRef]

Wemans, J.

G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B: Lasers Opt. (1)

C. Dorrer, E. M. Kosik, and I. A. Walmsley, Appl. Phys. B: Lasers Opt. 74, S209 (2002).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem. (1)

C. Dorrer, B. de Beauvoir, C. Le Blanc, J.-P. Rousseau, S. Ranc, P. Rousseau, J.-P. Chambaret, and F. Salin, Appl. Phys. B: Photophys. Laser Chem. 70, S77 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Iaconis and I. A. Walmsley, IEEE J. Quantum Electron. 35, 501 (1999).
[CrossRef]

Opt. Express (1)

T. M. Shuman, M. E. Anderson, J. Bromage, C. Iaconis, L. Waxer, and I. A. Walmsley, Opt. Express 5, 134143 (1999).
[CrossRef]

Opt. Lett. (4)

Proc. SPIE (2)

G. Figueira, N. Lopes, L. Cardoso, J. Wemans, J. M. Dias, M. Fajardo, C. Leitão, and J. T. Mendonça, in Proc. SPIE 5777, 636 (2005).
[CrossRef]

M. Takeda, H. Ina, and S. Kobayashi, in Proc. SPIE 72, 156 (1982).

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Figures (3)

Fig. 1
Fig. 1

Upconversion in SPIDER with chirped pulses. In the sum-frequency process, the linear chirp of the reference pulse changes the slope of the upconverted replica traces but preserves the higher-order spectral phase information.

Fig. 2
Fig. 2

Comparison between direct and corrected SPIDER readings of the relative quadratic phase k = ϕ i ϕ introduced by a grating pair as a function of total dispersion length. Crosses, theoretical value for k; circles, direct reading; squares, corrected with σ factor.

Fig. 3
Fig. 3

Comparison between direct and corrected SPIDER readings of the spectral phase of a chirped Gaussian pulse ( k = 0.2 , ϕ i = 0.001 ϕ ps , ϕ i = 0.0001 ϕ ps 2 ). Right axis, full spectral phase; left axis, third- and fourth-order terms highlighted. Gray curve, input spectral phase; black curve, direct reading from SPIDER; dashed curve, corrected ( σ = 0.86 ) reading.

Equations (5)

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ϕ ( ω ) = ϕ ω 0 + ϕ ω 0 Δ ω + ϕ ω 0 2 Δ ω 2 + Φ ω 0 ( Δ ω )
E u ± ( t ) = E i , c ( t ± τ 2 ) E r , c ( t ) exp [ ( Γ + Γ e ) ( t ± τ 2 ) 2 i ω ( t ± τ 2 ) ] ,
Ω c = 2 b e τ = τ ϕ 1 + k γ 2 + ( 1 + k ) 2 Ω 1 1 + k ,
ϕ u = ϕ i ( γ 2 k + k + 1 ) ( 1 + 2 k ) 4 γ 2 + ( 1 + 2 k ) 2 ϕ i 1 + k 1 + 2 k σ ϕ i .
τ c = τ [ 1 2 γ 2 + k ( 1 + 2 k ) 4 γ 2 + ( 1 + 2 k ) 2 ] τ ( 1 + k 1 + 2 k ) = σ τ ,

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