Abstract

We introduce and demonstrate a novel concept of frequency-resolved wavefront characterization. Our approach is particularly suitable for high-harmonic, extreme-UV (XUV) and soft X-ray radiation. The concept is based on an analysis of radiation diffracted from a slit scanned in front of a flat-field XUV spectrometer. With the spectrally resolved signal spread across one axis and the spatially resolved diffraction pattern in the other dimension, we reconstruct the wavefront. While demonstrated for high harmonics, the method is not restricted in wavelength.

© 2009 Optical Society of America

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2008

2006

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, Nat. Phys. 2, 101 (2006).
[CrossRef]

2005

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

2004

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

2003

2002

J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, Phys. Rev. Lett. 88, 173903 (2002).
[CrossRef] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

2001

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

2000

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, Nature 406, 752 (2000).
[CrossRef] [PubMed]

1999

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

1993

P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
[CrossRef] [PubMed]

D. J. Kane and R. Trebino, J. Quantum Electron. 29, 571 (1993).
[CrossRef]

1984

1983

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

Anderson, E. H.

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Attwood, D.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Attwood, D. T.

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Auge, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Backus, S.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Balcou, Ph.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Bartels, R. A.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

Bucourt, S.

Cai, Z.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, Nat. Phys. 2, 101 (2006).
[CrossRef]

Chao, W. L.

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Christov, I. P

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Constant, E.

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

Corkum, P. B.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, Phys. Rev. Lett. 88, 173903 (2002).
[CrossRef] [PubMed]

P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
[CrossRef] [PubMed]

Dorrer, C.

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

Dovillaire, G.

Fajardo, M.

Garzella, D.

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

Gautier, J.

Goddet, L. P.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Green, H.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Hajdu, J.

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, Nature 406, 752 (2000).
[CrossRef] [PubMed]

Harada, T.

Harteneck, B. D.

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Hauri, C.

Itatani, J.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, Phys. Rev. Lett. 88, 173903 (2002).
[CrossRef] [PubMed]

Ivanov, M. Yu.

J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, Phys. Rev. Lett. 88, 173903 (2002).
[CrossRef] [PubMed]

Jacobsen, C.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Kane, D. J.

D. J. Kane and R. Trebino, J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Kapteyn, H. C.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Kieffer, J. C.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

Kita, T.

Krausz, F.

J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, Phys. Rev. Lett. 88, 173903 (2002).
[CrossRef] [PubMed]

Kuroda, H.

Le Blanc, C.

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

Lee, D. G.

Levecq, X.

Levesque, J.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

Liddle, J. A.

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

Liu, Y. W.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Marchenko, T.

Mevel, E.

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

Muller, H. G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Murnane, M. M.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Nakano, N.

Nam, C. H.

Neutze, R.

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, Nature 406, 752 (2000).
[CrossRef] [PubMed]

Niikura, H.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

Nugent, K. A.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, Nat. Phys. 2, 101 (2006).
[CrossRef]

Papalazarou, E.

Park, J. J.

Paterson, D.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, Nat. Phys. 2, 101 (2006).
[CrossRef]

Paul, A.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Peele, A. G.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, Nat. Phys. 2, 101 (2006).
[CrossRef]

Pepin, H.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

Quéré, F.

J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, Phys. Rev. Lett. 88, 173903 (2002).
[CrossRef] [PubMed]

Quiney, H. M.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, Nat. Phys. 2, 101 (2006).
[CrossRef]

Rey, G.

Salin, F.

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

Scrick, O.

Sebban, S.

Sung, J. H.

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Trebino, R.

D. J. Kane and R. Trebino, J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Valentin, C.

van der Spoel, D.

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, Nature 406, 752 (2000).
[CrossRef] [PubMed]

Villeneuve, D. M.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

Weckert, E.

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, Nature 406, 752 (2000).
[CrossRef] [PubMed]

Wouts, R.

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, Nature 406, 752 (2000).
[CrossRef] [PubMed]

Yudin, G. L.

J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, Phys. Rev. Lett. 88, 173903 (2002).
[CrossRef] [PubMed]

Zeidler, D.

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

Zeitoun, P.

Appl. Opt.

J. Opt. Soc. Am. B

J. Quantum Electron.

D. J. Kane and R. Trebino, J. Quantum Electron. 29, 571 (1993).
[CrossRef]

Nat. Phys.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, Nat. Phys. 2, 101 (2006).
[CrossRef]

Nature

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, Nature 406, 752 (2000).
[CrossRef] [PubMed]

W. L. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, Nature 435, 1210 (2005).
[CrossRef] [PubMed]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, Phys. Rev. Lett. 88, 173903 (2002).
[CrossRef] [PubMed]

P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
[CrossRef] [PubMed]

E. Constant, D. Garzella, P. Breger, E. Mevel, C. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, Phys. Rev. Lett. 82, 1668 (1999).
[CrossRef]

Science

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. G. Muller, and P. Agostini, Science 292, 1689 (2001).
[CrossRef] [PubMed]

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental setup. The scanning slit (SS) is 20 μm wide, and the spectrometer slit (SE) width is 100 μm. The variable groove spacing flat field Hitachi imaging diffraction grating (model 001-0266) was used with nominal groove density of 1200 mm 1 [11].

Fig. 2
Fig. 2

(a) Logarithmic image of a high-harmonic spectrum diffracted through scanning slit. (b) The diffractogram. Each slice of the diffractogram shows the diffraction pattern for the particular scanning slit position printed below each slice. Only a small, sparse fragment of the complete diffractogram is shown. At each slice the intensity is normalized to maximum for the given slit position. In the experiment the slit was scanned and the diffraction pattern measured at 20 μm increments.

Fig. 3
Fig. 3

(a) Experimental results: phase and amplitude reconstruction of the 21st harmonic at the scanning slit position. Error bars for the reconstructed phase (∼0.3%) are unobservable on the figure scale. (b) Intensity profile on the MCP plane. The solid curve shows the measured profile. The dashed curve represents reconstructed intensity. The reconstructed intensity profile for a flat phase is shown by the solid curve with markers in the center.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

δ i = δ z y i z i d .
ϕ n = 2 π λ i = 0 n δ i .

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