Abstract

Extreme ultraviolet (EUV) optics play a key role in attosecond science since only with higher photon energies is it possible to achieve the wide spectral bandwidth required for ultrashort pulses. Multilayer EUV mirrors have been proposed and are being developed to temporally shape (compress) attosecond pulses. To fully characterize a multilayer optic for pulse applications requires not only knowledge of the reflectivity, as a function of photon energy, but also the reflected phase of the mirror. We develop the metrologies to determine the reflected phase of an EUV multilayer mirror using the photoelectric effect. The proposed method allows one to determine the optic’s impulse response and hence its pulse characteristics.

© 2008 Optical Society of America

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References

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E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, Science 317, 769 (2007).
[CrossRef] [PubMed]

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, Nature 449, 1029 (2007).
[CrossRef] [PubMed]

2006

2005

2003

T. Ejima, Jpn. J. Appl. Phys., Part 1 42, 6459 (2003).
[CrossRef]

2001

S. Bajt, D. Stearns, and P. Kearney, J. Appl. Phys. 90, 1017 (2001).
[CrossRef]

I. Walmsleya, L. Waxer, and C. Dorrer, Rev. Sci. Instrum. 72, 1 (2001).
[CrossRef]

E. M. Gullikson, S. Mrowka, and B. B. Kaufmann, Proc. SPIE 4343, 363 (2001).
[CrossRef]

1998

1997

1970

Appl. Opt.

J. Appl. Phys.

S. Bajt, D. Stearns, and P. Kearney, J. Appl. Phys. 90, 1017 (2001).
[CrossRef]

J. Opt. Soc. Am.

Jpn. J. Appl. Phys., Part 1

T. Ejima, Jpn. J. Appl. Phys., Part 1 42, 6459 (2003).
[CrossRef]

Nature

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, Nature 449, 1029 (2007).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Proc. SPIE

E. M. Gullikson, S. Mrowka, and B. B. Kaufmann, Proc. SPIE 4343, 363 (2001).
[CrossRef]

Rev. Sci. Instrum.

I. Walmsleya, L. Waxer, and C. Dorrer, Rev. Sci. Instrum. 72, 1 (2001).
[CrossRef]

Science

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, Science 317, 769 (2007).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Three samples were produced for this experiment: two quadratic depth-graded or chirped samples and one periodic sample. The two quadratic graded samples were designed to have opposite signs for their GDD and the positive GDD sample was designed to have twice the chirp compared to the negative GDD sample. Plotted are the measured reflectivity curves for the three samples (points as indicated in the inset) and their simulations (solid curves). The samples are labeled by their GDD.

Fig. 2
Fig. 2

Normalized TEY measurement is shown for the positive GDD sample plotted as ▴. The normalization is such that a value of 1 would correspond to the TEY value of sputtered Si. Plotted along the same graph, as a curve, is the simulated intensity of the surface electric field based on the reflectivity and the reflected phase.

Fig. 3
Fig. 3

Phase for the three samples was reconstructed from the reflectivity and TEY data. Plotted as solid curves is the calculated phase of the multilayers.

Equations (7)

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Δ τ Δ E 1.8 ,
φ = φ ( ω cent ) + φ ( ω cent ) ( ω ω cent ) + φ ( ω cent ) ( ω ω cent ) 2 2 ! + ,
τ = τ 0 1 + 16 ( ln 2 ) 2 { φ ( ω cent ) } 2 τ 0 4 ,
TEY = C ( ω ) I ( ω ) ,
I = E 2 = ( E inc + E ref ) 2 = E 0 2 ( 1 + r e i Δ φ ) 2 = E 0 2 ( 1 + r 2 + 2 r cos ( Δ φ ) ) ,
TEY m l TEY Si = C ( ω ) E m l 0 2 ( 1 + r 2 + 2 r cos ( Δ φ ) ) C ( ω ) E Si 0 2 J .
Δ φ = ± cos 1 ( J R 1 2 R ) + 2 π n ,

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