Abstract

A method is proposed that uses maximum entropy analysis of a Young’s two-slit interference pattern for the measurement of the spectrum of a high-harmonic-generation light source. The approach is tested using experimental data, and the results are found to be consistent with those obtained directly using a grazing incidence spectrometer.

© 2008 Optical Society of America

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References

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  1. A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
    [CrossRef] [PubMed]
  2. 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]
  3. R. A. Bartels, A. Paul, M. M. Murnane, H. C. Kapteyn, S. Backus, Y. Liu, and D. T. Attwood, Opt. Lett. 27, 707 (2002).
    [CrossRef]
  4. N. Agmon, Y. Alhassid, and R. D. Levine, J. Comput. Phys. 30, 250 (1979).
    [CrossRef]
  5. F. Izumi and R. A. Dilanian, Recent Res. Dev. Phys. 3, 699 (2002).
  6. D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
    [CrossRef]
  7. L. V. Dao, S. Teichmann, J. Davis, and P. Hannaford, J. Appl. Phys. 104, 023105 (2001).

2002

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]

R. A. Bartels, A. Paul, M. M. Murnane, H. C. Kapteyn, S. Backus, Y. Liu, and D. T. Attwood, Opt. Lett. 27, 707 (2002).
[CrossRef]

F. Izumi and R. A. Dilanian, Recent Res. Dev. Phys. 3, 699 (2002).

2001

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

L. V. Dao, S. Teichmann, J. Davis, and P. Hannaford, J. Appl. Phys. 104, 023105 (2001).

1998

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

1979

N. Agmon, Y. Alhassid, and R. D. Levine, J. Comput. Phys. 30, 250 (1979).
[CrossRef]

Agmon, N.

N. Agmon, Y. Alhassid, and R. D. Levine, J. Comput. Phys. 30, 250 (1979).
[CrossRef]

Alhassid, Y.

N. Agmon, Y. Alhassid, and R. D. Levine, J. Comput. Phys. 30, 250 (1979).
[CrossRef]

Allman, B. E.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

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.

Backus, S.

R. A. Bartels, A. Paul, M. M. Murnane, H. C. Kapteyn, S. Backus, Y. Liu, and D. T. Attwood, Opt. Lett. 27, 707 (2002).
[CrossRef]

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]

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[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]

R. A. Bartels, A. Paul, M. M. Murnane, H. C. Kapteyn, S. Backus, Y. Liu, and D. T. Attwood, Opt. Lett. 27, 707 (2002).
[CrossRef]

Chang, Z. H.

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Chantler, C. T.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

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]

Dao, L. V.

L. V. Dao, S. Teichmann, J. Davis, and P. Hannaford, J. Appl. Phys. 104, 023105 (2001).

Davis, J.

L. V. Dao, S. Teichmann, J. Davis, and P. Hannaford, J. Appl. Phys. 104, 023105 (2001).

Dilanian, R. A.

F. Izumi and R. A. Dilanian, Recent Res. Dev. Phys. 3, 699 (2002).

Durfee, C. G.

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

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]

Hannaford, P.

L. V. Dao, S. Teichmann, J. Davis, and P. Hannaford, J. Appl. Phys. 104, 023105 (2001).

Herne, C.

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Irving, T. H.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Izumi, F.

F. Izumi and R. A. Dilanian, Recent Res. Dev. Phys. 3, 699 (2002).

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]

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]

R. A. Bartels, A. Paul, M. M. Murnane, H. C. Kapteyn, S. Backus, Y. Liu, and D. T. Attwood, Opt. Lett. 27, 707 (2002).
[CrossRef]

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Levine, R. D.

N. Agmon, Y. Alhassid, and R. D. Levine, J. Comput. Phys. 30, 250 (1979).
[CrossRef]

Lin, J.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Liu, Y.

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]

Mancini, D. C.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

McMahon, P. J.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

McNulty, I.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Moldovan, N.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Murnane, M. M.

R. A. Bartels, A. Paul, M. M. Murnane, H. C. Kapteyn, S. Backus, Y. Liu, and D. T. Attwood, Opt. Lett. 27, 707 (2002).
[CrossRef]

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]

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Nugent, K. A.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Paterson, D.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[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]

R. A. Bartels, A. Paul, M. M. Murnane, H. C. Kapteyn, S. Backus, Y. Liu, and D. T. Attwood, Opt. Lett. 27, 707 (2002).
[CrossRef]

Retsch, C. C.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Rundquist, A.

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

Teichmann, S.

L. V. Dao, S. Teichmann, J. Davis, and P. Hannaford, J. Appl. Phys. 104, 023105 (2001).

J. Appl. Phys.

L. V. Dao, S. Teichmann, J. Davis, and P. Hannaford, J. Appl. Phys. 104, 023105 (2001).

J. Comput. Phys.

N. Agmon, Y. Alhassid, and R. D. Levine, J. Comput. Phys. 30, 250 (1979).
[CrossRef]

Opt. Commun.

D. Paterson, B. E. Allman, P. J. McMahon, J. Lin, N. Moldovan, K. A. Nugent, I. McNulty, C. T. Chantler, C. C. Retsch, T. H. K. Irving, and D. C. Mancini, Opt. Commun. 195, 79 (2001).
[CrossRef]

Opt. Lett.

Recent Res. Dev. Phys.

F. Izumi and R. A. Dilanian, Recent Res. Dev. Phys. 3, 699 (2002).

Science

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[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]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic representation of the Young’s double-slits experimental setup. (b) The idealized model of the HHG spectrum.

Fig. 2
Fig. 2

HHG spectrum obtained using MEM (solid curves) and FT (dashed curves) approaches from simulated interference patterns. Vertical lines are the precise peak positions in the simulated spectrum.

Fig. 3
Fig. 3

Experimental (asterisks) and reconstructed (solid curve) interference pattern.

Fig. 4
Fig. 4

Normalized intensity distributions of the reconstructed spectrum. Solid curve, S1; dashed curve, S2. Circles with error bars show the relative intensities of harmonics obtained using a spectrometer.

Equations (6)

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

I ( τ ν ) = 2 [ 1 + γ 12 cos ( 2 π ν τ ) ] sinc 2 ( π W D ν τ ) ,
I T ( τ j ) = k = 1 N F ( ν k ) I ( τ j ν k ) ,
S = k = 1 N p k log ( p k p k ( 0 ) ) ,
C = 1 M j = 1 M I T MEM ( τ j ) I T ( τ j ) 2 σ 2 ( I T ( τ j ) ) = 1 ,
p k ( n + 1 ) = p k ( n ) exp ( α C p k ( n ) ) T ,
R F ( % ) = 100 j = 1 M I T MEM ( τ j ) I T ( τ j ) j = 1 M I T ( τ j ) .

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