Abstract

The durations of extreme-ultraviolet femtosecond pulses (harmonics 21 and 27 of a Ti:sapphire femtosecond laser) have been measured by a cross-correlation technique. Photoelectron energy spectra resulting from ionization of helium atoms by one harmonic photon in the presence of the infrared laser field show sidebands that provide a cross-correlation signal from which the durations of the harmonic pulses can be obtained. The measurements yield a mean value of 130 fs for both harmonics. The accuracy of the method depends on the actual intensity dependence of the sidebands.

© 1997 Optical Society of America

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References

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  1. A. L’Huillier, L. A. Lompré, G. Mainfray, and C. Manus, in Atoms in Intense Laser Fields, M. Gavrila, ed., Suppl. 1 of Advances in Atomic, Molecular and Optical Physics (Academic, San Diego, Calif., 1992).
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    [CrossRef] [PubMed]
  3. J. L. Krause, K. J. Schafer, and K. C. Kulander, Phys. Rev. Lett. 68, 3535 (1992).
    [CrossRef] [PubMed]
  4. P. Salieres, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 75, 3776 (1995).
    [CrossRef]
  5. P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” submitted to Phys. Rev. A.
  6. J. M. Schins, A. Bouhal, P. Breyer, P. Agostini, A. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, J. Opt. Soc. Am. B 13, 197 (1996).
    [CrossRef]
  7. T. E. Glover, R. W. Schoenlein, A. H. Chin, and C. V. Shank, Phys. Rev. Lett. 76, 2468 (1996).
    [CrossRef] [PubMed]
  8. H. G. Muller, Comments At. Mol. Phys. 24, 355 (1990).
  9. V. Veniard, R. Taı̈eb, and A. Maquet, Phys. Rev. Lett. 74, 4161 (1995).
    [CrossRef]
  10. R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).
  11. J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
    [CrossRef] [PubMed]
  12. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964); F. Faisal, J. Phys. B 6, 89 (1973).
    [CrossRef]
  13. H. Reiss, Phys. Rev. A 22, 1786 (1980).
    [CrossRef]
  14. A. Gionga, V. Florescu, A. Maquet, and R. Taı̈eb, Phys. Rev. A 47, 1830 (1993).
    [CrossRef]
  15. C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, Opt. Lett. 18, 140 (1993).
    [CrossRef]
  16. J. Peatross, J. L. Chaloupka, and D. D. Meyerhofer, Opt. Lett. 19, 942 (1994).
    [CrossRef] [PubMed]
  17. J. P. Chauvineau, Rev. Phys. Appl. 23, 1645 (1994).
    [CrossRef]

1996 (2)

1995 (2)

V. Veniard, R. Taı̈eb, and A. Maquet, Phys. Rev. Lett. 74, 4161 (1995).
[CrossRef]

P. Salieres, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 75, 3776 (1995).
[CrossRef]

1994 (3)

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

J. Peatross, J. L. Chaloupka, and D. D. Meyerhofer, Opt. Lett. 19, 942 (1994).
[CrossRef] [PubMed]

J. P. Chauvineau, Rev. Phys. Appl. 23, 1645 (1994).
[CrossRef]

1993 (3)

A. Gionga, V. Florescu, A. Maquet, and R. Taı̈eb, Phys. Rev. A 47, 1830 (1993).
[CrossRef]

C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, Opt. Lett. 18, 140 (1993).
[CrossRef]

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

1992 (1)

J. L. Krause, K. J. Schafer, and K. C. Kulander, Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

1990 (1)

H. G. Muller, Comments At. Mol. Phys. 24, 355 (1990).

1980 (1)

H. Reiss, Phys. Rev. A 22, 1786 (1980).
[CrossRef]

1964 (1)

L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964); F. Faisal, J. Phys. B 6, 89 (1973).
[CrossRef]

Agostini, P.

J. M. Schins, A. Bouhal, P. Breyer, P. Agostini, A. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, J. Opt. Soc. Am. B 13, 197 (1996).
[CrossRef]

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Antonetti, A.

J. M. Schins, A. Bouhal, P. Breyer, P. Agostini, A. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, J. Opt. Soc. Am. B 13, 197 (1996).
[CrossRef]

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, Opt. Lett. 18, 140 (1993).
[CrossRef]

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Bijkerk, F.

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Bouhal, A.

J. M. Schins, A. Bouhal, P. Breyer, P. Agostini, A. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, J. Opt. Soc. Am. B 13, 197 (1996).
[CrossRef]

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Breger, P.

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Breyer, P.

Chaloupka, J. L.

Chambaret, J. P.

Chauvineau, J. P.

J. P. Chauvineau, Rev. Phys. Appl. 23, 1645 (1994).
[CrossRef]

Chin, A. H.

T. E. Glover, R. W. Schoenlein, A. H. Chin, and C. V. Shank, Phys. Rev. Lett. 76, 2468 (1996).
[CrossRef] [PubMed]

Constantinescu, A. C.

Constantinescu, R. C.

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Corkum, P.

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

Florescu, V.

A. Gionga, V. Florescu, A. Maquet, and R. Taı̈eb, Phys. Rev. A 47, 1830 (1993).
[CrossRef]

Gionga, A.

A. Gionga, V. Florescu, A. Maquet, and R. Taı̈eb, Phys. Rev. A 47, 1830 (1993).
[CrossRef]

Glover, T. E.

T. E. Glover, R. W. Schoenlein, A. H. Chin, and C. V. Shank, Phys. Rev. Lett. 76, 2468 (1996).
[CrossRef] [PubMed]

Grillon, G.

J. M. Schins, A. Bouhal, P. Breyer, P. Agostini, A. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, J. Opt. Soc. Am. B 13, 197 (1996).
[CrossRef]

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, Opt. Lett. 18, 140 (1993).
[CrossRef]

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Keldysh, L. V.

L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964); F. Faisal, J. Phys. B 6, 89 (1973).
[CrossRef]

Krause, J. L.

J. L. Krause, K. J. Schafer, and K. C. Kulander, Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

Kulander, K. C.

J. L. Krause, K. J. Schafer, and K. C. Kulander, Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

L’Huillier, A.

P. Salieres, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 75, 3776 (1995).
[CrossRef]

P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” submitted to Phys. Rev. A.

A. L’Huillier, L. A. Lompré, G. Mainfray, and C. Manus, in Atoms in Intense Laser Fields, M. Gavrila, ed., Suppl. 1 of Advances in Atomic, Molecular and Optical Physics (Academic, San Diego, Calif., 1992).

Le Blanc, C.

Lewenstein, M.

P. Salieres, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 75, 3776 (1995).
[CrossRef]

P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” submitted to Phys. Rev. A.

Lompré, L. A.

A. L’Huillier, L. A. Lompré, G. Mainfray, and C. Manus, in Atoms in Intense Laser Fields, M. Gavrila, ed., Suppl. 1 of Advances in Atomic, Molecular and Optical Physics (Academic, San Diego, Calif., 1992).

Louis, E.

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Mainfray, G.

A. L’Huillier, L. A. Lompré, G. Mainfray, and C. Manus, in Atoms in Intense Laser Fields, M. Gavrila, ed., Suppl. 1 of Advances in Atomic, Molecular and Optical Physics (Academic, San Diego, Calif., 1992).

Manus, C.

A. L’Huillier, L. A. Lompré, G. Mainfray, and C. Manus, in Atoms in Intense Laser Fields, M. Gavrila, ed., Suppl. 1 of Advances in Atomic, Molecular and Optical Physics (Academic, San Diego, Calif., 1992).

Maquet, A.

V. Veniard, R. Taı̈eb, and A. Maquet, Phys. Rev. Lett. 74, 4161 (1995).
[CrossRef]

A. Gionga, V. Florescu, A. Maquet, and R. Taı̈eb, Phys. Rev. A 47, 1830 (1993).
[CrossRef]

Meyerhofer, D. D.

Migus, A.

Muller, H. G.

J. M. Schins, A. Bouhal, P. Breyer, P. Agostini, A. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, J. Opt. Soc. Am. B 13, 197 (1996).
[CrossRef]

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

H. G. Muller, Comments At. Mol. Phys. 24, 355 (1990).

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Mysyrowicz, A.

J. M. Schins, A. Bouhal, P. Breyer, P. Agostini, A. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, J. Opt. Soc. Am. B 13, 197 (1996).
[CrossRef]

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Peatross, J.

Reiss, H.

H. Reiss, Phys. Rev. A 22, 1786 (1980).
[CrossRef]

Salieres, P.

P. Salieres, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 75, 3776 (1995).
[CrossRef]

P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” submitted to Phys. Rev. A.

Schafer, K. J.

J. L. Krause, K. J. Schafer, and K. C. Kulander, Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

Schins, J. M.

J. M. Schins, A. Bouhal, P. Breyer, P. Agostini, A. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, J. Opt. Soc. Am. B 13, 197 (1996).
[CrossRef]

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Schoenlein, R. W.

T. E. Glover, R. W. Schoenlein, A. H. Chin, and C. V. Shank, Phys. Rev. Lett. 76, 2468 (1996).
[CrossRef] [PubMed]

Shank, C. V.

T. E. Glover, R. W. Schoenlein, A. H. Chin, and C. V. Shank, Phys. Rev. Lett. 76, 2468 (1996).
[CrossRef] [PubMed]

Tai¨eb, R.

V. Veniard, R. Taı̈eb, and A. Maquet, Phys. Rev. Lett. 74, 4161 (1995).
[CrossRef]

A. Gionga, V. Florescu, A. Maquet, and R. Taı̈eb, Phys. Rev. A 47, 1830 (1993).
[CrossRef]

Veniard, V.

V. Veniard, R. Taı̈eb, and A. Maquet, Phys. Rev. Lett. 74, 4161 (1995).
[CrossRef]

Voorma, H. G.

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

Comments At. Mol. Phys. (1)

H. G. Muller, Comments At. Mol. Phys. 24, 355 (1990).

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Phys. Rev. A (2)

H. Reiss, Phys. Rev. A 22, 1786 (1980).
[CrossRef]

A. Gionga, V. Florescu, A. Maquet, and R. Taı̈eb, Phys. Rev. A 47, 1830 (1993).
[CrossRef]

Phys. Rev. Lett. (6)

J. M. Schins, P. Breger, P. Agostini, R. C. Constantinescu, H. G. Muller, G. Grillon, A. Antonetti, and A. Mysyrowicz, Phys. Rev. Lett. 73, 2180 (1994).
[CrossRef] [PubMed]

T. E. Glover, R. W. Schoenlein, A. H. Chin, and C. V. Shank, Phys. Rev. Lett. 76, 2468 (1996).
[CrossRef] [PubMed]

V. Veniard, R. Taı̈eb, and A. Maquet, Phys. Rev. Lett. 74, 4161 (1995).
[CrossRef]

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

J. L. Krause, K. J. Schafer, and K. C. Kulander, Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

P. Salieres, A. L’Huillier, and M. Lewenstein, Phys. Rev. Lett. 75, 3776 (1995).
[CrossRef]

Rev. Phys. Appl. (1)

J. P. Chauvineau, Rev. Phys. Appl. 23, 1645 (1994).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964); F. Faisal, J. Phys. B 6, 89 (1973).
[CrossRef]

Other (3)

A. L’Huillier, L. A. Lompré, G. Mainfray, and C. Manus, in Atoms in Intense Laser Fields, M. Gavrila, ed., Suppl. 1 of Advances in Atomic, Molecular and Optical Physics (Academic, San Diego, Calif., 1992).

P. Salieres, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” submitted to Phys. Rev. A.

R. C. Constantinescu, H. G. Muller, A. Bouhal, J. M. Schins, P. Breger, P. Agostini, G. Grillon, A. Antonetti, A. Mysyrowicz, H. G. Voorma, E. Louis, and F. Bijkerk, in Super-Intense Atom-Laser Physics IV , H. G. Muller and M. V. Fedorov, eds., NATO ASI Series 3/13 (Kluwer, Dordrecht, The Netherlands, 1996).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental setup.

Fig. 2
Fig. 2

Electron energy spectra. 30-eV mirror: (a) long delay and (b) zero delay. The peak labeled sdb in (b) is the one used for the cross-correlation measurement. 40-eV mirror: (c) long delay and (d) zero delay. The numbers are the harmonic orders, the labels sdb1, sdb2, and sdb3 in (d) refer to sidebands 1, 2, and 3, respectively.

Fig. 3
Fig. 3

Laser pulse obtained through a ω-2ω cross correlation (dots) fitted with a squared hyperbolic secant (curve) with a FWHM of 160 fs.

Fig. 4
Fig. 4

Experimental cross correlations and fits corresponding to different intensity dependences (see text): (a) first sideband of harmonic 21; (b), (c) second and third sidebands, respectively, of harmonic 27. lopt, Lowest-order perturbation theory; exprt, experimental intensity dependence.

Fig. 5
Fig. 5

Experimental intensity dependence of (a) the first sideband, (b) the second sideband, and (c) the third sideband of harmonic 27 (squares). The dotted lines show least-squares fits to the data.

Equations (6)

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

Eq,n=ωXUV±nωIR-IP-Up,
Jn(x, y)=m=-+ Jn-2m(x)Jm(y).
Isb(n)(τ)-+f[IIR(t-τ)]IXUV(t)dt.
f(IIR)pn3[1/(1+pn2)]4×0π sin θ cos2 θJn2[x(IIR), y(IIR)]dθ
τH=(τC2-τF2/α)1/2.
Isb(n)q=1923 hqpq,n3(1+pq,n2)-4×0π sin θ cos2 θJn2[x(IIR, n), y(IIR)]dθ,

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