Abstract

Angle-resolved photoelectron spectra of argon atoms by XUV attosecond pulses in the presence of a circularly polarized laser field are calculated to examine their dependence on the duration and the chirp of the attosecond pulses. From the calculated electron spectra, we show how to retrieve the duration and the chirp of the attosecond pulse using genetic algorithm. The method is expected to be used for characterizing the attosecond pulses which are produced by polarization gating of few-cycle left- and right-circularly polarized infrared laser pulses.

© 2005 Optical Society of America

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References

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    [CrossRef] [PubMed]
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Appl. Phys. B (1)

V. Strekov, A. Zair, O. Tcherbakoff, R. López-Martens, E. Cormier, E. Mével, and E. Constant, �??Generation of attosecond pulses with ellipticity-modulated fundamental,�?? Appl. Phys. B 78, 879�??884 (2004).
[CrossRef]

J. Modern. Optics (1)

Bing Shan, Shambhu Ghimire, and Zenghu Chang, �??Generation of attosecond extreme ultraviolet supercontinuum by a polarization gating,�?? J. Modern. Optics 52, 277�??283 (2004).
[CrossRef]

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

J. Phys. B (1)

E. S. Toma and H. G. Muller, �??Calculation of matrix elements for mixed extreme-ultraviolet-infrared two-photon above-threshold ionization of argon,�?? J. Phys. B 35, 3435�??3442 (2002).
[CrossRef]

Nature (London) (1)

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, �??Attosecond metrology,�?? Nature (London), 414, 509�??513 (2001).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (6)

Ph. Antonie, B. Piraux, D. B. Milosevic, and M. Gajda, �??Generation of ultrashort pulses of harmonics,�?? Phys. Rev. A 54, R1761-R1764 (1996).
[CrossRef]

D. J. Kennedy and S. T. Manson, �??Photoionization of the noble gases: Cross sections and angular distributions,�?? Phys. Rev. A 5, 227�??247 (1972).
[CrossRef]

F. A. Parpia, W. R. Jphnson, and V. Radojevic, �??Application of the relativistic local-density approximation to photoionization of the outer shells of neon, argon, krypton and xenon,�?? Phys. Rev. A 29, 3173�??3180 (1984).
[CrossRef]

M. Y. Adam, P. Morin, and G. Wendin. �??Photoelectron satellite spectrum in the region of 3s Cooper minimum of argon,�?? Phys. Rev. A 31, 1426�??1433 (1985).
[CrossRef] [PubMed]

Zenghu Chang, �??Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,�?? Phys. Rev. A 70, 043802-1�??8 (2004).
[CrossRef]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L�??Huillier, and P. B. Corkum, �??Theory of high-harmonic generation by low frequency laser fields,�?? Phys. Rev. A 49, 2117�??2132 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, �??Attosecond angle-resolved photoelectron spectroscopy,�?? Phys. Rev. Lett. 91, 223902-1�??4 (2003).
[CrossRef]

M. Ivanov, P. B. Corkum, T. Zuo, and A. Bandrauk, "Routes to control of intense-field atomic polarizability," Phys. Rev. Lett. 74, 2933�??2936 (1995).
[CrossRef] [PubMed]

Markus Kitzler, Nenad Milosevic, Armin Scrinzi, Ferenc Krausz, and Thomas Brabec, �??Quantum theory of attosecond xuv pulse measurement by laser dressed photoionization,�?? Phys. Rev. Lett. 88, 173904-1�??4 (2002).
[CrossRef]

J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, �??Attosecond streak camara,�?? Phys. Rev. Lett. 88, 173903-1�??4 (2002).
[CrossRef]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, �??Intense few-cycle laser fields: Frontiers of nonlinear optics,�?? Rev. Mod. Phys. 72, 545�??591 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Trebino, Kenneth W. DeLong, David N. Fittinghoff, John N. Sweetser, Marco A Krumbügel, and Bruce A. Richman, �??Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,�?? Rev. Sci. Instrum. 68, 3277�??3295 (1997).
[CrossRef]

Science (2)

Markus Drescher, Michael Hentschel, Reinhard Kienberger, Gabriel Tempea, Christian Spielmann, Georg A. Reider, Paul B. Corkum, and Ferenc Krausz, �??X-ray pulses approaching the attosecond frontier,�?? Science 291, 1923�??1927 (2001).
[CrossRef] [PubMed]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, �??Direct measuremnt of light waves,�?? Science 305, 1267�??1269 (2004).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

L. V. Keldysh, �??Ionization in the field of a strong electromagnetic wave,�?? Sov. Phys. JETP 20, 1307�??1314 (1965).

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Figures (9)

Fig. 1.
Fig. 1.

The time-dependence of the ellipticity and the two perpendicular electric field components of a laser pulse resulting from combining a left-hand circularly polarized pulse and a right-hand circularly polarized pulse. The pulse duration for both circular pulses is 5 fs and the delay between them is 5 fs. The solid and dotted lines represent the two orthogonal field components and the dashed line shows the ellipticity. Note that the small window of vanishing ellipticity or polarization gating where the combined field is nearly linearly polarized.

Fig. 2.
Fig. 2.

(a) The square of the dipole transition moment and (b)the asymmetry parameter β from the ground state of Ar by monochromatic light. (c) The ionization probability density vs photoelectron energy of Ar ionized by an XUV pulse which has mean photon energy of 35 eV, duration of 0.1 fs and peak intensity of 1012 W/cm2. Dashed lines represent the spectral shape of the XUV pulse.

Fig. 3.
Fig. 3.

(a) Energy and angular distributions of photoelectrons from Ar by a single XUV pulse of duration (FWHM) 100 as. The polarization of the XUV pulse is along the x-axis from which the angles of the photoelectrons are measured. (b) and (c), electron spectra by XUV pulses assisted by a circularly polarized laser with phase of π/2 and 0, respectively. The XUV pulse was assumed to be not chirped.

Fig. 4.
Fig. 4.

Dependence of photoelectron spectra on the XUV pulse durations. The upper row is for laser-free photoionization and the lower row is for laser-assisted photoionization where the laser phase was chosen to be π/2. From (a) to (c) the XUV pulse durations are 0.2, 0.5 and 2 fs, respectively. The XUV pulses are assumed to have no chirp.

Fig. 5.
Fig. 5.

Photoelectron spectra by laser-assisted XUV pulses with different chirp parameters and pulse durations as indicated in the figure. The frequency width of XUV pulse is fixed as 18.25 eV.

Fig. 6.
Fig. 6.

The center of gravity energy of the photoelectrons vs the electron’s angle for different chirp parameters from 0 to 20 of the XUV pulses. The width of the XUV pulse is fixed at 18.25 eV. Note the shift to the higher energy as the chirp parameter increases until at the highest chirp where the pulse duration is close to the optical period.

Fig. 7.
Fig. 7.

Photoelectron spectra by a train of two attosecond XUV pulses: (a) no laser ; (b),(c),(d), with lasers, of phase 0, π/4 and π/2, respectively.

Fig. 8.
Fig. 8.

Comparison of the retrieved electric field with the original field. The inset shows the intensity profile of the original and the retrieved pulses, in units of 1012W/cm2.

Fig. 9.
Fig. 9.

Comparison of the photoelectron spectra calculated using (a) the original pulse and (b) the retrieved pulse, at a different time delay of -0.2 fs.

Equations (15)

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V ( r ) = ( 1 + 5.4 e r + 11.6 e 3.682 r ) r .
R ( + ) = 0 r P 3 p P ε s ( ε d ) dr ,
d 2 = 6 ( 1 3 R 2 + 2 3 R + 2 )
d σ d Ω = σ tot 4 π [ 1 + β 3 cos 2 θ 1 2 ] ,
E x ( t ) = Re { E 0 x e σ ( 1 i ξ ) t 2 e i ω x t e x } ,
E l ( t ) = 1 2 E 0 ( t ) [ cos ( ω l t + ϕ ) e x + sin ( ω l t + ϕ ) e y ]
v l ( t ) = t E l ( t ) dt .
v l ( t ) 1 2 ω l E 0 ( t ) [ sin ( ω l t + ϕ ) e x + cos ( ω l t + ϕ ) e y ] .
b ( v ) = i dt d [ p ( t ) ] · E x ( t ) exp [ i t dt [ p ( t ) ] 2 2 + i I p t ]
1 2 [ v v l ( t s ) ] 2 = E 0 ,
Δ ω = 4 ln 2 τ x 1 + ξ 2 .
1 2 [ v v l ( t ) ] 2 = E 0 2 σ ξ t = Ω ( t ) .
E x ( t T 0 4 ) + E x ( t + T 0 4 ) .
b ( v ) = i dt d ( v ) · E x ( t ) exp [ i ( 1 2 ) v 2 t + i I p t ] .
ϕ ( ω ) = i = 1 N c i ( ω ω 0 ) i

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