## Circularly-polarized laser-assisted photoionization spectra of argon for attosecond pulse measurements

Optics Express, Vol. 13, Issue 6, pp. 1966-1977 (2005)

http://dx.doi.org/10.1364/OPEX.13.001966

Acrobat PDF (340 KB)

### 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

## 1. Introduction

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

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]

3. 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]

4. 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]

5. 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]

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]

6. 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]

7. P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, “Subfemtosecond pulses,” Opt. Lett. **19**, 1870–1872 (1994). [CrossRef] [PubMed]

8. 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]

9. Ph. Antonie, B. Piraux, D. B. Milosevic, and M. Gajda, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A **54**, R1761–R1764 (1996). [CrossRef]

10. V. T. Platonenko and V. V. Strelkov. “Single attosecond soft-x-ray pulse generated with a limited laser beam,” J. Opt. Soc. Am. B **16**, 435–440 (1999). [CrossRef]

11. 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]

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

13. 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]

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

*et al*. [5

5. 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]

## 2. Cross sections and asymmetry parameters for photoionization of Ar

14. 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]

*ε*s(

*R*-) and

*ε*d (

*R*+) continuum states are given by

*σ*

_{tot}is proportional to

*d*is the magnitude of the total transition dipole moment.

*θ*is the angle of the electron’s final momentum with respect to the light polarization direction, and

*β*is the asymmetry parameter that can be calculated using the method described in [15

15. 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]

*β*parameter and the total transition dipole moment, in the same spirit of obtaining differential cross section, we can define an effective angular dependent transition dipole moment for later calculation of laser-assisted photoionization.

*d*|

^{2}and (b) the

*β*parameter, versus the photon energy of the monochromatic XUV light. The results from this simple calculation show reasonable good agreement with the more elaborate many-electron calculations [16

16. F. A. Parpia, W. R. Jphnson, and V. Radojevic, “Applicattion 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]

17. 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]

## 3. XUV photoionization assisted by a circularly polarized laser

*ω*

_{x}can be generally described by

^{12}W/cm

^{2}and mean photon energy 35 eV. A circularly polarized laser field is characterized by an electric field

^{13}W/cm

^{2}. The central wavelength of the laser is taken to be 750 nm.

*t*, they gain a drift velocity (proportional to the vector potential of the laser field) given by

19. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by lowe frequency laser fields,” Phys. Rev. A **49**, 2117–2132 (1994). [CrossRef] [PubMed]

4. 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]

5. 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]

*b*(

*t*)=

_{l}(

*t*) is the instantaneous momentum of electron at time

*t*and

*I*

_{p}is the ionization energy. From the saddle point analysis, most of the contribution to the time integral comes from the time

*t*

_{s}satisfying the stationary phase condition

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]

3. 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]

*E*

_{0}=

*ω*

_{x}

*-I*

_{p}. In the calculation, integration over time in Eq. (9) is performed numerically.

### 3.1. Transform-limited XUV pulses

^{13}W/cm

^{2}such that the ionization probability by the XUV itself (intensity is 10

^{12}W/cm

^{2}) is two orders higher than that by the laser field. The two pulses peak at the same time

*t*=0. The polarization direction of the XUV pulse is defined as the x-axis (zero angle). The drift velocity at

*t*=0 is along y direction if the laser phase is zero and -x direction if laser phase is

*π*/2.

*β*is about 1.5, thus the laser-free photoelectrons peak at 0 and 180 degrees as shown in Fig. 3(a). Due to the stronger signal along the XUV polarization direction (x-axis), smaller detection angle is required when the detector is along the x-axis. When a laser field is present, the spectrum is deformed. Fig. 3(b) and Fig. 3(c) show the laser-assisted photoelectron spectra for laser phase of

*π*/2 and 0, respectively. When the drift velocity is along the -

*x*direction (

*ϕ=π*/2, Fig. 3(b)), more electrons are found in the -x direction and the energy distribution is stretched in the same direction which makes the detection more efficient than the case of laser phase of 0 (Fig. 3(c)). Clearly, phase-stabilized laser of phase

*ϕ=π*/2 is more desirable. In the following, we will only consider laser phase of

*ϕ=π*/2 unless mentioned otherwise.

20. 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]

21. 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]

*et al*. [5

**88**, 173903-1–4 (2002). [CrossRef]

### 3.2. Chirp-dependence

*τ*

_{x}=0.1 fs; (b) ξ=3,

*τ*

_{x}=0.32 fs; (c) ξ=5,

*τ*

_{x}=0.51 fs; (d) ξ=10,

*τ*

_{x}=1 fs; (e) ξ=15,

*τ*

_{x}=1.51 fs and (d) ξ=20,

*τ*

_{x}=2 fs.

*E*(

*θ*) (see Fig. 6). By focusing on this trace for angles larger than 180°, we note that

*E*(

*θ*) increases monotonically with increasing chirp, until for the large chirp parameter of 20 where the duration of the XUV pulse of 2.0 fs is close to the laser period. This trace, combining with the angular width, qualitatively illustrate the chirp and pulse duration dependence of the XUV pulses in the time-domain.

### 3.3. Double XUV pulses

*T*

_{0}/2 (i.e., one half of the laser period),

^{12}W/cm

^{2}. When the polarization gating is not short enough, such a train of two attosecond pulses are generated.

*ω*

_{l}, see Fig. 7(a). When the laser field is present, the spectra is distorted but are made of two identical pairs. In Fig. 7, the laser phases are 0,

*π*/4,

*π*/2, respectively, from (b) to (d). In (b) electrons generated by the left pulse experience a +x shift, while electrons generated by the right pulse experience a -

*x*shift. Thus the total electron spectra are stretched along the x-axis. In (c), electrons generated by the two pulses shift about half way toward the 45 degrees (and 225 degrees) line. In (d), the shifting to this diagonal line is complete and the electron spectrum shows a butterfly shape.

## 4. Retrieving the XUV pulse information

*b*(

^{2}is available experimentally. In order to obtain the phase information, one has to rely on the additional information supplemented by the laser-assisted photoionization measurement which builds the cross-correlation between the XUV pulse and the laser pulse. Our procedure of retrieving the XUV pulse can be described as follows: 1) using the measured laser-free spectra as input; 2) starting with a simple guess of the phase of

*b*(

*E*(

*θ*) defined earlier. In the simplest case, if we assume the XUV pulse has a Gaussian profile and is linearly chirped, then only one parameter needs to be fitted based on Eq. (11).

*ω*

_{0}is the center frequency, and the second order term corresponds to the linear chirp of the pulse. Our simulation shows that the latter method converges faster and is indeed used to retrieve the pulse information in the following example.

## 5. Summary and conclusion

## Acknowledgments

## References and links

1. | T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. |

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 |

3. | 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) , |

4. | 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. |

5. | J. Itatani, F. Quéré, G. L. Yudin, M. Yu. Ivanov, F. Krausz, and P. B. Corkum, “Attosecond streak camara,” Phys. Rev. Lett. |

6. | 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 |

7. | P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, “Subfemtosecond pulses,” Opt. Lett. |

8. | M. Ivanov, P. B. Corkum, T. Zuo, and A. Bandrauk, Routes to control of intense-field atomic polarizability.Phys. Rev. Lett. |

9. | Ph. Antonie, B. Piraux, D. B. Milosevic, and M. Gajda, “Generation of ultrashort pulses of harmonics,” Phys. Rev. A |

10. | V. T. Platonenko and V. V. Strelkov. “Single attosecond soft-x-ray pulse generated with a limited laser beam,” J. Opt. Soc. Am. B |

11. | 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 |

12. | Zenghu Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A |

13. | Bing Shan, Shambhu Ghimire, and Zenghu Chang, “Generation of attosecond extreme ultraviolet supercontinuum by a polarization gating,” J. Modern. Optics |

14. | 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 |

15. | D. J. Kennedy and S. T. Manson, “Photoionization of the noble gases: Cross sections and angular distributions,” Phys. Rev. A |

16. | F. A. Parpia, W. R. Jphnson, and V. Radojevic, “Applicattion of the relativistic local-density approximation to photoionization of the outer shells of neon, argon, krypton and xenon,” Phys. Rev. A |

17. | M. Y. Adam, P. Morin, and G. Wendin. “Photoelectron satellite spectrum in the region of 3s Cooper minimum of argon,” Phys. Rev. A |

18. | L. V. Keldysh, “Ionization in the field of a stong electromagnetic wave,” Sov. Phys. JETP |

19. | M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, Anne L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by lowe frequency laser fields,” Phys. Rev. A |

20. | S. A. Aseyev, Y. Ni, L. J. Frasinski, H. G. Muller, and M. J. J. Vrakking, “Attosecond angle-resolved photoelectron spectroscopy,” Phys. Rev. Lett. |

21. | 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. |

**OCIS Codes**

(260.7200) Physical optics : Ultraviolet, extreme

(320.5550) Ultrafast optics : Pulses

(320.7100) Ultrafast optics : Ultrafast measurements

**ToC Category:**

Research Papers

**History**

Original Manuscript: November 18, 2004

Revised Manuscript: March 6, 2005

Published: March 21, 2005

**Citation**

Z. Zhao, Zenghu Chang, X. Tong, and C. Lin, "Circularly-polarized laser-assisted photoionization spectra of argon for attosecond pulse measurements," Opt. Express **13**, 1966-1977 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-1966

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### References

- T. Brabec and F. Krausz, �??Intense few-cycle laser fields: Frontiers of nonlinear optics,�?? Rev. Mod. Phys. 72, 545�??591 (2000). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- P. B. Corkum, N. H. Burnett, and M. Y. Ivanov, �??Subfemtosecond pulses,�?? Opt. Lett. 19, 1870�??1872 (1994). [CrossRef] [PubMed]
- 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]
- Ph. Antonie, B. Piraux, D. B. Milosevic, and M. Gajda, �??Generation of ultrashort pulses of harmonics,�?? Phys. Rev. A 54, R1761-R1764 (1996). [CrossRef]
- V. T. Platonenko and V. V. Strelkov. �??Single attosecond soft-x-ray pulse generated with a limited laser beam,�?? J. Opt. Soc. Am. B 16, 435�??440 (1999). [CrossRef]
- 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]
- Zenghu Chang, �??Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,�?? Phys. Rev. A 70, 043802-1�??8 (2004). [CrossRef]
- 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]
- 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]
- 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]
- L. V. Keldysh, �??Ionization in the field of a strong electromagnetic wave,�?? Sov. Phys. JETP 20, 1307�??1314 (1965).
- 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]
- 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]
- 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]

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