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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 23857–23866
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Optimization of three-color laser field for the generation of single ultrashort attosecond pulse

Peng-Cheng Li, I-Lin Liu, and Shih-I Chu  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 23857-23866 (2011)
http://dx.doi.org/10.1364/OE.19.023857


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Abstract

We present an efficient and realizable scheme for the generation of an ultrashort single attosecond (as) pulse. The feasibility of such a scheme is demonstrated by solving accurately the time-dependent Schrödinger equation using the time-dependent generalized pseudospectral (TDGPS) method. This scheme involves the use of the optimization of the three-color laser fields. The optimized laser pulse is synthesized by three one-color laser pulses with proper relative phases. It can provide a longer acceleration time for the tunneling and oscillating electrons, and allows the electrons to gain more kinetic energy. We show that the plateau of high-order harmonic generation is extended dramatically and a broadband supercontinuum spectra is produced. As a result, an isolated 23 as pulse with a bandwidth of 163 eV can be obtained directly by superposing the supercontinuum harmonics near the cutoff region. We will show that such a metrology can be realized experimentally.

© 2011 OSA

1. Introduction

The availability of attosecond (as) extreme ultraviolet pulse is on the verge of opening up a new field of science [1

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]

3

3. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008). [CrossRef] [PubMed]

]. Attosecond laser permitted observation of control of electron wave packets [4

4. R. Kienberger, M. Hentschel, M. Uiberacker, Ch. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Steering attosecond electron wave packets with light,” Science 297, 1144–1148 (2002). [CrossRef] [PubMed]

], probing of nuclear dynamics [5

5. S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilä, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312, 424–427 (2006). [CrossRef] [PubMed]

] and electronic dynamics [6

6. M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz,“Attosecond real-time observation of electron tunnelling in atoms,” Nature (London) 446, 627–632 (2007). [CrossRef]

], attosecond time-resolved spectroscopy [7

7. M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature (London) 419, 803–807 (2002). [CrossRef]

], tomographic imaging of molecular orbital [8

8. J. Itatani, J. Levesque, D. Zeidler, Hiromichi Niikura, H. Ppin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432, 867–871 (2004). [CrossRef]

], etc. The generation of much shorter attosecond pulses has continued to attract much interest and has become one of the most active research directions in attosecond metrology today.

Among the approaches to produce attosecond pulses, the high-order harmonic generation (HHG) seems to be the most promising one[1

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]

, 9

9. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009). [CrossRef]

]. The HHG procedure can be well understood by the semiclassical three-step model [10

10. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]

]. According to the three-step model, the electron tunnels through the barrier formed by the Coulomb potential and the laser field in the beginning, then it oscillates quasifreely driven by the laser field and acquires additional kinetic energy, and finally it can recombine with the parent ion and emit radiation. The harmonic spectrum is characterized by a rapid drop at low orders followed by a broad plateau where all the harmonics have the same strength and a sharp cutoff around harmonic energy Ip + 3.17Up, where Ip is the atomic ionization potential and Up is the ponderomotive energy, i.e., the cycle-averaged kinetic energy of an electron gained in a monochromatic laser field.

At present, many schemes have been proposed to generate an ultrabroad supercontinuum spectrum and obtain extreme short attosecond pulse, such as using two-color laser fields [11

11. W. Y. Hong, P. X. Lu, P. F. Lan, Z. Y. Yang, Y. H. Li, and Q. Liao, “Broadband xuv supercontinuum generation via controlling quantum paths by a low-frequency field,” Phys. Rev. A 77, 033410 (2008). [CrossRef]

, 12

12. P. Zou, Z. N. Zeng, Y. H. Zheng, Y. Y. Lu, P. Liu, R. X. Li, and Z. Z. Xu, “Coherent control of broadband isolated attosecond pulses in a chirped two-color laser field,” Phys.Rev. A 81, 033428 (2010). [CrossRef]

], a few-cycle laser pulse [13

13. J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A 74(2), 023404 (2006). [CrossRef]

, 3

3. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008). [CrossRef] [PubMed]

], the chirped laser pulse [14

14. J. J. Xu, “Isolated short attosecond pulse generation in an orthogonally polarized multicycle chirped laser field,” Phys. Rev. A 83, 033823 (2011). [CrossRef]

, 15

15. J. Wu, G. T. Zhang, C. L. Xia, and X. S. Liu, “Control of the high-order harmonics cutoff and attosecond pulse generation through the combination of a chirped fundamental laser and a subharmonic laser field,” Phys. Rev. A 82, 013411 (2010). [CrossRef]

], quantum path control [16

16. K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004). [CrossRef] [PubMed]

, 17

17. I. L. Liu, P. C. Li, and S. I. Chu, “Coherent control of the electron quantum paths for the generation of single ultrashort attosecond laser pulse,” Phys. Rev. A 84, 033414 (2011). [CrossRef]

], polarization gating [18

18. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006). [CrossRef] [PubMed]

, 19

19. Z. H. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A 71, 023813 (2005). [CrossRef]

], and long-wavelength pumping [20

20. V. S. Yakovlev, M. Ivanov, and F. Krausz, “Enhanced phasematchingfor generation of soft x-ray harmonics and attosecond pulses in atomic gases,” Opt. Express 15, 15351–15364 (2007). [CrossRef] [PubMed]

, 21

21. P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4, 386–389 (2008). [CrossRef]

]. Among them, Sansone et al. have reported the generation of a 130 as isolated XUV pulse using the near-infrared driving pulse. Very recently, Goulielmakis et al. have experimentally demonstrated the generation of an isolated 80 attosecond pulses using only a single 3.3 fs pump pulse. Moreover, many theoretical works have been done to generate single sub-100 as pulse [22

22. L. E. Chipperfield, J. S. Robinson, J. W. G. Tisch, and J. P. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett. 102, 063003 (2009). [CrossRef] [PubMed]

, 23

23. I. A. Ivanov and A. S. Kheifets, “Tailoring the waveforms to extend the high-order harmonic generation cutoff,” Phys. Rev. A 80, 023809 (2009). [CrossRef]

].

In this paper, we present a realizable approach for efficiently ultrashort attosecond pulses generation by creating a longer acceleration time for the oscillating electrons allowing electrons to obtain more kinetic energy from laser fields. Our pulses are constructed by superposing a range of synchronized high harmonics driven by the optimized three-color laser field. We know that a one-color driving field interacts with an atom and generates coherent high-frequency radiation through ionizing, accelerating, and recombining processes. These three processes occur every half optical cycle [24

24. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̈ev, R. Taïeb, B. Carr, H. G. Muller, P. Agostini, and P. Salires, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003). [CrossRef] [PubMed]

, 25

25. R. López-Martens, K. Varj, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salires, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, Claes-Göran, Wahlström, and Anne L Huillier, “Amplitude and phase control of attosecond light pulses,” Phys. Rev. Lett. 94, 033001 (2005). [CrossRef] [PubMed]

]. In our method, we choose a optimized three-color laser field that can be realized experimentally. This shape of laser pulse allows that the processes of ionization, acceleration, and recombination occur more than half optical cycle and enables the HHG plateau extended significantly. It is also important to note that our approach can obtain an efficient and very broadband supercontinuum than those of some other published works, such as the cases of two color laser pulse, the longer wavelength, and so on. Although our simulation of the single attosecond pulse generation is single atom response, the recent studies show that the single-atom spectrum is similar even considering propagation effects [26

26. T. Auguste, P. Salires, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009). [CrossRef]

]. Our theoretical calculations show that this proposed scheme can obtain the efficient broadband supercontinuum harmonic spectra, which is used to produce a very short attosecond pulse less than one atomic unit of time (the atomic unit of time is about 24 as), which is the time scale of electron motion in atoms.

2. Theoretical methods

The HHG and attosecond pulse generation can be investigated by solving the time-dependent Schrödinger equation (TDSE). In the length gauge, the TDSE of hydrogen atom can be written as (in atomic units)
iψ(r,t)t=H^ψ(r,t)=[H^0+V^(r,t)]ψ(r,t),
(1)
where Ĥ0 is the Hamiltonian of the Hydrogen atom.
H^0=12d2dr2+L^22r21r,
(2)
and V(r,t) is the time-dependent atom-field interaction
V^(r,t)=E(t)r=zE(t).
(3)

The TDSE is solved accurately and efficiently by means of the time-dependent generalized pseudospectral (TDGPS) method [13

13. J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A 74(2), 023404 (2006). [CrossRef]

, 27

27. X. M. Tong and S. I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: A new generalized pseudospectral time-dependent method,” Chem. Phys. 217, 119–130 (1997). [CrossRef]

]. Once the time evolution of the wave function ψ (r, t) is determined, the HHG power spectrum can be obtained. The time-dependent induced dipole acceleration can be given by means of Ehrenfest’s theorem [27

27. X. M. Tong and S. I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: A new generalized pseudospectral time-dependent method,” Chem. Phys. 217, 119–130 (1997). [CrossRef]

]
dA(t)=<ψ(r,t)|dz2dt2|ψ(r,t)>=<ψ(r,t)|zr3+E(t)|ψ(r,t)>,
(4)
and the HHG power spectrum can be determined, which is proportional to the modulus squared of the Fourier transform of dA(t). It is given by
PA(ω)=|1tfti1ω2titfdA(t)eiωtdt|2.
(5)
By superposing several harmonics, an ultrashort pulse can be generated,
I(t)=|qaqeiqωt|2,
(6)
where aq = ∫dA(t)eiqωt dt.

To study the detailed spectral and temporal structures of HHG, we perform the time-frequency analysis by means of the wavelet transform,
Aω(t0,ω)=dA(t)ωW[ω(tt0)]dt.
(7)

For the harmonic emission, a natural choice of the mother wavelet is given by the Morlet wavelet:
W(x)=1τeixex22τ2.
(8)

3. Results and discussion

Considering several experimental demonstrations obtained a few-cycle pulse (∼5fs) [3

3. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008). [CrossRef] [PubMed]

], the laser pulses we choose are near 5 femtosecond for the experimental realizations. In our calculations, the optimized three-color laser field has the following form:
E(t)=i=13Eif(t)cos(ωit+ϕi),
(9)
where f (t) is the Gaussian pulse with 5-fs pulse duration. Ei, ωi, and ϕi are the amplitudes, frequencies, and relative phase for each laser pulse, respectively. We choose the intensity I1 = 1.0 × 1014W/cm2, I2 = 1.2 × 1014W/cm2 and I3 = 1.5 × 1014W/cm2. The frequencies ω1=0.057 a.u. (800 nm), ω2=0.023 a.u. (2000 nm) and ω3=0.021 a.u. (2200 nm), and the relative phase ϕ1 = π, ϕ2 = 0 and ϕ3=π2, respectively. This optimized pulse shape is presented in Fig. 1(d).

Fig. 1 (a) A 5-fs 800 nm laser pulse with peak intensity I = 1.0 × 1014W/cm2 (black solid line) and a 5-fs 2000 nm laser pulse with peak intensity I = 1.2 × 1014W/cm2 (red dotted line). (b) The combination of the 5-fs 800 nm and 2000 nm laser pulse shown in (a). (c) A 5-fs 2200 nm laser pulse with peak intensity I = 1.5 × 1014W/cm2 (black dotted line). For reference, two-color combination case (green solid line) is also presented. (d) The optimized three-color laser field.

In order to give an explanation of why such three-color combination was chosen, the optimizing process is presented in Fig. 1(a)–(d). Figure 1(a) shows a 5-fs 800 nm laser pulse with peak intensity I = 1.0 × 1014W/cm2 (black solid line) and a 5-fs 2000 nm laser pulse with peak intensity I = 1.2×1014W/cm2 (red dotted line), respectively. If we choose this few-cycle 800nm laser pulse to generate attosecond pulse, it can only obtain a single 200 as-300 as pusle [13

13. J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A 74(2), 023404 (2006). [CrossRef]

]. If we desire to extend the HHG plateau and obtain ever shorter attosecond pulse, the longer driving wavelength is a good choice [20

20. V. S. Yakovlev, M. Ivanov, and F. Krausz, “Enhanced phasematchingfor generation of soft x-ray harmonics and attosecond pulses in atomic gases,” Opt. Express 15, 15351–15364 (2007). [CrossRef] [PubMed]

, 21

21. P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4, 386–389 (2008). [CrossRef]

]. Such as this 2000 nm laser pulse is presented in Fig. 1(a), because the ponderomotive energy is proportional to 2, which implies that the harmonic cutoff can be extended using longer wavelength of the driving laser field. However, only using one-color longer wavelength driving field has a serious disadvantage that the harmonic yield is greatly decreased than the shorter wavelength laser pulse [28

28. J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98, 013901 (2007). [CrossRef] [PubMed]

]. To enhance the harmonic yield, some schemes have been proposed to use a longer wavelength laser pulse in combination with a higher frequency pulse [29

29. K. Ishikawa, “Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003). [CrossRef] [PubMed]

]. Figure 1(b) presents the combination of the 800 nm and 2000 nm laser pulses as shown in Fig. 1(a). Here, the major local maximum of peaks are marked by A, B, C, and D. We can see that the effective wavelength is increased for this combined pulse, and the intensity of the peaks is also. Therefore, the quasifreely electrons can obtain higher cutoff energy when the electrons are ionized from the major local ionization peak A and return to emit the HHG radiation at the major local emission peaks B and D. However, such simple combination of two-color laser field can not efficiently be used for generation of a broadband supercontinuum due to the interaction of HHG emission from peaks B and D. In order to generate a broadband supercontinuum, we must eliminate the impact of peak B. So we add a 5-fs 2200 nm laser pulse with peak intensity I = 1.5 × 1014W/cm2 (black dotted line) to the combined two-color laser pulse, as shown in Fig. 1(c). It just can eliminate the peak B. This results are presented in Fig. 1(d). Namely, We obtain a optimized three-color laser pulse. We can see that the intensity of peak B is deceased, and the intensity of peak A and D is increased. The advantages of such changes are not only to significantly extend the plateau of HHG, but also obtain a broadband supercontinuum. This is very important for the successful generation of the single ultrashort attosecond pulse.

To explain extension of the plateau of the HHG from the optimized combination of three-color laser pulse, we analyze the dependence of the returning kinetic energy on the travel time of the electrons for the 800 nm laser pulse, the 2000 nm laser pulse, and the optimized three-color laser pulse, respectively. The laser parameters are the same as Fig. 1(a) and Fig. 1(d). According to the semiclassical three-step model [10

10. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]

], the motion of the electron after tunneling ionization can be described by the classical mechanics. We can obtain the dependence of the returning kinetic energy on the travel time of electron by solving Newtonian equation. For the 800 nm laser pulse case, and travel time with the maximum return energy is around 0.6 optical cycle, the corresponding maximum return energy is about 30 eV. For the 2000 nm laser pulse case, and travel time with maximum return energy is about 1.65 optical cycles (using 800 nm laser period), and the corresponding maximum return energy is about 150 eV. For the optimized three-color laser case, the travel time with the maximum return energy is also about 1.65 optical cycles, and the corresponding maximum return energy is about 365 eV, which is much higher than the 2000 nm laser pulse case. Namely, the plateau of HHG can be effectively extended by the optimized three-color laser field. On the other hand, the shape of the optimized three-color laser pulse allows the processes of the ionization, acceleration, and recombination occur in 3.0 optical cycles. But for one-color 800 nm laser field case, these processes happen only in 1.0 optical cycle. Though the longer processes have happened for 2000 nm laser pulse case, it can not obtain a lager harmonic cutoff than the optimized three-color case [see Fig. 2(b)]. In Fig. 2(b), we compare the HHG spectra from hydrogen atom driven by these three corresponding laser fields, respectively. It is seen that the HHG cutoff for these three cases agree well with the semiclassical simulations shown in Fig. 2(a). For the 2000 nm laser pulse case, there are two plateaus, the cutoff energy of the first plateau is about 55 eV, which is generated from the first returning electrons. The cutoff energy of the second plateau is about 150 eV, which comes from the contribution of the multi-rescattering electrons. In general, the conversion efficiency of the harmonic by multi-rescattering electrons is lower. Though the higher cutoff energy of the HHG is obtained for the 2000 nm laser case, the harmonic yield is greatly decreased than the optimized three-color laser field. Moreover, it does not generate an efficient broadband supercontinuum. In fact, our optimized three-color laser pulse not only can significantly enhance the harmonic spectrum, but also greatly extend the harmonic generation cut-off. It is also important to note that our approach can obtain an efficient and very broadband supercontinuum.

Fig. 2 (a) The travel time versus returning energy for the 800 nm laser pulse (green line), the 2000 nm aser pulse (red line), and the optimized three-color laser field (blue line), respectively. The same laser parameters are used in Fig. 1(a) and Fig. 1(d). (b) Corresponding to the high-order harmonic spectra.

Fig. 3 (a) The HHG power spectra from hydrogen atom driven by the optimized three-color laser field shown as in Fig. 1(d). (b) Wavelet time-frequency profile of the HHG power spectra. (c) Dipole time profiles of consecutive harmonics near the cutoff. (d) The temporal profiles of the attosecond pulse by superposing the harmonic from 105th to 165th order.

Fig. 4 (a) Optimized three-color laser field. The green dashed line represents laser frequency ω2=0.019 a.u. (2400 nm). The blue solid line represents laser frequency ω2=0.019 a.u. (2400 nm) and intensity I1 = I2 = 1.5 × 1014W/cm2 and I3 = 1.7 × 1014W/cm2. The other laser parameters are the same as those in Fig. 1(d). (b) The corresponding HHG power spectrum and (c) Temporal profiles of the attosecond pulses by superposing the HHG near cutoff region. For comparison, the previous case (red dotted line) is also included in (a)–(c).

Fig. 5 (a) The optimized three-color laser pulse with 5-fs and 8-fs duration, respectively. The other laser parameters are the same as in Fig. 1(d). (b) Corresponding to the high-order harmonic spectra.

4. Conclusion

In conclusion, we present an efficient scheme to produce a single ultrashort attosecond pulse by using the optimized three-color laser field. This scheme is demonstrated by solving accurately the TDSE using the TDGPS method. Our study confirms that the optimized three-color laser pulse can provide a longer acceleration time for the oscillating electrons, and allows electrons to gain more kinetic energy from the laser field. We show that the plateau of high-order harmonic generation is extended dramatically and the broadband supercontinuous spectrum is produced. As a result, an isolated 23 as pulse with a bandwidth of 163 eV can be obtained directly by superposing the supercontinuum harmonics near the cutoff region. We hope to this proposed scheme can be be realized experimentally.

Acknowledgments

This work was partially supported by the Chemical Sciences, Geosciences, and Biosciences Division of the Office of Basic Energy Sciences, Office of Sciences, U.S. Department of Energy and by the U.S. National Science Foundation. We also would like to acknowledge the partial support of National Science Council of Taiwan (Grant No. 100-2119-M-002-013-MY3) and National Taiwan University (Grants No.Grant No. 10R80700). PCL is partially supported by the National Natural Science Foundation of China (Grant No. 11044007 and No. 11047016), and the Young Teachers Foundation of Northwest Normal University ( NWNU-LKQN-10-5).

References and links

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]

2.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic Generation,” Science 292, 1689–1692 (2001). [CrossRef] [PubMed]

3.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008). [CrossRef] [PubMed]

4.

R. Kienberger, M. Hentschel, M. Uiberacker, Ch. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Steering attosecond electron wave packets with light,” Science 297, 1144–1148 (2002). [CrossRef] [PubMed]

5.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilä, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312, 424–427 (2006). [CrossRef] [PubMed]

6.

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz,“Attosecond real-time observation of electron tunnelling in atoms,” Nature (London) 446, 627–632 (2007). [CrossRef]

7.

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature (London) 419, 803–807 (2002). [CrossRef]

8.

J. Itatani, J. Levesque, D. Zeidler, Hiromichi Niikura, H. Ppin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature (London) 432, 867–871 (2004). [CrossRef]

9.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009). [CrossRef]

10.

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]

11.

W. Y. Hong, P. X. Lu, P. F. Lan, Z. Y. Yang, Y. H. Li, and Q. Liao, “Broadband xuv supercontinuum generation via controlling quantum paths by a low-frequency field,” Phys. Rev. A 77, 033410 (2008). [CrossRef]

12.

P. Zou, Z. N. Zeng, Y. H. Zheng, Y. Y. Lu, P. Liu, R. X. Li, and Z. Z. Xu, “Coherent control of broadband isolated attosecond pulses in a chirped two-color laser field,” Phys.Rev. A 81, 033428 (2010). [CrossRef]

13.

J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A 74(2), 023404 (2006). [CrossRef]

14.

J. J. Xu, “Isolated short attosecond pulse generation in an orthogonally polarized multicycle chirped laser field,” Phys. Rev. A 83, 033823 (2011). [CrossRef]

15.

J. Wu, G. T. Zhang, C. L. Xia, and X. S. Liu, “Control of the high-order harmonics cutoff and attosecond pulse generation through the combination of a chirped fundamental laser and a subharmonic laser field,” Phys. Rev. A 82, 013411 (2010). [CrossRef]

16.

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004). [CrossRef] [PubMed]

17.

I. L. Liu, P. C. Li, and S. I. Chu, “Coherent control of the electron quantum paths for the generation of single ultrashort attosecond laser pulse,” Phys. Rev. A 84, 033414 (2011). [CrossRef]

18.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006). [CrossRef] [PubMed]

19.

Z. H. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A 71, 023813 (2005). [CrossRef]

20.

V. S. Yakovlev, M. Ivanov, and F. Krausz, “Enhanced phasematchingfor generation of soft x-ray harmonics and attosecond pulses in atomic gases,” Opt. Express 15, 15351–15364 (2007). [CrossRef] [PubMed]

21.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4, 386–389 (2008). [CrossRef]

22.

L. E. Chipperfield, J. S. Robinson, J. W. G. Tisch, and J. P. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett. 102, 063003 (2009). [CrossRef] [PubMed]

23.

I. A. Ivanov and A. S. Kheifets, “Tailoring the waveforms to extend the high-order harmonic generation cutoff,” Phys. Rev. A 80, 023809 (2009). [CrossRef]

24.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̈ev, R. Taïeb, B. Carr, H. G. Muller, P. Agostini, and P. Salires, “Attosecond synchronization of high-harmonic soft X-rays,” Science 302, 1540–1543 (2003). [CrossRef] [PubMed]

25.

R. López-Martens, K. Varj, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salires, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, Claes-Göran, Wahlström, and Anne L Huillier, “Amplitude and phase control of attosecond light pulses,” Phys. Rev. Lett. 94, 033001 (2005). [CrossRef] [PubMed]

26.

T. Auguste, P. Salires, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A 80, 033817 (2009). [CrossRef]

27.

X. M. Tong and S. I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: A new generalized pseudospectral time-dependent method,” Chem. Phys. 217, 119–130 (1997). [CrossRef]

28.

J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98, 013901 (2007). [CrossRef] [PubMed]

29.

K. Ishikawa, “Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003). [CrossRef] [PubMed]

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(020.2649) Atomic and molecular physics : Strong field laser physics

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: August 15, 2011
Revised Manuscript: October 10, 2011
Manuscript Accepted: October 30, 2011
Published: November 9, 2011

Citation
Peng-Cheng Li, I-Lin Liu, and Shih-I Chu, "Optimization of three-color laser field for the generation of single ultrashort attosecond pulse," Opt. Express 19, 23857-23866 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-23857


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References

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  7. M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature (London)419, 803–807 (2002). [CrossRef]
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  11. W. Y. Hong, P. X. Lu, P. F. Lan, Z. Y. Yang, Y. H. Li, and Q. Liao, “Broadband xuv supercontinuum generation via controlling quantum paths by a low-frequency field,” Phys. Rev. A77, 033410 (2008). [CrossRef]
  12. P. Zou, Z. N. Zeng, Y. H. Zheng, Y. Y. Lu, P. Liu, R. X. Li, and Z. Z. Xu, “Coherent control of broadband isolated attosecond pulses in a chirped two-color laser field,” Phys.Rev. A81, 033428 (2010). [CrossRef]
  13. J. J. Carrera, X. M. Tong, and S. I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A74(2), 023404 (2006). [CrossRef]
  14. J. J. Xu, “Isolated short attosecond pulse generation in an orthogonally polarized multicycle chirped laser field,” Phys. Rev. A83, 033823 (2011). [CrossRef]
  15. J. Wu, G. T. Zhang, C. L. Xia, and X. S. Liu, “Control of the high-order harmonics cutoff and attosecond pulse generation through the combination of a chirped fundamental laser and a subharmonic laser field,” Phys. Rev. A82, 013411 (2010). [CrossRef]
  16. K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett.92, 023003 (2004). [CrossRef] [PubMed]
  17. I. L. Liu, P. C. Li, and S. I. Chu, “Coherent control of the electron quantum paths for the generation of single ultrashort attosecond laser pulse,” Phys. Rev. A84, 033414 (2011). [CrossRef]
  18. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science314, 443–446 (2006). [CrossRef] [PubMed]
  19. Z. H. Chang, “Chirp of the single attosecond pulse generated by a polarization gating,” Phys. Rev. A71, 023813 (2005). [CrossRef]
  20. V. S. Yakovlev, M. Ivanov, and F. Krausz, “Enhanced phasematchingfor generation of soft x-ray harmonics and attosecond pulses in atomic gases,” Opt. Express15, 15351–15364 (2007). [CrossRef] [PubMed]
  21. P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys.4, 386–389 (2008). [CrossRef]
  22. L. E. Chipperfield, J. S. Robinson, J. W. G. Tisch, and J. P. Marangos, “Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period,” Phys. Rev. Lett.102, 063003 (2009). [CrossRef] [PubMed]
  23. I. A. Ivanov and A. S. Kheifets, “Tailoring the waveforms to extend the high-order harmonic generation cutoff,” Phys. Rev. A80, 023809 (2009). [CrossRef]
  24. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovac̈ev, R. Taïeb, B. Carr, H. G. Muller, P. Agostini, and P. Salires, “Attosecond synchronization of high-harmonic soft X-rays,” Science302, 1540–1543 (2003). [CrossRef] [PubMed]
  25. R. López-Martens, K. Varj, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salires, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, Claes-Göran, Wahlström, and Anne L Huillier, “Amplitude and phase control of attosecond light pulses,” Phys. Rev. Lett.94, 033001 (2005). [CrossRef] [PubMed]
  26. T. Auguste, P. Salires, A. S. Wyatt, A. Monmayrant, I. A. Walmsley, E. Cormier, A. Zaïr, M. Holler, A. Guandalini, F. Schapper, J. Biegert, L. Gallmann, and U. Keller, “Theoretical and experimental analysis of quantum path interferences in high-order harmonic generation,” Phys. Rev. A80, 033817 (2009). [CrossRef]
  27. X. M. Tong and S. I. Chu, “Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: A new generalized pseudospectral time-dependent method,” Chem. Phys.217, 119–130 (1997). [CrossRef]
  28. J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett.98, 013901 (2007). [CrossRef] [PubMed]
  29. K. Ishikawa, “Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett.91, 043002 (2003). [CrossRef] [PubMed]

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