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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26174–26185
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Isolated attosecond pulse generation with the stability against the carrier-envelope phase shift and with the high-beam quality from CO gas medium

Weiyi Hong, Qingbin Zhang, Xiaosong Zhu, and Peixiang Lu  »View Author Affiliations


Optics Express, Vol. 19, Issue 27, pp. 26174-26185 (2011)
http://dx.doi.org/10.1364/OE.19.026174


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Abstract

We theoretically investigate the isolated attosecond pulse generation with a 1300-nm infrared few-cycle laser pulse from the CO medium. It is found that the supercontinuum in the plateau from CO in the microscopic level can be generated for nearly all the carrier-envelop phase(CEP) of the driving pulse. The macroscopic investigation shows that when the molecular axis is parallel to the electric field, the supercontinuum can be phase-matched in broader spectral range than the antiparallel case and achieve a good beam quality with the divergence angle of 0.2 mrad, which benefits for some potential applications of ultrafast detections with high spatial and temporal resolutions.

© 2011 OSA

1. Introduction

The appearance and development of the attosecond pulses pave the way for the study and control of the ultrafast microscopic dynamics with unprecedented resolutions [1

1. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature (London) 427, 817–821 (2004).

, 2

2. M. I. Stockman, M. F. Kling, U. Kleineberg, and F. Krausz, “Attosecond nanoplasmonic-field microscope,” Nat. Photonics 1, 539–544 (2007).

]. Nowadays, attosecond pulses based on the high-order harmonic generation (HHG) have been successfully produced in experiment [3

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

]. It has been demonstrated that the harmonic signal bursts at the periodicity of half an optical cycle of the driving laser, resulting in an attosecond pulse train (APT) [4

4. P. Antoine, A. L’Huillier, and M. Lewenstein, “Attosecond pulse trains using high-order harmonics” Phys. Rev. Lett. 77, 1234–1237 (1996). [PubMed]

]. The isolated attosecond pulse can be obtained only if the harmonic process is confined within half a cycle.

Microscopically, the HHG process can be well depicted by the well-known three-step model [5

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

]: ionization, acceleration and recombination in the external laser field. This classical picture not only well explains the time-frequency properties of the high-order harmonics, but also suggests that the harmonic process can be controlled in both time and frequency domains to extract an isolated harmonic burst and further shorter the pulse duration. The few-cycle-pulse driving scheme [6

6. I. Christov, M. Murnane, and H. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the ‘Single-Cycle’ Regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).

] and the polarization gating technique [7

7. Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70, 043802 (2004).

] have been introduce in the earlier stage to generate an isolated attosecond pulse. However, the bandwidths of the generated xuv supercontinuum are limited to 20 eV. Recently, it has been proposed that wave-form-controlled two-color fields can significantly modulate the acceleration step of the harmonic processes and the form a broadband supercontinuum with bandwidth of several tens eV near the cutoff [8

8. P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A 76, 011402(R) (2007).

, 9

9. P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79, 043413 (2009).

, 10

10. Y. Zheng, Z. Zeng, X. Li, X. Chen, P. Liu, H. Xiong, H. Lu, S. Zhao, P. Wei, L. Zhang, X. Wang, J. Liu, Y. Cheng, R. Li, and Z. Xu, “Enhancement and broadening of extreme-ultraviolet supercontinuum in a relative phase controlled two-color laser field,” Opt. Lett. 33, 234–236 (2008). [PubMed]

]. However, the yields of the supercontinuum are much lower than that of the harmonics in the plateau, due to the intrinsic properties of the corresponding electron dynamics of the harmonic process [11

11. W. Hong, Q. Zhang, Z. Yang, and P. Lu, “Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse,” Phys. Rev. A 80, 053407 (2009).

]. An isolated attosecond pulse can also be generated by restricting the high harmonic generation within half an optical cycle of the driving laser, and the harmonics in the plateau merge to a supercontinuum [9

9. P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79, 043413 (2009).

, 12

12. P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801(R) (2007).

, 13

13. W. Hong, Y. Li, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Control of quantum paths in the multicycle regime and efficient broadband attosecond pulse generation,” J. Opt. Soc. Am. B 25, 1684–1689 (2009).

]. The restriction of the ionization, so-call “ionization gating”, can be realized by inducing the asymmetry of the ionization process in the adjacent half cycle. Such a gating is directly formed by synthesizing a second harmonic field [9

9. P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79, 043413 (2009).

, 12

12. P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801(R) (2007).

] or a very short uv pulse [13

13. W. Hong, Y. Li, P. Lu, P. Lan, Q. Zhang, and X. Wang, “Control of quantum paths in the multicycle regime and efficient broadband attosecond pulse generation,” J. Opt. Soc. Am. B 25, 1684–1689 (2009).

] to the fundamental field. It has also been found that the supercontinua with the ionization gating maintain the efficiency after propagation [9

9. P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79, 043413 (2009).

].

In this paper, we theoretically study the isolated attosecond pulse generation from the CO gas with a 1300-nm infrared few-cycle driving pulse. Here the infrared driving laser with longer wavelength is adopted to extend the harmonic cutoff and avoid breaking the inverse asymmetry of the CO molecule in the laser field. The ionization properties for the HHG in the single-atom response are presented. It is found that the generation of the isolated attosecond pulse from CO is robust against the carrier-envelop phase(CEP) of the driving pulse. The simulation of the 3-dimensional propagation for the supercontinuum generated from CO has been also carried out to investigate the spectral, temporal and spacial characteristics of the generated attosecond pulse.

2. Theoretical model

We employ the Lewenstein model [21

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

] to calculate the harmonic radiation. The time-dependent dipole moment is given by
dnl(t)=itdt[πɛ+i(tt)/2]3/2×drec[pst(t,t)A(t)]dion[pst(t,t)A(t)]×exp[iSst(t,t)]E(t)g(t)+c.c..
(1)
In this equation, E(t) is the electric field of the laser pulse, A(t) is the corresponding vector potential, ɛ is a positive regularization constant. pst and Sst are the stationary momentum and quasiclassical action, which are given by
pst(t,t)=1ttttA(t)dt,
(2)
Sst(t,t)=(tt)Ip12pst2(t,t)(tt)+12ttA2(t)dt,
(3)
where Ip is the ionization energy. g(t) in the equation(1) represents the ground state amplitude:
g(t)=Ef(t)exp[tw(t)dt].
(4)
w(t′) is the ionization rate, which is calculated by the molecular Ammosov-Delone-Krainov (MO-ADK) tunnelling model [22

22. X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66, 033402 (2002).

]:
w(E,R)=mB2(m)2|m||m|!1κ2Zc/κ1(2κ3E)2Zc/κ|m|1e2κ3/3E,
(5)
where
B(m)=lClDm,ml(R)Q(l,m),
(6)
Q(l,m)=(1)m(2l+1)(l+|m|!)2(l|m|)!
(7)
with Zc being the effective Coulomb charge, κ=2Ip, R being the Euler angles between the molecular axis and the field direction, and Dm,ml(R) the rotation matrix. The coefficients Cl for CO are calculated by the multiple-scattering method [22

22. X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66, 033402 (2002).

, 23

23. D. Dill and J. L. Dehmer, “Electronmolecule scattering and molecular photoionization using the multiplescattering method,” J. Chem. Phys. 61, 692–699 (1974).

].

The transition dipole moment between the ground and the continuum state is calculated by
dCO(p)=ΨCO(r)|r|eipr,
(8)
where ΨCO is the HOMO of CO obtained with the Gaussian 03 ab initio code [24

24. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, “Gaussian 03, Revision C.02,” Gaussian Inc., Wallingford, CT (2010).

].

In this model,the linear Stark shift of HOMO is considered, which will lead to the time-dependent ionization energy [25

25. M. Abu-samha and L. B. Madsen, “Photoelectron angular distributions from polar molecules probed by intense femtosecond lasers,” Phys. Rev. A 82, 043413 (2010).

, 26

26. A. Etches and L. B. Madsen, “Extending the strong-field approximation of high-order harmonic generation to polar molecules: gating mechanisms and extension of the harmonic cutoff,” J. Phys. B: At. Mol. Opt. Phys. 43, 155602 (2010).

]
Ip(t)=Ip0+μhE(t),
(9)
where Ip0 is the field free ionization energy, μh is the permanent dipole of HOMO of CO and E(t) is the external field. The permanent dipole of HOMO is calculated to be 1.72 a.u. (4.37 D) by [25

25. M. Abu-samha and L. B. Madsen, “Photoelectron angular distributions from polar molecules probed by intense femtosecond lasers,” Phys. Rev. A 82, 043413 (2010).

]
μh=drrρH(r),
(10)
where ρH(r) is the electron density of the HOMO calculated by ρH(r) = ∫drΨ*(r)Ψ(r).

The harmonic spectrum is then obtained by Fourier transforming the time-dependent dipole acceleration a⃗(t):
aq=|1T0Ta(t)exp(iqωt)|2,
(11)
where a(t)=d¨nl(t), T and ω are the duration and frequency of the driving pulse, respectively. q corresponds to the harmonic order.

The collective response of the macroscopic medium is described by the copropagation of the laser and the high harmonic fields, which can be written separately by [27

27. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61, 063801 (2000).

]
2Ef(ρ,z,t)1c22Ef(ρ,z,t)t2=ωp2(ρ,z,t)c2Ef(ρ,z,t)
(12)
2Eh(ρ,z,t)1c22Eh(ρ,z,t)t2=ωp2(ρ,z,t)c2Eh(ρ,z,t)+μ02Pnl(ρ,z,t)t2
(13)
where Ef and Eh are laser and harmonic fields, ωp=e4πne(ρ,z,t)/me is the plasma frequency, and Pnl(ρ,z,t) = [n0ne(ρ,z,t)]dnl(ρ,z,t) is the nonlinear polarization generated by the medium. n0 is the gas density and ne(t)=n0[1exp(tw(t)dt)] is the free-electron density in the gas. The equations here take into account both temporal plasma induced phase modulation and the spatial plasma lensing effects on the driving field. They do not consider the linear gas dispersion and the depletion of the fundamental beam during the HHG process, which is due to the low gas density (75 torr at room temperature in our scheme) [27

27. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61, 063801 (2000).

]. Then the induced refractive index n can be approximately described by the refractive index in vacuum (n=1). Equation (4) and (5) can be numerically solved using the Crank-Nicholson method. The calculation details can be found in [7

7. Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70, 043802 (2004).

].

3. Result and discussion

Fig. 1 The ionization rates of the CO molecules when the molecular axis is (a)parallel, (b)perpendicular and (c)antiparallel to the electric field.

In order to confirm the above predictions for the supercontinuum generation, we perform the quantum simulation by the MO-SFA to calculate the harmonic spectra from the CO molecule in the microscopic level. Figure 2(a) shows the high-energy part of the harmonic spectra for the parallel, antiparallel and perpendicular cases, depicted by the red, blue and black lines. One can clearly see that the harmonics from 55th to 100th become continuous for the parallel case, of which the bandwidth of the supercontinuum is 42 eV. The fringes in the supercontinuum is originated from the interference between the long and short quantum paths with nearly equivalent intensities. For the antiparallel case, the supercontinuum can also be observed in the plateau, but with lower cutoff energy and higher efficiency, due to the corresponding higher ionization rate and lower recollision energy of the electrons, as shown in Fig. 1(a). The harmonic spectrum for the perpendicular case is given for comparison. The harmonic yield in this case is 1 2 order lower than those in the parallel and antiparallel cases, and the supercontinuum can only be observed at the cutoff and the bandwidth is only 15 eV. A deeper insight is obtained by investigate the emission times of the harmonic spectra for the parallel and antiparallel cases in terms of the time-frequency analysis method, which is shown in Fig. 2(b) and (c), respectively. There are three main peaks corresponding to the harmonic generation during the pulse for both cases, marked by P1, P2 and P3. When the molecular axis is parallel to the laser electric field, the harmonic yield for P2 is much higher than those for P1 and P3 due to the ionization properties shown in Fig. 1(a). And for the antiparallel case, the harmonic yield for P3 is dominant during the pulse since the electric field and the molecule gate the ionization process of the electrons corresponding for P3.

Fig. 2 (a) The high-energy parts of the harmonic spectra for the parallel, antiparallel and perpendicular cases. (b)The time-frequency distribution for the parallel case. (c)The time-frequency distribution for the antiparallel case.

The driving pulse duration in our simulation is 13 fs, which contains only 2 optical cycles, then the carrier-envelope phase(CEP) plays an important role in the isolated attosecond pulse generation. We further investigate the ionization dynamics and the correspond high-harmonic generation with different CEPs in the microscopic level. Figure 3(a) and (b) shows the ionization rate and the continuous parts of the harmonic spectra as functions of the CEP, respectively. For comparison, those for the perpendicular case are also presented in Fig. 3(c) and (d). One can clearly see a significant difference in the ionization rates as functions of CEP between the parallel and perpendicular cases. As shown in Fig. 1(a), the ionization of the electrons corresponding to the high-harmonic generation is gated within a very short time for a wide range of CEP shift for the parallel case, leading to the supercontinuum generation in the plateau. For the CEP range in the vicinity of 0π, the two-peak structure of the ionization rate can also lead the the supercontinuum generation in the plateau, according to the above analysis. Then we can conclude that the supercontinuum can be produced in the plateau by using a two-cycle driving pulse with arbitrary CEPs. This can be confirmed by the result shown in Fig. 3(b), in which the harmonics in the plateau merge to supercontinua for nearly all the CEPs but different cutoff energies. For the perpendicular case, there are more than two ionization peaks during the pulse for all the CEPs, then the continuous harmonics can only be observed near the cutoff.

Fig. 3 (a) and (b) are the ionization rate and the high-energy part of the harmonics as functions of carrier-envelope phase for the parallel case. (c) and (d) are the ionization rate and the high-energy part of the harmonics as functions of carrier-envelope phase for the perpendicular case.

We further investigate the ionization properties of the CO molecule with different alignment angles. Figure 4 shows the ionization rate as a function of the alignment angle. Here the carrier-envelope phase is set to zero for convenience. As mentioned above, when the molecular axis of CO, i.e., the intrinsic dipole, is antiparallel to the electric field of the driving pulse, the ionization would be enhanced, and vice versa. This enhancement or suppression of the ionization by the intrinsic dipole is weakened as the alignment angle of the molecule tends from 0° or 180° to 90°, respectively. Therefore the inverse asymmetry of the high-harmonic generation in the adjacent two half-cycles is also diminished. Moreover, the ionization amplitude for the perpendicular case is much lower than those for other alignment angles, leading to the much lower harmonic efficiency shown in Fig. 2(a) by the black lines.

Fig. 4 The normalized ionization rates for different alignment angles.

The harmonic spectra of the CO molecule for different alignment angles calculated by the MO-SFA are presented in Fig. 5. Figure 5(a) shows the continuous parts of the harmonic spectra for the angles of 0°, 30°, and 60°, respectively. One can clearly see that the harmonic yields of the generated supercontinuum decrease as the alignment angle of the molecule increases. Moreover, the supercontinuum becomes slightly irregular for the case of 60°. The supercontinua for the cases of 120°, 150°, and 180° are also presented in Fig. 5(b). On the contrary, the harmonic yields of the generated supercontinuum increase as the alignment angle of the molecule increases, and some small irregular modulations appear on the supercontinuum for the case of 120°. This can be contributed to the ionization properties shown in Fig. 4. We can conclude that the the harmonic yields of the generated supercontinuum decrease and the supercontinuum becomes irregular as the CO molecule rotates from parallel orientation to perpendicular orientation.

Fig. 5 The high-energy parts of the harmonic spectra in microscopic level for the alignment angles of (a)0°, 30°, 60°, and 120° and (b) 120°, 150°, 180°, respectively.

In our calculation, the 1300-nm mid-infrared laser pulse is adopted. Such mid-infrared pulse can produce harmonics in nearly nonionized medium. Here the calculated ionization probability is below 0.1%, then such neutral medium enables one to adopt the standard phase-matching technique to macroscopically enhance the harmonic yields of an individual quantum path in the supercontinuum to obtain a pure isolated attosecond pulse. In this technique, the phase-matching condition for either quantum path (short or long) can be fully satisfied by adjusting the gas pressure and the position of the laser focus. To demonstrate this issue, we perform the nonadiabatic three-dimensional(3D) propagation simulations for both fundamental and harmonic fields in the gas medium. In order to realize the phase-matching condition of an individual quantum path of the supercontinuum, we consider a focused laser beam with the beam waist of 50 μm and 0.5-mm long gas jet with the gas density of 2.6×1018/cm3. The gas jet is placed 1 mm after the laser focus. Figure 6(a) and (b) show the spectra of the macroscopic harmonics for the alignment angles of 0°, 30°, 60°, and 120°, 150°, 180°, respectively. For comparison, the macroscopic spectrum for the perpendicular case is also presented in both Fig. 6(a) and (b) by the dashed lines. One can clearly see that the interference fringes through the plateau to the cutoff are mostly removed for all the angles. For the alignment angles of 0°, 30°, 60°, the supercontinua are well phase-matched from about 70th to the cutoff, while the phase-matched harmonics are only covered by about 20 harmonic orders for the angles of 120°, 150°, 180°. Moreover, there are some small irregular modulations in the supercontinuum for such angles.

Fig. 6 The high-energy parts of the harmonic spectra after propagation for the alignment angles of (a)0°, 30°, 60°, and 120° and (b) 120°, 150°, 180°, respectively. The dashed line in (a) and (b) is the case for the perpendicular cases.

Fig. 7 (a) and (b) are the temporal profiles of the attosecond pulses for parallel and antiparallel cases, respectively. (c) and (d) are the corresponding spatiotemporal profiles.

Finally, we go further to the beam qualities of the isolated attosecond pulses generated from the CO medium. We calculate the far-field distributions of the generated isolated attosecond pulses by the Hankel transformation from the near-field harmonic emissions at the exit face of the medium. The calculation details can be found in Ref. [27

27. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61, 063801 (2000).

]. The divergences of the isolated attosecond pulses for the parallel and antiparallel cases are presented in Fig. 8(a) and (b), respective. The insets show the spots with the distance of 1 m from the gas medium for these two case. It is clearly shown that the divergences for the parallel and antiparallel are both gaussian-like. The divergence angles for this two cases are 0.2 and 0.3 mrad, which indicates the better beam quality for the parallel case.

Fig. 8 The far-field profiles of the attosecond pulses for the parallel and antiparallel cases. The insets are the corresponding images with the distance of 1 m from the gas medium.

4. Conclusion

In conclusion, we have theoretically investigate the isolated attosecond pulse generation with a 1300-nm 13-fs infrared few-cycle laser pulse from the CO medium. It is found that the supercontinuum in the plateau from CO in the microscopic level can be generated for nearly all the carrier-envelop phase(CEP) of the driving pulse. The macroscopic investigation shows that the well phase-matched spectral region of the generated supercontinuum for the 0° of alignment angle is broader than that for the 180°. Further investigation implies that the spatiotemporal distribution structure of the isolated attosecond pulse for the parallel case is better than that for the antiparallel case. Moreover, the divergence of the isolated attosecond pulse for the parallel case is also smaller than that for the antiparallel case, indicating a better beam quality. Finally, we would like to point out that the intensity of the driving pulse should be carefully chosen to avoid breaking the inverse asymmetry and also producing high-density free electrons which distorts the electric field of the few-cycle pulses and limits the harmonic yields macroscopically. For the CO molecule, the intensity of the driving pulse should be less than 2 × 1014W/cm2 according to our calculation.

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants No. 60925021, 10904045, 10734080 and the National Basic Research Program of China under Grant No. 2011CB808103. This work was partially supported by the State Key Laboratory of Precision Spectroscopy of East China Normal University.

References and links

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I. Christov, M. Murnane, and H. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the ‘Single-Cycle’ Regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).

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Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A 70, 043802 (2004).

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P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Isolated sub-100-as pulse generation via controlling electron dynamics,” Phys. Rev. A 76, 011402(R) (2007).

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P. Lan, P. Lu, Q. Li, W. Hong, and Q. Zhang, “Macroscopic effects for quantum control of broadband isolated attosecond pulse generation with a two-color field,” Phys. Rev. A 79, 043413 (2009).

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Q. Li, W. Hong, Q. Zhang, S. Wang, and P. Lu, “Isolated-attosecond-pulse generation from asymmetric molecules with an ω+2ω/3 multicycle two-color field,” Phys. Rev. A 81, 053846 (2010).

19.

Q. Zhang, P. Lu, W. Hong, Q. Liao, and S. Wang, “Control of high-order harmonic generation from molecules lacking inversion symmetry with a polarization gating method,” Phys. Rev. A 79, 053406 (2009).

20.

S. De, I. Znakovskaya, D. Ray, F. Anis, N. G. Johnson, I. Bocharaova, M. Magrakvelidze, B. D. Esry, C. L. Cocke, I. V. Litvinyuk, and M. F. Kling, “Field-free orientation of CO molecules by femtosecond two-color laser fields,” Phys. Rev. Lett. 103, 153002 (2009). [PubMed]

21.

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

22.

X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66, 033402 (2002).

23.

D. Dill and J. L. Dehmer, “Electronmolecule scattering and molecular photoionization using the multiplescattering method,” J. Chem. Phys. 61, 692–699 (1974).

24.

M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, “Gaussian 03, Revision C.02,” Gaussian Inc., Wallingford, CT (2010).

25.

M. Abu-samha and L. B. Madsen, “Photoelectron angular distributions from polar molecules probed by intense femtosecond lasers,” Phys. Rev. A 82, 043413 (2010).

26.

A. Etches and L. B. Madsen, “Extending the strong-field approximation of high-order harmonic generation to polar molecules: gating mechanisms and extension of the harmonic cutoff,” J. Phys. B: At. Mol. Opt. Phys. 43, 155602 (2010).

27.

E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A 61, 063801 (2000).

28.

C. Jin, A. Le, and C. D. Lin, “Medium propagation effects in high-order harmonic generation of Ar and N2,” Phys. Rev. A 83, 023411 (2011).

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(260.3230) Physical optics : Ionization
(270.6620) Quantum optics : Strong-field processes

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: November 2, 2011
Revised Manuscript: November 24, 2011
Manuscript Accepted: November 25, 2011
Published: December 7, 2011

Citation
Weiyi Hong, Qingbin Zhang, Xiaosong Zhu, and Peixiang Lu, "Isolated attosecond pulse generation with the stability against the carrier-envelope phase shift and with the high-beam quality from CO gas medium," Opt. Express 19, 26174-26185 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26174


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References

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  19. Q. Zhang, P. Lu, W. Hong, Q. Liao, and S. Wang, “Control of high-order harmonic generation from molecules lacking inversion symmetry with a polarization gating method,” Phys. Rev. A79, 053406 (2009).
  20. S. De, I. Znakovskaya, D. Ray, F. Anis, N. G. Johnson, I. Bocharaova, M. Magrakvelidze, B. D. Esry, C. L. Cocke, I. V. Litvinyuk, and M. F. Kling, “Field-free orientation of CO molecules by femtosecond two-color laser fields,” Phys. Rev. Lett.103, 153002 (2009). [PubMed]
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  23. D. Dill and J. L. Dehmer, “Electronmolecule scattering and molecular photoionization using the multiplescattering method,” J. Chem. Phys.61, 692–699 (1974).
  24. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, “Gaussian 03, Revision C.02,” Gaussian Inc., Wallingford, CT (2010).
  25. M. Abu-samha and L. B. Madsen, “Photoelectron angular distributions from polar molecules probed by intense femtosecond lasers,” Phys. Rev. A82, 043413 (2010).
  26. A. Etches and L. B. Madsen, “Extending the strong-field approximation of high-order harmonic generation to polar molecules: gating mechanisms and extension of the harmonic cutoff,” J. Phys. B: At. Mol. Opt. Phys.43, 155602 (2010).
  27. E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimentional model of high-order harmonic generation in the few-optical cycle regime,” Phys. Rev. A61, 063801 (2000).
  28. C. Jin, A. Le, and C. D. Lin, “Medium propagation effects in high-order harmonic generation of Ar and N2,” Phys. Rev. A83, 023411 (2011).

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