OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 21337–21348
« Show journal navigation

Intense supercontinuum generation exceeding 300eV using a two-color field in combination with a 400-nm few-cycle control pulse

Hongchuan Du, Yizhen Wen, Xiaoshan Wang, and Bitao Hu  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 21337-21348 (2013)
http://dx.doi.org/10.1364/OE.21.021337


View Full Text Article

Acrobat PDF (999 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose a method to control the harmonic process by using a two-color field in combination with a 400-nm few-cycle control pulse for the generation of an ultra-broadband supercontinuum with high efficiency. The ionization and acceleration steps in the harmonic process can be simultaneously controlled by using a three-color field synthesized by a 2000-nm driving pulse and two weak 800-nm and 400-nm control pulses. Then an intense supercontinuum covered by the spectral range from 140eV to 445eV is produced. The 3D macroscopic propagation is also employed to select the short quantum path of the supercontinuum, then intense isolated sub-100-as pulses with tunable central wavelengths are directly obtained within water window region. In addition, the generation of isolated attosecond pulses in the far field is also investigated. An isolated 52-as pulse can be generated by using a filter centered on axis to select the harmonics in the far field.

© 2013 OSA

1. Introduction

The appearance and development of attosecond pulses have caused a breakthrough in metrology, which provides a powerful tool for resolving and controlling electronic dynamical processes occurring in the sub-femtosecond scale [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). [CrossRef]

3

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

]. The physical process exploited to produce attosecond pulses is high-order harmonic generation (HHG). To date, it has been experimentally demonstrated that isolated and multiple attosecond pulses can be produced by means of high-order harmonic generation in rare gases [4

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

10

10. K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37, 3891–3893 (2012). [CrossRef] [PubMed]

]. In particular, the generation of ever-shorter isolated attosecond pulses has continued to attract much interest. Experimentally, the 100-as barrier has been first brought through with a sub-4-fs near-single-cycle driving pulse by Goulielmakis et. al. [6

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

]. Very recently, Zhao et. al. [10

10. K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37, 3891–3893 (2012). [CrossRef] [PubMed]

] produced an isolated 67-as pulse by the double optical gating technique, which is the known shortest attosecond pulse at present. However, it is still a huge challenge to generate the isolated attosecond pulse under one atomic unit of time.

The physical mechanism of HHG can be well understood by the three-step model [11

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

]. In the first step, the electron tunnels through the potential barrier formed by the Coulomb potential and the laser field, then gains kinetic energy moving in the laser field, and finally returns to the ground state by recombining with the parent ion. During the recombination process, a photon with energy equaling to the ionization potential plus the kinetic energy is emitted. According to this model, several schemes have been proposed to generate isolated attosecond pulses, such as using a few-cycle laser pulse [12

12. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ’single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997). [CrossRef]

,13

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

], polarization gating [14

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

19

19. H. Du and B. Hu, “Broadband supercontinuum generation method combining mid-infrared chirped-pulse modulation and generalized polarization gating,” Opt. Express 18, 25958–25966 (2010). [CrossRef] [PubMed]

], ionization gating [20

20. K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub-50-attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69, 051805 (2004). [CrossRef]

22

22. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature (London) 432, 605–608 (2004). [CrossRef]

], and so on. Another effective way is the two-color or multi-color field scheme [23

23. E. Takahashi, P. Lan, O. Mücke, Y. Nabekawa, and K. Midorikawa, “Infrared two-color multicycle laser field synthesis for generating an intense attosecond pulse,” Phys. Rev. Lett. 104, 233901 (2010). [CrossRef] [PubMed]

36

36. C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A 81, 043420 (2010). [CrossRef]

], which can effectively extend the cutoff energy and generate the broadband supercontinuum by controlling the acceleration step. However, many applications are still limited by the low intensity of the isolated attosecond pulses at present. Therefore, new schemes are needed for generating intense isolated attosecond pulses. Very recently, we proposed a method to produce a broadband supercontinuum with high efficiency by enhancing the ionization within half optical cycle with a 400-nm few-cycle laser pulse [37

37. H. Du, L. Luo, X. Wang, and B. Hu, “Attosecond ionization control for broadband supercontinuum generation using a weak 400-nm few-cycle controlling pulse,” Opt. Express 20, 27226–27241 (2012). [CrossRef] [PubMed]

]. In this work, we further introduce this scheme to the two-color field. Microscopically, it is found that the three-color field can simultaneously control the ionization and acceleration steps, leading to the efficient generation of a 305-eV supercontinuum covered by the spectral range from ultraviolet to water window x ray. Macroscopically, the 3D propagation is carried out to select the short quantum path of the supercontinuum, then isolated sub-100-as pulses with tunable central wavelengths are directly obtained. In addition, we also investigate the generation of isolated attosecond pulses in the far field.

2. Theoretical methods

The simulation is carried out by taking into account both the single-atom response to the laser pulse and the collective response of the macroscopic gas to the laser and high-harmonic field. The single-atom response is calculated with the Lewenstein model [38

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

]. In this model, the instantaneous dipole moment of an atom is described as (in atom units)
dnl=itdt[πε+i(tt)/2]3/2×d*[pst(t,t)A(t)]d[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 its associated vector potential,and ε 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 of the atom, and d(p) is the dipole matrix element for transitions from the ground state to the continuum state. For hydrogenlike atoms, it can be approximated as
d(p)=i27/2π(2Ip)5/4p(p2+2Ip)3.
(4)
The g(t′) in Eq. (1) represents the ground state amplitude:
g(t)=exp[tω(t)dt],
(5)
where ω(t″) is the ionization rate which is calculated by ADK tunneling model [39

39. M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atoms ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

]:
ω(t)=ωp|Cn*|2(4ωpωt)2n*1exp(4ωp3ωt),
(6)
where
ωp=Ip,ωt=e|Ef(t)|2meIp,n*=Z(IphIp)1/2,|Cn*|2=22n*n*Γ(n*+1)Γ(n*),
(7)
where Z is the net resulting charge of the atom, and Iph is the ionization potential of the hydrogen atom, and e and me are electron charge and mass, respectively.

The harmonic spectrum is then obtained by Fourier transforming the time-dependent dipole acceleration a⃗(t):
aq=|1T0Ta(t)eiqωtdt|2,
(8)
where a⃗(t) = 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 propagation of the laser and the high harmonic field, which can be written separately [40

40. 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). [CrossRef]

]
2E(ρ,z,t)1c22E(ρ,z,t)t2=ωp2(ρ,z,t)c2E(ρ,z,t),
(9)
2Eh(ρ,z,t)1c22Eh(ρ,z,t)t2=ωp2(ρ,z,t)c2Eh(ρ,z,t)+μ02Pnl(ρ,z,t)t2.
(10)
Where E and Eh are the laser and high harmonic field; ωp is the plasma frequency and is given by ωp=ene(ρ,z,t)/meε0 and Pnl = [n0ne(ρ,z,t)]dnl(ρ,z,t) is the nonlinear polarization generated by the medium. n0 is the gas density and ne=n0[1exp(tω(t))dt] is the free-electron density in the gas. This propagation model takes into account both the temporal plasma-induced phase modulation and the spatial plasma lensing effects, but does not consider the linear gas dispersion, the depletion of the fundamental beam during the HHG process and absorption of high harmonics, which is due to the low gas density [40

40. 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). [CrossRef]

]. Then the induced refractive index n can be approximately described by the refractive index in vacuum (n = 1). These equations can be solved with Crank-Nicholson method. The calculation details can be found in [40

40. 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). [CrossRef]

].

The far-field harmonic emissions can be obtained from the near-field harmonic emissions at the exit face of a gas medium through a Hankel transformation [41

41. A. L’Huillier, P. Balcou, S. Candel, K. Schafer, and K. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064nm,” Phys. Rev. A 46, 2778–2790 (1992). [CrossRef]

43

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

]
Ehf(rf,zf,ω)=ikEh(r,z,ω)zfzJ0(krrfzfz)exp[ik(r2+rf2)2(zfz)]rdr,
(11)
where J0 is the zero-order Bessel function, z′ is the exit position of a gas medium, zf is the far-field position from the laser focus, rf is the transverse coordinate in the far field, r is the transverse coordinate at the exit face of a gas medium, and the wave vector k is given by k = ω/c.

3. Results and discussions

In our scheme, a 2000-nm laser pulse is selected as the driving pulse, and the two control laser pulses are a 800-nm pulse and a 400-nm few-cycle pulse, respectively. The synthesized three-color field has the following form:
E(t)=E1f1(t)cos(ω1t+ϕ1)+E2f2(t+τdelay2)cos[ω2(t+τdelay2)+ϕ2]+E3f3(t+τdelay3)cos[ω3(t+τdelay3)+ϕ3],
(12)
where, E1, E2 and E3 are the amplitudes of the driving and control electric fields, respectively. ω1, ω2 and ω3 are the frequencies of the driving and control pulses. f1(t)=exp[2ln(2)t2/τ12], f2(t)=exp[2ln(2)t2/τ22] and f3(t)=exp[2ln(2)t2/τ32] present the profiles of the three laser pulses. τ1 = τ2 = 2T1 and τ3 = 2T3 are the pulse durations of the driving and control pulses(full width at half maximum), where T1 and T3 are the optical periods of the driving and 400-nm control pulses. τdelay2 and τdelay3 are the time delays of the 800-nm and 400-nm control pulses. ϕ1, ϕ2 and ϕ3 are the carrier-envelope phases of the driving and control pulses, and are set as 0, 0 and π, respectively. In calculation, we choose E1 = 0.095a.u., E2 = 0.021a.u. and E3 = 0.06a.u., and the time delays of the 800-nm and 400-nm control pulses are set as τdelay2 = −0.45T2 and τdelay3 = 0.45T1, respectively. Experimentally, this scheme can be carried out by using a Ti: sapphire laser system. The 2000-nm driving pulse can be achieved via the optical parametric amplification (OPA) technology [44

44. M. -C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seabery, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-Ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105, 173901 (2010). [CrossRef]

,45

45. C. Trallero-Harrero, C. Jin, B. E. Schmidt, A. D. Shiner, J.-C. Kieffer, P. B. Corkum, D. M. Villeneuve, C. D. Lin, F. Légaré, and A. T. Le, “Generation of broad XUV continuous high harmonic spectra and isolated attosecond pulses with intense mid-infrared lasers,” J. Phys. B 45, 011001 (2012). [CrossRef]

], and the 400-nm control pulse can be realized through the second harmonic generation. The time delays can be adjusted by a piezoelectric translator stage [46

46. H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett. 100, 103906 (2008). [CrossRef] [PubMed]

].

In order to clarify the roles played by the two control pulses in our scheme, we firstly investigate the HHG process using the classical three-step model [11

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

]. Since the laser intensity is far below the saturation intensity of the target atom (here the helium atom is chosen), thus the HHG process can be well described in terms of the classical electron trajectories and the ADK ionization rate [39

39. M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atoms ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

]. Figure 1 presents the classical sketch of the HHG process in the 2000-nm driving pulse. It can be seen from Fig. 1(a) that there are three ionization peaks within the pulse duration. Therefore, as shown in Fig. 1(b), there are three quantum paths (marked as P1, P2 and P3) contributing to the harmonic generation, and their maximum energies are 644ω1, 535ω1 and 326ω1, respectively. Consequently, the harmonics above 535ω1 are mainly emitted by the quantum path P1, and form a supercontinuum with the bandwidth of 67eV. In order to further extend the harmonic cutoff and generate a broadband supercontinuum, we can control the acceleration process by adding a 800-nm control pulse. The results are shown in Fig. 2. One can clearly see that the maximum energy of the quantum path P1 is increased to 702ω1, and that of the quantum path P2 is decreased to 470ω1. Consequently, the harmonics above 470ω1 are mainly emitted by the quantum path P1, and form a supercontinuum with the bandwidth of 144eV. We also clearly see from Fig. 2(a) that the corresponding ionization rate of the quantum path P1 is enhanced, which leads to the efficient generation of the supercontinuum. Taking into account the above results, we can conclude that the 800-nm control pulse can simultaneously enhance the yields and extend the cutoff of the generated supercontinuum. To further enhance the yields of the supercontinuum, we introduce a 400-nm few-cycle control pulse to enhance the corresponding ionization rate of the quantum path P1. Figure 3 presents the classical sketch of the HHG process in the three-color field. As shown in Fig. 3(a), there is only one ionization peak within the pulse duration. Therefore, there is only one quantum path P1 contributing to the harmonic generation, as shown in Fig. 3(b). Moreover, the corresponding ionization rate of the quantum path P1 is approximately 2 orders of the magnitude higher than that in Fig. 2(a).

Fig. 1 (a) Electric field of the 2000-nm driving pulse (thin blue curve) and the corresponding ADK ionization rate (bold black curve), and (b) The dependence of the emitted photon energy on the ionization and recombination times of the electron in the driving pulse.
Fig. 2 (a) Electric field of the two-color field (thin blue curve) synthesized by a 2000-nm driving pulse and a 800-nm control pulse, and the corresponding ADK ionization rate(bold black curve), and (b) The dependence of the emitted photon energy on the ionization and recombination times of the electron in the two-color field.
Fig. 3 (a) Electric field of the three-color field (thin blue curve) synthesized by a 2000-nm driving pulse, a 800-nm control pulse and a 400-nm control pulse, and the corresponding ADK ionization rate (bold black curve), and (b) The dependence of the emitted photon energy on the ionization and recombination times of the electron in the three-color field. The labels ”increased” denote that the ionization rate is increased.

Thus we can conclude that an ultra-broadband supercontinuum with high efficiency can be produced in the three-color field scheme. In this scheme, the 800-nm control pulse is mainly used to extend the cutoff of the quantum path P1, and the 400-nm few-cycle control pulse is mainly used to select the quantum path P1 by enhancing the corresponding ionization rate. Therefore, the parameters of the 800-nm control pulse are chosen to maximize the cutoff of the quantum path P1. It is noted that the amplitude and time delay of the 400-nm few-cycle control pulse must be carefully chosen to successfully select the quantum path P1 and generate a broadband supercontinuum. Our calculations reveal that the main conclusions of this paper can be keep for E3 > 0.03a.u. and τdelay3 varying from 0.4T1 and 0.5T1.

To confirm the above sketch, we calculate the harmonic spectra using the Lewenstein model [38

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

]. Here the neutral species depletion is considered using the ADK model. Figure 4(a) shows the harmonic spectrum in the three-color field (solid blue curve). For comparison, the harmonic spectra in the 2000-nm driving field and in the two-color field are also given, respectively. The harmonic spectrum in the 2000-nm driving field has been shifted down 2 units for clarity. As shown in Fig. 4(a), the overall spectral structure is irregular for the harmonics below 554ω1, and only the harmonics near the cutoff are continuous in the 2000-nm driving pulse alone. A supercontinuum with bandwidth of 67eV is produced near the cutoff. The harmonic cutoff can be dramatically extended to 717ω1 and a broadband supercontinuum with the bandwidth of 144eV can be obtained by adding the 800-nm control pulse. Moreover, the yields of the supercontinuum are stronger than those of the harmonics in the driving pulse alone. When the 400-nm control pulse is added, the harmonics above 226ω1 is supercontinuous and an ultra-broadband supercontinuum with the bandwidth of 305eV is generated. The modulations on the supercontinuum are due to the interference of the short and the long quantum paths. Moreover, the harmonic intensity is 2 or 3 orders of the magnitude higher than that in the two-color field. Therefore, an intense ultra-broadband supercontinuum exceeding 300eV can be produced with the three-color field scheme. In order to further understand the emission times of the harmonics, figure 4(b) shows the time-frequency distribution in the three-color field. It is clear that there is only one quantum path P1 contributing to the generation of the supercontinuum. And the intensity of the short quantum path is comparable with that of the long quantum path, which leads to the modulations on the supercontinuum. These results are in good agreement with the above classical results in Fig. 3.

Fig. 4 (a) Harmonic spectra generated by using the 2000-nm driving field (dash black curve), the two-color field (dot red curve), and the three-color field (solid blue curve), and (b) time-frequency distribution in the three-color field.

To generate an isolated attosecond pulse from the modulated supercontinuum, one quantum path must be eliminated. This can be achieved by adjusting the focus position of the laser pulse relative to the gas jet since the short and long quantum paths have different phase-match conditions [47

47. P. Balcou, P. Salieres, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of the field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997). [CrossRef]

]. In order to achieve the generation of isolated attosecond pulses, we perform the nonadiabatic three-dimensional (3D) propagation simulations [40

40. 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). [CrossRef]

] for fundamental and harmonic field in the gas target. We consider a tightly focused Gaussian laser beam with a beam waist of 40μm and a 1.5-mm long gas jet with a density of 1.0 × 1018/cm3. The gas jet is placed 1mm after the laser focus. Other parameters are the same as in Fig. 3. Figure 5 presents the continuous part of the macroscopic harmonics in the three-color field. For comparison, the single-atom result is also presented (thin red curve). One can clearly see that the interference fringes through the plateau to the cutoff are all removed after propagation, which implies that only one quantum path is further selected. Then a macroscopic supercontinuum with the bandwidth of 305eV can be obtained, which covers the spectral range from ultraviolet to water window x ray.

Fig. 5 The harmonic spectrum after 3D propagation in the three-color field.

In the following, we investigate the generation of pure isolated attosecond pulses. The results are shown in Fig. 6. By applying a square window with a width of 50eV to the macroscopic supercontinuum at different orders, isolated sub-90-as pulses are directly obtained. This reveals that the isolated attosecond pulses with tunable central wavelengths from ultraviolet to water window x ray can be produced by this scheme. In addition, it is worth mentioning that the supercontinuum with bandwidth of over 300eV can support the generation of attosecond pulse with duration below 14as with proper chirp compensation.

Fig. 6 The temporal profiles of the isolated attosecond pulses centered at different frequencies by filtering the harmonics after 3D propagation.

The characteristics of the macroscopic attosecond pulses also include the spatial properties. Next, we further investigate the temporal profile and the spatiotemporal distribution of the attosecond pulses generated by filtering the 300th–380th and 380th–460th harmonics, which are shown in Fig. 7. As shown in this figure, a pure isolated attosecond pulse is directly obtained for the two cases. It can be judged from the emitted time of the isolated attosecond pulses that the short path of the supercontinuum is well phase-matched after propagation. Moreover, the attosecond pulse is always a single pulse at each radius and has some spatial chirps (The attosecond pulse is generated later off-axis than on-axis.) in the large radius region, as shown in Fig. 7(c) and (d).

Fig. 7 (a) and (b) are the temporal profiles of the attosecond pulses by filtering the 300th–380th and 380th–460th harmonics, respectively. (c) and (d) are the corresponding spatiotemporal profiles.

Finally, we further discuss the generation of attosecond pulses in the far field. In Fig. 8(a), the spatiotemporal distribution of the attosecond pulse generated by filtering the 300th–380th harmonics in the far field is shown. By using a spatial filter (indicated by a solid white curve, with a radius of 100μm) to select harmonics near the axis in the far field, an isolated 80-as pulse can be obtained, as shown in Fig. 8(b). To further shorten the duration of the attosecond pulse, one can superpose much more harmonics. In Fig. 9(a), the spatiotemporal distribution of the attosecond pulse generated by filtering the 270th–420th harmonics in the far field is shown. By using a spatial filter (indicated by a solid white curve, with a radius of 100μm) to select harmonics near the axis in the far field, an isolated 52-as pulse can be obtained, as shown in Fig. 9(b).

Fig. 8 Attosecond-pulse generation in the far field by filtering the 300th–380th harmonics. (a) spatiotemporal distribution of the attosecond pulse in the far field (z = 500mm). (b) The temporal profile of the attosecond pulse in the far field using a spatial filter with a radius of 100μm (shown by the solid white curve in (a)).
Fig. 9 Attosecond-pulse generation in the far field by filtering the 270th–420th harmonics. (a) spatiotemporal distribution of the attosecond pulse in the far field (z = 500mm). (b) The temporal profile of the attosecond pulse in the far field using a spatial filter with a radius of 100μm (shown by the solid white curve in (a)).

4. Conclusion

In summary, we propose a method to simultaneously control the ionization and acceleration processes of HHG for the generation of an intense ultra-broadband supercontinuum. It is found that the 800-nm control pulse mainly plays a role for controlling the acceleration process of HHG, and the 400-nm control pulse plays a role for controlling the ionization process of HHG in this scheme. Then the maximum kinetic energy and the ionization rate of the electrons contributing to the continuous harmonics are both increased, and an intense supercontinuum covered by the spectral range from ultraviolet to water window x ray is obtained. Moreover, the short quantum path is successfully selected after 3D propagation, which enables the generation of intense isolated sub-100-as pulses with tunable central wavelengths within the water window region. In addition, we also investigate the generation of isolated attosecond pulses in the far field. By using a filter with a radius of 100μm centered on axis to select the 270th–420th harmonics in the far field, an isolated 52-as pulse can be obtained.

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No. 91026021, 11075068, 10875054, 11175076 and 10975065), the Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2010-k08) and Scholarship Award for Excellent Doctoral Student granted by Ministry of Education.

References and links

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). [CrossRef]

2.

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

3.

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

4.

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

5.

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

6.

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

7.

F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010). [CrossRef]

8.

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]

9.

S. Gilbertson, S. Khan, Y. Wu, M. Chini, and Z. Chang, “Isolated attosecond pulse generation without the need to stabilize the carrier-envelope phase of driving lasers,” Phys. Rev. Lett. 105, 093902 (2010). [CrossRef] [PubMed]

10.

K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37, 3891–3893 (2012). [CrossRef] [PubMed]

11.

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

12.

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ’single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997). [CrossRef]

13.

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

14.

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

15.

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

16.

C. Altucci, V. Tosa, and R. Velotta, “Beyond the single-atom response in isolated attosecond-pulse generation,” Phys. Rev. A 75, 061401(R) (2007). [CrossRef]

17.

C. Altucci, R. Velotta, V. Tosa, P. Villoresi, F. Frassetto, L. Poletto, C. Vozzi, F. Calegari, M. Negro, S. De Silvestri, and S. Stagira, “Interplay between group-delay-dispersion-induced polarization gating and ionization to generate isolated attosecond pulses from multicycle lasers,” Opt. Lett. 35, 2798–2880 (2010). [CrossRef] [PubMed]

18.

W. Hong, P. Wei, Q. Zhang, S. Wang, and P. Lu, “Mid-infrared modulated polarization gating for ultra-broadband supercontinuum generation,” Opt. Express 18, 11308–11315 (2010). [CrossRef] [PubMed]

19.

H. Du and B. Hu, “Broadband supercontinuum generation method combining mid-infrared chirped-pulse modulation and generalized polarization gating,” Opt. Express 18, 25958–25966 (2010). [CrossRef] [PubMed]

20.

K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub-50-attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69, 051805 (2004). [CrossRef]

21.

M. J. Abel, T. Pfeifer, P. M. Nagel, W. Boutu, M. J. Bell, C. P. Steiner, D. M. Neumark, and S. R. Leone, “Isolated attosecond pulses from ionization gating of high-harmonic emission,” Chem. Phys. 366, 9–14 (2009). [CrossRef]

22.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature (London) 432, 605–608 (2004). [CrossRef]

23.

E. Takahashi, P. Lan, O. Mücke, Y. Nabekawa, and K. Midorikawa, “Infrared two-color multicycle laser field synthesis for generating an intense attosecond pulse,” Phys. Rev. Lett. 104, 233901 (2010). [CrossRef] [PubMed]

24.

T. Pfeifer, L. Gallmann, M. Abel, D. Neumark, and S. Leone, “Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field,” Opt. Lett. 31, 975–977 (2006). [CrossRef] [PubMed]

25.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98, 203901 (2007). [CrossRef] [PubMed]

26.

W. Hong, P. Lu, Q. Li, and Q. Zhang, “Broadband water window supercontinuum generation with a tailored mid-IR pulse in neutral media,” Opt. Lett. 34, 2102–2104 (2009). [CrossRef] [PubMed]

27.

H. Du and B. Hu, “Propagation effects of isolated attosecond pulse generation with a multicycle chirped and chirped-free two-color field,” Phys. Rev. A 84, 023817 (2011). [CrossRef]

28.

H. Du, H. Wang, and B. Hu, “Isolated short attosecond pulse generated using a two-color laser and a high-order pulse,” Phys. Rev. A 81, 063813 (2010). [CrossRef]

29.

H. Du, L. Luo, X. Wang, and B. Hu, “Isolated attosecond pulse generation from pre-excited medium with a chirped and chirped-free two-color field,” Opt. Express 20, 9713–9725 (2012). [CrossRef] [PubMed]

30.

F. Calegari, C. Vozzi, M. Negro, G. Sansone, F. Frassetto, L. Poletto, P. Villoresi, M. Nisoli, S. De Silvestri, and S. Stagira, “Efficient continuum generation exceeding 200 eV by intense ultrashort two-color driver,” Opt. Lett. 34, 3125–3127 (2009). [CrossRef] [PubMed]

31.

P. Lan, E. Takahashi, and K. Midorikawa, “Optimization of infrared two-color multicycle field synthesis for intense-isolated-attosecond-pulse generation,” Phys. Rev. A 82, 053413 (2010). [CrossRef]

32.

S. F. Zhao, X. X. Zhou, P. C. Li, and Z. J. Chen, “Isolated short attosecond pulse produced by using an intense few-cycle shaped laser and an ultraviolet attosecond pulse,” Phys. Rev. A 78, 063404 (2008). [CrossRef]

33.

J. G. Chen, S. L. Zeng, and Y. J. Yang, “Generation of isolated sub-50-as pulses by quantum path control in the multicycle regime,” Phys. Rev. A 82, 043401 (2010). [CrossRef]

34.

R. Lu, H. He, Y. Guo, and K. Han, “Theoretical study of single attosecond pulse generation with a three-colour laser field,” J. Phys. B 42, 225601 (2009). [CrossRef]

35.

P. C. Li and Shih.-I. Chu, “Effects of macroscopic propagation on spectra of broadband supercontinuum harmonics and isolated-attosecond-pulse generation: coherent control of the electron quantum trajectories in two-color laser fields,” Phys. Rev. A 86, 013411 (2012). [CrossRef]

36.

C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A 81, 043420 (2010). [CrossRef]

37.

H. Du, L. Luo, X. Wang, and B. Hu, “Attosecond ionization control for broadband supercontinuum generation using a weak 400-nm few-cycle controlling pulse,” Opt. Express 20, 27226–27241 (2012). [CrossRef] [PubMed]

38.

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

39.

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atoms ions in an alternating electromagnetic field,” Sov. Phys. JETP 64, 1191–1194 (1986).

40.

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). [CrossRef]

41.

A. L’Huillier, P. Balcou, S. Candel, K. Schafer, and K. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064nm,” Phys. Rev. A 46, 2778–2790 (1992). [CrossRef]

42.

V. Tosa, K. Kim, and C. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A 79, 043828 (2009). [CrossRef]

43.

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

44.

M. -C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seabery, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-Ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105, 173901 (2010). [CrossRef]

45.

C. Trallero-Harrero, C. Jin, B. E. Schmidt, A. D. Shiner, J.-C. Kieffer, P. B. Corkum, D. M. Villeneuve, C. D. Lin, F. Légaré, and A. T. Le, “Generation of broad XUV continuous high harmonic spectra and isolated attosecond pulses with intense mid-infrared lasers,” J. Phys. B 45, 011001 (2012). [CrossRef]

46.

H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett. 100, 103906 (2008). [CrossRef] [PubMed]

47.

P. Balcou, P. Salieres, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of the field-gradient forces,” Phys. Rev. A 55, 3204–3210 (1997). [CrossRef]

OCIS Codes
(190.4160) Nonlinear optics : Multiharmonic generation
(300.6560) Spectroscopy : Spectroscopy, x-ray
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Ultrafast Optics

History
Original Manuscript: June 18, 2013
Revised Manuscript: July 31, 2013
Manuscript Accepted: August 26, 2013
Published: September 4, 2013

Citation
Hongchuan Du, Yizhen Wen, Xiaoshan Wang, and Bitao Hu, "Intense supercontinuum generation exceeding 300eV using a two-color field in combination with a 400-nm few-cycle control pulse," Opt. Express 21, 21337-21348 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-21337


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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). [CrossRef]
  2. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys.81, 163–234 (2009). [CrossRef]
  3. M. I. Stockman, M. F. Kling, U. Kleineberg, and F. Krausz, “Attosecond nanoplasmonic-field microscope,” Nat. Photonics1, 539–544 (2007). [CrossRef]
  4. M. Hentschel, R. Kienberger, Ch. Spielmann, G. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature (London)414, 509–513 (2001). [CrossRef]
  5. P. Paul, E. Toma, P. Breger, G. Mullot, F. Auge, Ph. Balcou, H. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science292, 1689–1692 (2001). [CrossRef] [PubMed]
  6. E. Goulielmakis, M. Schultze, M. Hofstetter, V. Yakovlev, J. Gagnon, M. Uiberacker, A. Aquila, E. Gullikson, D. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science320, 1614–1617 (2008). [CrossRef] [PubMed]
  7. F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics4, 875–879 (2010). [CrossRef]
  8. 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]
  9. S. Gilbertson, S. Khan, Y. Wu, M. Chini, and Z. Chang, “Isolated attosecond pulse generation without the need to stabilize the carrier-envelope phase of driving lasers,” Phys. Rev. Lett.105, 093902 (2010). [CrossRef] [PubMed]
  10. K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett.37, 3891–3893 (2012). [CrossRef] [PubMed]
  11. P. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett.71, 1994–1997 (1993). [CrossRef] [PubMed]
  12. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ’single-cycle’ regime,” Phys. Rev. Lett.78, 1251–1254 (1997). [CrossRef]
  13. J. J. Carrera, X. M. Tong, and Shih.-I. Chu, “Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses,” Phys. Rev. A74, 023404 (2006). [CrossRef]
  14. P. Corkum, N. Burnett, and M. Ivanov, “Subfemtosecond pulses,” Opt. Lett.19, 1870–1872 (1994). [CrossRef] [PubMed]
  15. Z. Chang, “Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau,” Phys. Rev. A70, 043802 (2004). [CrossRef]
  16. C. Altucci, V. Tosa, and R. Velotta, “Beyond the single-atom response in isolated attosecond-pulse generation,” Phys. Rev. A75, 061401(R) (2007). [CrossRef]
  17. C. Altucci, R. Velotta, V. Tosa, P. Villoresi, F. Frassetto, L. Poletto, C. Vozzi, F. Calegari, M. Negro, S. De Silvestri, and S. Stagira, “Interplay between group-delay-dispersion-induced polarization gating and ionization to generate isolated attosecond pulses from multicycle lasers,” Opt. Lett.35, 2798–2880 (2010). [CrossRef] [PubMed]
  18. W. Hong, P. Wei, Q. Zhang, S. Wang, and P. Lu, “Mid-infrared modulated polarization gating for ultra-broadband supercontinuum generation,” Opt. Express18, 11308–11315 (2010). [CrossRef] [PubMed]
  19. H. Du and B. Hu, “Broadband supercontinuum generation method combining mid-infrared chirped-pulse modulation and generalized polarization gating,” Opt. Express18, 25958–25966 (2010). [CrossRef] [PubMed]
  20. K. T. Kim, C. M. Kim, M.-G. Baik, G. Umesh, and C. H. Nam, “Single sub-50-attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A69, 051805 (2004). [CrossRef]
  21. M. J. Abel, T. Pfeifer, P. M. Nagel, W. Boutu, M. J. Bell, C. P. Steiner, D. M. Neumark, and S. R. Leone, “Isolated attosecond pulses from ionization gating of high-harmonic emission,” Chem. Phys.366, 9–14 (2009). [CrossRef]
  22. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature (London)432, 605–608 (2004). [CrossRef]
  23. E. Takahashi, P. Lan, O. Mücke, Y. Nabekawa, and K. Midorikawa, “Infrared two-color multicycle laser field synthesis for generating an intense attosecond pulse,” Phys. Rev. Lett.104, 233901 (2010). [CrossRef] [PubMed]
  24. T. Pfeifer, L. Gallmann, M. Abel, D. Neumark, and S. Leone, “Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field,” Opt. Lett.31, 975–977 (2006). [CrossRef] [PubMed]
  25. Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett.98, 203901 (2007). [CrossRef] [PubMed]
  26. W. Hong, P. Lu, Q. Li, and Q. Zhang, “Broadband water window supercontinuum generation with a tailored mid-IR pulse in neutral media,” Opt. Lett.34, 2102–2104 (2009). [CrossRef] [PubMed]
  27. H. Du and B. Hu, “Propagation effects of isolated attosecond pulse generation with a multicycle chirped and chirped-free two-color field,” Phys. Rev. A84, 023817 (2011). [CrossRef]
  28. H. Du, H. Wang, and B. Hu, “Isolated short attosecond pulse generated using a two-color laser and a high-order pulse,” Phys. Rev. A81, 063813 (2010). [CrossRef]
  29. H. Du, L. Luo, X. Wang, and B. Hu, “Isolated attosecond pulse generation from pre-excited medium with a chirped and chirped-free two-color field,” Opt. Express20, 9713–9725 (2012). [CrossRef] [PubMed]
  30. F. Calegari, C. Vozzi, M. Negro, G. Sansone, F. Frassetto, L. Poletto, P. Villoresi, M. Nisoli, S. De Silvestri, and S. Stagira, “Efficient continuum generation exceeding 200 eV by intense ultrashort two-color driver,” Opt. Lett.34, 3125–3127 (2009). [CrossRef] [PubMed]
  31. P. Lan, E. Takahashi, and K. Midorikawa, “Optimization of infrared two-color multicycle field synthesis for intense-isolated-attosecond-pulse generation,” Phys. Rev. A82, 053413 (2010). [CrossRef]
  32. S. F. Zhao, X. X. Zhou, P. C. Li, and Z. J. Chen, “Isolated short attosecond pulse produced by using an intense few-cycle shaped laser and an ultraviolet attosecond pulse,” Phys. Rev. A78, 063404 (2008). [CrossRef]
  33. J. G. Chen, S. L. Zeng, and Y. J. Yang, “Generation of isolated sub-50-as pulses by quantum path control in the multicycle regime,” Phys. Rev. A82, 043401 (2010). [CrossRef]
  34. R. Lu, H. He, Y. Guo, and K. Han, “Theoretical study of single attosecond pulse generation with a three-colour laser field,” J. Phys. B42, 225601 (2009). [CrossRef]
  35. P. C. Li and Shih.-I. Chu, “Effects of macroscopic propagation on spectra of broadband supercontinuum harmonics and isolated-attosecond-pulse generation: coherent control of the electron quantum trajectories in two-color laser fields,” Phys. Rev. A86, 013411 (2012). [CrossRef]
  36. C. L. Xia, G. T. Zhang, J. Wu, and X. S. Liu, “Single attosecond pulse generation in an orthogonally polarized two-color laser field combined with a static electric field,” Phys. Rev. A81, 043420 (2010). [CrossRef]
  37. H. Du, L. Luo, X. Wang, and B. Hu, “Attosecond ionization control for broadband supercontinuum generation using a weak 400-nm few-cycle controlling pulse,” Opt. Express20, 27226–27241 (2012). [CrossRef] [PubMed]
  38. M. Lewenstein, Ph. Balcou, M. Ivanov, A. L’Huillier, and P. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A49, 2117–2132 (1994). [CrossRef] [PubMed]
  39. M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atoms ions in an alternating electromagnetic field,” Sov. Phys. JETP64, 1191–1194 (1986).
  40. 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). [CrossRef]
  41. A. L’Huillier, P. Balcou, S. Candel, K. Schafer, and K. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064nm,” Phys. Rev. A46, 2778–2790 (1992). [CrossRef]
  42. V. Tosa, K. Kim, and C. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A79, 043828 (2009). [CrossRef]
  43. C. Jin, A.-T. Le, and C. Lin, “Medium propagation effects in high-order harmonic generation of Ar and N2,” Phys. Rev. A83, 023411 (2011). [CrossRef]
  44. M. -C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seabery, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-Ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett.105, 173901 (2010). [CrossRef]
  45. C. Trallero-Harrero, C. Jin, B. E. Schmidt, A. D. Shiner, J.-C. Kieffer, P. B. Corkum, D. M. Villeneuve, C. D. Lin, F. Légaré, and A. T. Le, “Generation of broad XUV continuous high harmonic spectra and isolated attosecond pulses with intense mid-infrared lasers,” J. Phys. B45, 011001 (2012). [CrossRef]
  46. H. Mashiko, S. Gilbertson, C. Li, S. D. Khan, M. M. Shakya, E. Moon, and Z. Chang, “Double optical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers,” Phys. Rev. Lett.100, 103906 (2008). [CrossRef] [PubMed]
  47. P. Balcou, P. Salieres, A. L’Huillier, and M. Lewenstein, “Generalized phase-matching conditions for high harmonics: the role of the field-gradient forces,” Phys. Rev. A55, 3204–3210 (1997). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited