PHYSICAL REVIEW A 82, 023826 (2010)
Generation of an XUV supercontinuum by optimization of the angle between polarization planes of two linearly polarized pulses in a multicycle two-color laser field Jinping Yao,1,2 Yao Li,3 Bin Zeng,1,2 Hui Xiong,1 Han Xu,1 Yuxi Fu,1,2 Wei Chu,1,2 Jielei Ni,1,2 Xiaojun Liu,4 J. Chen,5,6,* Ya Cheng,1,† and Zhizhan Xu1,‡ 1
State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P. O. Box 800-211, Shanghai 201800, China 2 Graduate University of Chinese Academy of Sciences, Beijing 100049, China 3 Department of Physics, East China Normal University, Shanghai 200062, China 4 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China 5 Center for Applied Physics and Technology, Peking University, Beijing 100084, China 6 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China (Received 30 June 2010; published 30 August 2010) We theoretically investigate the high-order harmonic generation (HHG) in helium using a two-color laser field synthesized by an intense 25-fs laser pulse at 800 nm and a relatively weak ∼ 43-fs laser pulse at 1400 nm. When the polarization between the two pulses is arranged at an angle of ∼ 73◦ , supercontinuum spectra are dramatically broadened to 180 eV, which is sufficient to support an isolated ∼73-as pulse without any phase compensation. The physical mechanisms behind the phenomenon are well explained in terms of quantum and classical analyses. Furthermore, in the long-pulse regime, this method of extending the supercontinuum spectrum shows the significant advantage over previous two-color HHG schemes. DOI: 10.1103/PhysRevA.82.023826
PACS number(s): 42.65.Ky, 42.65.Re
I. INTRODUCTION −18
Attosecond (10 s) pulse generation has been intensively investigated recently due to its important application in probing ultrafast dynamic processes of electrons and molecules [1]. Attosecond pulses can be obtained by a series of methods such as stimulated Raman scattering [2], relativistic nonlinear Thomson scattering [3], and high-order harmonic generation (HHG) [4–6], among which HHG has been the only method to experimentally generate isolated attosecond pulses (IAPs) so far. At present, IAPs synthesized from high-order harmonics (HHs) can be achieved mainly with three approaches, namely, the use of the few-cycle driving pulses [7,8], polarization gating technology [9], and two-color scheme [10–16]. However, these methods usually require the pulse duration being sufficiently short in order to generate isolated single attosecond pulses. Although several well-developed pulse compression techniques [17–19] have enabled us to create ultrashort pulses with a pulse duration of 1 to 2 optical cycles, it is still a technical challenge to produce intense few-cycle laser pulses, which largely limit the output energy of IAPs. Therefore, it is highly desirable that IAPs can be created with lasers directly from the chirped pulse amplifier. To this end, one has explored several methods to broaden XUV supercontinua in the multicycle pulse regime. One way is to employ a noninteger wavelength ratio in the two-color field scheme to break the symmetry between the consecutive recombination events [20,21]. Another way is to introduce a nonlinear chirp in multicycle driver laser pulses [22]. In particular, Chang’s
*
chen
[email protected] ycheng-45277@hotmail. com ‡
[email protected] †
1050-2947/2010/82(2)/023826(5)
023826-1
group has recently experimentally demonstrated generation of IAPs with double optical gating [23] and generalized double optical gating [24], which represent an important step toward single attosecond pulse generation with multicycle driver pulses. In this paper, we propose an alternative method to generate sub-100-as IAPs by use of a multicycle two-color laser field. Theoretical simulation demonstrates that the supercontinuum spectrum can be significantly broadened when the polarization between the two fields is properly arranged. We also discuss the physical mechanisms dominating the supercontinuum extension. Lastly, we point out that in the multicycle regime, the method is particularly effective for enlarging the bandwidth of the supercontinuum. II. SIMULATION MODEL
In our simulation, the driver field consists of an intense 800-nm 25-fs laser field and a relatively weak 1400-nm ∼43-fs laser field. The 800-nm field polarizes at an angle θ with respect to the y axis, and the 1400-nm field polarizes exactly in the y direction. Thus, the synthesized field can be expressed as Ex = E1 exp −2 ln(2)(t − t0 )2 τ12 sin(ω1 t) sin θ, (1) Ey = E1 exp −2 ln(2)(t − t0 )2 τ12 sin(ω1 t) cos θ + E2 exp −2 ln(2)(t − t0 + Td )2 τ22 × sin[ω2 (t − t0 + Td )]. (2) Here, Ei , ωi , and τi (i = 1, 2) donate amplitude, angular frequency, and pulse duration of the 800-nm (i = 1) and 1400-nm (i = 2) fields, respectively. The peak intensities of the 800- and 1400-nm laser pulses are 1.2 × 1015 W/cm2 and ∼ 2.8 × 1014 W/cm2 , respectively. With the synthesized field, ©2010 The American Physical Society
JINPING YAO et al.
PHYSICAL REVIEW A 82, 023826 (2010)
the single-atom response is calculated using the Lewenstein model [25] based on a single-active-electron approximation. The atom used in the calculation is helium (He). The harmonic spectrum is obtained by Fourier transformation of the timedependent dipole moment. III. RESULTS AND DISCUSSION
By scanning the time delay Td and the relative angle θ between the two fields, we observe a broad supercontinuum generated under the conditions of Td ≈ 3.63 fs and θ ≈ 73◦ . Correspondingly, the synthesized electric field is shown in Fig. 1(a). The x component of the synthesized field is a one-color field at 800 nm, while the y component is a two-color field composed of 800- and 1400-nm laser pulses and, thus, exhibits high asymmetry. In such a synthesized field, the polarization state rapidly changes within an optical cycle, which allows us to manipulate the free-electron trajectories contributing to HHG. Surprisingly, with the optimized driver field, an XUV supercontinuum with a spectral width up to 180 eV is observed in both x and y directions, as illustrated in Fig. 1(b). Here, the harmonic intensity in the y direction is reduced by 2 orders of magnitude for display purposes only. One may notice that the supercontinuum shows a considerable modulation, particularly in the y direction, which is mainly
FIG. 1. (Color online) (a) x and y components of the synthesized driver field; (b) HH spectra generated with synthesized field as shown in (a); (c) HH spectra generated with 800-nm (dotted curve), 1400-nm (dashed curve), and synthesized (solid curve) fields.
caused by the interference of harmonics contributed by long and short trajectories. For comparison, HH spectra generated in three different laser fields, namely, the single-color 800-nm field, the single-color 1400-nm field, and the two-color synthesized field, are shown in Fig. 1(c). It can be clearly seen that no observable supercontinuum is generated with either an 800- or a 1400-nm laser field alone because their pulse durations are too long to support generation of IAPs. When the weak 1400-nm pulse is superposed onto the intense 800-nm pulse and the polarization between the two pulses is arranged to be ∼ 73◦ , the cutoff energy is effectively extended and a broad XUV supercontinuum is generated. Moreover, although the total intensity of HHs generated with the above-mentioned two-color field, defined as the sum of harmonic intensities in the x and y directions, is 1 to 2 orders of magnitude lower than that with an 800-nm field alone, it is still significantly higher than that with a 1400-nm laser field alone. Particularly, HH spectrum beyond 200 eV (i.e., the supercontinuum) does not show a sudden drop of conversion efficiency as compared to HH signal in the spectral range
