-
$ \begin{array}{l} {\rm{i}}\frac{{\partial \psi (z, R, t)}}{{\partial t}} = \left[ { - \frac{1}{{{m_{\rm{p}}}}}\frac{{{\partial ^2}}}{{\partial {R^2}}} - \frac{{2{m_{\rm{p}}} + 1}}{{4{m_{\rm{p}}}}}\frac{{{\partial ^2}}}{{\partial {z^2}}} + } \right.\\ \left. {V\left( {z, R} \right) + (1 + \frac{1}{{2{m_{\rm{p}}} + 1}})zE\left( t \right)} \right]\psi (z, R, t) \end{array} $
(1) 式中,mp为H或T的核质量;R为核间距; z为电子坐标; t表示时间; ψ(z, R, t)为波函数; V(z, R)为势能项,其可表示为:
$ \begin{array}{l} V\left( {z, R} \right) = {R^{ - 1}} - {\left[ {{{\left( {z - R/2} \right)}^2} + 1} \right]^{ - \frac{1}{2}}} - \\ \;\;\;\;\;\;\;\;\;\;\;{\left[ {{{\left( {z + R/2} \right)}^2} + 1} \right]^{ - \frac{1}{2}}} \end{array} $
(2) 式中,E(t)为激光场,其可表示为:
$ E\left( t \right) = E{\rm{exp}}[ - 4\left( {{t^2}/{\tau ^2}){\rm{ln}}2} \right]{\rm{cos}}\left( {{\omega _1}t} \right) $
(3) 式中,E, ω1和τ分别为激光振幅、频率和脉宽。
高次谐波谱图可表示为:
$ S(\omega ) = {\left| {\frac{1}{{\sqrt {2{\rm{\pi }}} }}\int {a(t){{\rm e}^{ - {\rm{i}}{\omega _1}{\rm{t}}}}{\rm d}t} } \right|^2} $
(4) 式中, $a\left( t \right) = - \left\langle {\psi \left( {z, R, t} \right)\left| {\partial V\left( {z, } \right)/\partial z + E\left( t \right)} \right|\psi \left( {z, R, t} \right)} \right\rangle $为偶极加速度。
方程求解采用2阶分裂算符的方法,具体参见参考文献[13]。谐波截止能量附近强度选择为谐波截止附近30阶谐波强度的平均值。
核运动对分子谐波强度及产生阿秒脉冲的影响
Effect of nuclear motion on molecular harmonic intensity and attosecond pulse generation
-
摘要: 为了了解核运动对H2+和T2+谐波辐射强度及产生阿秒脉冲的影响,采用数值求解薛定谔方程的方法,理论研究了10fs和20fs激光驱动下H2+和T2+谐波截止能量附近强度的变化。结果表明,短脉宽驱动下谐波强度满足H2+>T2+;而长脉宽驱动下谐波强度满足T2+>H2+;根据谐波强度变化规律,在最佳谐波辐射强度下引入半周期激光场可以获得高强度、高能量的谐波平台区,进而获得脉宽为37as的阿秒脉冲。该研究为探测同位素分子及产生高强度及高能量的阿秒脉冲提供了一种新的方案,对激光光学的发展有一定帮助。Abstract: In order to understand the effect of nuclear motion of H2+ and T+ 2on harmonic intensity and attosecond pulse generation, the intensity changes in the harmonic cutoff region from H2+ and T2+ driven by a 10fs and 20fs lasers were theoretically studied by numerically solving the time-dependent SchrÖdinger equation. The results show that the harmonic intensity follows as H2+ > T2+ under shorter pulse duration case; it follows as T2+ > H2+ under longer pulse duration case. According to the changing law of harmonic intensity, the high intensity and high energy harmonic plateau can be obtained by introducing the half-cycle laser pulse under the optimal harmonic emission intensity, and then the attosecond pulse with pulse duration of 37as can be obtained. The study provides a new way to detect isotopic molecules and generate high intensity and high energy attosecond pulses.
-
Key words:
- laser optics /
- high-order harmonic generation /
- nuclear motion /
- harmonic intensity /
- attosecond pulse
-
-
[1] L'HUILLIER A, BALCOU P. High-order harmonic generation in rare gases with a 1ps 1053nm laser[J]. Physical Review Letters, 1993, 70 (6): 774-777. doi: 10.1103/PhysRevLett.70.774 [2] FENG L Q, LI Y, LIU H. High intensity attosecond pulse generation by the improved multi-cycle polarization gating technology [J]. Laser Technology, 2018, 42(4): 451-456(in Chinese). [3] FENG L Q. Contributions of two-H nuclei in H2+ to high-order harmonic generation [J]. Journal of Atomic and Molecular Physics, 2018, 35(2): 267-271(in Chinese). [4] LIU H, FENG L Q. Contributions of charge-resonance-enhanced-ionization and dissociative ionization to high-order harmonic generation from H+2[J]. Journal of Atomic and Molecular Physics, 2018, 35(3): 461-465 (in Chinese). [5] CORKUM P B. Plasma perspective on strong field multiphoton ionization [J]. Physical Review Letters, 1993, 71(13): 1994-1997. doi: 10.1103/PhysRevLett.71.1994 [6] STEELKOV V V, STERJANTOV A F, SHUBIN N Y, et al. XUV generation with several-cycle laser pulse in barrier-suppression regime [J]. Journal of Physics, 2006, B39(3): 577-590. [7] ZUO T, CHELKOWSKI S, BANDRAUK A D. Harmonic-generation by the H2+ molecular ion in intense laser fields [J]. Physical Review, 1993, A48(5): 3837-3844. [8] LIU H, LI W L, FENG L Q. Chirp control of multi-photon resonance ionization and charge resonance enhanced ionization on molecular harmonic generation [J]. Chemical Physics Letters, 2017, 676: 118-123. doi: 10.1016/j.cplett.2017.03.049 [9] FENG L Q, LI Y, FENG A Y. Nano-plasmonic-pump-probe effect on the intensity enhancement of attosecond pulse from hydrogen molecular ion [J]. Laser Physics Letters, 2018, 15(11): 115301. doi: 10.1088/1612-202X/aadf73 [10] BIAN X B, BANDRAUK A D. Probing nuclear motion by frequency modulation of molecular high-order harmonic generation [J]. Physical Review Letters, 2014, 113(19): 193901. doi: 10.1103/PhysRevLett.113.193901 [11] FENG L Q, CHU T S. Nuclear signatures on the molecular harmonic emission and the attosecond pulse generation [J]. The Journal of Chemical Physics, 2012, 136(5): 054102. [12] HE L X, ZHANG Q B, LAN P F, et al. Monitoring ultrafast vibrational dynamics of isotopic molecules with frequency modulation of high-order harmonics [J]. Nature Communications, 2018, 9(1): 1108. doi: 10.1038/s41467-018-03568-3 [13] LU R F, ZHANG P Y, HAN K L. Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields [J]. Physical Review, 2008, E77(6): 066701. [14] LI Y, FENG L Q, QIAO Y. Selective enhancement of single-order and two-order harmonics from He atom via two-color and three-color laser fields [J]. Chemical Physics, 2019, 527: 110497. doi: 10.1016/j.chemphys.2019.110497 [15] FENG L Q, CHU T S. Generation of an isolated sub-40as pulse using two-color laser pulses: Combined chirp effects [J]. Physical Review, 2011, A84(5): 053853. [16] LI Y, FENG R L Q, QIAO Y. Improvement of harmonic spectra from superposition of initial state driven by homogeneous and inhomogeneous combined field [J]. Canadian Journal of Physics, 2019, 98(2):1139. [17] LI L, ZHENG M, FENG R L Q, et al. Waveform control in generations of intense water window attosecond pulses via multi-color combined field [J]. International Journal of Modern Physics, 2019, B33(13): 1950130. [18] FENG L Q, LIU H. Unipolar pulse assisted generation of the coherent XUV pulses [J]. Optics Communications, 2015, 348: 1-6. doi: 10.1016/j.optcom.2015.03.026 [19] WEI P F, MIAO J, ZENG Z N, et al. Selective enhancement of a single harmonic emission in a driving laser field with subcycle waveform control [J]. Physical Review Letters, 2013, 110(23): 233903. doi: 10.1103/PhysRevLett.110.233903