Subcycle interference in high-order harmonic generation from solids

Tao-Yuan Du, Dong Tang, and Xue-Bin Bian

Phys. Rev. A 98, 063416 – Published 14 December 2018

Abstract

Different from the high-order harmonic generation (HHG) from gases, we find that the yield of HHG from solids exhibits unexpected modulations as a function of the driving laser intensity and wavelength. Its mechanism can be unraveled by the interference between currents inside the solids induced by two adjacent Zener tunneling events. Our simulations agree well with the experimental measurements of HHG from ZnSe and solid Ar. We also find that the dephasing time plays a key role in this subcycle interference and can turn it on or off by controlling the overlap between the channels. It provides an avenue to optimize the ultrafast electron dynamics and HHG emission processes in solids, which will be useful for the compact ultrafast EUV light sources. We also propose an experimental scheme by using ultrashort lasers to explore this interference in other solid materials.

Received 2 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.063416

Physics Subject Headings (PhySH)

High-order harmonic generation

Nonlinear Dynamics

Authors & Affiliations

Tao-Yuan Du^1,2, Dong Tang^2,3, and Xue-Bin Bian^2,*

¹School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
²State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
³University of Chinese Academy of Sciences, Beijing 100049, China

^*xuebin.bian@wipm.ac.cn

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Vol. 98, Iss. 6 — December 2018

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Images

Figure 1
(a) Comparison of the yield of the tenth harmonic in ZnSe as a function of laser intensity obtained from experimental measurements (redrawn from the experimental data in Fig. S4(f) of Ref. [15]) and our simulation of the SBEs. (b) Comparison of the integral yields of the first and second plateaus in solid Ar as a function of laser intensity obtained from the experimental data in Fig. 2(a) of Ref. [10] and our theoretical simulations. The yields of the first and second plateaus are integrated in the range of 19–25 and 25–33 eV, respectively. The minimal yield in the experimental data implies a destructive points, as denoted by D $_{0, 1, 2, 3}$ in (a) and D $_{0, 1, 2}^{'}$ in (b), respectively. Temporal evolutions of the propagation phase $ϕ_{c v}$ at D $_{0}$ and D $_{0}^{'}$ points are shown in (c) and (e), respectively. (d) Relative band coupling strength $Φ$ , which is normalized and determines the times of the transition events. The transition events and its propagation phases are illustrated by the solid dots in (d) and hollow dot in (c) and (e), respectively. The dash-dotted line in (d) shows the electron wave vector $k (t)$ .
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Figure 2
Schematic of the subcycle interference. Two electron wave packets are pumped to the conduction band by Zener transition around the adjacent peaks which are separated by a half optical cycle. Temporal evolutions of the electron wave vector $k (t)$ is shown by the gray dash-dotted line in (a). The motion of wave packets in the same band shows the intraband current (solid arrows), while the ionization between valence and conduction bands illustrates the Zener transition (dashed arrows) in (b). The interference comes from the overlap between these two groups of the wave packets. $k = 0$ correspond to the $Γ$ point in the reduced BZ.
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Figure 3
Modulation of the HHG yields in ZnO crystal. (a) High harmonic spectra as a function of the laser intensity with constant laser frequency $ω =$ 0.0228 a.u., corresponding to a laser period $T_{0} = 6.7$ fs. The duration is eight optical cycles. The dephasing time is $T_{2} = 10$ fs. Two vertical dashed lines denote the minimal and maximal gap between the valence and conduction bands, which correspond to 3.3 and 12 eV, respectively. (b) Harmonic yields (blue solid line) which are the integrals of the plateau zone in the range of 3.3–12 eV as a function of the laser intensity. The destructive (downward triangle) and constructive (upward triangle) points of the HHG yield are predicted by the subcycle interference model. Two hollow triangles denote destructive and constructive points as an example, respectively. The role of dephasing time in modulation of HHG yields has been illustrated by the blue dash-dotted line in (b), where $T_{2}$ is about 3 fs in our simulations. Temporal evolutions of the propagation phase $ϕ_{c v}$ at the destructive and constructive points of the HHG yield are shown in (c) and (d), respectively. Time-frequency analysis of HHG with $A_{0} = 0.8 π / a$ is presented with $T_{2} = 10$ fs in (e) and $T_{2} = 3$ fs in (f). The solid and hollow dots indicate the short (S) and long (L) trajectories, respectively, which are predicted by the quasiclassical model [18].
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Figure 4
(a) High harmonic spectra as a function of the wavelength $λ$ with constant strength of the electric field $F_{0}$ = 0.0079 a.u. (b) Harmonic yields which are the integrals of the plateau zone as a function of the wavelength. (c) The propagation phase differences as function of the wavelength when the transition events occur at $t_{1} = - 0.5$ o.c. and $t_{2} = 0$ o.c., respectively.
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Figure 5
Demonstration of the subcycle interference in a single-cycle laser pulse. (a) HHG spectra as a function of the laser intensity. The laser frequency $ω =$ 0.0351 a.u., corresponding to a period about 4.3 fs. The FWHM of the laser pulse is about one cycle. HHGs in the plateau zone are divided into two zones which correspond to the interference opening (O) and closing (C) channels. (b) The harmonic yields which are the integrals of the zones in the HHG range of the interference opening (solid line) and closing (dash-dotted line) as a function of the laser intensity. The extreme points of the HHG yield in the interference opening zone are predicted by the above model, as shown by the downward and upward triangles in (b). Temporal evolution of the propagation phase $ϕ_{c v}$ at the destructive and constructive points of the HHG yield [two hollow triangles in (b)] are shown in (c) and (e), respectively. (d) Band coupling strength $Φ$ . The hollow dots in (c), (d), and (e) denote the transition events. (f) Time-frequency profile and quasiclassical prediction of HHG emission in (a) where the laser intensity is 9.67 TW/ ${cm}^{2}$ .
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Figure 6
The $k$ -dependent values of the transition dipoles $| d_{i j} (k) |$ (blue dashed lines) and relative band coupling strengths $Φ (k)$ (black solid lines) between the valence (V) and the conduction (C1) bands along the directions of the corresponding optical axes. The relative band coupling strengths $Φ (k)$ are normalized.
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