Shanghai Optical Machine has made progress in frequency shift of even harmonic of single layer MoS2

Recently, the research team of the State Key Laboratory of High-Field Laser Physics at the Shanghai Institute of Optics and Fine Mechanics of the Chinese Academy of Sciences has made progress in using high-field lasers to drive the even harmonic frequency shift of single-layer MoS2. The results were published in Optics Express under the title "Frequency shift of even-order high harmonic generation in monolayer MoS2".

High order harmonic radiation in solid materials is an important spectroscopy technique to detect the fundamental properties of matter, and has been successfully used to reconstruct crystal band structure, detect Berry curvature and detect topological phase transitions. In recent years, two-dimensional layered materials have received extensive attention, which brings new opportunities for further research on the generation of higher harmonics.

Since the thickness of the material is only a single or a few atomic layers, its spatial scale is much smaller than the wavelength of the driving laser, which can effectively avoid the influence of nonlinear transmission, and thus become an ideal material for studying the ultrafast-fast dynamics of laser field. Among them, monolayer molybdenum disulfide (MoS2) has attracted much attention due to its non-centrosymmetric structure and significant nonlinearity.

This research team [Opt.Express 29,4830 (2021)] observed an abnormal enhancement of even harmonics in the HHG spectrum of MoS2 and attributed this to spectral interference during different half-weeks of Berry contact control. In addition, quantum trajectory analysis suggests that the transition dipole moment phase and Berry linkage modulate the energy and momentum of the released photon, but no experimental observations have confirmed this so far.

The research team used the mid-infrared laser light source built by the laboratory to excite single-layer MoS2 to generate higher-order harmonic spectrum. It was found that when the laser polarization was driven along the armrest direction, the center frequency of even harmonics would shift significantly, and the harmonic energy of the frequency shift was close to the band gap energy of single-layer MoS2.

In addition, it is found that the frequency shift of even harmonics of adjacent order is opposite, that is, the 6th harmonic is red shifted, while the 8th harmonic is blue shifted. Based on the semiconductor Bloch equation and the saddle point calculation of electron orbit, the research team successfully revealed the microphysical mechanism of frequency shift, and confirmed that the frequency shift phenomenon of even harmonic is mainly from the interband polarization process.

The theoretical analysis further shows that the transition dipole moment phase and the Bailie connection jointly modulate the moment and momentum of the electron-hole pair recombination, resulting in a change in the frequency of the photon released by the adjacent half-period, which then changes the center frequency of different harmonic levels, and finally causes six redshifts and eight blue shifts of MoS2 spectrum. This work reveals that the transition dipole moment phase and Berry connection play an important role in the high-field optical response of non-centrosymmetric materials, and contributes to the fundamental understanding of ultrafine carrier dynamics in non-centrosymmetric materials.

Figure 1. The simulated higher-order harmonic spectra reproduce the experimental observations.

Figure 2. (a) the frequency shift of different levels of the spectrum between bands, and (b) the dependence of the harmonic frequency shift on the crystal azimuth.

Source: Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences