MATHEMATICAL SCIENCES

The frequency shift study of even-order harmonics of monolayer molybdenum disulfide has progressed


Recently, the research team of the State Key Laboratory of Strong-Field Laser Physics of the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences has made progress in using strong-field lasers to drive the even-order harmonic frequency shift of monolayer molybdenum disulfide. 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 spectroscopic technique for detecting the basic properties of materials, 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 attracted widespread attention, which has brought new opportunities for further research on the generation of higher harmonics. Since the material is only a single or a few atomic layers thick, its spatial scale is much smaller than the wavelength driving the laser, which can effectively avoid the influence of nonlinear transmission, so it has become an ideal material for studying the ultrafast dynamics of laser field drive. Among them, monolayer molybdenum disulfide (MoS2) has attracted widespread attention due to its non-central symmetric structure and significant nonlinearity. This research team[Opt. Express 29,4830 (2021)]In the HHG spectra of molybdenum disulfide, it was observed that even harmonics exhibited abnormal enhancement and attributed it to spectral interference between different half-periods controlled by the Berry link. In addition, quantum trajectory analysis shows that the transition dipole moment phase and the Berry connection modulate the energy and momentum of the released photons, but so far no experimental observations have confirmed this.

The research team used the laboratory’s self-built mid-infrared laser light source to excite the monolayer molybdenum disulfide to produce a high-order harmonic spectrum, and found that when driving the laser polarization along the armrest, the even-order harmonic center frequency will move significantly, and the harmonic energy of the frequency shift is close to the bandgap energy of the monolayer molybdenum disulfide. In addition, it is also found that the frequency shift of the adjacent order of even harmonics is in the opposite direction, that is, the 6th harmonic redshift, and the 8th harmonic blueshift. Based on the semiconductor Bloch equation and the calculation of the saddle point of the electronic orbit, the research team successfully revealed the microscopic physical mechanism of frequency shift, and confirmed that the frequency shift phenomenon of even harmonics mainly comes from the interband polarization process. The theoretical analysis further shows that the transition dipole moment phase and Bailey contact jointly modulate the moment and momentum of electron-hole pair recombination, resulting in the frequency change of photons released in the adjacent half-cycle, which in turn changes the center frequency of different harmonic levels, and finally causes the sixth redshift and eighth blue shift of the molybdenum disulfide spectrum. This work reveals that the transition dipole moment phase and the Berry connection play an important role in the strong field optical response of non-central symmetric materials, which is helpful for the fundamental understanding of ultrafast carrier dynamics in non-central symmetric materials. (Source: Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences)

Figure 1. The simulated higher-order harmonic spectrum reproduces the experimental observation.

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

Related paper information:https://doi.org/10.1364/OE.497154

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