Adjustable even and odd harmonic radiation characteristics of crystal target by strain engineering
Credit: ©Science China Press
As a cutting-edge subject in the cross research field, solid high-order harmonics not only provide a new strategy for high-efficiency, wide energy spectrum, short pulse light source, but also can be used to better study the electronic structure and nonlinear optical properties of condensed matter.
A recent study has revealed the novel harmonic spectrum distribution dependent on crystal orientation by adjusting the strain of single layer AlN, which is entitled “Strain effect on the orientation-dependent harmonic spectrum of monolayer aluminum nitride” and published in SCIENCE CHINA Physics, Mechanics & Astronomy. Prof. Ruifeng Lu from Nanjing University of Science and Technology is the corresponding author.
Using the theoretical model of multi-band semiconductor Bloch equation, the researchers found that the coherent enhancement of different quantum paths of electronic transitions resulted in different odd and even harmonics radiated by the strained target under the action of ultrafast and strong laser. This work provides a reference for the investigation of the electronic structure and dynamics of semiconductor in the strong laser field.
Since the scientists at Stanford University used ZnO crystal as the medium to obtain non-perturbed high-order harmonics in 2011 , the study on solid harmonics has attracted extensive interest of world-renowned research groups in related fields. Due to the high atomic density in the crystal materials, it is found that the harmonic signal intensity of SiO2 crystal is significantly higher than that of gas-phase medium under the same driving laser conditions . Also, the solid harmonic signal can be used to reconstruct band structure  as well as Berry curvature  of crystal. In 2015, the high-order harmonics of GaSe crystal were measured in experiment and the coherence mechanism of quantum paths was proposed .
In recent years, Prof. Ruifeng Lu and coworkers have made great progress in the theoretical research of solid harmonics. In 2018, the details of the first solid harmonic experimental data are qualitatively reproduced for the first time, and the generation mechanism of odd and even harmonics derived from crystal spatial symmetry is clarified . In 2019, it is further proved that the mechanisms of transition dipole moment, interband polarization and Berry curvature are essentially self-consistent, which are all the reflection of intrinsic symmetry .
At present, researchers try to obtain high-quality high-order harmonic signals by using light field regulation  or material regulation . As one of the common methods in condensed matter physics, strain control has not been discussed seriously in previous solid harmonic studies. This work focuses on the material control. It is found that the band gap of monolayer AlN crystal becomes narrow under strain condition, thus the efficiency of the first harmonic plateau (with a cut-off of the 11th order in Figure 1) mainly from the (V1, C1) band pair is obviously enhanced with the odd harmonics still dominant. For the second harmonic plateau (with a cut-off of the 29th order in Figure 1), odd harmonics are dominant along both Γ-M and Γ-K direction without strain, whereas even harmonics are dominant along Γ-M direction when strain is applied. Through the detailed analysis of the transition dipole moment, it is confirmed that the peculiar even harmonics of the second plateau come from the enhanced interference of direct transition (V1-C1) and indirect transition (V1-V2-C1) of valence electron by applying strain. The scheme of controlling the harmonic radiation by changing the electronic structure is of great scientific significance and reference value to the study of high-order harmonic in solid.
This research was funded by the National Natural Science Foundation of China (No. 11974185) & Natural Science Foundation of Jiangsu Province (No. BK20170032).
See the article:
WANG Ziwen, JIANG Shicheng, YUAN Guanglu, WU Tong, LI Cheng, QIAN Chen, JIN Cheng, YU Chao, HUA Weijie & LU Ruifeng, Strain effect on the orientation-dependent harmonic spectrum of monolayer aluminum nitride, SCIENCE CHINA Physics, Mechanics & Astronomy, 2020, 5: 257311
 S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, Observation of high-order harmonic generation in a bulk crystal, Nat. Phys. 7, 138 (2011).
 T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, Extreme ultraviolet high-harmonic spectroscopy of solids, Nature 521, 498 (2015).
 G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, All-optical reconstruction of crystal band structure, Phys. Rev. Lett. 115, 193603 (2015).
 T. T. Luu, and H. J. Wörner, Measurement of the Berry curvature of solids using high-harmonic spectroscopy, Nat. Commun. 9, 916 (2018).
 M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, Real-time observation of interfering crystal electrons in high-harmonic generation, Nature 523, 572 (2015).
 S. C. Jiang, J. G. Chen, H. Wei, C. Yu, R. F. Lu, and C. D. Lin, Role of transition dipole amplitude and phase on the generation of odd and even high-order harmonics in crystals, Phys. Rev. Lett. 120, 253201 (2018).
 S. C. Jiang, S. Gholam-Mirzaei, E. Crites, J. E. Beetar, M. Singh, R. F. Lu, M. Chini, and C. D. Lin, Crystal symmetry and polarization of high-order harmonics in ZnO, J. Phys. B: At. Mol. Opt. Phys. 52, 225601 (2019).
 N. Yoshikawa, T. Tamaya, and K. Tanaka, High-harmonic generation in graphene enhanced by elliptically polarized light excitation, Science 356, 736 (2017).
 H. Z. Liu, C. Guo, G. Vampa, J. Y. L. Zhang, T. Sarmiento, M. Xiao, P. H. Bucksbaum, J. Vučkovi?, S. H. Fan, and D. A. Reis, Enhanced high-harmonic generation from an all-dielectric metasurface, Nat. Phys. 14, 1006 (2018).
Related Journal Article