- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Impact of incident photon energy and pulse intensity on circularly polarized high harmonic generation in monolayer graphene

Yu-Ze Li1, Ting-Ting Xi1,*, Yu-Hui Song2,3, Huan-Cheng Yang2,3, Kai Liu2,3,†, and Zhong-Yi Lu2,3,‡

  • *Contact author: ttxi@ucas.ac.cn
  • †Contact author: kliu@ruc.edu.cn
  • ‡Contact author: zlu@ruc.edu.cn
PDF

Phys. Rev. B 112, 235418 – Published 17 December, 2025

DOI: https://doi.org/10.1103/qhcm-fh67

Abstract

Circularly polarized high harmonics provide important light sources for ultrafast detection of chiral molecules and solid materials. Although the circularly polarized high harmonic generation (HHG) has been reported in many solid materials, the comprehensive study about its dependence on the driving pulse parameters is still rare. Here, by using time-dependent density functional theory calculations, we have systematically simulated the generation of high harmonics from monolayer graphene driven by circularly polarized femtosecond pulses with different photon energies and peak intensities. Our calculation results show that when the driving pulses with high photon energy or low peak intensity are adopted, circularly polarized high harmonics can be generated, in which the harmonic radiation is dominated by intraband process and the harmonic order/polarization fulfill the selection rule. However, under driving pulses with low photon energy and high peak intensity, some of low-order harmonics exhibit noise spectra and their corresponding polarizations deviate significantly from the selection rule, which is because under this condition the number of incident photons is increased and the interband transitions between the empty and occupied bands with large density of states are enhanced. Our study clarifies the conditions for the generation of circularly polarized high harmonics in graphene and provides an important reference for selecting driving pulse parameters with the knowledge of electronic band structure. We also discover the correspondence between the HHG noise spectrum and the polarization, which can serve as a simple experimental criterion on whether the interband transitions become prominent in solid materials.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (34)

  1. Y.-J. Chen, D. Haase, J. Manz, H.-H. Wang, and Y.-G. Yang, From chiral laser pulses to femto- and attosecond electronic chirality flips in achiral molecules, Nat. Commun. 15, 565 (2024).
  2. J.-T. Liang, M. Han, Y.-J. Liao, J.-B. Ji, C. S. Leung, W.-C. Jiang, K. Ueda, Y.-M. Zhou, P.-X. Lu, and H. J. Wörner, Attosecond-resolved non-dipole photoionization dynamics, Nat. Photon. 18, 311 (2024).
  3. T. Xiang, L. Cheng, and J.-B. Qi, Ultrafast charge and spin dynamics on topological insulators, Acta Phys. Sin. 68, 227202 (2019).
  4. J. Hasaien, K.-J. Zhu, F. Sun, Y.-L. Wu, Y.-G. Shi, and J.-M. Zhao, Generation and control of photo-excited thermal currents in triple degenerate topological semimetal mop with circularly polarized ultrafast light pulses, Acta Phys. Sin. 69, 207801 (2020).
  5. X. Yang, H.-M. Feng, J.-N. Liu, X.-Q. Zhang, W. He, and Z.-H. Cheng, Ultrafast spin dynamics: From femtosecond magnetism to attosecond magnetism, Acta Phys. Sin. 73, 157501 (2024).
  6. H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, Polarization-dependent high-order two-color mixing, Phys. Rev. A 51, R3414 (1995).
  7. S. Long, W. Becker, and J. K. McIver, Model calculations of polarization-dependent two-color high-harmonic generation, Phys. Rev. A 52, 2262 (1995).
  8. A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen, Spin angular momentum and tunable polarization in high-harmonic generation, Nat. Photon. 8, 543 (2014).
  9. N. Saito, P.-Y. Xia, F.-M. Lu, T. Kanai, J. Itatani, and N. Ishii, Observation of selection rules for circularly polarized fields in high-harmonic generation from a crystalline solid, Optica 4, 1333 (2017).
  10. N. Klemke, N. Tancogne-Dejean, G. M. Rossi, Y.-D. Yang, R. E. Mainz, G. D. Sciacca, A. Rubio, F. X. Kärtner, and O. D. Mücke, Polarization-state-resolved high-harmonic spectroscopy of solids, Nat. Commun. 10, 1319 (2019).
  11. T. T. Luu and H. J. Wörner, Generation of circularly polarized extreme-ultraviolet harmonics from solids, Eur. Phys. J. Spec. Top. 230, 4057 (2021).
  12. C. L. Tang and H. Rabin, Selection rules for circularly polarized waves in nonlinear optics, Phys. Rev. B 3, 4025 (1971).
  13. O. E. Alon, V. Averbukh, and N. Moiseyev, Selection rules for the high harmonic generation spectra, Phys. Rev. Lett. 80, 3743 (1998).
  14. N. Yoshikawa, T. Tamaya, and K. Tanaka, High-harmonic generation in graphene enhanced by elliptically polarized light excitation, Science 356, 736 (2017).
  15. C.-D. Liu, Y.-H. Zheng, Z.-N. Zeng, and R.-X. Li, Driving-laser ellipticity dependence of high-order harmonic generation in graphene, Phys. Rev. A 97, 063412 (2018).
  16. S. A. Sato, H. Hirori, Y. Sanari, Y. Kanemitsu, and A. Rubio, High-order harmonic generation in graphene: Nonlinear coupling of intraband and interband transitions, Phys. Rev. B 103, L041408 (2021).
  17. M. S. Mrudul and G. Dixit, High-harmonic generation from monolayer and bilayer graphene, Phys. Rev. B 103, 094308 (2021).
  18. Y.-K. Feng, S.-X. Shi, J.-B. Li, Y.-J. Ren, X. Zhang, J.-H. Chen, and H.-C. Du, Semiclassical analysis of ellipticity dependence of harmonic yield in graphene, Phys. Rev. A 104, 043525 (2021).
  19. Z.-Y. Chen and R. Qin, Circularly polarized extreme ultraviolet high harmonic generation in graphene, Opt. Express 27, 3761 (2019).
  20. E. Runge and E. K. U. Gross, Density-functional theory for time-dependent systems, Phys. Rev. Lett. 52, 997 (1984).
  21. M. A. L. Marques, A. Castro, G. F. Bertsch, and A. Rubio, Octopus: A first-principles tool for excited electron-ion dynamics, Comput. Phys. Commun. 151, 60 (2003).
  22. A. Castro, H. Appel, M. Oliveira, C. A. Rozzi, X. Andrade, F. Lorenzen, M. A. L. Marques, E. K. U. Gross, and A. Rubio, Octopus: A tool for the application of time-dependent density functional theory, Phys. Status Solidi B 243, 2465 (2006).
  23. X. Andrade, J. Alberdi-Rodriguez, D. A. Strubbe, M. J. T. Oliveira, F. Nogueira, A. Castro, J. Muguerza, A. Arruabarrena, S. G. Louie, A. Aspuru-Guzik, A. Rubio, and M. A. L. Marques, Time-dependent densityfunctional theory in massively parallel computer architectures: The octopus project, J. Phys.: Condens. Matter 24, 233202 (2012).
  24. X. Andrade, D. A. Strubbe, U. D. Giovannini, A. H. Larsen, M. J. T. Oliveira, J. Alberdi-Rodriguez, A. Varas, I. Theophilou, N. Helbig, M. Verstraete, L. Stella, F. Nogueira, A. Aspuru-Guzik, A. Castro, M. A. L. Marques, and A. Rubio, Real-space grids and the octopus code as tools for the development of new simulation approaches for electronic systems, Phys. Chem. Chem. Phys. 17, 31371 (2015).
  25. C. Yu, S.-C. Jiang, and R.-F. Lu, High order harmonic generation in solids: A review on recent numerical methods, Adv Phys: X 4, 1562982 (2019).
  26. N. Tancogne-Dejean, O. D. Mücke, F. X. Kärtner, and A. Rubio, Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics, Nat. Commun. 8, 745 (2017).
  27. N. Tancogne-Dejean, O. D. Mücke, F. X. Kärtner, and A. Rubio, Impact of the electronic band structure in high-harmonic generation spectra of solids, Phys. Rev. Lett. 118, 087403 (2017).
  28. See Supplemental Material at http://link.aps.org/supplemental/10.1103/qhcm-fh67 for the convergence test of k-point meshes, the test of different exchange-correlation functionals, the test of different pulse durations, the test of carrier-envelope phases, the joint density of states of monolayer graphene, and the comparison of our results with prior experimental results.
  29. M.-X. Wu, S. Ghimire, D. A. Reis, K. J. Schafer, and M. B. Gaarde, High-harmonic generation from Bloch electrons in solids, Phys. Rev. A 91, 043839 (2015).
  30. T. Otobe, High-harmonic generation in α-quartz by the electron-hole recombination, Phys. Rev. B 94, 235152 (2016).
  31. A. F. Kemper, B. Moritz, J. K. Freericks, and T. P. Devereaux, Theoretical description of high-order harmonic generation in solids, New J. Phys. 15, 023003 (2013).
  32. U. Huttner, K. Schuh, J. V. Moloney, and S. W. Koch, Similarities and differences between high-harmonic generation in atoms and solids [Invited], J. Opt. Soc. Am. B 33, C22 (2016).
  33. G. Vampa, C. R. McDonald, G. Orlando, D. D. Klug, P. B. Corkum, and T. Brabec, Theoretical analysis of high-harmonic generation in solids, Phys. Rev. Lett. 113, 073901 (2014).
  34. R.-X. Zuo, X.-H. Song, X.-W. Liu, S.-D. Yang, and W.-F. Yang, Influence of intraband motion on the interband excitation and high harmonic generation, Chin. Phys. B 28, 094208 (2019).

Outline

Information

Phys. Rev. B 112, 235418– Published 17 December, 2025
  • Received 14 July 2025
  • Revised 4 November 2025
  • Accepted 3 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation