Abstract
Dynamical control of the nonlinear optical properties of solids – with light itself – will be essential for future ultrafast photonic technologies. Previously, methods to modulate nonlinear processes including second-harmonic generation (SHG) have relied primarily on non-resonant light-matter interaction or photo-generation of hot electrons in nanoscale materials. However, these approaches are typically constrained by limited interaction lengths and the initial frequency conversion is relatively weak under equilibrium conditions. Here, a ~ 30% modulation of efficient phase-matched SHG in bulk beta-barium borate (β-BaB2O4) is achieved through transient lattice deformation by intense terahertz (THz) pulses that are tuned to resonance with an infrared-active phonon mode. The effect originates from modification of the index of refraction ellipsoid and the corresponding nonlinear phase-matching conditions, rather than from direct modulation of the nonlinear susceptibility through THz-mediated \({\chi }^{(3)}\) processes. This mechanism, of resonant selective lattice excitation, points toward novel THz-control schemes to tune the nonlinear optical response in materials.
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Data availability
The data supporting the findings of this study, including those presented in the Supplementary Information, are available in Figshare at https://doi.org/10.6084/m9.figshare.31254352.
Code availability
The DFT and DFPT calculations presented in this study are available on Materials Cloud at https://doi.org/10.24435/materialscloud:k3-ns.
References
Boyd, R. W. Nonlinear Optics 3rd edn (Academic Press, Burlington, 2008).
Dutt, A., Mohanty, A., Gaeta, A. L. & Lipson, M. Nonlinear and quantum photonics using integrated optical materials. Nat. Rev. Mater. 9, 321–346 (2024).
Chang, D. E., Vuletić, V. & Lukin, M. D. Quantum nonlinear optics - photon by photon. Nat. Photonics 8, 685–694 (2014).
Hickstein, D. D. et al. Self-organized nonlinear gratings for ultrafast nanophotonics. Nat. Photonics 13, 494–499 (2019).
Casacio, C. A. et al. Quantum-enhanced nonlinear microscopy. Nature 594, 201–206 (2021).
Parodi, V. et al. Nonlinear optical microscopy: from fundamentals to applications in live bioimaging. Front. Bioeng. Biotechnol. 8, 585363 (2020).
Bogaerts, W. et al. Programmable photonic circuits. Nature 586, 207–216 (2020).
Lukin, D. M. et al. 4H-silicon-carbide-on-insulator for integrated quantum and nonlinear photonics. Nat. Photonics 14, 330–334 (2020).
Moody, G., Chang, L., Steiner, T. J. & Bowers, J. E. Chip-scale nonlinear photonics for quantum light generation. AVS Quantum Sci. 2, 041702 (2020).
Liu, X. & Fu, H. Highly-coherent second-harmonic generation in a chip-scale source. Light Sci. Appl. 13, 20 (2024).
Widhalm, A. et al. Electric-field-induced second harmonic generation in silicon dioxide. Opt. Express 30, 4867–4874 (2022).
Chen, S., Li, K. F., Li, G., Cheah, K. W. & Zhang, S. Gigantic electric-field-induced second harmonic generation from an organic conjugated polymer enhanced by a band-edge effect. Light Sci. Appl. 8, 17 (2019).
Puckett, M. W. et al. Observation of second-harmonic generation in silicon nitride waveguides through bulk nonlinearities. Opt. Express 24, 16923–16933 (2016).
Timurdogan, E., Poulton, C. V., Byrd, M. J. & Watts, M. R. Electric field-induced second-order nonlinear optical effects in silicon waveguides. Nat. Photonics 11, 200–206 (2017).
Franchi, R., Castellan, C., Ghulinyan, M. & Pavesi, L. Second-harmonic generation in periodically poled silicon waveguides with lateral p-i-n junctions. Opt. Lett. 45, 3188–3191 (2020).
Huang, B. et al. Electrical control of 2D magnetism in bilayer CrI3. Nat. Nanotechnol. 13, 544–548 (2018).
Seyler, K. L. et al. Electrical control of second-harmonic generation in a WSe2 monolayer transistor. Nat. Nanotechnol. 10, 407–411 (2015).
Lee, K. T. et al. Electrically biased silicon metasurfaces with magnetic mie resonance for tunable harmonic generation of light. ACS Photonics 6, 2663–2670 (2019).
Cai, W., Vasudev, A. P. & Brongersma, M. L. Electrically controlled nonlinear generation of light with plasmonics. Science 333, 1720–1723 (2011).
Klimmer, S. et al. All-optical polarization and amplitude modulation of second-harmonic generation in atomically thin semiconductors. Nat. Photonics 15, 837–842 (2021).
Liu, D. et al. Light-triggered reversible tuning of second-harmonic generation in a photoactive plasmonic molecular nanocavity. Nano Lett. 23, 5851–5858 (2023).
Taghinejad, M., Xu, Z., Lee, K. T., Lian, T. & Cai, W. Transient second-order nonlinear media: breaking the spatial symmetry in the time domain via hot-electron transfer. Phys. Rev. Lett. 124, 013901 (2020).
Li, G. C. et al. Light-induced symmetry breaking for enhancing second-harmonic generation from an ultrathin plasmonic nanocavity. Nat. Commun. 12, 4326 (2021).
Belvin, C. A. et al. Exciton-driven antiferromagnetic metal in a correlated van der Waals insulator. Nat. Commun. 12, 4837 (2021).
Bodrov, S. B., Sergeev, Y.uA., Korytin, A. I. & Stepanov, A. N. Terahertz-field-induced second optical harmonic generation from Si(111) surface. Phys. Rev. B 105, 035306 (2022).
Cornet, M., Degert, J., Abraham, E. & Freysz, E. Terahertz-field-induced second harmonic generation through Pockels effect in zinc telluride crystal. Opt. Lett. 39, 5921–5924 (2014).
Chen, J., Han, P. & Zhang, X.-C. Terahertz-field-induced second-harmonic generation in a beta barium borate crystal and its application in terahertz detection. Appl. Phys. Lett. 95, 011118 (2009).
Bodrov, S. B., Sergeev, Y.uA., Korytin, A. I., Burova, E. A. & Stepanov, A. N. Terahertz pulse induced femtosecond optical second harmonic generation in transparent media with cubic nonlinearity. J. Opt. Soc. Am. B 37, 789–796 (2020).
Ovchinnikov, A. V., Chefonov, O. V., Mishina, E. D. & Agranat, M. B. Second harmonic generation in the bulk of silicon induced by an electric field of a high power terahertz pulse. Sci. Rep. 9, 9753 (2019).
Cammarata, A. & Rondinelli, J. M. Contributions of correlated acentric atomic displacements to the nonlinear second harmonic generation and response. ACS Photonics 1, 96–100 (2014).
Li, R. Vibrational contributions to the electro-optic effect of BBO, KTP and RTP crystals. Comput. Mater. Sci. 230, 112529 (2023).
Lin, J., Lee, M.-H., Liu, Z.-P., Chen, C. & Pickard, C. J. Mechanism for linear and nonlinear optical effects in β-BaB2O4 crystals. Phys. Rev. B 60, 13380–13389 (1999).
Li, R. et al. Optical properties of barium borate crystal in the THz range revisited. Opt. Lett. 50, 686–689 (2025).
Vicario, C., Trisorio, A., Allenspach, S., Rüegg, C. & Giorgianni, F. Narrow-band and tunable intense terahertz pulses for mode-selective coherent phonon excitation. Appl. Phys. Lett. 117, 101101 (2020).
Kozina, M. et al. Terahertz-driven phonon upconversion in SrTiO3. Nat. Phys. 15, 387–392 (2019).
Melnikov, A. A. et al. Coherent phonons in a Bi2Se3 film generated by an intense single-cycle THz pulse. Phys. Rev. B 97, 214304 (2018).
Mankowsky, R., von Hoegen, A., Först, M. & Cavalleri, A. Ultrafast reversal of the ferroelectric polarization. Phys. Rev. Lett. 118, 197601 (2017).
Grishunin, K. A. et al. THz electric field-induced second harmonic generation in inorganic ferroelectric. Sci. Rep. 7, 687 (2017).
McDonnell, C. et al. THz field induced second harmonic generation in epsilon near zero indium tin oxide thin films. Nano Lett. 25, 12201–12206 (2025).
Itoh, H. et al. Terahertz field control of electronic-ferroelectric anisotropy at room temperature in LuFe2O4. Phys. Rev. Lett. 135, 106504 (2025).
Stegeman, G. I., Hagan, D. J. & Torner, L. χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons. Opt. Quantum Electron. 28, 1691–1740 (1996).
Sutherland, R. L. Handbook of Nonlinear Optics 2nd edn (CRC Press, Boca Raton, 2003).
Gerber, S. et al. Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser. Science 357, 71–75 (2017).
Chelladurai, D. et al. Barium titanate and lithium niobate permittivity and Pockels coefficients from megahertz to sub-terahertz frequencies. Nat. Mater. 24, 868–875 (2025).
Goodno, G. D. et al. Investigation of β-BaB2O4 as a Q switch for high power applications. Appl. Phys. Lett. 66, 1575–1577 (1995).
Disa, A. S., Nova, T. F. & Cavalleri, A. Engineering crystal structures with light. Nat. Phys. 17, 1087–1092 (2021).
Fu, W. et al. Phononic integrated circuitry and spin–orbit interaction of phonons. Nat. Commun. 10, 2743 (2019).
von Hoegen, A., Mankowsky, R., Fechner, M., Först, M. & Cavalleri, A. Probing the interatomic potential of solids with strong-field nonlinear phononics. Nature 555, 79–82 (2018).
Baroni, S., de Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515–562 (2001).
Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).
Giannozzi, P. et al. Advanced capabilities for materials modelling with quantum ESPRESSO. J. Phys. Condens. Matter 29, 465901 (2017).
Hamann, D. R. Optimized norm-conserving Vanderbilt pseudopotentials. Phys. Rev. B 88, 085117 (2013).
Schlipf, M. & Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 196, 36–44 (2015).
Materials Project. Materials Data on Ba(BO2)2, https://doi.org/10.17188/1276454.
Umari, P. & Pasquarello, A. Ab initio molecular dynamics in a finite homogeneous electric field. Phys. Rev. Lett. 89, 157602 (2002).
Acknowledgements
The authors thank the PSI-LNO GL group for support during the experiments and R. Li for helpful discussions. This work was supported by the Swiss National Science Foundation (SNSF) under grant number 10001644 and SNSF Spark grant number 221173, and by the French government through the UCA J.E.D.I. Investments in the Future project managed by the National Research Agency (ANR) under reference number ANR-15-IDEX-01.
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F.G. and C.V. conceived the project and designed the experiment. F.G., C.V., and G.M. performed the THz spectroscopy measurements. F.G., C.V., A.T., G.N., and L.S. carried out the THz experiments. F.G. performed the FDTD simulations. N.C. carried out the DFT and DFPT calculations. N.F., N.C., and F.G. developed the analytical model and interpreted the data. F.G. prepared the figures. F.G., A.L.C., and C.V. wrote the manuscript with input from all authors. All authors discussed the results.
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Giorgianni, F., Colonna, N., Nagamine, G. et al. All-optical control of second-harmonic generation in β-BaB2O4 via coherent, terahertz-driven acentric lattice displacement. Nat Commun (2026). https://doi.org/10.1038/s41467-026-70532-x
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DOI: https://doi.org/10.1038/s41467-026-70532-x
