journal article·2025-05-01Open access

Theory of terahertz pump optical probe spectroscopy of phonon polaritons in noncentrosymmetric systems

Niccolò Sellati, Jacopo Fiore, Stefano Paolo Villani, Lara Benfatto, Mattia Udina

npj Quantum Materials· Volume 10· Issue 1

Abstract

Abstract Hybrid lattice-light modes, known as phonon polaritons, represent the backbone of advanced protocols based on THz pumping of infrared modes. Here we provide a theoretical framework able to capture the different roles played by phonon polaritons in experimental protocols based either on Raman-like pump and probe schemes, typical of four-wave mixing processes, or on THz pump-visible probe three-wave mixing protocols. By using a many-body description of the nonlinear optical kernel, along with a perturbative solution of nonlinear Maxwell’s equations, we discuss the limitations of all-optical four-wave mixing protocols and we highlight the advantages of exploiting broadband THz pumps to enlarge the phase space of the phonon polariton dispersion at low momenta accessible in a single experiment. Besides providing a quantitative description of existing and future experiments, our results offer a general framework for the theoretical modeling of the hybridization between light and lattice degrees of freedom in time-resolved experiments.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Mechanical and Optical Resonators · Photonic and Optical Devices · Terahertz technology and applications

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (63)

Show source-provided references
1. Basov, D. N., Fogler, M. M. & de Abajo, F. J. G. Polaritons in van der waals materials. Science 354, aag1992 (2016).10.1126/science.aag1992 ↗
2. Caldwell, J. D. et al. Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons. Nanophotonics 4, 44–68 (2015).10.1515/nanoph-2014-0003 ↗
3. Planken, P. C. M., Noordam, L. D., Kennis, J. T. M. & Lagendijk, A. Femtosecond time-resolved study of the generation and propagation of phonon polaritons in linbo3. Phys. Rev. B 45, 7106–7114 (1992).10.1103/PhysRevB.45.7106 ↗
4. Feurer, T. et al. Terahertz polaritonics. Annu. Rev. Mater. Res. 37, 317–350 (2007).10.1146/annurev.matsci.37.052506.084327 ↗
5. Feurer, T., Vaughan, J. C. & Nelson, K. A. Spatiotemporal coherent control of lattice vibrational waves. Science 299, 374–377 (2003).10.1126/science.1078726 ↗
6. Kojima, S., Tsumura, N., Kitahara, H., Takeda, M. W. & Nishizawa, S. Terahertz time domain spectroscopy of phonon-polaritons in ferroelectric lithium niobate crystals. Jpn. J. Appl. Phys. 41, 7033 (2002).10.1143/JJAP.41.7033 ↗
7. Xu, C. & Zong, A. Time-domain study of coupled collective excitations in quantum materials. npj Quantum Mater. 10, 21 (2025).10.1038/s41535-025-00726-x ↗
8. Cartella, A. et al. An effective magnetic field from optically driven phonons. Nat. Phys. 13, 132 (2017).10.1038/nphys3925 ↗
9. Cheung, K. P. & Auston, D. H. Excitation of coherent phonon polaritons with femtosecond optical pulses. Phys. Rev. Lett. 55, 2152–2155 (1985).10.1103/PhysRevLett.55.2152 ↗
10. Dougherty, T. P., Wiederrecht, G. P. & Nelson, K. A. Impulsive stimulated raman scattering experiments in the polariton regime. J. Opt. Soc. Am. B 9, 2179–2189 (1992).10.1364/JOSAB.9.002179 ↗
11. Bakker, H. J., Hunsche, S. & Kurz, H. Observation of thz phonon-polariton beats in litao3. Phys. Rev. Lett. 69, 2823–2826 (1992).10.1103/PhysRevLett.69.2823 ↗
12. Loulergue, J. C. & Etchepare, J. e-symmetry phonon polaritons in pbtio3. Phys. Rev. B 52, 15160–15164 (1995).10.1103/PhysRevB.52.15160 ↗
13. Gautier, C. A., Mérian, M. & Etchepare, J. Low frequency e-symmetry phonon modes in litao3: a non-linear temporal domain approach. J. Phys. Condens. Matter 12, 7175 (2000).10.1088/0953-8984/12/32/302 ↗
14. Knighton, B. E., Dastrup, B. S., Johnson, C. L. & Johnson, J. A. Measurement of a phonon-polariton dispersion curve by varying the excitation wavelength. Phys. Rev. B 97, 214307 (2018).10.1103/PhysRevB.97.214307 ↗
15. Crimmins, T. F., Stoyanov, N. S. & Nelson, K. A. Heterodyned impulsive stimulated Raman scattering of phonon-polaritons in LiTaO3 and LiNbO3. J. Chem. Phys. 117, 2882–2896 (2002).10.1063/1.1491948 ↗
16. Hebling, J. Determination of the momentum of impulsively generated phonon polaritons. Phys. Rev. B 65, 092301 (2002).10.1103/PhysRevB.65.092301 ↗
17. Wahlstrand, J. K. & Merlin, R. Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons. Phys. Rev. B 68, 054301 (2003).10.1103/PhysRevB.68.054301 ↗
18. Ikegaya, Y., Sakaibara, H., Minami, Y., Katayama, I. & Takeda, J. Real-time observation of phonon-polariton dynamics in ferroelectric LiNbO3 in time-frequency space. Appl. Phys. Lett. 107, 062901 (2015).10.1063/1.4928480 ↗
19. Henry, C. H. & Hopfield, J. J. Raman scattering by polaritons. Phys. Rev. Lett. 15, 964–966 (1965).10.1103/PhysRevLett.15.964 ↗
20. Irmer, G., Röder, C., Himcinschi, C. & Kortus, J. Phonon polaritons in uniaxial crystals: A raman scattering study of polaritons in α-gan. Phys. Rev. B 88, 104303 (2013).10.1103/PhysRevB.88.104303 ↗
21. Barker, A. S. & Loudon, R. Response functions in the theory of raman scattering by vibrational and polariton modes in dielectric crystals. Rev. Mod. Phys. 44, 18–47 (1972).10.1103/RevModPhys.44.18 ↗
22. 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).10.1063/5.0015612 ↗
23. Juvé, V. et al. Ultrafast tunable modulation of light polarization at terahertz frequencies. Opt. Lett. 43, 5905–5908 (2018).10.1364/OL.43.005905 ↗
24. Huber, T., Ranke, M., Ferrer, A., Huber, L. & Johnson, S. L. Coherent phonon spectroscopy of non-fully symmetric modes using resonant terahertz excitation. Appl. Phys. Lett. 107, 091107 (2015).10.1063/1.4930021 ↗
25. Kojima, S. Broadband terahertz spectroscopy of phonon-polariton dispersion in ferroelectrics. Photonics 5, https://www.mdpi.com/2304-6732/5/4/55 (2018).10.3390/photonics5040055 ↗
26. Dastrup, B. S., Hall, J. R. & Johnson, J. A. Experimental determination of the interatomic potential in LiNbO3 via ultrafast lattice control. Appl. Phys. Lett. 110, 162901 (2017).10.1063/1.4980112 ↗
27. Johnson, C. L., Knighton, B. E. & Johnson, J. A. Distinguishing nonlinear terahertz excitation pathways with two-dimensional spectroscopy. Phys. Rev. Lett. 122, 073901 (2019).10.1103/PhysRevLett.122.073901 ↗
28. Knighton, B. E. et al. Terahertz waveform considerations for nonlinearly driving lattice vibrations. J. Appl. Phys. 125, 144101 (2019).10.1063/1.5052638 ↗
29. Lin, H.-W., Mead, G. & Blake, G. A. Mapping linbo3 phonon-polariton nonlinearities with 2d thz-thz-raman spectroscopy. Phys. Rev. Lett. 129, 207401 (2022).10.1103/PhysRevLett.129.207401 ↗
30. Fu, Z. & Yamaguchi, M. Coherent excitation of optical phonons in gaas by broadband terahertz pulses. Sci. Rep. 6, 38264 (2016).10.1038/srep38264 ↗
31. Faust, W. L. & Henry, C. H. Mixing of visible and near-resonance infrared light in gap. Phys. Rev. Lett. 17, 1265–1268 (1966).10.1103/PhysRevLett.17.1265 ↗
32. Hwang, D. & Solin, S. Raman scattering from tuneable hot phonons and polaritons. Solid State Commun. 13, 983–987 (1973).10.1016/0038-1098(73)90414-6 ↗
33. Hwang, D. M. & Solin, S. A. Mixing of argon-ion and carbon dioxide laser radiation in uniaxial rubidium chlorate crystals. Phys. Rev. B 9, 1884–1896 (1974).10.1103/PhysRevB.9.1884 ↗
34. Wagner, W. D. & Claus, R. Phase matching for difference frequency generation in the view of spontaneous raman scattering by hot polaritons. Phys. Status Solidi A 64, 647–656 (1981).10.1002/pssa.2210640229 ↗
35. Mayer, A. & Keilmann, F. Far-infrared nonlinear optics. i. χ(2) near ionic resonance. Phys. Rev. B 33, 6954–6961 (1986).10.1103/PhysRevB.33.6954 ↗
36. Dekorsy, T., Yakovlev, V. A., Seidel, W., Helm, M. & Keilmann, F. Infrared-phonon–polariton resonance of the nonlinear susceptibility in gaas. Phys. Rev. Lett. 90, 055508 (2003).10.1103/PhysRevLett.90.055508 ↗
37. Wiederrecht, G. P. et al. Explanation of anomalous polariton dynamics in litao3. Phys. Rev. B 51, 916–931 (1995).10.1103/PhysRevB.51.916 ↗
38. Bakker, H. J., Hunsche, S. & Kurz, H. Investigation of anharmonic lattice vibrations with coherent phonon polaritons. Phys. Rev. B 50, 914–920 (1994).10.1103/PhysRevB.50.914 ↗
39. Bakker, H. J., Hunsche, S. & Kurz, H. Coherent phonon polaritons as probes of anharmonic phonons in ferroelectrics. Rev. Mod. Phys. 70, 523–536 (1998).10.1103/RevModPhys.70.523 ↗
40. Cavalleri, A. et al. Tracking the motion of charges in a terahertz light field by femtosecond x-ray diffraction. Nature 442, 664–666 (2006).10.1038/nature05041 ↗
41. Mankowsky, R., Von Hoegen, A., Först, M. & Cavalleri, A. Ultrafast reversal of the ferroelectric polarization. Phys. Rev. Lett. 118, 197601 (2017).10.1103/PhysRevLett.118.197601 ↗
42. Henstridge, M., Först, M., Rowe, E., Fechner, M. & Cavalleri, A. Nonlocal nonlinear phononics. Nat. Phys. 18, 461 (2022).10.1038/s41567-022-01512-3 ↗
43. Taherian, N. et al. Squeezed josephson plasmons in driven YBa2Cu3O6+x. ArXiv https://arxiv.org/abs/2401.01115 (2024).
44. Luo, T. et al. Time-of-flight detection of terahertz phonon-polariton. Nat. Commun. 15, 2276 (2024).10.1038/s41467-024-46515-1 ↗
45. Nagaosa, N. & Heusler, S. Quantum Field Theory in Condensed Matter Physics Texts and monographs in physics (Springer, 1999). https://books.google.it/books?id=C9uAXYIlFhMC.10.1007/978-3-662-03774-4 ↗
46. Mahan, G. D. Many Particle Physics, 3rd ed (Plenum, New York, 2000).10.1007/978-1-4757-5714-9 ↗
47. Udina, M., Cea, T. & Benfatto, L. Theory of coherent-oscillations generation in terahertz pump-probe spectroscopy: From phonons to electronic collective modes. Phys. Rev. B 100, 165131 (2019).10.1103/PhysRevB.100.165131 ↗
48. Shalaby, M. & Hauri, C. P. Demonstration of a low-frequency three-dimensional terahertz bullet with extreme brightness. Nat. Commun. 6, 5976 (2015).10.1038/ncomms6976 ↗
49. Somma, C. et al. Ultra-broadband terahertz pulses generated in the organic crystal dstms. Opt. Lett. 40, 3404–3407 (2015).10.1364/OL.40.003404 ↗
50. Sivarajah, P. et al. THz-frequency magnon-phonon-polaritons in the collective strong-coupling regime. J. Appl. Phys. 125, 213103 (2019).10.1063/1.5083849 ↗
51. Först, M. et al. Nonlinear phononics as an ultrafast route to lattice control. Nat. Phys. 7, 854–856 (2011).10.1038/nphys2055 ↗
52. Basini, M. et al. Terahertz ionic kerr effect: Two-phonon contribution to the nonlinear optical response in insulators. Phys. Rev. B 109, 024309 (2024).10.1103/PhysRevB.109.024309 ↗
53. Sun, Z., Gutiérrez-Rubio, Á., Basov, D. N. & Fogler, M. M. Hamiltonian optics of hyperbolic polaritons in nanogranules. Nano Lett. 15, 4455–4460 (2015).10.1021/acs.nanolett.5b00814 ↗
54. Bergeron, A., Gradziel, C., Leonelli, R. & Francoeur, S. Probing hyperbolic and surface phonon-polaritons in 2d materials using raman spectroscopy. Nat. Commun. 14, 5976 (2023).10.1038/s41467-023-39809-3 ↗
55. Zhang, Q. et al. Interface nano-optics with van der waals polaritons. Nature 597, 187–195 (2022).10.1038/s41586-021-03581-5 ↗
56. Wu, Y. et al. Manipulating polaritons at the extreme scale in van der waals materials. Nat. Rev. Phys. 4, 578–594 (2022).10.1038/s42254-022-00472-0 ↗
57. Galiffi, E. et al. Extreme light confinement and control in low-symmetry phonon-polaritonic crystals. Nat. Rev. Mater. 9, 9–28 (2024).10.1038/s41578-023-00620-7 ↗
58. Niemann, R. et al. Long-wave infrared super-resolution wide-field microscopy using sum-frequency generation. Appl. Phys. Lett. 120, 131102 (2022).10.1063/5.0081817 ↗
59. Niemann, R. et al. Spectroscopic and interferometric sum-frequency imaging of strongly coupled phonon polaritons in sic metasurfaces. Adv. Mater. 36, 2312507 (2024).10.1002/adma.202312507 ↗
60. Gubbin, C. R. & De Liberato, S. Theory of four-wave-mixing in phonon polaritons. ACS Photonics 5, 284–288 (2018).10.1021/acsphotonics.7b00863 ↗
61. DelPo, C. A. et al. Polariton transitions in femtosecond transient absorption studies of ultrastrong light-molecule coupling. J. Phys. Chem. Lett. 11, 2667–2674 (2020).10.1021/acs.jpclett.0c00247 ↗
62. Fassioli, F., Park, K. H., Bard, S. E. & Scholes, G. D. Femtosecond photophysics of molecular polaritons. J. Phys. Chem. Lett. 12, 11444–11459 (2021).10.1021/acs.jpclett.1c03183 ↗
63. Bourzutschky, A. N., Lev, B. L. & Keeling, J. Raman-phonon-polariton condensation in a transversely pumped cavity. npj Quantum Mater. 9, 81 (2024).10.1038/s41535-024-00693-9 ↗