Mapping LiNbO₃ Phonon-Polariton Nonlinearities with 2D-THz-THz-Raman (2D-TTR) Spectroscopy

Coherent control of vibrational modes is a promising route to achieving ultrafast manipulation of material properties with light. Through excitation of specific phonon modes that are strongly coupled to bulk material properties of interest, researchers have shown examples including enhancement of superconductivity and switching of the magnetic, ferroelectric, and structural phases with ultrafast optical pulses. With the development of intense terahertz (THz) sources, coherent control with THz frequency pulses, which provide phase-sensitive access to phonon modes with no parasitic electronic excitation, has gained significant attention. To achieve this future degree of control over matter, it is essential to characterize the multitude of different linear and nonlinear excitations that occur when pumped with an intense, broadband THz pulse. Lithium niobate (LiNbO₃) is an ideal candidate for developing techniques that can provide detailed information on the potential energy landscape due to its importance in nonlinear THz polaritonic applications. Here, we report two-dimension THz-THz-Raman (2D-TTR) measurements on x-cut LiNbO₃ with selective detection of the third-order nonlinear signal and significantly improved THz bandwidth (up to 9 THz). We demonstrate that 2D-TTR spectroscopy can provide insight into the excitation mechanism, nonlinear phonon-phonon couplings, and sources of anharmonicity in the system. We show that the E(TO₁) and E(TO₃) phonon-polaritons are excited through resonant THz one-photon absorption (1PA) as opposed to THz sum-frequency (SF) excitation. We directly observe THz and Raman nonlinear transitions between the E(TO₁) and E(TO₃) modes. Due to selection rules of the E-symmetry phonon modes, distinct symmetry-allowed Feynman pathways are observed for different THz polarizations. Further, our models show that the set of Feynman pathways observed are induced via mechanical anharmonicity of the phonon-polariton modes as opposed to electronic anharmonicity. Such information is traditionally only available via density functional theory (DFT) calculations. These findings provide a concrete foundation for future coherent control applications. For example, the nonlinear transitions between E(TO₁) and E(TO₃) may be optimized using tailored THz pulse sequences to achieve efficient population transfer between the two modes.