Mapping ${\mathrm{LiNbO}}_3$ Phonon-Polariton Nonlinearities with 2D THz-THz-Raman Spectroscopy

Two-dimensional terahertz-terahertz-Raman spectroscopy can provide insight into the anharmonicities of low-energy phonon modes—knowledge of which can help develop strategies for coherent control of material properties. Measurements on ${\mathrm{LiNbO}}_3$ reveal THz and Raman nonlinear transitions between the $E({\mathrm{TO}}_1$) and $E({\mathrm{TO}}_3$) phonon polaritons. Distinct coherence pathways are observed with different THz polarizations. The observed pathways suggest that the origin of the third-order nonlinear responses is due to mechanical anharmonicities, as opposed to electronic anharmonicities. Further, we confirm that the $E({\mathrm{TO}}_1$) and $E({\mathrm{TO}}_3$) phonon polaritons are excited through resonant one-photon THz excitation.

Figure 1

(a) ${\text{LiNbO}}_3$ crystal structure in the hexagonal unit cell [33, 34]. (b) Schematic of the 2D-TTR experiment, pulse sequence, and time definitions. The polarization of each pulse is indicated in the circles. Coordinates $\{x,y,z\}$ refer to the crystal axes of $x$-cut ${\mathrm{LiNbO}}_3$, where $x$ and $z$ coincide with unit cell vectors $a$ and $c$, and $y$ is orthogonal to $x$ and $z$. (c) Red: PHP dispersion curve for $E$-symmetry phonon modes [35]. Black: wave vector matching condition of the 800 nm probe for forward ($k_{+}$, solid) and backward ($k_{-}$, dashed) propagating PHPs [19]. The shaded regions show the THz bandwidth of $E_A^{\mathrm{THz}}$ and $E_B^{\mathrm{THz}}$.

Figure 2

(a) 2D-TTR spectra in the frequency domain for four pump-probe polarization configurations, taken from the combination of two crystal orientations and two THz polarization orderings (positive and negative $t_1$ quadrants). The spectra have been deconvolved by the IRF to reveal true intensity and frequency positions. Guiding lines are provided at $f_1=3.85\mathrm{THz}$ (violet), $f_1=7.1\mathrm{THz}$ (teal), $f_2=\pm 3.25\mathrm{THz}$ (violet) and $f_2=\pm 3.85\mathrm{THz}$ (teal). (b) Close-up of peaks II to IV for polarization $R_{zyzy}^{(3)}$. (c) Select Feynman pathways for the observed nonlinear peaks (I, I’) and III. Depending on the THz polarizations, III ($yz$) or III ($zy$) is selectively observed. See SM [26] for full assignment. (d) THz polarization dependence of the fourier transform (FT) amplitude of peaks III and IV. (e) THz field strength dependence of the $E({\mathrm{TO}}_1)$ ($A_{3.85}$) and $E({\mathrm{TO}}_3)$ ($A_{7.1}$) features along $f_1$. Best linear fits are shown as dashed lines.

Figure 3

Third-order models based on different excitation mechanisms and sources of anharmonicity. Identical guiding lines are added. For reference, the overlayed contours depict the $R_{zyzy}^{(3)}$ experimental spectra.