Second-harmonic phonon spectroscopy of $\alpha$-quartz

We demonstrate midinfrared second-harmonic generation as a highly sensitive phonon spectroscopy technique that we exemplify using $\alpha$-quartz (SiO${}_2$) as a model system. A midinfrared free-electron laser provides direct access to optical phonon resonances ranging from $350{\mathrm{c}\mathrm{m}}^{-1}$ to $1400
$\mathrm{c}\mathrm{m}$^{-1}$. While the extremely wide tunability and high peak fields of an free-electron laser promote nonlinear spectroscopic studies—complemented by simultaneous linear reflectivity measurements—azimuthal scans reveal crystallographic symmetry information of the sample. Additionally, temperature-dependent measurements show how damping rates increase, phonon modes shift spectrally and in certain cases disappear completely when approaching $T_c=846\mathrm{K}$ where quartz undergoes a structural phase transition from trigonal $\alpha$-quartz to hexagonal $\beta$-quartz, demonstrating the technique’s potential for studies of phase transitions.