  We investigate optical nonlinearities that are induced and enhanced due to
the strong phonon resonance in hexagonal boron nitride. We predict and observe
large sub-picosecond duration signals due to four-wave mixing (FWM) during
resonant excitation. The resulting FWM signal allows for time-resolved
observation of the crystal motion. In addition, we observe enhancements of
third-harmonic generation with resonant pumping at the hBN transverse optical
phonon. Phonon-induced nonlinear enhancements are also predicted to yield large
increases in high-harmonic efficiencies.
