  We study the effects of crystal anisotropy on optical phonon resonances in
the second harmonic generation (SHG) from silicon carbide (SiC) in its
Reststrahl region. By comparing experiments and simulations for isotropic
3C-SiC and anisotropic 4H-SiC in two crystal cuts, we identify several
pronounced effects in the nonlinear response which arise solely from the
crystal anisotropy. Specifically, we demonstrate that the axial and planar
transverse optical phonon resonances selectively and exclusively appear in the
corresponding tensor elements of the nonlinear susceptibility, enabling
observation of an intense SHG peak originating from a weak phonon mode due to
zone-folding along the c-axis of 4H-SiC. Similarly, we identify an anisotropy
factor $\zeta \equiv \epsilon_\perp/\epsilon_\parallel$ responsible for a steep
enhancement of the transmitted fundamental fields at the axial longitudinal
optical phonon frequency, resulting in strongly enhanced SHG. We develop a
general recipe to extract all these features that is directly applicable to all
wurtzite-structure polar dielectrics, where a very similar behavior is
expected. Our model study illustrates the opportunities for utilizing the
crystal anisotropy for selectively enhancing nonlinear-optical effects in polar
dielectrics, which could potentially be extended to built-in anisotropy in
artificially designed hybrid materials.
