Effects of Crystal Anisotropy on Optical Phonon Resonances in the   Mid-Infrared Second Harmonic Response of SiC
  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. 
Alexander Paarmann, Ilya Razdolski, Sandy Gewinner, Wieland   Schoellkopf, Martin Wolf
cond-mat.mtrl-sci