Probing Noncentrosymmetric 2D Materials by Fourier Space Second Harmonic Imaging

Second-harmonic generation (SHG) has been established
as a powerful
tool for probing noncentrosymmetric materials. In the typical implementation,
the SHG intensity is detected while rotating the polarization of the
incident laser field and of the second harmonic relative to the sample.
Although effective, this approach can be time-consuming and laborious.
Here, we present a novel experimental approach for directly determining
the symmetry and crystal orientation of noncentrosymmetric 2D materials.
This approach involves capturing SH images generated by tightly focused
laser beams in Fourier space and exploits the material’s symmetry
and SHG’s coherent nature. For a Gaussian laser beam, the crystal
orientation of the 2D material can be derived from the ellipticity
of the observed SHG patterns, whereas for an azimuthally polarized
laser beam, the detected SHG pattern directly reveals the crystal
lattice together with its orientation. A microscopic model that treats
SHG as a coherent superposition of fields radiated by dipolar emitters
within the laser-illuminated area and that considers the symmetry
of the χ(2)-tensor quantitatively describes the detected
patterns. The approach presented provides a fast and precise tool
for determining crystal symmetry and orientation and will be applicable
to materials with broken inversion symmetry.