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.