Polarization-Resolved Interferometric Description of Second-Harmonic Generation in Hetero-Bilayer Transition Metal Dichalcogenides

Optical second-harmonic generation (SHG) has been widely used in determining the crystallographic orientation of various 2D single crystals, but has yet to prove to be applicable to artificially stacked heterocrystals. In this work, we anatomize SHG by hetero-bilayer transition metal dichalcogenides (TMDs) using a polarization-resolved spectral interferometry,[1] which quantifies the phase and intensity of two orthogonal polarizations. As the far-field SHG signals are a superposition of two signals originating from each layer, they contain the crystallographic information in addition to the 2^nd-order susceptibility tensor of each. We show that a newly devised matrix formalism enables the complete description of the superposed signals and allows the analytical expression for any of the phase, amplitude, and crystallographic orientation in terms of the other. As a proof of concept, the stack angle of MoS₂/WS₂ bilayers could be precisely determined by measuring the crystallographic orientations of both layers simultaneously, which could also be operated in a raster-scanning mode. The matrix method can be generalized to multiple-layered heterostructures with susceptibility tensors of other symmetries.

[1] W. Kim, J. Y. Ahn, J. Oh, J. H. Shim and S. Ryu, “Second-Harmonic Young's Interference in Atom-Thin Heterocrystals”, Nano Lett. 20, 8825 (2020)