Fig. 1: Modeling of Quasi-phase matching (QPM) by van der Waals stacking of 3R-MoS₂.

a Schematic of second harmonic generation (SHG) through a 3R-MoS₂ flake, with a thickness of t. A fundamental pump with a wavelength at \(\lambda\) is incident onto the flake, generating a second-harmonic (SH) signal with a wavelength at \(\lambda /2\). b Schematic of van der Waals stacking of two 3R-MoS₂ flakes, with a twist angle \(\theta\). The top flake, bottom flake, and the stack area are labeled as B, A and AB, respectively. Each flake has a coherence length of \({t}_{c}\). c Simulated SHG as a function of thickness t, for two scenarios: (1) non QPM (black line) and (2) QPM (pink line). For non QPM scenario, the SHG adds constructively (destructively) at a thickness of odd (even) times of the coherence length \({t}_{c}\). For the QPM scenario, multiple layers of 3R-MoS₂ (each layer with the same thickness of \({t}_{c}\)) are stacked together. The orientation angles of the odd and even number of layers are set to be 0° and 60°, respectively.