Universal Imaging of Full Strain Tensor in 2D Crystals with Third-Harmonic Generation

Quantitatively mapping and monitoring the strain distribution in 2D materials is essential for their physical understanding and function engineering. Optical characterization methods are always appealing due to unique noninvasion and high-throughput advantages. However, all currently available optical spectroscopic techniques have application limitation, e.g., photoluminescence spectroscopy is for direct-bandgap semiconducting materials, Raman spectroscopy is for ones with Raman-active and strain-sensitive phonon modes, and second-harmonic generation spectroscopy is only for noncentrosymmetric ones. Here, a universal methodology to measure the full strain tensor in any 2D crystalline material by polarization-dependent third-harmonic generation is reported. This technique utilizes the third-order nonlinear optical response being a universal property in 2D crystals and the nonlinear susceptibility has a one-to-one correspondence to strain tensor via a photoelastic tensor. The photoelastic tensor of both a noncentrosymmetric D-3h WS2 monolayer and a centrosymmetric D-3d WS2 bilayer is successfully determined, and the strain tensor distribution in homogenously strained and randomly strained monolayer WS2 is further mapped. In addition, an atlas of photoelastic tensors to monitor the strain distribution in 2D materials belonging to all 32 crystallographic point groups is provided. This universal characterization on strain tensor should facilitate new functionality designs and accelerate device applications in 2D-materials-based electronic, optoelectronic, and photovoltaic devices.