Vector beams for real-time monitoring of crystalline symmetry on µm length scale

Abstract

Symmetry constrains and determines the physical properties of crystalline solids. Determining crystalline symmetry often requires large-scale diffraction facilities and advanced analysis software and therefore cannot be realized with real-time feedback. Alternatively, optical anisotropy has also been exploited for elucidating the rotation, mirror, and inversion symmetries of solids on smaller tabletop setups. Second-harmonic generation (SHG), in particular, has demonstrated a remarkable sensitivity to subtle changes in these symmetries during phase transitions. To access the full nonlinear susceptibility of a crystal in a cryogenic or vacuum environment, angle-by-angle rotation of the scattering plane of an obliquely incident and outgoing beam in co-ordination with their polarization states is required. This often results in a bulky and wobbly setup, significant feedback latency, and a focal spot size >20µm unsuitable for microscopic samples such as 2D materials. In this work, we make use of vector beams to realize a non-rotating oblique incidence setup, demonstrating a real-time (up to 15 fps) visualization of SHG rotation anisotropy on a sample area of ∼2×2µm 2 . Both the feedback latency and focal spot size represent more than an order of magnitude improvement over previous designs based on a Gaussian beam and mechanically rotating stages. Here, the use of a vector beam greatly simplifies and reduces the cost of nonlinear optical anisotropy measurements, heralding widespread applications of this approach in both research and industrial settings, for example, for strain monitoring and crystal alignment. Our work may also promote broader integration of the structured optical field into solid-state and condensed matter research in the future.