Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it is very necessary to employ diffraction theories to analyze the obstacle effects on structured light beams during propagation. The aim of this work is to provide a systematic summary and comparison of the scalar diffraction theories for structured light beams. We first present the scalar fields of typical structured light beams in the source plane, including the fundamental Gaussian beams, higher-order Hermite–Gaussian beams, Laguerre–Gaussian vortex beams, non-diffracting Bessel beams, and self-accelerating Airy beams. Then, we summarize and compare the main scalar diffraction theories of structured light beams, including the Fresnel diffraction integral, Collins formula, angular spectrum representation, and Rayleigh–Sommerfeld diffraction integral. Finally, based on these theories, we derive in detail the analytical propagation expressions of typical structured light beams under different conditions. In addition, the propagation of typical structured light beams is simulated. We hope this work can be helpful for the efficient study of the propagation of structured light beams.

Twisted light carrying orbital angular momentum inherently possesses a handedness, which would produce chiroptical responses by chiral matter. In this work, a scheme of vortical differential scattering (VDS) was utilized to investigate the chiroptical responses of dielectric chiral particles to the twisted light. The simulation results showed that the dielectric chiral particles have obvious VDS signals under the illumination of twisted light with opposite topological charges. The larger the relative chiral parameter of the particles, the more obvious the VDS signals. The extreme value of the VDS signals can be enhanced by reducing the waist radius of the twisted light or by adopting the circularly polarized twisted light. In addition, non-spherical dielectric chiral particles exhibit more obvious VDS signals compared with spherical ones. These findings are expected to find potential applications in the detection and identification of chiral substances.