Simulations of the optical caustics in the primary rainbow region for single-layered spherical droplets

Vector ray tracing (VRT) model is used to simulate the propagation process of rays entering layered particles. The (1, 2, 2) exiting rays causing one of the primary twin rainbows of the layered droplet are extracted, and the primary rainbow fringe of the rays is obtained. When the core-shell ratio approaches 0, the layered droplet with a tiny core is approximately homogeneous and their rainbow scattering angle curves are highly consistent. According to the number of exiting rays at the same elevation angle in the same scattering section, the rays are partitioned and the hyperbolic umbilical fringe is obtained.