Optical caustics associated with the primary rainbow for coated spheroidal droplets

In this study, the optical caustics (i.e., rainbow fringes and hyperbolic umbilical fringes) of a coated spheroidal droplet illuminated by a Gaussian beam are examined using a vector ray tracing (VRT) model. For a more comprehensive investigation, this study only focuses on the (1, 2, 2) type of rays [J. Opt. Soc. Am. A29(8), 1489 (2012)10.1364/JOSAA.29.001489]. First, the relations between the scattering angle and incident angle are investigated by using the VRT model and are compared with those obtained by the analytical solution. For coated droplets with different core-shell ratios (i.e., the ratio of the core radius to shell radius), aspect ratios of core, aspect ratios of shell, and refractive indices of shell, the curvature of the rainbow fringes and the location of the cusp caustics are investigated. Furthermore, the effect that tilt angles of the droplet and the relative position of the incident Gaussian beam have on the caustics is investigated. This model provides perspectives for studying the rainbow scattering from multilayer droplets with illumination of any kind of shaped beam and droplets with regular, convex shapes, whose surfaces can be described by analytical functions.