Numerical implementation of three-dimensional vectorial complex ray model and application to rainbow scattering of spheroidal drops

The rainbow patterns of oblate spheroidal drops have been observed in experiments nearly forty years ago [ Nature 312 , 529 ( 1984 ) 10.1038/312529a0 ]. However, the prediction for those complex patterns has been a challenge for conventional light scattering models. The vectorial complex ray model (VCRM) allows to account for the direction, the polarization, the phase, the amplitude and the wavefront curvature of waves and provides a powerful tool for the study of the light/electromagnetic wave interaction with a homogeneous object of any shape with smooth surface. In [ Opt. Lett. 46 , 4585 ( 2021 ) 10.1364/OL.434149 ], the authors have reported an important breakthrough of VCRM for the three-dimensional scattering (VCRM3D) and the simulated rainbow patterns of oblate drops. The present paper is devoted to the detailed description of the numerical implementation allowing the simulation of the 3D scattering field by a nonspherical particle. Its ability to predict both the fine and coarse intensity structures of the rainbows and the near-backward scattering patterns of spheroids is demonstrated. This work opens perspectives for exploring the 3D scattering characteristics of large objects with any smooth shape and developing relevant optical techniques for particle characterization.