Generalized rainbow patterns of oblate drops simulated by a ray model in three dimensions

TL;DR

This paper extends the vectorial complex ray model to three dimensions to simulate and analyze the detailed rainbow scattering patterns of oblate drops, achieving good agreement with experimental data.

Contribution

It introduces a 3D extension of the VCRM with a line-by-line triangulation interpolation, enabling comprehensive simulation of rainbow patterns of oblate drops.

Findings

Successfully simulates geometrical, coarse, and fine rainbow structures

Achieves qualitative and quantitative agreement with experiments

Provides physical interpretation of generalized rainbow patterns

Abstract

The scattering patterns near the primary rainbow of oblate drops are simulated by extending the vectorial complex ray model (VCRM) [1] to three-dimensional (3D) calculations. With the curvature of wavefront as intrinsic property of a ray, this advanced ray model permits, in principle, to predict the amplitudes and phases of all emergent rays with a rigorous algebraic formalism. This letter reports a breakthrough of VCRM for 3D scattering with a line-by-line triangulation interpolation algorithm allowing to calculate the total complex amplitude of scattered f eld. This makes possible to simulate not only the skeleton (geometrical rainbow angles, hyperbolic-umbilic caustics), but also the coarse (Airy bows, lattice) and f ne (ripple fringes) structures of the generalized rainbow patterns (GRPs) of oblate drops. The simulated results are found qualitatively and quantitatively in good agreement with experimental scattering patterns for drops of different aspect ratios. The physical interpretation of the GRPs is also given. This work opens up prominent perspectives for simulating and understanding the 3D scattering of large particles of any shape with smooth surface by VCRM.