TITLE:
Effect of the Relative Position with Gaussian Beam Center and Droplet Center on Optical Caustics
AUTHORS:
Yutong Hao
KEYWORDS:
Vector Ray-Tracing Model, Optical Caustics, Gaussian Beam, Rainbow
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.5,
May
16,
2022
ABSTRACT: In this paper, a vector ray-tracing model (VRT) is used to simulate the optical caustic structures associated with the secondary rainbow for an ellipsoidal droplet illuminated by a Gaussian beam. The optical caustics of drops with an equatorial radius a = 50 μm, 100 μm, 200 μm, and 500 μm are studied at the same drop/beam ratios (i.e. γ the ratio between the droplet equatorial radius and the Gaussian beam waist) using concentric illumination with a Gaussian beam, and the effect of droplet size on the optical caustics is analyzed. The curvature of the rainbow fringe and the evolution of the cusp caustics position, in this case, are obtained; the diameter range of droplet shape (ellipsoid) measured by Gaussian beam illumination is broadened. Based on this model, the effects of the relative positions d = 0, 0.5yR, and yR on the optical caustics of the droplet when the center of the Gaussian beam deviates from the droplet center (the center of the Gaussian beam waist is on the same y-axis as the droplet center) are discussed. The optical caustics of the droplet when the center of the Gaussian beam is off the droplet center (the center of the Gaussian beam waist is on the z-axis with the droplet center) are also discussed. The effects of the relative positions of the center of the beam waist and the droplet center d = 0, 0.5yR, and yR on the optical caustics are also discussed. A method of measuring droplet shape with Gaussian beam illumination is proposed when the beam waist center is coaxial with the droplet center.