Optical caustics observed in light scattered by an oblate spheroid

Abstract

The electromagnetic fields scattered when a plane wave is incident on an oblate spheroid in the side-on orientation may be calculated using a generalization of Mie theory, and the results may be decomposed in a Debye series expansion. A number of optical caustics are observed in the computed scattered intensity for the one internal reflection portion of the Debye series for scattering angles in the vicinity of the firstorder rainbow, and are analyzed in terms of the rainbow, transverse cusp, and hyperbolic umbilic caustics of catastrophe optics. The specific features of these three caustics are described, as is their assembly into the global structure of the observed caustics for spheroid scattering. It is found that, for a spheroid whose radius is an order of magnitude larger than the wavelength of the incident light, the interference structure accompanying the transverse cusp and hyperbolic umbilic caustics is only partially formed.

Debye series for light scattering by a spheroid

“…Increasing the eccentricity leads to a coalescence of the rays leaving the droplet in the same direction above and below its equatorial plane, creating the cusped diffraction catastrophe, a hyperbolic umbilic diffraction catastrophe, or a symbolic umbilic diffraction catastrophe for increasing a / b [15][16][17]. All these eccentricity-related phenomena are demonstrated and analyzed in the present and companion papers [18] by use of Debye series developed in the context of electromagnetic scattering.…”

Debye series for light scattering by a nonspherical particle

“…4(e) of Ref. [46] since the spheroid is somewhat larger than it was before, the angular size of the diffraction structure is correspondingly smaller, so corresponding more of it can fit into a given angular interval. This agreement for p = 0,1,2, along with the fact that the EBCM formalism is capable of being used for larger particle sizes than the spheroidal coordinate VSM formulism can, underscores the predictive power of the EBCM Debye series.…”

“…2. These parameters were chosen because the p = 2 Debye series component of this system has already been extensively studied using VSM Debye series in oblate spheroidal coordinates [46]. The p = 0 scattering contribution of Fig.…”

“…4(b), it is seen that the increasing angular attenuation effect is somewhat larger than the decreasing angular attenuation effect. [46], which were computed for b = 6.00 µm (or a = 6.00 µm in Ref. [46]) using the VSM Debye series in spheroidal coordinates.…”

“…[46], which were computed for b = 6.00 µm (or a = 6.00 µm in Ref. [46]) using the VSM Debye series in spheroidal coordinates. More detail of the interference structure is visible in Figs.…”