Supernumerary bows: interference theory with the zero wavefront as a basic element.

This study relates to the prediction of the angular positions of supernumerary screenbows and rainbows, in the case of a refractive sphere illuminated by a point source placed at a distance of h from its center; for h→∞, the incident light beam becomes parallel. The screenbow appears on a spherical screen whose center is that of the sphere and which intercepts the tangential caustic surface. The rainbow, specific to the water drop, but here generalized to any refractive sphere, corresponds to a screenbow produced on a "screen" placed at an infinite distance.

Refractive sphere and light point source: shortcut to the zero wavefronts.

A somewhat basic way to find an expression for the zero wavefront of a given illuminated refractive medium starts from a wavefront arbitrary point E, belonging to this medium, whose position analytical expression is already known. Then, one derives a new virtual wavefront-the zero wavefront-equivalent to the point source of light. The spatial path length of the resulting direct equivalent ray between E and the corresponding point E0, belonging to the zero wavefront, equals the optical path length of the more or less complicated succession of ray segments, caused by refraction and/or reflection, between E and the point source.

Supernumerary bows: caustics of a refractive sphere and analysis of the relative overall Gouy phase shift of supernumerary rays.

The modified Young's theory of interference related to supernumerary rainbows is based on a difference of 90° in the Gouy phase shifts for the parallel rays producing these bows. An observation screen placed at a given distance from a refractive sphere illuminated by a point source of light should also show supernumerary screen bows. An extensive description and analysis of the caustics involved are given.

Geometric optics of a refringent sphere illuminated by a point source: caustics, wavefronts, and zero phase-fronts for every rainbow "k" order.

This study relates to a refringent sphere illuminated by a point source placed at a distance h from its center; for h→∞ the light beam becomes parallel. A selection of variables, principally angular with the center of the sphere as a common point, allows a global, straightforward, and geometrically transparent way to the rays, caustics, and wavefronts, internal as well as external, for every k order, k being the number of internal reflections. One obtains compact formulas for generating the rays and the wavefronts.