Caustics of wave fronts reflected by a surface

Abstract

One can often see caustic by reflection in nature, but it is rather hard to understand the way of how caustic arise and which geometric properties of a mirror surface define the geometry of the caustic. The caustic by reflection has complicated topology and much more complicated geometry. From engineering point of view, the geometry of caustic by reflection is important for antenna's theory because it can be considered as a surface of concentration of the reflected wave front. In this paper, we give purely geometric description of the caustics of a wave front (flat or spherical) after reflection from a mirror surface. The description clarifies the dependence of caustic on geometrical characteristics of a surface and allows rather simple and fast computer visualization of the caustics in dependence of location of the rays source or direction of the pencil of parallel rays.