Optical Caustics and Diffraction Catastrophes

Abstract

It is well known that the stable caustics of geometrical optics fall into Thom’s classification of the elementary catastrophes of codimension up to 3. The caustics formed by an irregular water drop lens are a good example. By allowing the shape of the drop to change under the control of one or more parameters catastrophes of higher codimension can be formed, in particular, the parabolic umbilic (D₅) and the symbolic umbilic (E₆). They correspond to reactions between umbilic points on the surface of the drop. Each stable caustic singularity of geometrical optics is clothed with a structurally stable diffraction pattern. The elliptic umbilic diffraction catastrophe has been studied in detail and shown to be built on a skeleton of dislocation lines, consisting of rings and hairpins, which is itself structurally stable.