Critical point explosions in two-dimensional wave fields

Abstract

We discuss degenerate critical points in two-dimensional fields described by complex wave functions. Typical examples include the familiar optical field in a plane normal to the direction of propagation, electrons in two-dimensional heterojunctions, the Abrikosov lattice in superconductors, thin films of liquid helium at low temperatures, etc. Using simple topological arguments, we show that under the influence of small perturbations a degenerate critical point can decay explosively into a large number of irreducible (nondegenerate) components, and that this explosion may trigger a chain reaction that fragments other aspects of the wave field. We also discuss controlled explosions designed to produce particular decay products. We show that vortices (phase singularities) may be divided into two classes, generic and nongeneric, and that each class has its own special properties and modes of decay. The fallout from a critical point explosion can be extensive. The mound of debris resulting from decay of a single 5th-order optical vortex can easily contain over 150 new critical points. In superconductors vortex orders can approach 10 3, and the number of new critical points generated during explosion of vortices of this order can exceed 5×10 6.