Focusing and twinkling: critical exponents from catastrophes in non-Gaussian random short waves

Abstract

The critical exponent of the intensity moment is computed from the Thorn-Arnol'd classification of caustics as catastrophes. The caustics are studied on the torus whose coordinates are 16 N random phases theta ₁... theta _N for members of the ensemble describing the phase screen or inhomogeneous medium responsible for the disorder of the wave. The results indicate that when N to infinity (Gaussian random medium) the exponents depend only on whether the waves propagate in two or three space dimensions.