Anomalous reflections near a caustic

Abstract

Waves propagating in a medium with highly variable refractive index tend to focus forming caustics. The energy content of the wave field in the vicinity of a caustic is higher than that of the ambient field away from the caustic. Consequently, waves scattering from heterogeneities located near caustics have more energy than a field scattering a little further away from the caustic. For a suitable choice of Sobolev norms for the domain and range spaces of the scattering operator, the restriction to scatterers supported away from caustics is a bounded operator, whereas the restriction to scatterers supported in a neighborhood of caustics is unbounded.