On radiation conditions for rough surface scattering problems

Abstract

It is well. known that Sommerfeld's radiation condition is not a valid characterization of outgoing waves for scattering problems at rough surfaces. Instead, a radiation condition called upward propagating radiation condition (UPRC) is commonly used. Recently, a different radiation condition called the pole condition has been investigated for scattering problems at bounded obstacles. In this paper we show the equivalence between the UPRC and the pole condition. In doing so, we give a rigorous interpretation of a formula called the angular spectrum representation for Dirichlet data in the space of bounded continuous functions.