Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides

Abstract

We extend classic  Sommerfeld  and  Silver-Müller  radiation  conditions  for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If x=(x₁,x₂,x₃)∈R³, with x₃ denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x₃|>‖x‖^r, for γ∈(1/4,1/2) and x large. For |x₃|<‖x‖^r and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.