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= (x 1,x2,x3) ∈ℝ3, with x 3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x3| > ||x||γ, for γ∈ (1/4,1/2) and x large. For |x 3| ≤ ||x||γ and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator. © 2012 Global-Science Press.