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

We extend classic Sommerfeld and Silver-Muller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If x = (x(1), x(2), x(3)) is an element of R-3, with x(3) denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x(3) | > parallel to x parallel to(gamma), for gamma is an element of (1/4, 1/2) and x large. For |x(3)| < parallel to x parallel to(gamma). and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.