Asymptotics for helmholtz and maxwell solutions in 3-D open waveguides. http://doi.dx.org/10.4208/cicp.231209.150910s

Abstract

We extend classic Sommerfeld and Silver-Muller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three iso-tropic homogeneous layers in three dimensions. If x=(x_1,x_2,x_3)inR^3$, with $x_{3}$ denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region $abs{x_3}>norm{Vx}^gamma$, for $gammain(1/4,1/2)$ and $Vx$ large. For $abs{x_3}<norm{Vx}^gamma$ and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.