TY - JOUR
T1 - Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides
AU - Carlos Jerez-Hanckes & Jean-Claude Nédélec
JO - Communications in Computational Physics
VL - 2
SP - 629
EP - 646
PY - 2012
DA - 2012/12
SN - 11
DO - http://doi.org/10.4208/cicp.231209.150910s
UR - https://global-sci.org/intro/article_detail/cicp/7382.html
KW - 
AB - <p style="text-align: justify;">We extend classic&nbsp; Sommerfeld&nbsp; and&nbsp; Silver-Müller&nbsp; radiation&nbsp; conditions&nbsp; for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If <strong>x</strong>=(x<sub>1</sub>,x<sub>2</sub>,x<sub>3</sub>)∈<strong>R</strong><sup>3</sup>, with x<sub>3</sub> denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x<sub>3</sub>|&gt;‖<strong>x</strong>‖<sup>r</sup>, for γ∈(1/4,1/2) and x large. For |x<sub>3</sub>|&lt;‖<strong>x</strong>‖<sup>r</sup>&nbsp;and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.</p>