TY - JOUR
T1 - Asymptotics for helmholtz and maxwell solutions in 3-D open waveguides
AU - Jerez-Hanckes, Carlos
AU - Nedelec, Jean Claude
PY - 2012/2
Y1 - 2012/2
N2 - 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.
AB - 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.
KW - Helmholtz equation
KW - Open waveguide
KW - Radiation condition
UR - http://www.scopus.com/inward/record.url?scp=84055190612&partnerID=8YFLogxK
U2 - 10.4208/cicp.231209.150910s
DO - 10.4208/cicp.231209.150910s
M3 - Article
AN - SCOPUS:84055190612
SN - 1815-2406
VL - 11
SP - 629
EP - 646
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 2
ER -