Volume 11, Issue 2
Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides

Carlos Jerez-Hanckes & Jean-Claude Nédélec

Commun. Comput. Phys., 11 (2012), pp. 629-646.

Published online: 2012-12

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  • 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=(x1,x2,x3)∈R3, with x3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x3|>‖xr, for γ∈(1/4,1/2) and x large. For |x3|<‖xr and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

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@Article{CiCP-11-629, author = {}, title = {Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {629--646}, 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=(x1,x2,x3)∈R3, with x3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x3|>‖xr, for γ∈(1/4,1/2) and x large. For |x3|<‖xr and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.231209.150910s}, url = {http://global-sci.org/intro/article_detail/cicp/7382.html} }
TY - JOUR T1 - Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides 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 -

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=(x1,x2,x3)∈R3, with x3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region |x3|>‖xr, for γ∈(1/4,1/2) and x large. For |x3|<‖xr and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

Carlos Jerez-Hanckes & Jean-Claude Nédélec. (2020). Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides. Communications in Computational Physics. 11 (2). 629-646. doi:10.4208/cicp.231209.150910s
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