no. 4
Computing guided modes for an unbounded stratified medium in integrated optics
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 4, pp. 799-824.

We present a finite element method to compute guided modes in a stratified medium. The major difficulty to overcome is related to the unboundedness of the stratified medium. Our method is an alternative to the use of artificial boundary conditions and to the use of integral representation formulae. The domain is bounded in such a way we can write the solution on its lateral boundaries in terms of Fourier series. The series is then truncated for the computations over the bounded domain. The problem is scalar and 2-dimensional.

Classification : 65N30, 65N25, 35Q60, 78M10, 68U20
Mots clés : finite element method, exact boundary condition, unbounded domain, stratified medium, guided modes, optics, series expansion 
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     title = {Computing guided modes for an unbounded stratified medium in integrated optics},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {799--824},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {4},
     year = {2001},
     mrnumber = {1863281},
     zbl = {0993.78017},
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     url = {http://www.numdam.org/item/M2AN_2001__35_4_799_0/}
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Mahé, Fabrice. Computing guided modes for an unbounded stratified medium in integrated optics. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 4, pp. 799-824. http://www.numdam.org/item/M2AN_2001__35_4_799_0/

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