Geodesic
Gap Opening and Split Band Edges in Waveguides Coupled by a Periodic System of Small Windows
Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 665-683

Voir la notice de l'article provenant de la source Math-Net.Ru

As an example of two coupled waveguides, we construct a periodic second-order differential operator acting in a Euclidean domain and having spectral gaps whose edges are attained strictly inside the Brillouin zone. The waveguides are modeled by the Laplacian in two infinite strips of different width that have a common interior boundary. On this common boundary, we impose the Neumann boundary condition, but cut out a periodic system of small holes, while on the remaining exterior boundary we impose the Dirichlet boundary condition. It is shown that, by varying the widths of the strips and the distance between the holes, one can control the location of the extrema of the band functions as well as the number of the open gaps. We calculate the leading terms in the asymptotics for the gap lengths and the location of the extrema.
Keywords: Laplacian, periodic operator, waveguide, band spectrum, spectral gap, dispersion laws, matching of asymptotic expansions, boundary conditions. 
@article{MZM_2013_93_5_a2,
     author = {D. I. Borisov and K. V. Pankrashin},
     title = {Gap {Opening} and {Split} {Band} {Edges} in {Waveguides} {Coupled} by a {Periodic} {System} of {Small} {Windows}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {665--683},
     publisher = {mathdoc},
     volume = {93},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a2/}
}
TY  - JOUR
AU  - D. I. Borisov
AU  - K. V. Pankrashin
TI  - Gap Opening and Split Band Edges in Waveguides Coupled by a Periodic System of Small Windows
JO  - Matematičeskie zametki
PY  - 2013
SP  - 665
EP  - 683
VL  - 93
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a2/
LA  - ru
ID  - MZM_2013_93_5_a2
ER  - 
%0 Journal Article
%A D. I. Borisov
%A K. V. Pankrashin
%T Gap Opening and Split Band Edges in Waveguides Coupled by a Periodic System of Small Windows
%J Matematičeskie zametki
%D 2013
%P 665-683
%V 93
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a2/
%G ru
%F MZM_2013_93_5_a2
D. I. Borisov; K. V. Pankrashin. Gap Opening and Split Band Edges in Waveguides Coupled by a Periodic System of Small Windows. Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 665-683. http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a2/