Geodesic
On the Extrema of Band Functions in Periodic Waveguides
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 87-90

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In the work we construct an example of a periodic differential operator whose spectrum has gaps with edges attained by the band functions at interior points of the Brillouin zone. This example is the Laplacian on a pair of infinite parallel strips with common boundary from which a periodic system of small holes is cut out. At that, on the outer boundaries the Dirichlet condition is imposed, while on the common boundary the Neumann condition is considered.
Keywords: periodic operator, gap, spectrum, dispersion law, waveguide.
Mots-clés : Brillouin zone 
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     title = {On the {Extrema} of {Band} {Functions} in {Periodic} {Waveguides}},
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D.I. Borisov; K. V. Pankrashin. On the Extrema of Band Functions in Periodic Waveguides. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 87-90. http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a7/