Analytic representation formulas and power series are developed describing the band structure inside periodic photonic and acoustic crystals made from high contrast inclusions. Central to this approach is the identification and utilization of a resonance spectrum for quasi-periodic source free modes. These modes are used to represent solution operators associated with electromagnetic and acoustic waves inside periodic high contrast media. Convergent power series for the Bloch wave spectrum is recovered from the representation formulas. Explicit conditions on the contrast are found that provide lower bounds on the convergence radius. These conditions are sufficient for the separation of spectral branches of the dispersion relation.
Accepté le :
DOI : 10.1051/m2an/2016046
Mots clés : Bloch waves, band structure, high contrast, periodic medium
@article{M2AN_2017__51_3_889_0, author = {Lipton, Robert and Viator, Robert Jr.}, title = {Bloch waves in crystals and periodic high contrast media}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {889--918}, publisher = {EDP-Sciences}, volume = {51}, number = {3}, year = {2017}, doi = {10.1051/m2an/2016046}, mrnumber = {3666650}, zbl = {1375.35109}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2016046/} }
TY - JOUR AU - Lipton, Robert AU - Viator, Robert Jr. TI - Bloch waves in crystals and periodic high contrast media JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 889 EP - 918 VL - 51 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016046/ DO - 10.1051/m2an/2016046 LA - en ID - M2AN_2017__51_3_889_0 ER -
%0 Journal Article %A Lipton, Robert %A Viator, Robert Jr. %T Bloch waves in crystals and periodic high contrast media %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 889-918 %V 51 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016046/ %R 10.1051/m2an/2016046 %G en %F M2AN_2017__51_3_889_0
Lipton, Robert; Viator, Robert Jr. Bloch waves in crystals and periodic high contrast media. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 889-918. doi : 10.1051/m2an/2016046. http://www.numdam.org/articles/10.1051/m2an/2016046/
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