Volume 51, Number 3, May-June 2017
|Page(s)||889 - 918|
|Published online||14 April 2017|
Bloch waves in crystals and periodic high contrast media
Received: 25 November 2015
Revised: 20 April 2016
Accepted: 16 June 2016
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.
Mathematics Subject Classification: 35J15 / 78A40 / 78A45
Key words: Bloch waves / band structure / high contrast / periodic medium
© EDP Sciences, SMAI 2017
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.