R. Lipton, Robert Viator, Silvia Jiménez Bolanos, A. Adili
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Bloch waves in high contrast electromagnetic crystals
Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielectric contrast inclusions. Central to this approach is the identifcation and utilization of a resonance spectrum for quasiperiodic source-free modes. These modes are used to represent solution operators associated with electromagnetic and acoustic waves inside periodic high contrast media. A 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 for any fixed quasi-momentum.
期刊介绍:
M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem.
Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.