Silvia Jimenez Bolanos, Colgate University
Authors: Abiti Adili, Silvia Jimenez Bolanos, Robert P. Lipton, and Robert Viator Jr.
2022 AWM Research Symposium
Recent Advancements in the Mathematics of Materials

In this talk, we present the derivation of analytic representation formulas and power series describing the band structure inside non-magnetic periodic photonic crystals, made from high dielectric contrast inclusions. We identify a resonance spectrum for quasi-periodic source-free modes, which 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 obtained from the representation formulas and 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.

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