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Creators/Authors contains: "Adili, Abiti"

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  1. 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 identification 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. 
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  2. We provide a platform to examine the effect of inclusion geometry on three-dimensional metamaterial crystals to tune frequency-dependent effective properties for control of leading order dispersive behaviour. The crystal is non-magnetic and made from all dielectric components. The design provides novel dispersive properties using subwavelength resonances controlled by the geometry of the media. We numerically calculate the effective tensors of the metamaterial to identify frequency intervals where the metamaterial exhibits band gaps as well as intervals of normal dispersion and double negative dispersion. The frequency intervals can be explicitly controlled by adjusting the geometry and placement of the dielectric inclusions within the period cell of the crystal. 
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