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Dirac cone dispersions in photonic and phononic crystals

Last modified: 2011-12-30

#### Abstract

We show that by employing accidental degeneracy, dielectric photonic crystals can be designed and fabricated that exhibit Dirac cone dispersion at k=0 at a finite frequency. Under some circumstances, effective medium theory can be used to relate the photonic crystal to a material with effectively zero permittivity and permeability at and near the Dirac point frequency. This concept can also be extended to acoustic and elastic waves. For the case of acoustic waves, we can find direct correspondence with the photonic crystal system. For the case of elastic waves, we show that Dirac cone dispersion at k=0 can be related to a special kind of elastic crystal in which only longitudinal wave is allowed in certain directions and only transverse wave is allowed in some other directions. Effective medium theory finds that this phononic crystal has effectively zero mass density and zero effective

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