Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability.

We consider a dielectric photonic crystal made of cylindrical holes in a high index matrix. We show that a given finite size photonic crystal can mimic a homogeneous material whose permittivity and permeability are negative. We pay attention to the limitation of the homogeneous medium model and the vital role of the truncation of the crystal.

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