Left-handed media and homogenization of photonic crystals

Using homogenization theory, we derive the effective permittivity and permeability of a wire-mesh photonic crystal from first principles. We show that this structure does not lead to a left-handed medium when it is embedded in a matrix with a negative μ, but that resonators in a medium with a negative E do form a left-handed medium in the correct range of frequencies. © 2005 Optical Society of America.