Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

We show that the two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values for both the electric permittivity ϵ and the magnetic permeability μ in some frequency range. This follows from a recently proven general theorem. The negative values of ϵ and μ are found by a numerical simulation. Using values |ϵ| and |μ| for the medium surrounding the PC slab we simulate the Veselago lens, a unique optical device predicted by Veselago. An approximate analytical theory is proposed to calculate the values of ϵ and μ from the PC band structure. It gives the results that are close to those obtained by the numerical simulation. The theory explains how a non-zero magnetization arises in a non-magnetic PC.