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 epsilon and the magnetic permeability mu in some frequency range. This follows from a recently proven general theorem. The negative values of epsilon and mu are found by a numerical simulation. Using values \epsilon\ and \mu\ 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 epsilon and mu 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. (C) 2003 Elsevier Ltd. All rights reserved.