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

Abstract

We show that a 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 of 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 these values we demonstrate 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.

11 pages 4 figures

References in corpus (4)

• Determination of Effective Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients
• Electrodynamics of metallic photonic crystals and problem of left-handed materials
• Sign of refractive index and group velocity in left-handed media
• Diffraction theory and focusing of light by left-handed materials

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• Far field imaging by a planar lens: diffraction versus superresolution
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• A new Heterogeneous Multiscale Method for time-harmonic Maxwell's equations based on divergence-regularization
• Localized Orthogonal Decomposition for two-scale Helmholtz-type problems
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