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

TL;DR

This paper demonstrates that a two-dimensional dielectric photonic crystal can exhibit negative electric permittivity and magnetic permeability, acting as a left-handed material, and explores its optical properties and theoretical underpinnings.

Contribution

It shows that non-magnetic dielectric photonic crystals can have negative permittivity and permeability, and provides both numerical and analytical methods to determine these properties.

Findings

Photonic crystal exhibits negative ε and μ in certain frequency ranges.

Demonstration of Veselago lens using the photonic crystal.

Analytical theory closely matches numerical simulation results.

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.