All-Dielectric Rod-Type Metamaterials Operating at Optical Frequencies

Light propagation in all-dielectric rod-type metamaterials is studied theoretically. The electric and magnetic dipole moments of the rods are derived analytically in the long-wavelength limit. The photonic band structure of a square array of rods is retrieved by homogenizing the corresponding array of dipoles. It is found that such a structure exhibits a true left-handed behavior, confirming previous experimental results [L. Peng \textit{et al.}, Phys. Rev. Lett. \textbf{98}, 157403 (2007)]. A scaling analysis proves that this effect holds at optical frequencies and can be obtained, for instance, by using silicon rods.