Abstract
We calculate analytically the effective index of refraction ${n}_{eff}$ of a periodic arrangement of nonmagnetic metallic cylinders in the low-frequency limit. At $\ensuremath{\omega}\ensuremath{\rightarrow}0$ the dielectric constant of the cylinders is singular, ${ϵ}_{m}(\ensuremath{\omega})\ensuremath{\approx}\ensuremath{-}({\ensuremath{\omega}}_{p}∕\ensuremath{\omega}{)}^{2}$, allowing propagation in the plane of periodicity of a mode with the magnetic field parallel to the cylinders ($H$ polarization). The in-plane electric field induces eddy currents, which are localized in a narrow skin layer. We show that the magnetic moment of the eddy currents leads to diamagnetic response if the radius of the cylinders is larger than the skin depth $\ensuremath{\delta}\ensuremath{\sim}{10}^{\ensuremath{-}5}\phantom{\rule{0.3em}{0ex}}\mathrm{cm}$. Otherwise, the cylinders are transparent for the electromagnetic field and their magnetic moment can be neglected. Magnetization of the cylinders gives rise to distinct values of the quasistatic and static indices of refraction and explains a paradox with noncommuting limits ${ϵ}_{m}\ensuremath{\rightarrow}\ensuremath{\infty}$ and $\ensuremath{\omega}\ensuremath{\rightarrow}0$.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.