Diamagnetism and the dispersion of the magnetic permeability

Abstract

It is well known that the usual Kramers--Kronig relations for the relative permeability function $\mu (\omega )$ are not compatible with diamagnetism ($\mu (0)<1$) and a positive imaginary part ($\text{Im}\mu (\omega )>0$ for $\omega >0$). We demonstrate that a certain physical meaning can be attributed to $\mu$ for all frequencies, and that in the presence of spatial dispersion, $\mu$ does not necessarily tend to 1 for high frequencies $\omega$ and fixed wavenumber $\mathbf{k}$. Taking the asymptotic behavior into account, diamagnetism can be compatible with Kramers--Kronig relations even if the imaginary part of the permeability is positive. We provide several examples of diamagnetic media and metamaterials for which $\mu (\omega ,\mathbf{k})\nrightarrow 1$ as $\omega \to \infty$.

References in corpus (1)

• First-Principle Homogenization Theory for Periodic Metamaterials

Cited by in corpus (3)

• Four definitions of magnetic permeability for periodic metamaterials
• Is diamagnetism really acausal?
• Is there a conflict between causality and diamagnetism?