Abstract
It is well known that the usual Kramers–Kronig relations for the relative permeability function μ(ω) are not compatible with diamagnetism (μ(0) < 1) and a positive imaginary part (Im μ(ω) > 0 for ω > 0). We demonstrate that a certain physical meaning can be attributed to μ for all frequencies, and that in the presence of spatial dispersion, μ does not necessarily tend to 1 for high frequencies ω and fixed wavenumber 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 μ(ω, k) ↛ 1 as ω →∞.
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Dirdal, C.A., Skaar, J. Diamagnetism and the dispersion of the magnetic permeability. Eur. Phys. J. B 91, 131 (2018). https://doi.org/10.1140/epjb/e2018-80515-1
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DOI: https://doi.org/10.1140/epjb/e2018-80515-1