Abstract: For more than a century after the seminal paper by Gustav Mie (1908) on scattering of electromagnetic waves by a dielectric substance, the concept of "leaky modes" has been central in the interpretation of observed spectra from these media. Leaky modes occur because outwardly travelling waves of light scattered by a dielectric medium will not be polluted by backward waves if the surrounding medium is very large (infinite in theory): the waves leak out of the system. Surprisingly, the leaky mode spectra are completely determined by the scattering substance, and not at all by the very large outer medium. Moreover, the leaky modes become exponentially large at infinity, so that they are to be rejected in the standard solution of differential equations! Only at the end of last century, these amazing facts have been justified by the theory of regularisation. In a recent paper, we (Goedbloed & Keppens, J. Plasma Physics, 92(3):E89, 1--38, 2026) have investigated whether this magic also works for magnetohydrodynamic waves scattered by solar magnetic loops.
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