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Correlations between helicity and optical losses within general electromagnetic scattering theory

Helicity preserving nanostructures and metasurfaces have been recently proposed as suitable candidates to enhance spectroscopic features of chiral matter. With this in mind, we highlight that losses in the constituent nonmagnetic materials dramatically affect the possibility of constructing structures which conserve helicity. We first present a general procedure that permits the evaluation of the normalized helicity expectation value, $\langle\hatΛ\rangle$, i.e. the observable that permits the identification of helicity preserving scatterers. We then apply this procedure to the case of a chiral sphere, which in an orientation averaged picture can capture the optical response of chiral inorganic nanostructures, obtaining a widely applicable analytical expression of $\langle\hatΛ\rangle$ for this type of objects. Finally, we numerically show that optical losses impose an upper bound to the helicity expectation value on nonmagnetic core-shells and chiral spheres.