  We present a general theory of circular dichroism in planar chiral
nanostructures with rotational symmetry. It is demonstrated, analytically, that
the handedness of the incident field's polarization can control whether a
nanostructure induces either absorption or scattering losses, even when the
total optical loss (extinction) is polarization-independent. We show that this
effect is a consequence of modal interference so that strong circular dichroism
in absorption and scattering can be engineered by combining Fano resonances
with planar chiral nanoparticle clusters.
