We experimentally demonstrate a three-dimensional chiral optical metamaterial
that exhibits an asymmetric transmission for forwardly and backwardly
propagating linearly polarized light. The observation of this novel effect
requires a metamaterial composed of three-dimensional chiral metaatoms without
any rotational symmetry. Our analysis is supported by a systematic
investigation of the transmission matrices for arbitrarily complex, lossy media
that allows deriving a simple criterion for asymmetric transmission in an
arbitrary polarization base. Contrary to physical intuition, in general the
polarization eigenstates in such three-dimensional and low-symmetry
metamaterials do not obey fxed relations and the associated transmission
matrices cannot be symmetrized