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 fixed relations and the associated transmission matrices cannot be symmetrized.PACS numbers: XX.XX.XX During the past several years optical metamaterials (MMs) have attracted an enormous interest since they promise to allow for a manipulation of light propagation to a seemingly arbitrary extent. MMs are usually obtained by assembling sub-wavelength unit cell structures called metaatoms. Initial studies on MMs were based on rather simple and highly symmetric metaatoms [1][2][3]. Recently, more and more sophisticated structures were explored in order to achieve customized functionalities like, e.g. a negative refractive index due to chirality [4-6]. Also, a large variety of plasmonic metaatoms were investigated that evoke a huge polarization rotation like gammadions, omega shaped particles or helices [7][8][9]. Studying the characteristics of light propagation in such low-symmetry MMs also revealed unexpected phenomena like asymmetric transmission for circularly polarized light [10][11][12]. Although at first sight this effect of nonreciprocal transmission, to date not observed for linearly polarized light, is counterintuitive, it does not violate Lorentz' reciprocity theorem. This asymmetric transmission of circularly polarized light was demonstrated at so-called planar chiral MMs. Such MMs are composed of metaatoms without structural variation in the principal propagation direction. They preserve symmetry in this direction and are only chiral in the two-dimensional space [13]; thus, strictly speaking, they are intrinsically achiral in three dimensions since the mirror image of a structure is congruent with the structure itself if operated from the backside. The remaining mirroring plane is perpendicular to the propagation direction.In this Letter we theoretically and experimentally demonstrate a novel MM design which breaks the latter symmetry. For the first time our approach reveals that the very structures exhibit asymmetric transmission for linearly polarized light. We emphasize that also in this case the reciprocity theorem is not violated since only reciprocal materials are involved.Prior to any further considerations we concisely discuss the effect of a potential MM substrate that is, after all, in most cases required for fabricating planar MMs. Generally speaking, just this supporting substrate breaks the mirror symmetry for ...

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By relying on an advanced Jones calculus we analyze the polarization properties of light upon propagation through metamaterial slabs in a comprehensive manner. Based on symmetry considerations, we show that all periodic metamaterials may be divided into five different classes only. It is shown that each class differently affects the polarization of the transmitted light and sustains different eigenmodes. We show how to deduce these five classes from symmetry considerations and provide a simple algorithm that can be applied to decide by measuring transmitted intensities to which class a given metamaterial is belonging to only.

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