Most fundamentally, planar chirality is a mathematical term, finding use in chemistry, physics and related physical sciences, for example, in astronomy, optics and metamaterials. Recent occurrences in latter two fields are dominated by microwave applications and micro- and nanostructured planar interfaces for visible and infrared light.
Planar chirality in chemistry
This term is used in chemistry contexts, e.g., for a chiral molecule lacking an asymmetric carbon atom, but possessing two non-coplanar rings that are each dissymmetric and which cannot easily rotate about the chemical bond connecting them: 2,2'-dimethylbiphenyl is perhaps the simplest example of this case. Planar chirality is also exhibited by molecules like (E)-cyclooctene, some di- or poly-substituted metallocenes, and certain monosubstituted paracyclophanes. Nature rarely provides planar chiral molecules, cavicularin being an exception.
Assigning the configuration of planar chiral molecules
To assign the configuration of a planar chiral molecule, begin by selecting the pilot atom, which is the highest priority of the atoms that is not in the plane, but are directly attached to an atom in the plane. Next, assign the priority of three adjacent in-plane atoms, starting with the atom attached to the pilot atom as priority 1, and preferentially assigning in order of highest priority if there is a choice. When viewed from the side of the pilot atom, if the three atoms form a clockwise direction when followed in order of priority, the molecule is assigned as R, otherwise it is assigned as S.
Planar chirality in optics and metamaterials
The study of planar chiral metamaterials has revealed that planar chirality is associated with an optical effect: the directionally asymmetric transmission (reflection and absorption) of circularly polarized waves. Planar chiral metamaterials, which are also anisotropic and lossy exhibit different total transmission (reflection and absorption) levels for the same circularly polarized wave incident on their front and back. The asymmetric transmission phenomenon arises from different, e.g. left-to-right, circular polarization conversion efficiencies for opposite propagation directions of the incident wave and therefore the effect is referred to as circular conversion dichroism. Like the twist of a planar chiral pattern appears reversed for opposite directions of observation, planar chiral metamaterials have interchanged properties for left-handed and right-handed circularly polarized waves that are incident on their front and back. In particular left-handed and right-handed circularly polarized waves experience opposite directional transmission (reflection and absorption) asymmetries. 
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