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Planar chirality, also known as 2D chirality, is the special case of chirality for two dimensions. Most fundamentally, planar chirality is a mathematical term, finding use in chemistry , physics and related physical sciences, for example, in astronomy , optics and metamaterials .
2D chirality is associated with directionally asymmetric transmission (reflection and absorption) of circularly polarized electromagnetic waves. 2D-chiral materials, 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.
2D-chiral patterns, such as flat spirals, cannot be superposed with their mirror image by translation or rotation in two-dimensional space (a plane). 2D chirality is associated with directionally asymmetric transmission (reflection and absorption) of circularly polarized waves. 2D-chiral materials, which are also anisotropic and lossy exhibit ...
An object that is not chiral is said to be achiral. A chiral object and its mirror image are said to be enantiomorphs. The word chirality is derived from the Greek χείρ (cheir), the hand, the most familiar chiral object; the word enantiomorph stems from the Greek ἐναντίος (enantios) 'opposite' + μορφή (morphe) 'form'.
The chiral angle α is then the angle between u and w. [6] [7] [8] The pairs (n,m) that describe distinct tube structures are those with 0 ≤ m ≤ n and n > 0. All geometric properties of the tube, such as diameter, chiral angle, and symmetries, can be computed from these indices. The type also determines the electronic structure of the tube.
The affine space group type is determined by the underlying abstract group of the space group. In three dimensions, Fifty-four of the affine space group types preserve chirality and give chiral crystals. The two enantiomorphs of a chiral crystal have the same affine space group. Arithmetic crystal classes (73 in three dimensions)
The concept of 2D chirality also exists and a planar object is said to be chiral if it cannot be superposed onto its mirror image unless it is lifted from the plane. 2D-chiral metamaterials that are anisotropic and lossy have been observed to exhibit directionally asymmetric transmission (reflection, absorption) of circularly polarized waves ...
In a two-dimensional conformal field theory, properties are called chiral if they follow from the action of one of the two Virasoro algebras. If the space of states can be decomposed into factorized representations of the product of the two Virasoro algebras, then all consequences of conformal symmetry are chiral.