Planar chirality is the special case of chirality

Chirality (mathematics)

In geometry, a figure is chiral if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. For example, a right shoe is different from a left shoe, and clockwise is different from counterclockwise.A chiral object...

 for two dimension

Dimension

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

s.

Most fundamentally, planar chirality

Chirality (mathematics)

In geometry, a figure is chiral if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. For example, a right shoe is different from a left shoe, and clockwise is different from counterclockwise.A chiral object...

 is a mathematical

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 term, finding use in chemistry

Chemistry

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 and related physical sciences, for example, in astronomy

Astronomy

Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

, optics

Optics

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

 and metamaterials. Recent occurrences in latter two fields are dominated by microwave

Microwave

Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...

 applications and micro- and nanostructure

Nanostructure

A nanostructure is an object of intermediate size between molecular and microscopic structures.In describing nanostructures it is necessary to differentiate between the number of dimensions on the nanoscale. Nanotextured surfaces have one dimension on the nanoscale, i.e., only the thickness of the...

d planar interfaces for visible and infrared

Infrared

Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

 light

Light

Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

.

Planar chirality in chemistry

This term is used in chemistry

Chemistry

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

 contexts, e.g., for a chiral

Chirality (chemistry)

A chiral molecule is a type of molecule that lacks an internal plane of symmetry and thus has a non-superimposable mirror image. The feature that is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom....

 molecule

Molecule

A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 lacking an asymmetric carbon

Asymmetric carbon

An asymmetric carbon atom is a carbon atom that is attached to four different types of atom or four different groups of atoms. Knowing the number of asymmetric carbon atoms, one can calculate the maximum possible number of stereoisomers for any given molecule as follows:As an example, malic acid...

 atom, but possessing two non-coplanar rings that are each dissymmetric and which cannot easily rotate about the chemical bond

Chemical bond

A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

 connecting them: 2,2'-dimethylbiphenyl is perhaps the simplest example of this case. Planar chirality is also exhibited by molecules like (E)-cyclooctene

Cyclooctene

Cyclooctene is a cycloalkene with an eight-membered ring. It is notable because it is the smallest cycloalkene that can exist as either the cis- or trans-isomer with the cis-isomer more common...

, some di- or poly-substituted metallocene

Metallocene

A metallocene is a compound typically consisting of two cyclopentadienyl anions bound to a metal center in the oxidation state II, with the resulting general formula 2M. Closely related to the metallocenes are the metallocene derivatives, e.g. titanocene dichloride, vanadocene dichloride...

s, and certain monosubstituted paracyclophanes. Nature rarely provides planar chiral molecules, cavicularin

Cavicularin

Cavicularin is a natural phenolic secondary metabolite isolated from the liverwort Cavicularia densa. This macrocycle is unusual because it was the first compound isolated from nature displaying optical activity due to the presence of planar chirality and axial chirality. The specific rotation for...

 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 are 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 metamaterial

Metamaterial

Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....

s has revealed that planar chirality is associated with an optical effect: the directionally asymmetric transmission (reflection and absorption) of circularly polarized

Circular polarization

In electrodynamics, circular polarization of an electromagnetic wave is a polarization in which the electric field of the passing wave does not change strength but only changes direction in a rotary type manner....

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 tranmission 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
.