Planar chirality

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Planar chirality, also known as 2D chirality, is the special case of chirality for two dimensions.

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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 and terahertz applications as well as micro- and nanostructured planar interfaces for infrared and visible light.

In chemistry

A planar chiral derivative of ferrocene, used for kinetic resolution of some racemic secondary alcohols Planar chiral ferrocene derivative.svg
A planar chiral derivative of ferrocene, used for kinetic resolution of some racemic secondary alcohols

This term is used in chemistry contexts, [2] 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 is directly attached to an atom in the plane. Next, assign the priority of the 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. Then set the pilot atom to in front of the three atoms in question. If the three atoms reside in a clockwise direction when followed in order of priority, the molecule is assigned as R; when counterclockwise it is assigned as S. [3]

In optics and metamaterials

Chiral diffraction

Papakostas et al. observed in 2003 that planar chirality affects the polarization of light diffracted by arrays of planar chiral microstructures, where large polarization changes of opposite sign were detected in light diffracted from planar structures of opposite handedness. [4]

Circular conversion dichroism

The study of planar chiral metamaterials has revealed that planar chirality is also associated with an optical effect in non-diffracting structures: 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. [5] [6]

Extrinsic planar chirality

Achiral components may form a chiral arrangement. In this case, chirality is not an intrinsic property of the components, but rather imposed extrinsically by their relative positions and orientations. This concept is typically applied to experimental arrangements, for example, an achiral (meta)material illuminated by a beam of light, where the illumination direction makes the whole experiment different from its mirror image. Extrinsic planar chirality results from illumination of any periodically structured interface for suitable illumination directions. Starting from normal incidence onto a periodically structured interface, extrinsic planar chirality arises from tilting the interface around any axis that does not coincide with a line of mirror symmetry of the interface. In the presence of losses, extrinsic planar chirality can result in circular conversion dichroism, as described above. [7]

Chiral mirrors

Conventional mirrors reverse the handedness of circularly polarized waves upon reflection. In contrast, a chiral mirror reflects circularly polarized waves of one handedness without handedness change[ dubious ], while absorbing circularly polarized waves of the opposite handedness. A perfect chiral mirror exhibits circular conversion dichroism with ideal efficiency. Chiral mirrors can be realized by placing a planar chiral metamaterial in front of a conventional mirror. [8] The concept has been exploited in holography to realize independent holograms for left-handed and right-handed circularly polarized electromagnetic waves. [9] Active chiral mirrors that can be switched between left and right, or chiral mirror and conventional mirror, have been reported. [10]

See also

Related Research Articles

<span class="mw-page-title-main">Optical rotation</span> Concept in enantioselective synthesis

Optical rotation, also known as polarization rotation or circular birefringence, is the rotation of the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials. Circular birefringence and circular dichroism are the manifestations of optical activity. Optical activity occurs only in chiral materials, those lacking microscopic mirror symmetry. Unlike other sources of birefringence which alter a beam's state of polarization, optical activity can be observed in fluids. This can include gases or solutions of chiral molecules such as sugars, molecules with helical secondary structure such as some proteins, and also chiral liquid crystals. It can also be observed in chiral solids such as certain crystals with a rotation between adjacent crystal planes or metamaterials.

<span class="mw-page-title-main">Circular polarization</span> Polarization state

In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave.

<span class="mw-page-title-main">Polarization (physics)</span> Property of waves that can oscillate with more than one orientation

Polarization is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves in solids.

Circular dichroism (CD) is dichroism involving circularly polarized light, i.e., the differential absorption of left- and right-handed light. Left-hand circular (LHC) and right-hand circular (RHC) polarized light represent two possible spin angular momentum states for a photon, and so circular dichroism is also referred to as dichroism for spin angular momentum. This phenomenon was discovered by Jean-Baptiste Biot, Augustin Fresnel, and Aimé Cotton in the first half of the 19th century. Circular dichroism and circular birefringence are manifestations of optical activity. It is exhibited in the absorption bands of optically active chiral molecules. CD spectroscopy has a wide range of applications in many different fields. Most notably, UV CD is used to investigate the secondary structure of proteins. UV/Vis CD is used to investigate charge-transfer transitions. Near-infrared CD is used to investigate geometric and electronic structure by probing metal d→d transitions. Vibrational circular dichroism, which uses light from the infrared energy region, is used for structural studies of small organic molecules, and most recently proteins and DNA.

<span class="mw-page-title-main">Enantiomer</span> Stereoisomers which are non-superposable mirror images of each other

In chemistry, an enantiomer – also called optical isomer, antipode, or optical antipode – is one of two stereoisomers that are non-superposable onto their own mirror image. Enantiomers are much like one's right and left hands, when looking at the same face, they cannot be superposed onto each other. No amount of reorientation in three spatial dimensions will allow the four unique groups on the chiral carbon to line up exactly. The number of stereoisomers a molecule has can be determined by the number of chiral carbons it has. Stereoisomers include both enantiomers and diastereomers.

<span class="mw-page-title-main">Stereocenter</span> Atom which is the focus of stereoisomerism in a molecule

In stereochemistry, a stereocenter of a molecule is an atom (center), axis or plane that is the focus of stereoisomerism; that is, when having at least three different groups bound to the stereocenter, interchanging any two different groups creates a new stereoisomer. Stereocenters are also referred to as stereogenic centers.

<span class="mw-page-title-main">Specular reflection</span> Mirror-like wave reflection

Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface.

<span class="mw-page-title-main">Metamaterial</span> Materials engineered to have properties that have not yet been found in nature

A metamaterial is any material engineered to have a property that is not found in naturally occurring materials. They are made from assemblies of multiple elements fashioned from composite materials such as metals and plastics. These materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials.

<span class="mw-page-title-main">Chirality (chemistry)</span> Geometric property of some molecules and ions

In chemistry, a molecule or ion is called chiral if it cannot be superposed on its mirror image by any combination of rotations, translations, and some conformational changes. This geometric property is called chirality. The terms are derived from Ancient Greek χείρ (cheir) 'hand'; which is the canonical example of an object with this property.

<span class="mw-page-title-main">Polarimetry</span> Measurement and interpretation of the polarization of transverse waves

Polarimetry is the measurement and interpretation of the polarization of transverse waves, most notably electromagnetic waves, such as radio or light waves. Typically polarimetry is done on electromagnetic waves that have traveled through or have been reflected, refracted or diffracted by some material in order to characterize that object.

Homochirality is a uniformity of chirality, or handedness. Objects are chiral when they cannot be superposed on their mirror images. For example, the left and right hands of a human are approximately mirror images of each other but are not their own mirror images, so they are chiral. In biology, 19 of the 20 natural amino acids are homochiral, being L-chiral (left-handed), while sugars are D-chiral (right-handed). Homochirality can also refer to enantiopure substances in which all the constituents are the same enantiomer, but some sources discourage this use of the term.

Negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for (electric) permittivity (ε) and (magnetic) permeability (μ); in such cases the material can be assigned a negative refractive index. Such materials are sometimes called "double negative" materials.

<span class="mw-page-title-main">Raman optical activity</span>

Raman optical activity (ROA) is a vibrational spectroscopic technique that is reliant on the difference in intensity of Raman scattered right and left circularly polarised light due to molecular chirality.

A superlens, or super lens, is a lens which uses metamaterials to go beyond the diffraction limit. For example, in 1995, Guerra combined a transparent grating having 50nm lines and spaces with a conventional microscope immersion objective. The resulting "superlens" resolved a silicon sample also having 50nm lines and spaces, far beyond the classical diffraction limit imposed by the illumination having 650nm wavelength in air. The diffraction limit is a feature of conventional lenses and microscopes that limits the fineness of their resolution depending on the illumination wavelength and the numerical aperture NA of the objective lens. Many lens designs have been proposed that go beyond the diffraction limit in some way, but constraints and obstacles face each of them.

<span class="mw-page-title-main">Absolute configuration</span> Stereochemistry term

Absolute configuration refers to the spatial arrangement of atoms within a chiral molecular entity and its resultant stereochemical description. Absolute configuration is typically relevant in organic molecules, where carbon is bonded to four different substituents. This type of construction creates two possible enantiomers. Absolute configuration uses a set of rules to describe the relative positions of each bond around the chiral center atom. The most common labeling method uses the descriptors R or S is based on the Cahn–Ingold–Prelog priority rules. R and S refer to Rectus and Sinister, which are Latin for right and left, respectively.

Vibrational circular dichroism (VCD) is a spectroscopic technique which detects differences in attenuation of left and right circularly polarized light passing through a sample. It is the extension of circular dichroism spectroscopy into the infrared and near infrared ranges.

<span class="mw-page-title-main">Negative-index metamaterial</span> Material with a negative refractive index

Negative-index metamaterial or negative-index material (NIM) is a metamaterial whose refractive index for an electromagnetic wave has a negative value over some frequency range.

<span class="mw-page-title-main">Chiral media</span> Applied to electromagnetism

The term chiral describes an object, especially a molecule, which has or produces a non-superposable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism. The term "chiral" comes from the Greek word for the human hand, which itself exhibits such non-superimposeability of the left hand precisely over the right. Due to the opposition of the fingers and thumbs, no matter how the two hands are oriented, it is impossible for both hands to exactly coincide. Helices, chiral characteristics (properties), chiral media, order, and symmetry all relate to the concept of left- and right-handedness.

<span class="mw-page-title-main">Chirality</span> Difference in shape from a mirror image

Chirality is a property of asymmetry important in several branches of science. The word chirality is derived from the Greek χειρ (kheir), "hand", a familiar chiral object.

<span class="mw-page-title-main">Sergei Tretyakov (scientist)</span>

Sergei Anatolyevich Tretyakov is a Russian-Finnish scientist, focused in electromagnetic field theory, complex media electromagnetics and microwave engineering. He is currently a professor at Department of Electronics and Nanoengineering, Aalto University, Finland. His main research area in recent years is metamaterials and metasurfaces from fundamentals to applications. He was the president of the European Virtual Institute for Artificial Electromagnetic Materials and Metamaterials and general chair of the Metamaterials Congresses from 2007 to 2013. He is a fellow/member of many scientific associations such as IEEE, URSI, the Electromagnetics Academy, and OSA. He is also an Honorary Doctor of Francisk Skorina Gomel State University.

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