Chirality (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, chiral media, order, and symmetry all relate to the concept of left- and right-handedness.

Types of chirality

Chirality describes that something is different from its mirror image. Chirality can be defined in two or three dimensions. It can be an intrinsic property of an object, such as a molecule, crystal or metamaterial. It can also arise from the relative position and orientation of different components, such as the propagation direction of a beam of light relative to the structure of an achiral material.

Intrinsic 3d chirality

Any object that cannot be superimposed with its mirror image by translation or rotation in three dimensions has intrinsic 3d chirality. Intrinsic means that the chirality is a property of the object. In most contexts, materials described as chiral have intrinsic 3d chirality. Typical examples are homogeneous/homogenizable chiral materials that have a chiral structure on the subwavelength scale. For example, an isotropic chiral material can comprise a random dispersion of handed molecules or inclusions, such as a liquid consisting of chiral molecules. Handedness can also be present at the macroscopic level in structurally chiral materials. For example, the molecules of cholesteric liquid crystals are randomly positioned but macroscopically they exhibit a helicoidal orientational order. Other examples of structurally chiral materials can be fabricated either as stacks of uniaxial laminas or using sculptured thin films. Remarkably, artificial examples of both types of chiral materials were produced by J. C. Bose more than 11 decades ago. 3D chirality causes the electromagnetic effects of optical activity and linear conversion dichroism.

Extrinsic 3d chirality

Any arrangement that cannot be superimposed with its mirror image by translation or rotation in three dimensions has extrinsic 3d chirality. Extrinsic means that the chirality is a consequence of the arrangement of different components, rather than an intrinsic property of the components themself. For example, the propagation direction of a beam of light through an achiral crystal can form an experimental arrangement that is different from its mirror image. In particular, oblique incidence onto any planar structure that does not posess two-fold rotational symmetry results in a 3D-chiral experimental arrangement, except for the special case when the structure has a line of mirror symmetry in the plane of incidence.
Bunn predicted in 1945 that extrinsic 3d chirality would cause optical activity and the effect was later detected in liquid crystals.
Extrinsic 3d chirality causes large optical activity and linear conversion dichroism in metamaterials. These effects are inherently tuneable by changing the relative orientation of incident wave and material. Both extrinsic 3d chirality and the resulting optical activity are reversed for opposite angles of incidence.

Intrinsic 2d chirality

Any object that cannot be superimposed with its mirror image by translation or rotation in two dimensions has intrinsic 2d chirality, also known as planar chirality. Intrinsic means that the chirality is a property of the object. Any planar pattern that does not have a line of mirror symmetry is 2d-chiral, and examples include flat spirals and letters such as S, G, P. In contrast to 3d-chiral objects, the perceived sense of twist of 2d-chiral patterns is reversed for opposite directions of observation. 2d chirality is associated with circular conversion dichroism, which causes directionally asymmetric transmission of circularly polarized electromagnetic waves.

Extrinsic 2d chirality

Also 2d chirality can arise from the relative arrangement of different components. In particular, oblique illumination of any planar periodic structure will result in extrinsic 2d chirality, except for the special cases where the plane of incidence is either parallel or perpendicular to a line of mirror symmetry of the structure. Strong circular conversion dichroism due to extrinsic 2d chirality has been observed in metamaterials.

Handedness of electromagnetic waves

waves can have handedness associated with their polarization. Polarization of an electromagnetic wave is the property that describes the orientation, i.e., the time-varying direction and amplitude, of the electric field vector. For example, the electric field vectors of left-handed or right-handed circularly polarized waves form helices of opposite handedness in space as illustrated by the adjacent animation.
Polarizations are described in terms of the figures traced by the electric field vector as a function of time at a fixed position in space. In general, polarization is elliptical and is traced in a clockwise or counterclockwise sense. If, however, the major and minor axes of the ellipse are equal, then the polarization is said to be circular . If the minor axis of the ellipse is zero, the polarization is said to be linear. Rotation of the electric vector in a clockwise sense is designated right-hand polarization, and rotation in a counterclockwise sense is designated left-hand polarization. When deciding whether the rotation is clockwise or counterclockwise, a convention is needed. Optical physicists tend to determine handedness from the perspective of an observer looking towards the source from within the wave, like an astronomer looking at a star. Engineers tend to determine handedness looking along the wave from behind the source, like an engineer standing behind a radiating antenna. Both conventions yield opposite definitions of left-handed and right-handed polarizations and therefore care must be taken to understand which convention is being followed.
Mathematically, an elliptically polarized wave may be described as the vector sum of two waves of equal wavelength but unequal amplitude, and in quadrature.

Circular polarization

, regarding electromagnetic wave propagation, is polarization such that the tip of the electric field vector describes a helix. The magnitude of the electric field vector is constant. The projection of the tip of the electric field vector upon any fixed plane intersecting, and normal to, the direction of propagation, describes a circle. A circularly polarized wave may be resolved into two linearly polarized waves in phase quadrature with their planes of polarization at right angles to each other. Circular polarization may be referred to as "right-hand" or "left-hand," depending on whether the helix describes the thread of a right-hand or left-hand screw, respectively
in support of the series on U.S. military standards relating to telecommunications, MIL-STD-188

Optical activity

3D-chiral materials can exhibit optical activity, which manifests itself as circular birefringence, causing polarization rotation for linearly polarized waves, and circular dichroism, causing different attenuation of left- and right-handed circularly polarized waves. The former can be exploited to realize polarization rotators, while the latter can be used to realize circular polarizers. Optical activity is weak in natural chiral materials, but it can be enhanced by orders of magnitude in an artificial chiral materials, i.e., chiral metamaterials.
Just like the perceived sense of twist of a helix is the same for opposite directions of observation, optical activity is the same for opposite directions of wave propagation.

Circular birefringence

In 3d-chiral media, circularly polarized electromagnetic waves of opposite handedness can propagate with different speed. This phenomenon is known as circular birefringence and described by different real parts of refracive indices for left- and right-handed circularly polarized waves. As a consequence, left- and right-handed circularly polarized waves accumulate different amounts of phase upon propagation through a chiral medium. This phase difference causes rotation of the polarization state of linearly polarized waves, which may be thought of as superposition of left- and right-handed circularly polarized waves. Circular birefringence can yield a negative index of refraction for waves of one handedness when the effect is sufficiently large.

Circular dichroism

In 3d-chiral media, circularly polarized electromagnetic waves of opposite handedness can propagate with different losses. This phenomenon is known as circular dichroism and described by different imaginary parts of refracive indices for left- and right-handed circularly polarized waves.

Specular optical activity

While optical activity is normally observed for transmitted light, polarization rotation and different attenuation of left-handed and right-handed circularly polarized waves can also occur for light reflected by chiral substances. These phenomena of specular circular birefringence and specular circular dichroism are jointly known as specular optical activity. Specular optical avtivity is weak in natural materials. Extrinsic 3d chirality associated with oblique illumination of metasurfaces lacking two-fold rotational symmetry leads to large specular optical activity.

Nonlinear optical activity

Optical activity that depends on the intensity of light has been predicted and then observed in lithium iodate crystals.
In comparison to lithium iodate, extrinsic 3d chirality associated with oblique illumination of metasurfaces lacking two-fold rotational symmetry was found to lead to 30 million times stronger nonlinear optical activity in the optical part of the spectrum. At microwave frequencies, a 12 orders of magnitude stronger effect than in lithium iodate was observed for an intrinsically 3d-chiral structure.

Circular conversion dichroism

2D chirality is associated with directionally asymmetric transmission of circularly polarized electromagnetic waves. 2D-chiral materials, which are also anisotropic and lossy exhibit different total transmission 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 2d-chiral pattern appears reversed for opposite directions of observation, 2d-chiral materials 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 asymmetries.
Circular conversion dichroism with almost ideal efficiency has been achieved in metamaterial-based chiral mirrors. In contrast to conventional mirrors, a chiral mirror reflects circularly polarized waves of one handedness without handedness change, while absorbing circularly polarized waves of the other handedness. Chiral mirrors can be realized by placing a 2d-chiral metamaterial in front of a conventional mirror. The concept has been exploited in holography to realize independent holograms for left-handed and right-handed circularly polarized electromagnetic waves. Active chiral mirrors that can be switched between left and right, or chiral mirror and conventional mirror, have been reported.

Linear conversion dichroism

3D chirality of anisotropic structures is associated with directionally asymmetric transmission of linearly polarized electromagnetic waves. Different levels of total transmission for the same linearly polarized wave incident on their front and back arise from different, e.g. x-to-y, linear polarization conversion efficiencies for opposite propagation directions of the incident wave and therefore the effect is referred to as linear conversion dichroism. The x-to-y and y-to-x polarization conversion efficiencies are interchanged for opposite directions of wave propagation. Linear conversion dichroism has been observed in metamaterials with intrinsic and extrinsic 3d chirality. Active metamaterials, where the effect can be turned on and off have been realized by controlling 3d chirality with phase transitions.

Repulsive Casimir force in chiral metamaterials

observed experimentally in nature have almost always been attractive and have rendered nanoscale and microscale machines inoperable by causing their moving parts to permanently stick together. This has been a long-standing problem that some researchers have tried to solve.
Nanoscale machines expected to have wide application in industry, energy, medicine and other fields may someday operate far more efficiently thanks to important theoretical discoveries concerning the manipulation of famous Casimir forces that took place at the U.S. Department of Energy's Ames Laboratory.
The ground breaking research, conducted through mathematical simulations, revealed the possibility of a new class of materials able to exert a repulsive force when they are placed in extremely close proximity to each other. The repulsive force, which harnesses a quantum phenomenon known as the Casimir effect, may someday allow nanoscale machines to overcome mechanical friction.
Though the frictional forces in nanoscale environments are small, they significantly inhibit the function of the tiny devices designed to operate in that realm, explained Costas Soukoulis, a senior physicist at the Ames Lab and Distinguished Professor of physics at Iowa State University, who led the research effort.
Soukoulis and his teammates, including Ames Laboratory assistant scientist Thomas Koschny, were the first to study the use of exotic materials known as chiral metamaterials as a way to harness the Casimir effect. Their efforts have demonstrated that it is indeed possible to manipulate the Casimir force. The findings were published in the Sept. 4, 2009 issue of Physical Review Letters, in an article entitled, "Repulsive Casimir Force in Chiral Metamaterials." This work was however discredited because it was based on an unphysical model of the chiral materials.
Understanding the importance of their discovery requires a basic understanding of both the Casimir effect and the unique nature of chiral metamaterials.
The Casimir effect was named after Dutch physicist Hendrik Casimir, who postulated its existence in 1948. Using quantum theory, Casimir predicted that energy should exist even in a vacuum, which can give rise to forces acting on the bodies brought into close proximity of each other. For the simple case of two parallel plates, he postulated that the energy density inside the gap should decrease as the size of the gap decreases, also meaning work must be done to pull the plates apart. Alternatively, an attractive force that pushes the plates closer together can be said to exist.
Remarkably, this new discovery demonstrates that a repulsive Casimir effect is possible using chiral metamaterials. Chiral materials share an interesting characteristic: their molecular structure prevents them from being superimposed over a reverse copy of themselves, in the same way a human hand cannot fit perfectly atop a reverse image of itself. Chiral materials are fairly common in nature. The sugar molecule is one example. However, natural chiral materials are incapable of producing a repulsive Casimir effect that is strong enough to be of practical use.
For that reason, the group turned its attention to chiral metamaterials, so named because they do not exist in nature and must instead be made in the lab. The fact that they are artificial gives them a unique advantage, commented Koschny. "With natural materials you have to take what nature gives you; with metamaterials, you can create a material to exactly meet your requirements," he said.
The chiral metamaterials the researchers focused on have a unique geometric structure that enabled them to change the nature of energy waves, such as those located in the gap between the two closely positioned plates, causing those waves to exert a repulsive Casimir force.
The present study was carried out using mathematical simulations because of the difficulties involved in fabricating these materials with semiconductor lithographic techniques. While more work needs to be done to determine if chiral materials can induce a repulsive Casimir force strong enough to overcome friction in nanoscale devices, practical applications of the Casimir effect are already under close study at other DOE facilities, including Los Alamos and Sandia National Laboratories. Both have expressed considerable interest in using the chiral metamaterials designed at Ames Laboratory to fabricate new structures and reduce the attractive Casimir force, and possibly to obtain a repulsive Casimir force.
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