![Polarimeter (Optical rotation)](https://upload.wikimedia.org/wikipedia/commons/5/5d/Polarimeter_%28Optical_rotation%29.svg)
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
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...
materials, those lacking microscopic mirror symmetry. Unlike other sources of
birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
which alter a beam's state of polarization, optical activity can be observed in
fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
s. This can include gases or solutions of
chiral molecules such as sugars, molecules with helical
secondary structure
Protein secondary structure is the three dimensional conformational isomerism, form of ''local segments'' of proteins. The two most common Protein structure#Secondary structure, secondary structural elements are alpha helix, alpha helices and beta ...
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
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
planes (such as
quartz
Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical form ...
) or
metamaterial
A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...
s.
When looking at the source of light, the rotation of the plane of polarization may be either to the right (dextrorotatory or dextrorotary — ''d''-rotary, represented by (+), clockwise), or to the left (levorotatory or levorotary — ''l''-rotary, represented by (−), counter-clockwise) depending on which
stereoisomer
In stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in ...
is dominant. For instance,
sucrose
Sucrose, a disaccharide, is a sugar composed of glucose and fructose subunits. It is produced naturally in plants and is the main constituent of white sugar. It has the molecular formula .
For human consumption, sucrose is extracted and refined ...
and
camphor
Camphor () is a waxy, colorless solid with a strong aroma. It is classified as a terpenoid and a cyclic ketone. It is found in the wood of the camphor laurel ('' Cinnamomum camphora''), a large evergreen tree found in East Asia; and in the k ...
are ''d''-rotary whereas
cholesterol
Cholesterol is any of a class of certain organic molecules called lipids. It is a sterol (or modified steroid), a type of lipid. Cholesterol is biosynthesized by all animal cells and is an essential structural component of animal cell mem ...
is ''l''-rotary. For a given substance, the angle by which the polarization of light of a specified wavelength is rotated is proportional to the path length through the material and (for a solution) proportional to its concentration.
Optical activity is measured using a polarized source and
polarimeter
A polarimeter is a scientific instrument used to measure the angle of rotation caused by passing polarized light through an optically active substance.[sugar industry
The sugar industry subsumes the production, processing and marketing of sugars (mostly sucrose and fructose). Globally, most sugar is extracted from sugar cane (~80% predominantly in the tropics) and sugar beet (~ 20%, mostly in temperate cli ...]
to measure the sugar concentration of syrup, and generally in chemistry to measure the concentration or
enantiomeric ratio of chiral molecules in solution. Modulation of a liquid crystal's optical activity, viewed between two sheet
polarizers, is the principle of operation of
liquid-crystal display
A liquid-crystal display (LCD) is a flat-panel display
A flat-panel display (FPD) is an electronic display used to display visual content such as text or images. It is present in consumer, medical, transportation, and industrial equipmen ...
s (used in most modern televisions and computer monitors).
Forms
Dextrorotation and laevorotation (also spelled levorotation)
[The first word component '']dextro-
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. Circul ...
'' comes from the Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
word ''dexter
Dexter may refer to:
Arts and entertainment
* Dexter, the main character of the American animated series ''Dexter's Laboratory'' that aired from 1996 to 2003
* Dexter, a fictional character in the British Diary of a Bad Man#Main, web series ''Diar ...
'', meaning "right" (as opposed to left). ''Laevo-
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. Circul ...
'' or ''levo-
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. Circul ...
'' comes from the Latin '' laevus'', meaning "left side". are terms used in
chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
and
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
to describe the optical rotation of
plane-polarized light
Polarization (also polarisation) 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 ...
. From the point of view of the observer, ''dextrorotation'' refers to clockwise or right-handed rotation, and ''laevorotation'' refers to counterclockwise or left-handed rotation.
A
chemical compound
A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...
that causes dextrorotation is called ''dextrorotatory'' or ''dextrorotary'', while a compound that causes laevorotation is called ''laevorotatory'' or ''laevorotary''.
Compounds with these properties consist of
chiral
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...
molecules and are said to have optical activity. If a chiral molecule is dextrorotary, its
enantiomer
In chemistry, an enantiomer ( /ɪˈnænti.əmər, ɛ-, -oʊ-/ ''ih-NAN-tee-ə-mər''; from Ancient Greek ἐνάντιος ''(enántios)'' 'opposite', and μέρος ''(méros)'' 'part') – also called optical isomer, antipode, or optical ant ...
(geometric mirror image) will be laevorotary, and vice versa. Enantiomers rotate plane-polarized light the same number of degrees, but in opposite directions.
Chirality prefixes
A compound may be labeled as dextrorotary by using the "(+)-" or "''d''-" prefix. Likewise, a laevorotary compound may be labeled using the "(−)-" or "''l''-" prefix. The lowercase "''d''-" and "''l''-" prefixes are obsolete, and are distinct from the
SMALL CAPS
In typography, small caps (short for "small capitals") are characters typeset with glyphs that resemble uppercase letters (capitals) but reduced in height and weight close to the surrounding lowercase letters or text figures. This is technicall ...
"
D-" and "
L-" prefixes. The "
D-" and "
L-" prefixes are used to specify the enantiomer of chiral
organic compounds
In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The s ...
in
biochemistry
Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
and are based on the compound's
absolute configuration
Absolute configuration refers to the spatial arrangement of atoms within a chiral molecular entity (or group) and its resultant stereochemical description. Absolute configuration is typically relevant in organic molecules, where carbon is bonded ...
relative to (+)-
glyceraldehyde
Glyceraldehyde (glyceral) is a triose monosaccharide with chemical formula C3 H6 O3. It is the simplest of all common aldoses. It is a sweet, colorless, crystalline solid that is an intermediate compound in carbohydrate metabolism. The word comes ...
, which is the
D-form by definition. The prefix used to indicate absolute configuration is not directly related to the (+) or (−) prefix used to indicate optical rotation in the same molecule. For example, nine of the nineteen
L-
amino acid
Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha am ...
s naturally occurring in proteins are, despite the
L- prefix, actually dextrorotary (at a wavelength of 589 nm), and
D-
fructose
Fructose, or fruit sugar, is a Ketose, ketonic monosaccharide, simple sugar found in many plants, where it is often bonded to glucose to form the disaccharide sucrose. It is one of the three dietary monosaccharides, along with glucose and galacto ...
is sometimes called "laevulose" because it is laevorotary.
The
D- and
L- prefixes describe the molecule as a whole, as do the (+) and (−) prefixes for optical rotation. In contrast, the (''R'')- and (''S'')- prefixes from the
Cahn–Ingold–Prelog priority rules
In organic chemistry, the Cahn–Ingold–Prelog (CIP) sequence rules (also the CIP priority convention; named for R.S. Cahn, C.K. Ingold, and Vladimir Prelog) are a standard process to completely and unequivocally name a stereoisomer of a ...
characterize the
absolute configuration
Absolute configuration refers to the spatial arrangement of atoms within a chiral molecular entity (or group) and its resultant stereochemical description. Absolute configuration is typically relevant in organic molecules, where carbon is bonded ...
of each specific chiral
stereocenter
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 cr ...
with the molecule, rather than a property of the molecule as a whole. A molecule having exactly one chiral stereocenter (usually an
asymmetric carbon An asymmetric carbon atom (chiral carbon) is a carbon atom that is attached to four different types of atoms or groups of atoms. Le Bel-van't Hoff rule states that the number of stereoisomers of an organic compound is 2n, where n represents the num ...
atom) can be labeled (''R'') or (''S''), but a molecule having multiple stereocenters needs more than one label. For example, the essential amino acid
L-threonine contains two chiral stereocenters and is written (2''S'',3''S'')-threonine. There is no strict relationship between the R/S, the
D/
L, and (+)/(−) designations, although some correlations exist. For example, of the naturally occurring amino acids, all are
L, and most are (''S''). For some molecules the (''R'')-enantiomer is the dextrorotary (+) enantiomer, and in other cases it is the laevorotary (−) enantiomer. The relationship must be determined on a case-by-case basis with experimental measurements or detailed computer modeling.
[See, for example,]
History
The rotation of the orientation of
linearly polarized light was first observed in 1811 in
quartz
Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical form ...
by French physicist
François Arago
Dominique François Jean Arago ( ca, Domènec Francesc Joan Aragó), known simply as François Arago (; Catalan: ''Francesc Aragó'', ; 26 February 17862 October 1853), was a French mathematician, physicist, astronomer, freemason, supporter of t ...
. In 1820, the English astronomer
Sir John F.W. Herschel discovered that different individual quartz crystals, whose crystalline structures are mirror images of each other (see illustration), rotate linear polarization by equal amounts but in opposite directions.
Jean Baptiste Biot
Jean-Baptiste Biot (; ; 21 April 1774 – 3 February 1862) was a French physicist, astronomer, and mathematician who co-discovered the Biot–Savart law of magnetostatics with Félix Savart, established the reality of meteorites, made an early b ...
also observed the rotation of the axis of polarization in certain liquids and vapors of organic substances such as
turpentine
Turpentine (which is also called spirit of turpentine, oil of turpentine, terebenthene, terebinthine and (colloquially) turps) is a fluid obtained by the distillation of resin harvested from living trees, mainly pines. Mainly used as a special ...
. In 1822,
Augustin-Jean Fresnel
Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Isaac Newton, Newton's co ...
found that optical rotation could be explained as a species of
birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
: whereas previously known cases of birefringence were due to the different speeds of light polarized in two perpendicular planes, optical rotation was due to the different speeds of right-hand and left-hand circularly polarized light.
[A. Fresnel, "Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant les directions parallèles à l'axe", read 9 December 1822; printed in H. de Senarmont, E. Verdet, and L. Fresnel (eds.), ''Oeuvres complètes d'Augustin Fresnel'', vol. 1 (1866), pp.731–51; translated as "Memoir on the double refraction that light rays undergo in traversing the needles of quartz in the directions parallel to the axis", , 2021 (open access); especially §13.] Simple
polarimeter
A polarimeter is a scientific instrument used to measure the angle of rotation caused by passing polarized light through an optically active substance.[glucose
Glucose is a simple sugar with the molecular formula . Glucose is overall the most abundant monosaccharide, a subcategory of carbohydrates. Glucose is mainly made by plants and most algae during photosynthesis from water and carbon dioxide, using ...]
, in solution. In fact one name for
D-glucose (the biological isomer), is ''dextrose'', referring to the fact that it causes linearly polarized light to rotate to the right or
dexter
Dexter may refer to:
Arts and entertainment
* Dexter, the main character of the American animated series ''Dexter's Laboratory'' that aired from 1996 to 2003
* Dexter, a fictional character in the British Diary of a Bad Man#Main, web series ''Diar ...
side. In a similar manner, levulose, more commonly known as
fructose
Fructose, or fruit sugar, is a Ketose, ketonic monosaccharide, simple sugar found in many plants, where it is often bonded to glucose to form the disaccharide sucrose. It is one of the three dietary monosaccharides, along with glucose and galacto ...
, causes the
plane of polarization
The term ''plane of polarization'' refers to the direction of polarization of '' linearly-polarized'' light or other electromagnetic radiation. Unfortunately the term is used with two contradictory meanings. As originally defined by Étienne-Lou ...
to rotate to the left. Fructose is even more strongly levorotatory than glucose is dextrorotatory.
Invert sugar syrup, commercially formed by the
hydrolysis
Hydrolysis (; ) is any chemical reaction in which a molecule of water breaks one or more chemical bonds. The term is used broadly for substitution reaction, substitution, elimination reaction, elimination, and solvation reactions in which water ...
of
sucrose
Sucrose, a disaccharide, is a sugar composed of glucose and fructose subunits. It is produced naturally in plants and is the main constituent of white sugar. It has the molecular formula .
For human consumption, sucrose is extracted and refined ...
syrup to a mixture of the component simple sugars, fructose, and glucose, gets its name from the fact that the conversion causes the direction of rotation to "invert" from right to left.
In 1849,
Louis Pasteur
Louis Pasteur (, ; 27 December 1822 – 28 September 1895) was a French chemist and microbiologist renowned for his discoveries of the principles of vaccination, microbial fermentation and pasteurization, the latter of which was named afte ...
resolved a problem concerning the nature of
tartaric acid
Tartaric acid is a white, crystalline organic acid that occurs naturally in many fruits, most notably in grapes, but also in bananas, tamarinds, and citrus. Its salt, potassium bitartrate, commonly known as cream of tartar, develops naturally i ...
. A solution of this compound derived from living things (to be specific,
wine lees) rotates the plane of
polarization of light passing through it, but tartaric acid derived by
chemical synthesis
As a topic of chemistry, chemical synthesis (or combination) is the artificial execution of chemical reactions to obtain one or several products. This occurs by physical and chemical manipulations usually involving one or more reactions. In moder ...
has no such effect, even though its reactions are identical and its elemental composition is the same. Pasteur noticed that the crystals come in two asymmetric forms that are mirror images of one another. Sorting the crystals by hand gave two forms of the compound: Solutions of one form rotate polarized light clockwise, while the other form rotate light counterclockwise. An equal mix of the two has no polarizing effect on light. Pasteur deduced that the molecule in question is asymmetric and could exist in two different forms that resemble one another as would left- and right-hand gloves, and that the organic form of the compound consists of purely the one type.
In 1874,
Jacobus Henricus van 't Hoff and
Joseph Achille Le Bel
Joseph Achille Le Bel (21 January 1847 in Pechelbronn – 6 August 1930, in Paris, France) was a French chemist. He is best known for his work in stereochemistry. Le Bel was educated at the École Polytechnique in Paris. In 1874 he announced his ...
independently proposed that this phenomenon of optical activity in carbon compounds could be explained by assuming that the 4 saturated chemical bonds between carbon atoms and their neighbors are directed towards the corners of a regular tetrahedron. If the 4 neighbors are all different, then there are two possible orderings of the neighbors around the tetrahedron, which will be mirror images of each other. This led to a better understanding of the three-dimensional nature of molecules.
In 1945, Charles William Bunn predicted optical activity of achiral structures, if the wave's propagation direction and the achiral structure form an experimental arrangement that is different from its mirror image. Such optical activity due to
extrinsic chirality was observed in the 1960s in liquid crystals.
In 1950,
Sergey Vavilov predicted optical activity that depends on the intensity of light and the effect of nonlinear optical activity was observed in 1979 in
lithium iodate
Lithium iodate (LiIO3) is a negative uniaxial crystal for nonlinear, acousto-optical and piezoelectric applications. It has been utilized for 347 nm ruby lasers.
Properties
Mohs hardness of lithium iodate is 3.5–4. Its linear thermal expan ...
crystals.
Optical activity is normally observed for transmitted light. However, in 1988, M. P. Silverman discovered that polarization rotation can also occur for light reflected from chiral substances. Shortly after, it was observed that chiral media can also reflect left-handed and right-handed circularly polarized waves with different efficiencies. These phenomena of specular circular birefringence and specular circular dichroism are jointly known as specular optical activity. Specular optical activity is very weak in natural materials.
In 1898
Jagadish Chandra Bose
Sir Jagadish Chandra Bose
(;, ; 30 November 1858 – 23 November 1937) was a biologist, physicist, Botany, botanist and an early writer of science fiction. He was a pioneer in the investigation of radio microwave optics, made significant contr ...
described the ability of twisted artificial structures to rotate the polarization of
microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
s. Since the early 21st century, the development of artificial materials has led to the prediction and realization of chiral metamaterials with optical activity exceeding that of natural media by orders of magnitude in the optical part of the spectrum. Extrinsic chirality associated with oblique illumination of metasurfaces lacking two-fold rotational symmetry has been observed to lead to large linear optical activity in transmission and reflection, as well as nonlinear optical activity exceeding that of lithium iodate by 30 million times.
Theory
Optical activity occurs due to molecules dissolved in a fluid or due to the fluid itself only if the molecules are one of two (or more)
stereoisomer
In stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in ...
s; this is known as an
enantiomer
In chemistry, an enantiomer ( /ɪˈnænti.əmər, ɛ-, -oʊ-/ ''ih-NAN-tee-ə-mər''; from Ancient Greek ἐνάντιος ''(enántios)'' 'opposite', and μέρος ''(méros)'' 'part') – also called optical isomer, antipode, or optical ant ...
. The structure of such a molecule is such that it is ''not'' identical to its
mirror image
A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface. As an optical effect it results from reflection off from substances ...
(which would be that of a different stereoisomer, or the "opposite enantiomer"). In mathematics, this property is also known as
chirality
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...
. For instance, a metal rod is ''not'' chiral, since its appearance in a mirror is not distinct from itself. However a screw or light bulb base (or any sort of
helix
A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, ...
) ''is'' chiral; an ordinary right-handed screw thread, viewed in a mirror, would appear as a left-handed screw (very uncommon) which could not possibly screw into an ordinary (right-handed) nut. A human viewed in a mirror would have their heart on the right side, clear evidence of chirality, whereas the mirror reflection of a doll might well be indistinguishable from the doll itself.
In order to display optical activity, a fluid must contain only one, or a preponderance of one, stereoisomer. If two enantiomers are present in equal proportions then their effects cancel out and no optical activity is observed; this is termed a
racemic
In chemistry, a racemic mixture, or racemate (), is one that has equal amounts of left- and right-handed enantiomers of a chiral molecule or salt. Racemic mixtures are rare in nature, but many compounds are produced industrially as racemates. ...
mixture. But when there is an
enantiomeric excess
In stereochemistry, enantiomeric excess (ee) is a measurement of purity used for chiral substances. It reflects the degree to which a sample contains one enantiomer in greater amounts than the other. A racemic mixture has an ee of 0%, while a sin ...
, more of one enantiomer than the other, the cancellation is incomplete and optical activity is observed. Many naturally occurring molecules are present as only one enantiomer (such as many sugars). Chiral molecules produced within the fields of
organic chemistry
Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; ...
or
inorganic chemistry
Inorganic chemistry deals with synthesis and behavior of inorganic and organometallic compounds. This field covers chemical compounds that are not carbon-based, which are the subjects of organic chemistry. The distinction between the two disci ...
are racemic unless a chiral reagent was employed in the same reaction.
At the fundamental level, polarization rotation in an optically active medium is caused by circular birefringence, and can best be understood in that way. Whereas
linear birefringence in a crystal involves a small difference in the
phase velocity
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...
of light of two different linear polarizations, circular birefringence implies a small difference in the velocities between right and left-handed ''
circular polarization
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 t ...
s''.
Think of one enantiomer in a solution as a large number of little helices (or screws), all right-handed, but in random orientations. Birefringence of this sort is possible even in a fluid because the handedness of the helices is not dependent on their orientation: even when the direction of one helix is reversed, it still appears right handed. And circularly polarized light itself is chiral: as the wave proceeds in one direction the electric (and magnetic) fields composing it are rotating clockwise (or counterclockwise for the opposite circular polarization), tracing out a right (or left) handed screw pattern in space. In addition to the bulk
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
which substantially lowers the phase velocity of light in any dielectric (transparent) material compared to the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
(in vacuum), ''there is an additional interaction between the chirality of the wave and the chirality of the molecules.'' Where their chiralities are the same, there will be a small additional effect on the wave's velocity, but the opposite circular polarization will experience an opposite small effect as its chirality is opposite that of the molecules.
Unlike linear birefringence, however, natural optical rotation (in the absence of a magnetic field) cannot be explained in terms of a local material
permittivity
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
tensor (i.e., a charge response that only depends on the local electric field vector), as symmetry considerations forbid this. Rather, circular birefringence only appears when considering nonlocality of the material response, a phenomenon known as
spatial dispersion In the physics of continuous media, spatial dispersion is a phenomenon where material parameters such as permittivity or conductivity have dependence on wavevector. Normally, such a dependence is assumed to be absent for simplicity, however spatial ...
.
Nonlocality means that electric fields in one location of the material drive currents in another location of the material. Light travels at a finite speed, and even though it is much faster than the electrons, it makes a difference whether the charge response naturally wants to travel along with the electromagnetic wavefront, or opposite to it. Spatial dispersion means that light travelling in different directions (different wavevectors) sees a slightly different permittivity tensor. Natural optical rotation requires a special material, but it also relies on the fact that the wavevector of light is nonzero, and a nonzero wavevector bypasses the symmetry restrictions on the local (zero-wavevector) response. However, there is still reversal symmetry, which is why the direction of natural optical rotation must be 'reversed' when the direction of the light is reversed, in contrast to magnetic
Faraday rotation
The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the ...
. All optical phenomena have some nonlocality/wavevector influence but it is usually negligible; natural optical rotation, rather uniquely, absolutely requires it.
The phase velocity of light in a medium is commonly expressed using the
index of refraction
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
''n'', defined as the speed of light (in free space) divided by its speed in the medium. The difference in the refractive indices between the two circular polarizations quantifies the strength of the circular birefringence (polarization rotation),
:
.
While
is small in natural materials, examples of giant circular birefringence resulting in a negative refractive index for one circular polarization have been reported for chiral metamaterials.
The familiar rotation of the axis of ''linear'' polarization relies on the understanding that a linearly polarized wave can as well be described as the
superposition (addition) of a left and right circularly polarized wave in equal proportion. The phase difference between these two waves is dependent on the orientation of the linear polarization which we'll call
, and their electric fields have a relative phase difference of
which then add to produce linear polarization:
:
where
is the
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
of the net wave, while
and
are the two circularly polarized
basis functions
In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be repres ...
(having zero phase difference). Assuming propagation in the ''+z'' direction, we could write
and
in terms of their ''x'' and ''y'' components as follows:
:
:
where
and
are unit vectors, and ''i'' is the
imaginary unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...
, in this case representing the 90 degree phase shift between the ''x'' and ''y'' components that we have decomposed each circular polarization into. As usual when dealing with
phasor
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude (''A''), angular frequency (''ω''), and initial phase (''θ'') are time-invariant. It is related to ...
notation, it is understood that such quantities are to be multiplied by
and then the actual electric field at any instant is given by the ''real part'' of that product.
Substituting these expressions for
and
into the equation for
we obtain:
:
::
::
The last equation shows that the resulting vector has the ''x'' and ''y'' components in phase and oriented exactly in the
direction, as we had intended, justifying the representation of any linearly polarized state at angle
as the superposition of right and left circularly polarized components with a relative phase difference of
. Now let us assume transmission through an optically active material which induces an additional phase difference between the right and left circularly polarized waves of
. Let us call
the result of passing the original wave linearly polarized at angle
through this medium. This will apply additional phase factors of
and
to the right and left circularly polarized components of
:
:
Using similar math as above we find:
:
thus describing a wave linearly polarized at angle
, thus rotated by
relative to the incoming wave:
We defined above the difference in the refractive indices for right and left circularly polarized waves of
. Considering propagation through a length ''L'' in such a material, there will be an additional phase difference induced between them of
(as we used above) given by:
:
,
where
is the wavelength of the light (in vacuum). This will cause a rotation of the linear axis of polarization by
as we have shown.
In general, the refractive index depends on wavelength (see
dispersion
Dispersion may refer to:
Economics and finance
*Dispersion (finance), a measure for the statistical distribution of portfolio returns
*Price dispersion, a variation in prices across sellers of the same item
*Wage dispersion, the amount of variatio ...
) and the differential refractive index
will also be wavelength dependent. The resulting variation in rotation with the wavelength of the light is called
optical rotatory dispersion
Optical rotatory dispersion is the variation in the optical rotation of a substance with a change in the wavelength of light. Optical rotatory dispersion can be used to find the absolute configuration of metal complexes. For example, when plane-pol ...
(ORD). ORD spectra and
circular dichroism spectra are related through the
Kramers–Kronig relations. Complete knowledge of one spectrum allows the calculation of the other.
So we find that the degree of rotation depends on the color of the light (the yellow sodium D line near 589 nm
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
is commonly used for measurements), and is directly proportional to the path length
through the substance and the amount of circular birefringence of the material
which, for a solution, may be computed from the substance's
specific rotation
In chemistry, specific rotation ( '') is a property of a chiral chemical compound. It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance–concentration product, as the light passes through a sampl ...
and its concentration in solution.
Although optical activity is normally thought of as a property of fluids, particularly
aqueous solutions
An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be rep ...
, it has also been observed in crystals such as
quartz
Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical form ...
(SiO
2). Although quartz has a substantial linear birefringence, that effect is cancelled when propagation is along the
optic axis
An optical axis is a line along which there is some degree of rotational symmetry in an optics, optical system such as a camera lens, microscope or telescopic sight.
The optical axis is an imaginary line that defines the path along which light ...
. In that case, rotation of the plane of polarization is observed due to the relative rotation between crystal planes, thus making the crystal formally chiral as we have defined it above. The rotation of the crystal planes can be right or left-handed, again producing opposite optical activities. On the other hand,
amorphous
In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal.
Etymology
The term comes from the Greek ''a'' ("wi ...
forms of
silica
Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is one ...
such as
fused quartz
Fused quartz, fused silica or quartz glass is a glass consisting of almost pure silica (silicon dioxide, SiO2) in amorphous (non-crystalline) form. This differs from all other commercial glasses in which other ingredients are added which change ...
, like a racemic mixture of chiral molecules, has no net optical activity since one or the other crystal structure does not dominate the substance's internal molecular structure.
Applications
For a pure substance in solution, if the color and path length are fixed and the
specific rotation
In chemistry, specific rotation ( '') is a property of a chiral chemical compound. It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance–concentration product, as the light passes through a sampl ...
is known, the observed rotation can be used to calculate the concentration. This usage makes a
polarimeter
A polarimeter is a scientific instrument used to measure the angle of rotation caused by passing polarized light through an optically active substance.[plane of polarization
The term ''plane of polarization'' refers to the direction of polarization of '' linearly-polarized'' light or other electromagnetic radiation. Unfortunately the term is used with two contradictory meanings. As originally defined by Étienne-Lou ...]
may also occur through the
Faraday effect
The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the m ...
which involves a static
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
. However, this is a distinct phenomenon that is not classified as "optical activity." Optical activity is reciprocal, i.e. it is the same for opposite directions of wave propagation through an optically active medium, for example clockwise polarization rotation from the point of view of an observer. In case of optically active isotropic media, the rotation is the same for any direction of wave propagation. In contrast, the Faraday effect is non-reciprocal, i.e opposite directions of wave propagation through a Faraday medium will result in clockwise and anti-clockwise polarization rotation from the point of view of an observer. Faraday rotation depends on the propagation direction relative to that of the applied magnetic field. All compounds can exhibit polarization rotation in the presence of an applied magnetic field, provided that (a component of) the magnetic field is oriented in the direction of light propagation. The Faraday effect is one of the first discoveries of the relationship between light and electromagnetic effects.
See also
*
Cryptochirality In stereochemistry, cryptochirality is a special case of chirality in which a molecule is chiral but its specific rotation is non-measurable. The underlying reason for the lack of rotation is the specific electronic properties of the molecule. The t ...
*
Specific rotation
In chemistry, specific rotation ( '') is a property of a chiral chemical compound. It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance–concentration product, as the light passes through a sampl ...
*
Circular dichroism
*
Birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...
*
Geometric phase In classical and quantum mechanics, geometric phase is a phase difference acquired over the course of a cycle, when a system is subjected to cyclic adiabatic processes, which results from the geometrical properties of the parameter space of the Ha ...
*
Polarization
*
Levorotation and dextrorotation
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. Circul ...
*
Chirality (chemistry)
In chemistry, a molecule or ion is called chiral () if it cannot be superposed on its mirror image by any combination of rotation (geometry), rotations, translation (geometry), translations, and some Conformational isomerism, conformational ch ...
*
Chirality (electromagnetism)
300px, The direction of current flow and induced magnetic flux follow a "handness" relationship
The term chiral describes an object, especially a molecule, which has or produces a non-superposable mirror image of itself. In chemistry, such a m ...
*
Polarization rotator
A polarization rotator is an optical device that rotates the polarization axis of a linearly polarized light beam by an angle of choice. Such devices can be based on the Faraday effect, on birefringence, or on total internal reflection. F. J. ...
*
Hyper Rayleigh Scattering Optical Activity
*
Raman optical activity
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.
History of Raman optical activity
...
(ROA)
References
Further reading
* Eugene Hecht, ''Optics'', 3rd Ed., Addison-Wesley, 1998,
*
Akhlesh Lakhtakia
Akhlesh Lakhtakia is Evan Pugh University Professor and Charles Godfrey Binder Professor of engineering science and mechanics at the Pennsylvania State University. His research focuses on electromagnetic fields in complex materials, such as scul ...
Beltrami Fields in Chiral Media World Scientific, Singapore, 1994
* A step by step tutorial o
* Morrison. Robert. T, and Boyd. Robert. N, "Organic Chemistry (6th ed)". Prentice-Hall Inc (1992).
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Polarization (waves)
Stereochemistry