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Optical Activity

Definition: the ability of a transparent substance to exhibit polarization rotation or circular dichroism

German: optische Aktivität

Category: general optics

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Optical activity is the ability of a substance to cause optical rotation or circular dichroism:

  • Optical rotation is the phenomenon that the polarization direction of light is gradually rotated clockwise (dextrorotary) or anti-clockwise (levorotary) when linearly polarized light passes through certain transparent substances. It is related to circular birefringence, as explained below.
  • Circular dichroism is a difference in optical absorption coefficients for different circular polarization directions.

There are also related phenomena of polarization-dependent reflectance and various nonlinear effects. Optical activity can also occur in the area of terahertz radiation [7].

Note that because optical activity is a principal ability of a substance to exhibit such effects, it does not depend on the presence of polarized light, i.e., on the actual occurrence of optical rotation or polarization-dependent absorption. In other words, a substance can be optically active even when being in the dark.

Causes of Optical Activity

For reasons of symmetry, optical rotation can not occur in many situations – essentially because there is nothing which could favor a rotation of the polarization to the left against a rotation to the right, for example. A typical situation, however, where such symmetry is broken, is a medium containing molecules with a structure such that the mirror image of that structure is not identical to the original structure. Such molecules are called chiral; for each of them, two different versions (called enantiomers, or more generally stereoisomers) exist. The simplest situation to imagine would be molecules in the form of a helix, wound in a certain direction.

One may then expect that the chiral symmetry could effectively be restored by a random orientation of such molecules, but this is not the case; for example, a left-handed helical molecule rotated by 180° stays left-handed, i.e., interacts with light in the same way as for the original orientation.

Note that optical rotation can still not be observed in a liquid containing such molecules, if the left-handed and right-handed form occur with the same density (racemic mixture). That is often the case in synthetically fabricated substances, while living organisms often produce only one form of a molecule. The earliest finding in this context was that of Louis Pasteuer in 1849 [1]. He observed that natural tartaric acid causes optical rotation, while chemically synthesized tartaric acid does not. He then also discovered that single crystals of tartaric acid come in two different shapes, one being the mirror image of the other one, and that finally led to the finding that tartaric acid consists of chiral molecules. It was later found that such chiral asymmetries are actually quite common in the living world, e.g. in sugars like natural sucrose (ordinary sugar), which contains only the dextrorotary version. That striking asymmetry is related to the fact that biological organisms producing sugar have the same kind of asymmetry for a number of other types of important molecules, and that the relative chirality of molecules can substantially influence their chemical reaction dynamics, although different enantiomers otherwise exhibit the exactly same chemical behavior.

Interestingly, optical activity is not found in physical models exhibiting the basic property of locality. Optical activity is related to a nonlocal material response, where the polarization at one location depends on the electric field at slightly different locations.

Optical activity can also occur in crystalline materials, where chirality arises from the lattice structure. For example, α-quartz is unidirectionally birefringent, thus has no linear birefringence for light propagating along its optical axis, and yet exhibits optical rotation. (The same effect is observed in various other birefringent crystal materials, e.g. in calcite.) This can be interpreted as resulting from the periodic repetition of three different crystal planes. A detailed analysis, however, is quite complicated [2].

Strong optical activity can also obtained in suitably constructed photonic metamaterials [8].

While optical activity is usually related to naturally chiral substances, as explained above, polarization rotation can also be obtained by exposing some substances to a magnetic field. That is called the Faraday effect, which is exploited particularly in Faraday rotators and Faraday isolators. The Faraday effect may be called a magnetically induced optical rotation, although it is not common to call this optical activity, which is a property of a medium.

Circular Birefringence

One can also describe optical activity as a difference of the velocity of light (phase velocity) between two opposite rotation directions of circularly polarized light. That property of the medium is called circular birefringence.

Linearly polarized light can be considered as a superposition of circularly polarized light in both directions with equal amplitudes. During propagation in a circularly birefringent medium, one obtains a linearly increasing phase shift between the two circularly polarized components. That phase shift then leads to a change of linear polarization direction. Therefore, circular birefringence is directly related to optical rotation; it is not possible to have circular birefringence but no optical rotation, and optical activity implies both.

The amount of polarization rotation can quite easily be calculated when the refractive index difference related to the circular birefringence is known; the resulting formula is the following:

optical rotation

where L is the length of the medium and λ is the vacuum wavelength.

There are also media where Raman scattering intensities differ between left and right polarized light; this phenomenon is called Raman optical activity in analogy to ordinary optical activity. A more general term, also comprising vibrational circular dichroism, is vibrational optical activity [6].

Measurement of Optical Activity

The magnitude of optical activity (called optical rotatory power) can be measured with a polarimeter, for example in sugar solutions. It generally depends not only on the concentration of chiral molecules, but also on wavelength, temperature and the used solvent.

While the basic measurement principle is rather old, these instruments have been substantially revised over the years and now allow for highly accurate measurements. There are even automated polarimeters which are for the combination of convenience, high speed and high accuracy.

Nonlinear Polarization Rotation

The polarization state of light can also undergo changes for nonlinear propagation in birefringent media. This is often called nonlinear polarization rotation, although in that case one cannot generally assume that a linear polarization direction is maintained. Only, the polarization state may be changed such that optimum transmission through a linear polarizer is obtained for different orientation of the polarizer then it would be for linear (low-intensity) propagation.

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Bibliography

[1]L. Pasteur, “Recherches sur les propriétés spécifiques des deux acides qui composent l'acide racémique” (Researches on the specific properties of the two acids that compose the racemic acid), Annales de chimie et de physique, 3rd series, 28, 56 (1850)
[2]S. Chandrasekhar, “Theoretical interpretation of the optical activity of quartz” (1953), https://www.ias.ac.in/public/Volumes/seca/037/03/0468-0484.pdf
[3]D. Eimerl, “Quantum electrodynamics of optical activity in birefringent crystals”, J. Opt. Soc. Am. B 5 (7), 1453 (1988), doi:10.1364/JOSAB.5.001453
[4]D. F. Nelson, “Mechanisms and dispersion of crystalline optical activity”, J. Opt. Soc. Am. B 6 (6), 1110 (1989), doi:10.1364/JOSAB.6.001110
[5]I. J. Tebbutt, “Effect of optical activity on type-I and type-II phase matching in second-harmonic generation”, Appl. Opt. 31 (27), 5810 (1992), doi:10.1364/AO.31.005810
[6]L. A. Nafie, “Vibrational optical activity”, Appl. Spectroscopy 50 (5), 14A (1996)
[7]F. Hache and G: Gallo, “Optical activity of metallic helices in the terahertz domain: a theoretical investigation”, J. Opt. Soc. Am. B 29 (10), 2675 (2012), doi:10.1364/JOSAB.29.002675
[8]J. Kaschke, J. K. Gansel and M. Wegener, “On metamaterial circular polarizers based on metal N-helices”, Opt. Express 20 (23), 26012 (2012), doi:10.1364/OE.20.026012

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See also: polarization of light, Faraday rotators, polarimeters
and other articles in the category general optics

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