3068:. 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.
739:. 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
714:. 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
486:
27:
636:. 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.
474:
590:
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.
3020:. 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,
2514:
601:
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
624:
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
676:
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
589:
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
1058:
1809:
3426:
A. Fresnel, "Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant les directions parallÚles à l'axe", read 9 December 1822; printed in H. de
Senarmont, E. Verdet, and L. Fresnel (eds.),
1986:
2647:
3389:
Biot (1818 & 1819) "Extrait d'un mémoire sur les rotations que certaines substances impriment aux axes de polarisation des rayons lumineux" (Extract from a memoir on the rotations that certain substances impress on the axes of polarization of light rays),
734:
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
680:
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
689:, 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
605:
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
2341:
753:, 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),
526:: 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. Simple
625:
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.
726:
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.
3217:
465:)-enantiomer is the dextrorotary (+) enantiomer, and in other cases it is the levorotary (â) enantiomer. The relationship must be determined on a case-by-case basis with experimental measurements or detailed computer modeling.
185:-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.
1435:
1346:
3633:
Silverman, M.; Ritchie, N.; Cushman, G.; Fisher, B. (1988). "Experimental configurations using optical phase modulation to measure chiral asymmetries in light specularly reflected from a naturally gyrotropic medium".
2084:
919:
1673:
367:-form by definition. The prefix used to indicate absolute configuration is not directly related to the (+) or (â) prefix used to indicate optical rotation in the same molecule. For example, nine of the nineteen
2856:
509:
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.
3205:
1819:
856:(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
602:
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.
2525:
3431:, vol. 1 (1866), pp. 731â751; translated as "Memoir on the double refraction that light rays undergo in traversing the needles of quartz in the directions parallel to the axis",
845:
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.
3790:
Kuwata-Gonokami, M.; Saito, N.; Ino, Y.; Kauranen, M.; Jefimovs, K.; Vallius, T.; Turunen, J.; Svirko, Y. (2005). "Giant
Optical Activity in Quasi-Two-Dimensional Planar Nanostructures".
566:
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.
2745:
2686:
2333:
1665:
1097:
816:
3337:"Mémoire sur une modification remarquable qu'éprouvent les rayons lumineux dans leur passage à travers certains corps diaphanes et sur quelques autres nouveaux phénomÚnes d'optique"
3301:
Stephens, P. J.; Devlin, F. J.; Cheeseman, J. R.; Frisch, M. J.; Bortolini, O.; Besse, P. (2003). "Determination of absolute configuration using calculation of optical rotation".
3032:, 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.
2228:
1629:
1594:
1249:
1214:
1171:
1136:
2800:
2274:
2193:
3252:
2903:
2709:
2509:{\displaystyle \mathbf {E} _{out}={\frac {\sqrt {2}}{2}}(e^{-i\Delta \theta }e^{-i\theta _{0}}\mathbf {E} _{RHC}+e^{i\Delta \theta }e^{i\theta _{0}}\mathbf {E} _{LHC})\,\,.}
2297:
1552:
2169:. 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
911:
2124:
881:
3354:"On the rotation impressed by plates of rock crystal on the planes of polarization of the rays of light, as connected with certain peculiarities in its crystallization,"
1496:
1467:
2995:
2933:
2880:
2770:
2167:
843:
3339:(Memoir on a remarkable modification that light rays experience during their passage through certain translucent substances and on some other new optical phenomena),
2248:
2144:
743:. All optical phenomena have some nonlocality/wavevector influence but it is usually negligible; natural optical rotation, rather uniquely, absolutely requires it.
4359:
700:
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
2972:
285:(geometric mirror image) will be laevorotary, and vice versa. Enantiomers rotate plane-polarized light the same number of degrees, but in opposite directions.
4364:
1354:
1265:
730:
Unlike linear birefringence, however, natural optical rotation (in the absence of a magnetic field) cannot be explained in terms of a local material
708:
of light of two different linear polarizations, circular birefringence implies a small difference in the velocities between right and left-handed
4225:
1998:
1053:{\displaystyle \mathbf {E} _{\theta _{0}}={\frac {\sqrt {2}}{2}}(e^{-i\theta _{0}}\mathbf {E} _{RHC}+e^{i\theta _{0}}\mathbf {E} _{LHC})\,\,,}
1804:{\displaystyle \mathbf {E} _{\theta _{0}}={\frac {\sqrt {2}}{2}}(e^{-i\theta _{0}}\mathbf {E} _{RHC}+e^{i\theta _{0}}\mathbf {E} _{LHC})\,\,}
3833:
Plum, E.; Fedotov, V. A.; Schwanecke, A. S.; Zheludev, N. I.; Chen, Y. (2007). "Giant optical gyrotropy due to electromagnetic coupling".
2808:
644:
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)
3123:
617:
predicted optical activity that depends on the intensity of light and the effect of nonlinear optical activity was observed in 1979 in
3614:
Akhmanov, S. A.; Zhdanov, B. V.; Zheludev, N. I.; Kovrigin, A. I.; Kuznetsov, V. I. (1979). "Nonlinear optical activity in crystals".
407:
418:
with the molecule, rather than a property of the molecule as a whole. A molecule having exactly one chiral stereocenter (usually an
3229:
1981:{\displaystyle ={\frac {1}{2}}({\hat {x}}(e^{-i\theta _{0}}+e^{i\theta _{0}})+{\hat {y}}i(e^{-i\theta _{0}}-e^{i\theta _{0}}))\,\,}
607:
3270:
3494:"Sur les relations qui existent entre les formules atomiques des corps organiques et le pouvoir rotatoire de leurs dissolutions"
660:(which would be that of a different stereoisomer, or the "opposite enantiomer"). In mathematics, this property is also known as
4054:
3496:(On the relations that exist between the atomic formulas of organic substances and the rotatory power of their solutions),
453:, and (+)/(â) designations, although some correlations exist. For example, of the naturally occurring amino acids, all are
4120:
Zhang, S.; Park, Y.-S.; Li, J.; Lu, X.; Zhang, W.; Zhang, X. (2009). "Negative
Refractive Index in Chiral Metamaterials".
3564:
R. Williams (1969). "Optical-rotary power and linear electro-optic effect in nematic liquid crystals of p-azoxyanisole".
668:
chiral, since its appearance in a mirror is not distinct from itself. However a screw or light bulb base (or any sort of
2642:{\displaystyle \mathbf {E} _{out}={\hat {x}}\cos(\theta _{0}+\Delta \theta )+{\hat {y}}\sin(\theta _{0}+\Delta \theta )}
4218:
3929:
4175:
3284:
3246:
2950:
So we find that the degree of rotation depends on the color of the light (the yellow sodium D line near 589 nm
398:- prefixes describe the molecule as a whole, as do the (+) and (â) prefixes for optical rotation. In contrast, the (
4397:
3755:
Svirko, Y.; Zheludev, N. I.; Osipov, M. (2001). "Layered chiral metallic microstructures with inductive coupling".
3712:
Bose, Jagadis
Chunder (1898). "On the Rotation of Plane of Polarisation of Electric Waves by a Twisted Structure".
514:
also observed the rotation of the axis of polarization in certain liquids and vapors of organic substances such as
3016:). Although quartz has a substantial linear birefringence, that effect is cancelled when propagation is along the
2935:
will also be wavelength dependent. The resulting variation in rotation with the wavelength of the light is called
594:
430:), but a molecule having multiple stereocenters needs more than one label. For example, the essential amino acid
119:
2714:
2655:
2302:
1634:
1066:
759:
718:
which substantially lowers the phase velocity of light in any dielectric (transparent) material compared to the
4459:
4382:
4211:
3472:
2882:
is the wavelength of the light (in vacuum). This will cause a rotation of the linear axis of polarization by
200:
of chiral molecules in solution. Modulation of a liquid crystal's optical activity, viewed between two sheet
3407:
3353:
4392:
3113:
2749:
We defined above the difference in the refractive indices for right and left circularly polarized waves of
2146:
as the superposition of right and left circularly polarized components with a relative phase difference of
137:
When looking at the source of light, the rotation of the plane of polarization may be either to the right (
3669:
Silverman, M.; Badoz, J.; Briat, B. (1992). "Chiral reflection from a naturally optically active medium".
3336:
2944:
2936:
2198:
1599:
1564:
1219:
1184:
1141:
1106:
852:
polarization relies on the understanding that a linearly polarized wave can as well be described as the
724:
there is an additional interaction between the chirality of the wave and the chirality of the molecules.
196:
to measure the sugar concentration of syrup, and generally in chemistry to measure the concentration or
4235:
3276:
20:
2126:
direction, as we had intended, justifying the representation of any linearly polarized state at angle
122:. It can also be observed in chiral solids such as certain crystals with a rotation between adjacent
4354:
4070:
Plum, E.; Zhou, J.; Dong, J.; Fedotov, V. A.; Koschny, T.; Soukoulis, C. M.; Zheludev, N. I. (2009).
3493:
3399:
2779:
2253:
2172:
3451:
2885:
2691:
2279:
1521:
4464:
4280:
3373:
554:
to rotate to the left. Fructose is even more strongly levorotatory than glucose is dextrorotatory.
485:
886:
3017:
2102:
859:
853:
3199:
1472:
1443:
3193:
3128:
3044:
is known, the observed rotation can be used to calculate the concentration. This usage makes a
1514:
components that we have decomposed each circular polarization into. As usual when dealing with
1174:
411:
356:
300:
205:
3341:
Mémoires de la classe des sciences mathématiques et physiques de l'Institut Impérial de France
2977:
2915:
2865:
2752:
2149:
825:
4418:
4332:
4249:
4184:
4046:
3529:
R. Williams (1968). "Optical
Rotatory Effect in the Nematic Liquid Phase of p-Azoxyanisole".
3108:
3057:
2233:
2129:
710:
629:
598:
551:
519:
294:
278:
243:
111:
4428:
4413:
4264:
4129:
4086:
3991:
3944:
3894:
3842:
3799:
3764:
3678:
3643:
3573:
3538:
3452:"Recherches sur les propriétés spécifiques des deux acides qui composent l'acide racémique"
3118:
3103:
582:
555:
281:
molecules and are said to have optical activity. If a chiral molecule is dextrorotary, its
201:
83:
4191:
542:, referring to the fact that it causes linearly polarized light to rotate to the right or
8:
4326:
4203:
2909:
2776:
in such a material, there will be an additional phase difference induced between them of
747:
694:
686:
578:
494:
115:
87:
16:
Rotation of the plane of linearly polarized light as it travels through a chiral material
4133:
4090:
3995:
3948:
3898:
3846:
3803:
3768:
3682:
3647:
3577:
3542:
3454:(Researches on the specific properties of the two acids that compose the racemic acid),
4387:
4285:
4102:
3910:
3884:
3737:
3729:
3088:
3004:
Although optical activity is normally thought of as a property of fluids, particularly
2957:
2940:
736:
586:
530:
have been used since this time to measure the concentrations of simple sugars, such as
511:
91:
4374:
4180:
4171:
4145:
4106:
4050:
4009:
3914:
3815:
3694:
3318:
3280:
3242:
3083:
3041:
3005:
2998:
690:
632:
described the ability of twisted artificial structures to rotate the polarization of
419:
348:
258:
3741:
3613:
2954:
is commonly used for measurements), and is directly proportional to the path length
502:
489:
Sucrose solution concentration measuring experiment, demonstrating optical rotation.
4423:
4259:
4141:
4137:
4094:
3999:
3960:
3952:
3902:
3850:
3807:
3772:
3721:
3686:
3651:
3581:
3546:
3310:
740:
715:
44:
3832:
3811:
677:
mirror reflection of a doll might well be indistinguishable from the doll itself.
131:
4433:
4321:
4301:
4275:
4034:
3098:
3078:
3040:
For a pure substance in solution, if the color and path length are fixed and the
1430:{\displaystyle \mathbf {E} _{LHC}={\frac {\sqrt {2}}{2}}({\hat {x}}-i{\hat {y}})}
1341:{\displaystyle \mathbf {E} _{RHC}={\frac {\sqrt {2}}{2}}({\hat {x}}+i{\hat {y}})}
26:
313:-" prefix. Likewise, a levorotary compound may be labeled using the "(â)-" or "
106:
which alter a beam's state of polarization, optical activity can be observed in
4098:
4071:
4038:
3869:
3550:
3156:
3065:
3061:
2974:
through the substance and the amount of circular birefringence of the material
1503:
1100:
719:
705:
618:
614:
360:
217:
193:
3179:
3161:
3048:
a tool of great importance to those trading in or using sugar syrups in bulk.
543:
102:
materials, those lacking microscopic mirror symmetry. Unlike other sources of
4453:
4316:
3093:
701:
574:
570:
523:
506:
478:
103:
4438:
4311:
4254:
4149:
4013:
3819:
3789:
3725:
3698:
3655:
3374:"Phenomene de polarisation successive, observés dans des fluides homogenes"
3322:
3204:. These are used infrequently in English, but sometimes they are, see e.g.
3029:
731:
657:
645:
415:
352:
162:
3151:
2947:. Complete knowledge of one spectrum allows the calculation of the other.
577:. A solution of this compound derived from living things (to be specific,
90:
light as it travels through certain materials. Circular birefringence and
3690:
3632:
3376:(Phenomenon of successive polarization, observed in homogeneous fluids),
3045:
527:
189:
178:
59:
31:
3167:
2079:{\displaystyle ={\hat {x}}\cos(\theta _{0})+{\hat {y}}\sin(\theta _{0})}
1518:
notation, it is understood that such quantities are to be multiplied by
746:
The phase velocity of light in a medium is commonly expressed using the
4306:
4030:
4029:
4004:
3979:
3964:
3314:
2951:
697:
are racemic unless a chiral reagent was employed in the same reaction.
649:
559:
515:
372:
327:
282:
197:
3956:
3906:
3854:
3776:
3733:
3585:
3173:
477:
The two asymmetric crystal forms, dextrorotatory and levorotatory, of
379:- prefix, actually dextrorotary (at a wavelength of 589 nm), and
3021:
661:
633:
431:
235:
3437:
2230:
the result of passing the original wave linearly polarized at angle
547:
384:
161:-rotary, represented by (â), counter-clockwise) depending on which
4069:
3889:
2851:{\displaystyle 2\Delta \theta ={\frac {\Delta nL2\pi }{\lambda }}}
1554:
and then the actual electric field at any instant is given by the
1506:, in this case representing the 90 degree phase shift between the
473:
445:)-threonine. There is no strict relationship between the R/S, the
309:
A compound may be labeled as dextrorotary by using the "(+)-" or "
3927:
3867:
2250:
through this medium. This will apply additional phase factors of
682:
563:
531:
239:
170:
166:
123:
3977:
883:, and their electric fields have a relative phase difference of
3754:
3432:
3025:
3009:
1515:
522:
found that optical rotation could be explained as a species of
498:
304:
127:
99:
3980:"Giant nonlinear optical activity in a plasmonic metamaterial"
3300:
3236:
2997:
which, for a solution, may be computed from the substance's
669:
107:
4119:
2908:
In general, the refractive index depends on wavelength (see
1177:(having zero phase difference). Assuming propagation in the
546:
side. In a similar manner, levulose, more commonly known as
3668:
3378:
Bulletin des
Sciences, par la Société Philomatique de Paris
4233:
2091:
The last equation shows that the resulting vector has the
585:
of light passing through it, but tartaric acid derived by
188:
Optical activity is measured using a polarized source and
3477:
Archives NĂ©erlandaises des
Sciences Exactes et Naturelles
3262:
3230:"Determination of optical rotation and specific rotation"
2299:
to the right and left circularly polarized components of
387:
is sometimes called "levulose" because it is levorotary.
347:-" prefixes are used to specify the enantiomer of chiral
208:(used in most modern televisions and computer monitors).
149:-rotary, represented by (+), clockwise), or to the left (
3870:"Optical activity in extrinsically chiral metamaterial"
652:. The structure of such a molecule is such that it is
2980:
2960:
2918:
2888:
2868:
2811:
2782:
2755:
2717:
2694:
2658:
2528:
2344:
2305:
2282:
2256:
2236:
2201:
2175:
2152:
2132:
2105:
2001:
1822:
1676:
1637:
1602:
1567:
1524:
1475:
1446:
1357:
1268:
1222:
1187:
1144:
1109:
1069:
922:
889:
862:
828:
762:
82:, is the rotation of the orientation of the plane of
325:-" prefixes are obsolete, and are distinct from the
254:
refers to counterclockwise or left-handed rotation.
4072:"Metamaterial with negative index due to chirality"
3978:Ren, M.; Plum, E.; Xu, J.; Zheludev, N. I. (2012).
3930:"Specular optical activity of achiral metasurfaces"
3357:
Transactions of the
Cambridge Philosophical Society
3051:
2652:thus describing a wave linearly polarized at angle
437:
contains two chiral stereocenters and is written (2
3928:Plum, E.; Fedotov, V. A.; Zheludev, N. I. (2016).
3868:Plum, E.; Fedotov, V. A.; Zheludev, N. I. (2008).
2989:
2966:
2927:
2897:
2874:
2850:
2794:
2764:
2739:
2703:
2680:
2641:
2508:
2327:
2291:
2268:
2242:
2222:
2187:
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2138:
2118:
2078:
1980:
1803:
1659:
1623:
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1546:
1490:
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1429:
1340:
1243:
1208:
1165:
1130:
1091:
1052:
905:
875:
837:
810:
250:refers to clockwise or right-handed rotation, and
4365:Ultravioletâvisible spectroscopy of stereoisomers
3008:, it has also been observed in crystals such as
375:naturally occurring in proteins are, despite the
4451:
3518:. New York: Oxford University Press. p. 88.
3422:
3420:
3410:; for Biot's experiments with turpentine vapor (
3269:Solomons, T.W. Graham; Fryhle, Graig B. (2008).
2099:components in phase and oriented exactly in the
704:in a crystal involves a small difference in the
269:, while a compound that causes laevorotation is
913:which then add to produce linear polarization:
3603:. Moscow: USSR Academy of Sciences Publishing.
3601:Mikrostruktura Sveta (Microstructure of Light)
3462: : 56â99; see also appendix, pp. 99â117.
3268:
610:was observed in the 1960s in liquid crystals.
4219:
3473:"Sur les formules de structure dans l'espace"
3417:
277:. Compounds with these properties consist of
573:resolved a problem concerning the nature of
216:"Levo" redirects here. For the company, see
52:Sample tube containing molecules under study
3636:Journal of the Optical Society of America A
3563:
3528:
2772:. Considering propagation through a length
4226:
4212:
4196:Morrison. Robert. T, and Boyd. Robert. N,
3441:, 2021 (open access); especially §13.
3124:Hyper Rayleigh Scattering Optical Activity
2740:{\displaystyle \mathbf {E} _{\theta _{0}}}
2681:{\displaystyle \theta _{0}+\Delta \theta }
2328:{\displaystyle \mathbf {E} _{\theta _{0}}}
1660:{\displaystyle \mathbf {E} _{\theta _{0}}}
1092:{\displaystyle \mathbf {E} _{\theta _{0}}}
811:{\displaystyle \Delta n=n_{RHC}-n_{LHC}\,}
246:. From the point of view of the observer,
192:. This is a tool particularly used in the
4025:
4023:
4003:
3888:
3436:
2502:
2501:
1977:
1976:
1800:
1799:
1046:
1045:
807:
110:. This can include gases or solutions of
3498:Bulletin de la Société Chimique de Paris
3165:, meaning "right" (as opposed to left).
2912:) and the differential refractive index
484:
472:
25:
3598:
3293:
114:such as sugars, molecules with helical
4452:
4020:
4207:
2519:Using similar math as above we find:
848:The familiar rotation of the axis of
538:-glucose (the biological isomer), is
288:
4200:(6th ed.), Prentice-Hall Inc (1992).
3711:
3513:
3475:(On structural formulas in space),
3429:Oeuvres complĂštes d'Augustin Fresnel
534:, in solution. In fact one name for
497:light was first observed in 1811 in
4187:, World Scientific, Singapore, 1994
4043:Electrodynamics of Continuous Media
3241:. World Health Organization. 2017.
3143:
3001:and its concentration in solution.
1561:Substituting these expressions for
493:The rotation of the orientation of
204:, is the principle of operation of
13:
4160:
3218:LibreTexts Chemistry â Polarimetry
2981:
2919:
2889:
2827:
2815:
2786:
2756:
2695:
2672:
2630:
2584:
2452:
2392:
2283:
2260:
2223:{\displaystyle \mathbf {E} _{out}}
2179:
1624:{\displaystyle \mathbf {E} _{LHC}}
1589:{\displaystyle \mathbf {E} _{RHC}}
1244:{\displaystyle \mathbf {E} _{LHC}}
1209:{\displaystyle \mathbf {E} _{RHC}}
1166:{\displaystyle \mathbf {E} _{LHC}}
1131:{\displaystyle \mathbf {E} _{RHC}}
829:
763:
505:. In 1820, the English astronomer
98:. Optical activity occurs only in
14:
4476:
4360:NMR spectroscopy of stereoisomers
4170:, 3rd ed., Addison-Wesley, 1998,
1173:are the two circularly polarized
408:CahnâIngoldâPrelog priority rules
55:Optical rotation due to molecules
4398:Diastereomeric recrystallization
3714:Proceedings of the Royal Society
3456:Annales de chimie et de physique
3412:vapeur d'essence de térébenthine
3392:Annales de Chimie et de Physique
3258:from the original on 2022-10-09.
3192:The equivalent French terms are
3052:Comparison to the Faraday effect
2943:spectra are related through the
2720:
2531:
2482:
2425:
2347:
2308:
2204:
1780:
1739:
1679:
1640:
1605:
1570:
1360:
1271:
1225:
1190:
1147:
1112:
1072:
1026:
985:
925:
355:and are based on the compound's
118:such as some proteins, and also
34:for measuring optical rotation.
4185:Beltrami Fields in Chiral Media
4113:
4063:
3971:
3921:
3861:
3826:
3783:
3748:
3705:
3662:
3626:
3607:
3592:
3557:
3522:
3507:
3486:
3465:
3444:
3383:
3238:The International Pharmacopoeia
3035:
2795:{\displaystyle 2\Delta \theta }
2711:relative to the incoming wave:
2269:{\displaystyle -\Delta \theta }
2188:{\displaystyle 2\Delta \theta }
664:. For instance, a metal rod is
4142:10.1103/PhysRevLett.102.023901
4045:. Vol. 8 (2nd ed.).
3366:
3346:
3329:
3222:
3211:
3186:
2898:{\displaystyle \Delta \theta }
2704:{\displaystyle \Delta \theta }
2636:
2614:
2602:
2590:
2568:
2556:
2498:
2378:
2292:{\displaystyle \Delta \theta }
2073:
2060:
2048:
2036:
2023:
2011:
1973:
1970:
1921:
1912:
1900:
1851:
1845:
1836:
1796:
1711:
1547:{\displaystyle e^{-i\omega t}}
1482:
1453:
1424:
1418:
1400:
1391:
1335:
1329:
1311:
1302:
1042:
957:
685:mixture. But when there is an
261:that causes dextrorotation is
1:
3812:10.1103/PhysRevLett.95.227401
3136:
2802:(as we used above) given by:
558:, commercially formed by the
4393:Chiral column chromatography
3114:Chirality (electromagnetism)
906:{\displaystyle 2\theta _{0}}
595:Jacobus Henricus van 't Hoff
242:are the optical rotation of
7:
4190:A step by step tutorial on
3566:Journal of Chemical Physics
3277:John Wiley & Sons, Inc.
3071:
3060:may also occur through the
2937:optical rotatory dispersion
2119:{\displaystyle \theta _{0}}
876:{\displaystyle \theta _{0}}
461:). For some molecules the (
165:is dominant. For instance,
10:
4481:
4355:Chiral derivatizing agents
4236:enantioselective synthesis
4099:10.1103/PhysRevB.79.035407
3551:10.1103/PhysRevLett.21.342
1491:{\displaystyle {\hat {y}}}
1462:{\displaystyle {\hat {x}}}
1181:direction, we could write
468:
317:-" prefix. The lowercase "
298:
292:
215:
94:are the manifestations of
86:about the optical axis of
21:circularly polarized light
18:
4406:
4373:
4342:
4294:
4242:
3471:van 't Hoff, J.H. (1874)
3343:, 1st part : 93â134.
3275:(9th ed.). Hoboken:
3149:The first word component
639:
30:Operating principle of a
4281:Supramolecular chirality
3516:Chemical Crystallography
3352:Herschel, J.F.W. (1820)
3064:which involves a static
2990:{\displaystyle \Delta n}
2945:KramersâKronig relations
2928:{\displaystyle \Delta n}
2875:{\displaystyle \lambda }
2765:{\displaystyle \Delta n}
2162:{\displaystyle 2\theta }
838:{\displaystyle \Delta n}
414:of each specific chiral
211:
49:Linearly polarized light
19:Not to be confused with
4122:Physical Review Letters
3937:Applied Physics Letters
3877:Applied Physics Letters
3835:Applied Physics Letters
3792:Physical Review Letters
3757:Applied Physics Letters
3599:Vavilov, S. I. (1950).
3531:Physical Review Letters
3206:Patrick Mailliet et al.
2939:(ORD). ORD spectra and
2243:{\displaystyle \theta }
2139:{\displaystyle \theta }
1631:into the equation for
1259:components as follows:
1103:of the net wave, while
581:) rotates the plane of
206:liquid-crystal displays
3726:10.1098/rspl.1898.0019
3656:10.1364/JOSAA.5.001852
3183:, meaning "left side".
3129:Raman optical activity
2991:
2968:
2929:
2899:
2876:
2852:
2796:
2766:
2741:
2705:
2682:
2643:
2510:
2329:
2293:
2270:
2244:
2224:
2189:
2163:
2140:
2120:
2080:
1982:
1805:
1661:
1625:
1590:
1548:
1498:are unit vectors, and
1492:
1463:
1431:
1342:
1245:
1210:
1167:
1132:
1093:
1054:
907:
877:
839:
812:
711:circular polarizations
648:; this is known as an
507:Sir John F.W. Herschel
490:
482:
422:atom) can be labeled (
412:absolute configuration
357:absolute configuration
301:Absolute configuration
120:chiral liquid crystals
80:circular birefringence
68:
4419:Chiral pool synthesis
4333:Diastereomeric excess
4047:Butterworth-Heinemann
3984:Nature Communications
3492:Le Bel, J.-A. (1874)
3177:comes from the Latin
3109:Chirality (chemistry)
3058:plane of polarization
2992:
2969:
2930:
2900:
2877:
2853:
2797:
2767:
2742:
2706:
2683:
2644:
2511:
2330:
2294:
2271:
2245:
2225:
2190:
2164:
2141:
2121:
2081:
1983:
1806:
1662:
1626:
1591:
1549:
1493:
1464:
1432:
1343:
1246:
1211:
1168:
1133:
1094:
1055:
908:
878:
840:
813:
630:Jagadish Chandra Bose
599:Joseph Achille Le Bel
552:plane of polarization
520:Augustin-Jean Fresnel
488:
476:
406:)- prefixes from the
295:Chirality (chemistry)
244:plane-polarized light
76:polarization rotation
29:
4460:Polarization (waves)
4429:Asymmetric catalysis
4414:Asymmetric induction
4049:. pp. 362â365.
3720:(389â400): 146â152.
3691:10.1364/OL.17.000886
3514:Bunn, C. W. (1945).
3119:Polarization rotator
3056:Rotation of light's
2978:
2958:
2916:
2886:
2866:
2809:
2780:
2753:
2715:
2692:
2656:
2526:
2342:
2303:
2280:
2254:
2234:
2199:
2173:
2150:
2130:
2103:
1999:
1820:
1674:
1635:
1600:
1565:
1522:
1473:
1444:
1355:
1266:
1220:
1185:
1142:
1107:
1067:
920:
887:
860:
826:
760:
702:linear birefringence
501:by French physicist
4327:Enantiomeric excess
4134:2009PhRvL.102b3901Z
4091:2009PhRvB..79c5407P
3996:2012NatCo...3..833R
3949:2016ApPhL.108n1905P
3899:2008ApPhL..93s1911P
3847:2007ApPhL..90v3113P
3804:2005PhRvL..95v7401K
3769:2001ApPhL..78..498S
3683:1992OptL...17..886S
3648:1988JOSAA...5.1852S
3578:1969JChPh..50.1324W
3543:1968PhRvL..21..342W
3450:Pasteur, L. (1850)
3372:Biot, J. B. (1815)
2688:, thus rotated by
748:index of refraction
695:inorganic chemistry
687:enantiomeric excess
608:extrinsic chirality
116:secondary structure
4424:Chiral auxiliaries
4388:Kinetic resolution
4286:Inherent chirality
4271:-symmetric ligands
4005:10.1038/ncomms1805
3315:10.1002/chir.10270
3299:See, for example,
3089:Circular dichroism
2987:
2964:
2941:circular dichroism
2925:
2905:as we have shown.
2895:
2872:
2848:
2792:
2762:
2737:
2701:
2678:
2639:
2506:
2325:
2289:
2266:
2240:
2220:
2185:
2159:
2136:
2116:
2076:
1978:
1801:
1657:
1621:
1586:
1544:
1488:
1459:
1427:
1338:
1251:in terms of their
1241:
1206:
1163:
1128:
1089:
1050:
903:
873:
835:
808:
737:spatial dispersion
587:chemical synthesis
556:Invert sugar syrup
512:Jean Baptiste Biot
495:linearly polarized
491:
483:
339:-" prefixes. The "
289:Chirality prefixes
198:enantiomeric ratio
92:circular dichroism
88:linearly polarized
69:
4447:
4446:
4383:Recrystallization
4375:Chiral resolution
4198:Organic Chemistry
4181:Akhlesh Lakhtakia
4079:Physical Review B
4056:978-0-7506-2634-7
3957:10.1063/1.4944775
3907:10.1063/1.3021082
3855:10.1063/1.2745203
3777:10.1063/1.1342210
3586:10.1063/1.1671194
3483: : 445â454.
3414:), see pp. 72â81.
3272:Organic Chemistry
3208:, page 12 and 15.
3084:Specific rotation
3042:specific rotation
3006:aqueous solutions
2999:specific rotation
2967:{\displaystyle L}
2846:
2605:
2559:
2376:
2372:
2051:
2014:
1915:
1848:
1834:
1709:
1705:
1558:of that product.
1485:
1456:
1421:
1403:
1389:
1385:
1332:
1314:
1300:
1296:
955:
951:
691:organic chemistry
656:identical to its
537:
456:
452:
448:
434:
420:asymmetric carbon
410:characterize the
397:
393:
382:
378:
370:
366:
349:organic compounds
346:
342:
338:
334:
330:
259:chemical compound
41:Unpolarized light
4472:
4350:Optical rotation
4295:Chiral molecules
4260:Planar chirality
4228:
4221:
4214:
4205:
4204:
4192:Optical Rotation
4154:
4153:
4117:
4111:
4110:
4076:
4067:
4061:
4060:
4027:
4018:
4017:
4007:
3975:
3969:
3968:
3934:
3925:
3919:
3918:
3892:
3874:
3865:
3859:
3858:
3830:
3824:
3823:
3787:
3781:
3780:
3752:
3746:
3745:
3709:
3703:
3702:
3666:
3660:
3659:
3630:
3624:
3623:
3611:
3605:
3604:
3596:
3590:
3589:
3561:
3555:
3554:
3526:
3520:
3519:
3511:
3505:
3504: : 337â347.
3490:
3484:
3469:
3463:
3448:
3442:
3440:
3424:
3415:
3387:
3381:
3370:
3364:
3350:
3344:
3333:
3327:
3326:
3297:
3291:
3290:
3266:
3260:
3259:
3257:
3234:
3226:
3220:
3215:
3209:
3190:
3184:
3147:
2996:
2994:
2993:
2988:
2973:
2971:
2970:
2965:
2934:
2932:
2931:
2926:
2904:
2902:
2901:
2896:
2881:
2879:
2878:
2873:
2857:
2855:
2854:
2849:
2847:
2842:
2825:
2801:
2799:
2798:
2793:
2771:
2769:
2768:
2763:
2746:
2744:
2743:
2738:
2736:
2735:
2734:
2733:
2723:
2710:
2708:
2707:
2702:
2687:
2685:
2684:
2679:
2668:
2667:
2648:
2646:
2645:
2640:
2626:
2625:
2607:
2606:
2598:
2580:
2579:
2561:
2560:
2552:
2546:
2545:
2534:
2515:
2513:
2512:
2507:
2497:
2496:
2485:
2479:
2478:
2477:
2476:
2459:
2458:
2440:
2439:
2428:
2422:
2421:
2420:
2419:
2399:
2398:
2377:
2368:
2367:
2362:
2361:
2350:
2334:
2332:
2331:
2326:
2324:
2323:
2322:
2321:
2311:
2298:
2296:
2295:
2290:
2275:
2273:
2272:
2267:
2249:
2247:
2246:
2241:
2229:
2227:
2226:
2221:
2219:
2218:
2207:
2194:
2192:
2191:
2186:
2168:
2166:
2165:
2160:
2145:
2143:
2142:
2137:
2125:
2123:
2122:
2117:
2115:
2114:
2085:
2083:
2082:
2077:
2072:
2071:
2053:
2052:
2044:
2035:
2034:
2016:
2015:
2007:
1987:
1985:
1984:
1979:
1969:
1968:
1967:
1966:
1946:
1945:
1944:
1943:
1917:
1916:
1908:
1899:
1898:
1897:
1896:
1876:
1875:
1874:
1873:
1850:
1849:
1841:
1835:
1827:
1810:
1808:
1807:
1802:
1795:
1794:
1783:
1777:
1776:
1775:
1774:
1754:
1753:
1742:
1736:
1735:
1734:
1733:
1710:
1701:
1700:
1695:
1694:
1693:
1692:
1682:
1666:
1664:
1663:
1658:
1656:
1655:
1654:
1653:
1643:
1630:
1628:
1627:
1622:
1620:
1619:
1608:
1595:
1593:
1592:
1587:
1585:
1584:
1573:
1553:
1551:
1550:
1545:
1543:
1542:
1497:
1495:
1494:
1489:
1487:
1486:
1478:
1468:
1466:
1465:
1460:
1458:
1457:
1449:
1436:
1434:
1433:
1428:
1423:
1422:
1414:
1405:
1404:
1396:
1390:
1381:
1380:
1375:
1374:
1363:
1347:
1345:
1344:
1339:
1334:
1333:
1325:
1316:
1315:
1307:
1301:
1292:
1291:
1286:
1285:
1274:
1250:
1248:
1247:
1242:
1240:
1239:
1228:
1215:
1213:
1212:
1207:
1205:
1204:
1193:
1172:
1170:
1169:
1164:
1162:
1161:
1150:
1137:
1135:
1134:
1129:
1127:
1126:
1115:
1098:
1096:
1095:
1090:
1088:
1087:
1086:
1085:
1075:
1059:
1057:
1056:
1051:
1041:
1040:
1029:
1023:
1022:
1021:
1020:
1000:
999:
988:
982:
981:
980:
979:
956:
947:
946:
941:
940:
939:
938:
928:
912:
910:
909:
904:
902:
901:
882:
880:
879:
874:
872:
871:
844:
842:
841:
836:
817:
815:
814:
809:
806:
805:
787:
786:
741:Faraday rotation
716:refractive index
535:
457:, and most are (
454:
450:
446:
432:
395:
391:
380:
376:
368:
364:
359:relative to (+)-
344:
340:
336:
332:
326:
177:-rotary whereas
126:planes (such as
112:chiral molecules
96:optical activity
74:, also known as
72:Optical rotation
45:Linear polarizer
4480:
4479:
4475:
4474:
4473:
4471:
4470:
4469:
4465:Stereochemistry
4450:
4449:
4448:
4443:
4434:Organocatalysis
4402:
4369:
4338:
4322:Racemic mixture
4290:
4276:Axial chirality
4270:
4243:Chirality types
4238:
4232:
4163:
4161:Further reading
4158:
4157:
4118:
4114:
4074:
4068:
4064:
4057:
4039:L.P. Pitaevskii
4028:
4021:
3976:
3972:
3932:
3926:
3922:
3872:
3866:
3862:
3831:
3827:
3788:
3784:
3753:
3749:
3710:
3706:
3667:
3663:
3631:
3627:
3612:
3608:
3597:
3593:
3562:
3558:
3527:
3523:
3512:
3508:
3491:
3487:
3470:
3466:
3449:
3445:
3425:
3418:
3388:
3384:
3371:
3367:
3363: : 43â51.
3351:
3347:
3334:
3330:
3298:
3294:
3287:
3267:
3263:
3255:
3249:
3232:
3228:
3227:
3223:
3216:
3212:
3191:
3187:
3155:comes from the
3148:
3144:
3139:
3134:
3099:Geometric phase
3079:Cryptochirality
3074:
3054:
3038:
3015:
2979:
2976:
2975:
2959:
2956:
2955:
2917:
2914:
2913:
2887:
2884:
2883:
2867:
2864:
2863:
2826:
2824:
2810:
2807:
2806:
2781:
2778:
2777:
2754:
2751:
2750:
2729:
2725:
2724:
2719:
2718:
2716:
2713:
2712:
2693:
2690:
2689:
2663:
2659:
2657:
2654:
2653:
2621:
2617:
2597:
2596:
2575:
2571:
2551:
2550:
2535:
2530:
2529:
2527:
2524:
2523:
2486:
2481:
2480:
2472:
2468:
2464:
2460:
2448:
2444:
2429:
2424:
2423:
2415:
2411:
2404:
2400:
2385:
2381:
2366:
2351:
2346:
2345:
2343:
2340:
2339:
2317:
2313:
2312:
2307:
2306:
2304:
2301:
2300:
2281:
2278:
2277:
2255:
2252:
2251:
2235:
2232:
2231:
2208:
2203:
2202:
2200:
2197:
2196:
2174:
2171:
2170:
2151:
2148:
2147:
2131:
2128:
2127:
2110:
2106:
2104:
2101:
2100:
2067:
2063:
2043:
2042:
2030:
2026:
2006:
2005:
2000:
1997:
1996:
1962:
1958:
1954:
1950:
1939:
1935:
1928:
1924:
1907:
1906:
1892:
1888:
1884:
1880:
1869:
1865:
1858:
1854:
1840:
1839:
1826:
1821:
1818:
1817:
1784:
1779:
1778:
1770:
1766:
1762:
1758:
1743:
1738:
1737:
1729:
1725:
1718:
1714:
1699:
1688:
1684:
1683:
1678:
1677:
1675:
1672:
1671:
1649:
1645:
1644:
1639:
1638:
1636:
1633:
1632:
1609:
1604:
1603:
1601:
1598:
1597:
1574:
1569:
1568:
1566:
1563:
1562:
1529:
1525:
1523:
1520:
1519:
1477:
1476:
1474:
1471:
1470:
1448:
1447:
1445:
1442:
1441:
1413:
1412:
1395:
1394:
1379:
1364:
1359:
1358:
1356:
1353:
1352:
1324:
1323:
1306:
1305:
1290:
1275:
1270:
1269:
1267:
1264:
1263:
1229:
1224:
1223:
1221:
1218:
1217:
1194:
1189:
1188:
1186:
1183:
1182:
1175:basis functions
1151:
1146:
1145:
1143:
1140:
1139:
1116:
1111:
1110:
1108:
1105:
1104:
1081:
1077:
1076:
1071:
1070:
1068:
1065:
1064:
1030:
1025:
1024:
1016:
1012:
1008:
1004:
989:
984:
983:
975:
971:
964:
960:
945:
934:
930:
929:
924:
923:
921:
918:
917:
897:
893:
888:
885:
884:
867:
863:
861:
858:
857:
827:
824:
823:
795:
791:
776:
772:
761:
758:
757:
642:
471:
363:, which is the
307:
297:
291:
221:
214:
67:
60:linear analyzer
24:
17:
12:
11:
5:
4478:
4468:
4467:
4462:
4445:
4444:
4442:
4441:
4436:
4431:
4426:
4421:
4416:
4410:
4408:
4404:
4403:
4401:
4400:
4395:
4390:
4385:
4379:
4377:
4371:
4370:
4368:
4367:
4362:
4357:
4352:
4346:
4344:
4340:
4339:
4337:
4336:
4330:
4324:
4319:
4314:
4309:
4304:
4298:
4296:
4292:
4291:
4289:
4288:
4283:
4278:
4273:
4268:
4262:
4257:
4252:
4246:
4244:
4240:
4239:
4231:
4230:
4223:
4216:
4208:
4202:
4201:
4194:
4188:
4178:
4166:Eugene Hecht,
4162:
4159:
4156:
4155:
4112:
4062:
4055:
4019:
3970:
3943:(14): 141905.
3920:
3883:(19): 191911.
3860:
3841:(22): 223113.
3825:
3798:(22): 227401.
3782:
3747:
3704:
3671:Optics Letters
3661:
3625:
3606:
3591:
3556:
3521:
3506:
3485:
3464:
3458:, 3rd series,
3443:
3416:
3394:, 2nd series,
3382:
3365:
3345:
3328:
3292:
3285:
3261:
3247:
3221:
3210:
3185:
3141:
3140:
3138:
3135:
3133:
3132:
3126:
3121:
3116:
3111:
3106:
3101:
3096:
3091:
3086:
3081:
3075:
3073:
3070:
3066:magnetic field
3062:Faraday effect
3053:
3050:
3037:
3034:
3013:
2986:
2983:
2963:
2924:
2921:
2894:
2891:
2871:
2860:
2859:
2845:
2841:
2838:
2835:
2832:
2829:
2823:
2820:
2817:
2814:
2791:
2788:
2785:
2761:
2758:
2732:
2728:
2722:
2700:
2697:
2677:
2674:
2671:
2666:
2662:
2650:
2649:
2638:
2635:
2632:
2629:
2624:
2620:
2616:
2613:
2610:
2604:
2601:
2595:
2592:
2589:
2586:
2583:
2578:
2574:
2570:
2567:
2564:
2558:
2555:
2549:
2544:
2541:
2538:
2533:
2517:
2516:
2505:
2500:
2495:
2492:
2489:
2484:
2475:
2471:
2467:
2463:
2457:
2454:
2451:
2447:
2443:
2438:
2435:
2432:
2427:
2418:
2414:
2410:
2407:
2403:
2397:
2394:
2391:
2388:
2384:
2380:
2375:
2371:
2365:
2360:
2357:
2354:
2349:
2320:
2316:
2310:
2288:
2285:
2265:
2262:
2259:
2239:
2217:
2214:
2211:
2206:
2195:. Let us call
2184:
2181:
2178:
2158:
2155:
2135:
2113:
2109:
2089:
2088:
2087:
2086:
2075:
2070:
2066:
2062:
2059:
2056:
2050:
2047:
2041:
2038:
2033:
2029:
2025:
2022:
2019:
2013:
2010:
2004:
1991:
1990:
1989:
1988:
1975:
1972:
1965:
1961:
1957:
1953:
1949:
1942:
1938:
1934:
1931:
1927:
1923:
1920:
1914:
1911:
1905:
1902:
1895:
1891:
1887:
1883:
1879:
1872:
1868:
1864:
1861:
1857:
1853:
1847:
1844:
1838:
1833:
1830:
1825:
1812:
1811:
1798:
1793:
1790:
1787:
1782:
1773:
1769:
1765:
1761:
1757:
1752:
1749:
1746:
1741:
1732:
1728:
1724:
1721:
1717:
1713:
1708:
1704:
1698:
1691:
1687:
1681:
1652:
1648:
1642:
1618:
1615:
1612:
1607:
1583:
1580:
1577:
1572:
1541:
1538:
1535:
1532:
1528:
1504:imaginary unit
1484:
1481:
1455:
1452:
1438:
1437:
1426:
1420:
1417:
1411:
1408:
1402:
1399:
1393:
1388:
1384:
1378:
1373:
1370:
1367:
1362:
1349:
1348:
1337:
1331:
1328:
1322:
1319:
1313:
1310:
1304:
1299:
1295:
1289:
1284:
1281:
1278:
1273:
1238:
1235:
1232:
1227:
1203:
1200:
1197:
1192:
1160:
1157:
1154:
1149:
1125:
1122:
1119:
1114:
1101:electric field
1084:
1080:
1074:
1061:
1060:
1049:
1044:
1039:
1036:
1033:
1028:
1019:
1015:
1011:
1007:
1003:
998:
995:
992:
987:
978:
974:
970:
967:
963:
959:
954:
950:
944:
937:
933:
927:
900:
896:
892:
870:
866:
834:
831:
820:
819:
804:
801:
798:
794:
790:
785:
782:
779:
775:
771:
768:
765:
720:speed of light
706:phase velocity
641:
638:
619:lithium iodate
615:Sergey Vavilov
503:François Arago
470:
467:
361:glyceraldehyde
293:Main article:
290:
287:
263:dextrorotatory
248:dextrorotation
230:(also spelled
224:Dextrorotation
218:Levo (company)
213:
210:
194:sugar industry
139:dextrorotatory
66:
65:
62:
56:
53:
50:
47:
42:
39:
35:
15:
9:
6:
4:
3:
2:
4477:
4466:
4463:
4461:
4458:
4457:
4455:
4440:
4437:
4435:
4432:
4430:
4427:
4425:
4422:
4420:
4417:
4415:
4412:
4411:
4409:
4405:
4399:
4396:
4394:
4391:
4389:
4386:
4384:
4381:
4380:
4378:
4376:
4372:
4366:
4363:
4361:
4358:
4356:
4353:
4351:
4348:
4347:
4345:
4341:
4334:
4331:
4328:
4325:
4323:
4320:
4318:
4317:Meso compound
4315:
4313:
4310:
4308:
4305:
4303:
4300:
4299:
4297:
4293:
4287:
4284:
4282:
4279:
4277:
4274:
4272:
4267:
4263:
4261:
4258:
4256:
4253:
4251:
4248:
4247:
4245:
4241:
4237:
4229:
4224:
4222:
4217:
4215:
4210:
4209:
4206:
4199:
4195:
4193:
4189:
4186:
4182:
4179:
4177:
4176:0-201-30425-2
4173:
4169:
4165:
4164:
4151:
4147:
4143:
4139:
4135:
4131:
4128:(2): 023901.
4127:
4123:
4116:
4108:
4104:
4100:
4096:
4092:
4088:
4085:(3): 035407.
4084:
4080:
4073:
4066:
4058:
4052:
4048:
4044:
4040:
4036:
4035:E.M. Lifshitz
4032:
4026:
4024:
4015:
4011:
4006:
4001:
3997:
3993:
3989:
3985:
3981:
3974:
3966:
3962:
3958:
3954:
3950:
3946:
3942:
3938:
3931:
3924:
3916:
3912:
3908:
3904:
3900:
3896:
3891:
3886:
3882:
3878:
3871:
3864:
3856:
3852:
3848:
3844:
3840:
3836:
3829:
3821:
3817:
3813:
3809:
3805:
3801:
3797:
3793:
3786:
3778:
3774:
3770:
3766:
3762:
3758:
3751:
3743:
3739:
3735:
3731:
3727:
3723:
3719:
3715:
3708:
3700:
3696:
3692:
3688:
3684:
3680:
3676:
3672:
3665:
3657:
3653:
3649:
3645:
3641:
3637:
3629:
3621:
3617:
3610:
3602:
3595:
3587:
3583:
3579:
3575:
3571:
3567:
3560:
3552:
3548:
3544:
3540:
3536:
3532:
3525:
3517:
3510:
3503:
3499:
3495:
3489:
3482:
3478:
3474:
3468:
3461:
3457:
3453:
3447:
3439:
3434:
3430:
3423:
3421:
3413:
3409:
3405:
3401:
3397:
3393:
3386:
3379:
3375:
3369:
3362:
3358:
3355:
3349:
3342:
3338:
3335:Arago (1811)
3332:
3324:
3320:
3316:
3312:
3308:
3304:
3296:
3288:
3286:9780471684961
3282:
3279:p. 195.
3278:
3274:
3273:
3265:
3254:
3250:
3248:9789241550031
3244:
3240:
3239:
3231:
3225:
3219:
3214:
3207:
3203:
3202:
3197:
3196:
3189:
3182:
3181:
3176:
3175:
3170:
3169:
3164:
3163:
3158:
3154:
3153:
3146:
3142:
3130:
3127:
3125:
3122:
3120:
3117:
3115:
3112:
3110:
3107:
3105:
3102:
3100:
3097:
3095:
3094:Birefringence
3092:
3090:
3087:
3085:
3082:
3080:
3077:
3076:
3069:
3067:
3063:
3059:
3049:
3047:
3043:
3033:
3031:
3027:
3023:
3019:
3011:
3007:
3002:
3000:
2984:
2961:
2953:
2948:
2946:
2942:
2938:
2922:
2911:
2906:
2892:
2869:
2843:
2839:
2836:
2833:
2830:
2821:
2818:
2812:
2805:
2804:
2803:
2789:
2783:
2775:
2759:
2747:
2730:
2726:
2698:
2675:
2669:
2664:
2660:
2633:
2627:
2622:
2618:
2611:
2608:
2599:
2593:
2587:
2581:
2576:
2572:
2565:
2562:
2553:
2547:
2542:
2539:
2536:
2522:
2521:
2520:
2503:
2493:
2490:
2487:
2473:
2469:
2465:
2461:
2455:
2449:
2445:
2441:
2436:
2433:
2430:
2416:
2412:
2408:
2405:
2401:
2395:
2389:
2386:
2382:
2373:
2369:
2363:
2358:
2355:
2352:
2338:
2337:
2336:
2318:
2314:
2286:
2263:
2257:
2237:
2215:
2212:
2209:
2182:
2176:
2156:
2153:
2133:
2111:
2107:
2098:
2094:
2068:
2064:
2057:
2054:
2045:
2039:
2031:
2027:
2020:
2017:
2008:
2002:
1995:
1994:
1993:
1992:
1963:
1959:
1955:
1951:
1947:
1940:
1936:
1932:
1929:
1925:
1918:
1909:
1903:
1893:
1889:
1885:
1881:
1877:
1870:
1866:
1862:
1859:
1855:
1842:
1831:
1828:
1823:
1816:
1815:
1814:
1813:
1791:
1788:
1785:
1771:
1767:
1763:
1759:
1755:
1750:
1747:
1744:
1730:
1726:
1722:
1719:
1715:
1706:
1702:
1696:
1689:
1685:
1670:
1669:
1668:
1650:
1646:
1616:
1613:
1610:
1581:
1578:
1575:
1559:
1557:
1539:
1536:
1533:
1530:
1526:
1517:
1513:
1509:
1505:
1501:
1479:
1450:
1415:
1409:
1406:
1397:
1386:
1382:
1376:
1371:
1368:
1365:
1351:
1350:
1326:
1320:
1317:
1308:
1297:
1293:
1287:
1282:
1279:
1276:
1262:
1261:
1260:
1258:
1254:
1236:
1233:
1230:
1201:
1198:
1195:
1180:
1176:
1158:
1155:
1152:
1123:
1120:
1117:
1102:
1082:
1078:
1047:
1037:
1034:
1031:
1017:
1013:
1009:
1005:
1001:
996:
993:
990:
976:
972:
968:
965:
961:
952:
948:
942:
935:
931:
916:
915:
914:
898:
894:
890:
868:
864:
855:
854:superposition
851:
846:
832:
802:
799:
796:
792:
788:
783:
780:
777:
773:
769:
766:
756:
755:
754:
752:
749:
744:
742:
738:
733:
728:
725:
722:(in vacuum),
721:
717:
713:
712:
707:
703:
698:
696:
692:
688:
684:
678:
675:
671:
667:
663:
659:
655:
651:
647:
646:stereoisomers
637:
635:
631:
626:
622:
620:
616:
611:
609:
603:
600:
596:
591:
588:
584:
580:
576:
575:tartaric acid
572:
571:Louis Pasteur
567:
565:
561:
557:
553:
550:, causes the
549:
545:
541:
533:
529:
525:
524:birefringence
521:
517:
513:
508:
504:
500:
496:
487:
480:
479:tartaric acid
475:
466:
464:
460:
444:
440:
436:
429:
425:
421:
417:
413:
409:
405:
401:
388:
386:
374:
362:
358:
354:
350:
329:
324:
320:
316:
312:
306:
302:
296:
286:
284:
280:
276:
272:
271:laevorotatory
268:
264:
260:
255:
253:
252:laevorotation
249:
245:
241:
237:
233:
229:
228:laevorotation
225:
219:
209:
207:
203:
199:
195:
191:
186:
184:
180:
176:
172:
168:
164:
160:
156:
152:
148:
144:
140:
135:
133:
132:metamaterials
129:
125:
121:
117:
113:
109:
105:
104:birefringence
101:
97:
93:
89:
85:
81:
77:
73:
63:
61:
57:
54:
51:
48:
46:
43:
40:
37:
36:
33:
28:
22:
4439:Biocatalysis
4349:
4312:Diastereomer
4302:Stereoisomer
4265:
4255:Stereocenter
4234:Concepts in
4197:
4167:
4125:
4121:
4115:
4082:
4078:
4065:
4042:
3987:
3983:
3973:
3940:
3936:
3923:
3880:
3876:
3863:
3838:
3834:
3828:
3795:
3791:
3785:
3760:
3756:
3750:
3717:
3713:
3707:
3674:
3670:
3664:
3642:(11): 1852.
3639:
3635:
3628:
3619:
3616:JETP Letters
3615:
3609:
3600:
3594:
3569:
3565:
3559:
3534:
3530:
3524:
3515:
3509:
3501:
3497:
3488:
3480:
3476:
3467:
3459:
3455:
3446:
3428:
3411:
3403:
3395:
3391:
3385:
3377:
3368:
3360:
3356:
3348:
3340:
3331:
3306:
3302:
3295:
3271:
3264:
3237:
3224:
3213:
3200:
3194:
3188:
3178:
3172:
3166:
3160:
3150:
3145:
3104:Polarization
3055:
3039:
3036:Applications
3030:fused quartz
3003:
2949:
2907:
2861:
2773:
2748:
2651:
2518:
2096:
2092:
2090:
1560:
1555:
1511:
1507:
1499:
1439:
1256:
1252:
1178:
1062:
849:
847:
821:
750:
745:
732:permittivity
729:
723:
709:
699:
679:
673:
665:
658:mirror image
653:
643:
627:
623:
612:
604:
592:
583:polarization
568:
539:
528:polarimeters
492:
462:
458:
442:
438:
427:
423:
416:stereocenter
403:
399:
389:
353:biochemistry
322:
318:
314:
310:
308:
274:
270:
267:dextrorotary
266:
262:
256:
251:
247:
232:levorotation
231:
227:
223:
222:
187:
182:
174:
163:stereoisomer
158:
154:
151:levorotatory
150:
146:
143:dextrorotary
142:
138:
136:
95:
84:polarization
79:
75:
71:
70:
38:Light source
4031:L.D. Landau
3965:10220/40854
3677:(12): 886.
3572:(3): 1324.
3046:polarimeter
1667:we obtain:
518:. In 1822,
373:amino acids
275:laevorotary
190:polarimeter
179:cholesterol
32:polarimeter
4454:Categories
4307:Enantiomer
3763:(4): 498.
3537:(6): 342.
3380:, 190â192.
3309:: S57â64.
3195:dextrogyre
3137:References
3018:optic axis
2952:wavelength
2910:dispersion
650:enantiomer
634:microwaves
621:crystals.
560:hydrolysis
516:turpentine
435:-threonine
328:SMALL CAPS
299:See also:
283:enantiomer
202:polarizers
155:levorotary
58:Rotatable
4407:Reactions
4250:Chirality
4107:119259753
3915:117891131
3890:0807.0523
3406: :
3398: :
3303:Chirality
3024:forms of
3022:amorphous
2982:Δ
2920:Δ
2893:θ
2890:Δ
2870:λ
2844:λ
2840:π
2828:Δ
2819:θ
2816:Δ
2790:θ
2787:Δ
2757:Δ
2727:θ
2699:θ
2696:Δ
2676:θ
2673:Δ
2661:θ
2634:θ
2631:Δ
2619:θ
2612:
2603:^
2588:θ
2585:Δ
2573:θ
2566:
2557:^
2470:θ
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2453:Δ
2413:θ
2406:−
2396:θ
2393:Δ
2387:−
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2287:θ
2284:Δ
2264:θ
2261:Δ
2258:−
2238:θ
2183:θ
2180:Δ
2157:θ
2134:θ
2108:θ
2065:θ
2058:
2049:^
2028:θ
2021:
2012:^
1960:θ
1948:−
1937:θ
1930:−
1913:^
1890:θ
1867:θ
1860:−
1846:^
1768:θ
1727:θ
1720:−
1686:θ
1647:θ
1556:real part
1537:ω
1531:−
1483:^
1454:^
1419:^
1407:−
1401:^
1330:^
1312:^
1079:θ
1014:θ
973:θ
966:−
932:θ
895:θ
865:θ
830:Δ
789:−
764:Δ
662:chirality
613:In 1950,
593:In 1874,
579:wine lees
569:In 1849,
236:chemistry
4343:Analysis
4150:19257274
4041:(1984).
4014:22588295
3820:16384264
3742:89292757
3699:19794663
3323:12884375
3253:Archived
3201:lévogyre
3072:See also
3028:such as
628:In 1898
548:fructose
540:dextrose
402:)- and (
385:fructose
343:-" and "
335:-" and "
321:-" and "
64:Detector
4130:Bibcode
4087:Bibcode
3992:Bibcode
3990:: 833.
3945:Bibcode
3895:Bibcode
3843:Bibcode
3800:Bibcode
3765:Bibcode
3679:Bibcode
3644:Bibcode
3574:Bibcode
3539:Bibcode
3438:4745976
3435::
3400:372â389
3152:dextro-
1502:is the
1099:is the
683:racemic
564:sucrose
532:glucose
469:History
240:physics
171:camphor
167:sucrose
124:crystal
4174:
4168:Optics
4148:
4105:
4053:
4012:
3913:
3818:
3740:
3734:115973
3732:
3697:
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3433:Zenodo
3321:
3283:
3245:
3180:laevus
3168:Laevo-
3162:dexter
3026:silica
3010:quartz
2862:where
1516:phasor
1440:where
1063:where
850:linear
822:While
640:Theory
544:dexter
499:quartz
426:) or (
394:- and
305:Aldose
279:chiral
128:quartz
108:fluids
100:chiral
4103:S2CID
4075:(PDF)
3933:(PDF)
3911:S2CID
3885:arXiv
3873:(PDF)
3738:S2CID
3730:JSTOR
3408:63â81
3256:(PDF)
3233:(PDF)
3174:levo-
3159:word
3157:Latin
3131:(ROA)
670:helix
234:) in
212:Forms
130:) or
4335:(de)
4329:(ee)
4172:ISBN
4146:PMID
4051:ISBN
4010:PMID
3816:PMID
3695:PMID
3319:PMID
3281:ISBN
3243:ISBN
3198:and
3012:(SiO
2276:and
2095:and
1596:and
1510:and
1469:and
1255:and
1216:and
1138:and
597:and
390:The
303:and
238:and
226:and
173:are
169:and
4138:doi
4126:102
4095:doi
4000:doi
3961:hdl
3953:doi
3941:108
3903:doi
3851:doi
3808:doi
3773:doi
3722:doi
3687:doi
3652:doi
3582:doi
3547:doi
3311:doi
3171:or
2609:sin
2563:cos
2055:sin
2018:cos
693:or
666:not
654:not
562:of
351:in
273:or
265:or
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