3079:. 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.
750:. 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
725:. 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
497:
647:. 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.
38:
485:
601:
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.
3031:. 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,
2525:
612:
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
635:
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
687:
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
600:
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
1069:
1820:
3437:
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.),
1997:
2658:
3400:
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),
745:
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
691:
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
700:, 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
616:
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
2352:
764:, 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),
537:: 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
636:
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.
737:
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.
3228:
476:)-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.
196:-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.
1446:
1357:
3644:
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".
2095:
930:
1684:
378:-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
2867:
520:
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.
3216:
1830:
867:(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
613:
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.
2536:
3442:, 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",
856:
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.
3801:
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".
577:
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.
4370:
2756:
2697:
2344:
1676:
1108:
827:
3348:"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"
4375:
3312:
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".
3043:, 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.
2239:
1640:
1605:
1260:
1225:
1182:
1147:
2811:
2285:
2204:
3263:
2914:
2720:
2520:{\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})\,\,.}
2308:
1563:
2180:. 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
922:
2135:
892:
3365:"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,"
1507:
1478:
3006:
2944:
2891:
2781:
2178:
854:
3350:(Memoir on a remarkable modification that light rays experience during their passage through certain translucent substances and on some other new optical phenomena),
2259:
2155:
754:. All optical phenomena have some nonlocality/wavevector influence but it is usually negligible; natural optical rotation, rather uniquely, absolutely requires it.
711:
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
4236:
2983:
296:(geometric mirror image) will be laevorotary, and vice versa. Enantiomers rotate plane-polarized light the same number of degrees, but in opposite directions.
3134:
418:
1365:
1276:
741:
Unlike linear birefringence, however, natural optical rotation (in the absence of a magnetic field) cannot be explained in terms of a local material
719:
of light of two different linear polarizations, circular birefringence implies a small difference in the velocities between right and left-handed
2009:
1064:{\displaystyle \mathbf {E} _{\theta _{0}}={\frac {\sqrt {2}}{2}}(e^{-i\theta _{0}}\mathbf {E} _{RHC}+e^{i\theta _{0}}\mathbf {E} _{LHC})\,\,,}
4065:
1815:{\displaystyle \mathbf {E} _{\theta _{0}}={\frac {\sqrt {2}}{2}}(e^{-i\theta _{0}}\mathbf {E} _{RHC}+e^{i\theta _{0}}\mathbf {E} _{LHC})\,\,}
3844:
Plum, E.; Fedotov, V. A.; Schwanecke, A. S.; Zheludev, N. I.; Chen, Y. (2007). "Giant optical gyrotropy due to electromagnetic coupling".
2819:
655:
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)
628:
predicted optical activity that depends on the intensity of light and the effect of nonlinear optical activity was observed in 1979 in
4229:
3625:
Akhmanov, S. A.; Zhdanov, B. V.; Zheludev, N. I.; Kovrigin, A. I.; Kuznetsov, V. I. (1979). "Nonlinear optical activity in crystals".
4186:
3295:
3257:
429:
with the molecule, rather than a property of the molecule as a whole. A molecule having exactly one chiral stereocenter (usually an
3240:
1992:{\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}}))\,\,}
4408:
3281:
3505:"Sur les relations qui existent entre les formules atomiques des corps organiques et le pouvoir rotatoire de leurs dissolutions"
671:(which would be that of a different stereoisomer, or the "opposite enantiomer"). In mathematics, this property is also known as
605:
3507:(On the relations that exist between the atomic formulas of organic substances and the rotatory power of their solutions),
464:, and (+)/(â) designations, although some correlations exist. For example, of the naturally occurring amino acids, all are
4470:
4393:
4222:
4131:
Zhang, S.; Park, Y.-S.; Li, J.; Lu, X.; Zhang, W.; Zhang, X. (2009). "Negative
Refractive Index in Chiral Metamaterials".
496:
3575:
R. Williams (1969). "Optical-rotary power and linear electro-optic effect in nematic liquid crystals of p-azoxyanisole".
679:
chiral, since its appearance in a mirror is not distinct from itself. However a screw or light bulb base (or any sort of
4403:
3124:
2653:{\displaystyle \mathbf {E} _{out}={\hat {x}}\cos(\theta _{0}+\Delta \theta )+{\hat {y}}\sin(\theta _{0}+\Delta \theta )}
618:
2955:
3940:
2947:
2961:
So we find that the degree of rotation depends on the color of the light (the yellow sodium D line near 589 nm
409:- prefixes describe the molecule as a whole, as do the (+) and (â) prefixes for optical rotation. In contrast, the (
4246:
3766:
Svirko, Y.; Zheludev, N. I.; Osipov, M. (2001). "Layered chiral metallic microstructures with inductive coupling".
3723:
Bose, Jagadis
Chunder (1898). "On the Rotation of Plane of Polarisation of Electric Waves by a Twisted Structure".
3287:
525:
also observed the rotation of the axis of polarization in certain liquids and vapors of organic substances such as
31:
3027:). Although quartz has a substantial linear birefringence, that effect is cancelled when propagation is along the
2946:
will also be wavelength dependent. The resulting variation in rotation with the wavelength of the light is called
4365:
441:), but a molecule having multiple stereocenters needs more than one label. For example, the essential amino acid
2725:
2666:
2313:
1645:
1077:
770:
729:
which substantially lowers the phase velocity of light in any dielectric (transparent) material compared to the
4475:
4291:
3483:
2893:
is the wavelength of the light (in vacuum). This will cause a rotation of the linear axis of polarization by
211:
of chiral molecules in solution. Modulation of a liquid crystal's optical activity, viewed between two sheet
3418:
3364:
3028:
864:
2760:
We defined above the difference in the refractive indices for right and left circularly polarized waves of
2157:
as the superposition of right and left circularly polarized components with a relative phase difference of
148:
When looking at the source of light, the rotation of the plane of polarization may be either to the right (
3680:
Silverman, M.; Badoz, J.; Briat, B. (1992). "Chiral reflection from a naturally optically active medium".
3139:
1185:
422:
367:
311:
216:
3347:
4429:
4343:
4260:
4057:
3119:
3068:
2209:
1610:
1575:
1230:
1195:
1152:
1117:
863:
polarization relies on the understanding that a linearly polarized wave can as well be described as the
735:
there is an additional interaction between the chirality of the wave and the chirality of the molecules.
721:
640:
609:
562:
530:
305:
289:
254:
207:
to measure the sugar concentration of syrup, and generally in chemistry to measure the concentration or
122:
2137:
direction, as we had intended, justifying the representation of any linearly polarized state at angle
133:. It can also be observed in chiral solids such as certain crystals with a rotation between adjacent
4439:
4424:
4275:
4140:
4097:
4081:
Plum, E.; Zhou, J.; Dong, J.; Fedotov, V. A.; Koschny, T.; Soukoulis, C. M.; Zheludev, N. I. (2009).
4002:
3955:
3905:
3853:
3810:
3775:
3689:
3654:
3584:
3549:
3504:
3410:
3129:
3114:
2790:
2264:
2183:
593:
566:
94:
3462:
2896:
2702:
2290:
1532:
4337:
3384:
2920:
758:
705:
697:
589:
565:
to rotate to the left. Fructose is even more strongly levorotatory than glucose is dextrorotatory.
505:
126:
98:
897:
37:
4398:
4296:
4113:
3921:
3895:
3748:
3740:
3099:
2951:
2113:
870:
747:
597:
522:
102:
3210:
1483:
1454:
3204:
3055:
is known, the observed rotation can be used to calculate the concentration. This usage makes a
1525:
components that we have decomposed each circular polarization into. As usual when dealing with
4385:
4191:
4182:
4156:
4061:
4020:
3826:
3705:
3352:
Mémoires de la classe des sciences mathématiques et physiques de l'Institut Impérial de France
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2926:
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2763:
2160:
836:
701:
513:
430:
359:
269:
4195:
3540:
R. Williams (1968). "Optical
Rotatory Effect in the Nematic Liquid Phase of p-Azoxyanisole".
2244:
2140:
4434:
4270:
4148:
4105:
4010:
3971:
3963:
3913:
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3662:
3592:
3557:
3321:
751:
726:
55:
3463:"Recherches sur les propriétés spécifiques des deux acides qui composent l'acide racémique"
292:
molecules and are said to have optical activity. If a chiral molecule is dextrorotary, its
4444:
4332:
4312:
4286:
4202:
4045:
3109:
3089:
553:, referring to the fact that it causes linearly polarized light to rotate to the right or
4214:
2787:
in such a material, there will be an additional phase difference induced between them of
27:
Rotation of the plane of linearly polarized light as it travels through a chiral material
4144:
4101:
4006:
3959:
3909:
3857:
3814:
3779:
3693:
3658:
3588:
3553:
3465:(Researches on the specific properties of the two acids that compose the racemic acid),
4049:
3167:
3076:
3072:
3015:
Although optical activity is normally thought of as a property of fluids, particularly
2968:
1514:
1111:
730:
716:
629:
625:
541:
have been used since this time to measure the concentrations of simple sugars, such as
371:
228:
204:
130:
4464:
4327:
4117:
3925:
3104:
712:
643:
described the ability of twisted artificial structures to rotate the polarization of
585:
581:
534:
517:
489:
114:
3752:
2965:
is commonly used for measurements), and is directly proportional to the path length
500:
Sucrose solution concentration measuring experiment, demonstrating optical rotation.
4449:
4322:
4265:
4152:
3040:
742:
668:
656:
426:
363:
173:
142:
3822:
688:
mirror reflection of a doll might well be indistinguishable from the doll itself.
3051:
For a pure substance in solution, if the color and path length are fixed and the
1441:{\displaystyle \mathbf {E} _{LHC}={\frac {\sqrt {2}}{2}}({\hat {x}}-i{\hat {y}})}
1352:{\displaystyle \mathbf {E} _{RHC}={\frac {\sqrt {2}}{2}}({\hat {x}}+i{\hat {y}})}
3056:
538:
324:-" prefix. Likewise, a levorotary compound may be labeled using the "(â)-" or "
200:
189:
117:
which alter a beam's state of polarization, optical activity can be observed in
70:
42:
4109:
4082:
3880:
3561:
2985:
through the substance and the amount of circular birefringence of the material
4317:
4041:
3190:
3172:
3059:
a tool of great importance to those trading in or using sugar syrups in bulk.
2962:
660:
570:
554:
526:
484:
383:
338:
293:
208:
113:
materials, those lacking microscopic mirror symmetry. Unlike other sources of
17:
3032:
672:
644:
442:
246:
212:
4160:
4024:
3830:
3736:
3709:
3666:
3385:"Phenomene de polarisation successive, observés dans des fluides homogenes"
3333:
3215:. These are used infrequently in English, but sometimes they are, see e.g.
3162:
2958:. Complete knowledge of one spectrum allows the calculation of the other.
588:. A solution of this compound derived from living things (to be specific,
101:
light as it travels through certain materials. Circular birefringence and
3701:
3387:(Phenomenon of successive polarization, observed in homogeneous fluids),
558:
395:
3178:
2090:{\displaystyle ={\hat {x}}\cos(\theta _{0})+{\hat {y}}\sin(\theta _{0})}
1529:
notation, it is understood that such quantities are to be multiplied by
757:
The phase velocity of light in a medium is commonly expressed using the
4015:
3990:
3975:
3325:
708:
are racemic unless a chiral reagent was employed in the same reaction.
693:
574:
542:
250:
181:
177:
134:
3967:
3917:
3865:
3787:
3744:
3596:
3184:
488:
The two asymmetric crystal forms, dextrorotatory and levorotatory, of
390:- prefix, actually dextrorotary (at a wavelength of 589 nm), and
3443:
3036:
3020:
1526:
509:
315:
138:
110:
3448:
2241:
the result of passing the original wave linearly polarized at angle
172:-rotary, represented by (â), counter-clockwise) depending on which
3900:
2862:{\displaystyle 2\Delta \theta ={\frac {\Delta nL2\pi }{\lambda }}}
1565:
and then the actual electric field at any instant is given by the
1517:, in this case representing the 90 degree phase shift between the
680:
495:
483:
456:)-threonine. There is no strict relationship between the R/S, the
320:
A compound may be labeled as dextrorotary by using the "(+)-" or "
118:
36:
2261:
through this medium. This will apply additional phase factors of
894:, and their electric fields have a relative phase difference of
4218:
533:
found that optical rotation could be explained as a species of
3991:"Giant nonlinear optical activity in a plasmonic metamaterial"
3247:
3008:
which, for a solution, may be computed from the substance's
2919:
In general, the refractive index depends on wavelength (see
1188:(having zero phase difference). Assuming propagation in the
557:
side. In a similar manner, levulose, more commonly known as
3389:
Bulletin des
Sciences, par la Société Philomatique de Paris
2102:
The last equation shows that the resulting vector has the
596:
of light passing through it, but tartaric acid derived by
199:
Optical activity is measured using a polarized source and
3488:
Archives NĂ©erlandaises des
Sciences Exactes et Naturelles
3241:"Determination of optical rotation and specific rotation"
2310:
to the right and left circularly polarized components of
398:
is sometimes called "levulose" because it is levorotary.
358:-" prefixes are used to specify the enantiomer of chiral
219:(used in most modern televisions and computer monitors).
160:-rotary, represented by (+), clockwise), or to the left (
3881:"Optical activity in extrinsically chiral metamaterial"
663:. The structure of such a molecule is such that it is
2991:
2971:
2929:
2899:
2879:
2822:
2793:
2766:
2728:
2705:
2669:
2539:
2355:
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2247:
2212:
2186:
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2143:
2116:
2012:
1833:
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1613:
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1535:
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1457:
1368:
1279:
1233:
1198:
1155:
1120:
1080:
933:
900:
873:
839:
773:
93:, is the rotation of the orientation of the plane of
336:-" prefixes are obsolete, and are distinct from the
265:
refers to counterclockwise or left-handed rotation.
4417:
4384:
4353:
4305:
4253:
4083:"Metamaterial with negative index due to chirality"
3989:Ren, M.; Plum, E.; Xu, J.; Zheludev, N. I. (2012).
3941:"Specular optical activity of achiral metasurfaces"
3368:
Transactions of the
Cambridge Philosophical Society
2663:thus describing a wave linearly polarized at angle
448:
contains two chiral stereocenters and is written (2
3939:Plum, E.; Fedotov, V. A.; Zheludev, N. I. (2016).
3879:Plum, E.; Fedotov, V. A.; Zheludev, N. I. (2008).
3000:
2977:
2938:
2908:
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2714:
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1991:
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1557:
1501:
1472:
1440:
1351:
1254:
1219:
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1141:
1102:
1063:
916:
886:
848:
821:
261:refers to clockwise or right-handed rotation, and
4376:Ultravioletâvisible spectroscopy of stereoisomers
3019:, it has also been observed in crystals such as
386:naturally occurring in proteins are, despite the
3529:. New York: Oxford University Press. p. 88.
3433:
3431:
3421:; for Biot's experiments with turpentine vapor (
3280:Solomons, T.W. Graham; Fryhle, Graig B. (2008).
2110:components in phase and oriented exactly in the
715:in a crystal involves a small difference in the
280:, while a compound that causes laevorotation is
924:which then add to produce linear polarization:
3614:. Moscow: USSR Academy of Sciences Publishing.
3612:Mikrostruktura Sveta (Microstructure of Light)
3473: : 56â99; see also appendix, pp. 99â117.
621:was observed in the 1960s in liquid crystals.
4230:
3484:"Sur les formules de structure dans l'espace"
288:. Compounds with these properties consist of
8:
584:resolved a problem concerning the nature of
227:"Levo" redirects here. For the company, see
63:Sample tube containing molecules under study
3647:Journal of the Optical Society of America A
2783:. Considering propagation through a length
4237:
4223:
4215:
4207:Morrison. Robert. T, and Boyd. Robert. N,
3452:, 2021 (open access); especially §13.
3135:Hyper Rayleigh Scattering Optical Activity
2751:{\displaystyle \mathbf {E} _{\theta _{0}}}
2692:{\displaystyle \theta _{0}+\Delta \theta }
2339:{\displaystyle \mathbf {E} _{\theta _{0}}}
1671:{\displaystyle \mathbf {E} _{\theta _{0}}}
1103:{\displaystyle \mathbf {E} _{\theta _{0}}}
822:{\displaystyle \Delta n=n_{RHC}-n_{LHC}\,}
257:. From the point of view of the observer,
203:. This is a tool particularly used in the
4036:
4034:
4014:
3899:
3447:
2990:
2970:
2928:
2898:
2878:
2835:
2821:
2792:
2765:
2740:
2735:
2730:
2727:
2704:
2674:
2668:
2632:
2608:
2607:
2586:
2562:
2561:
2546:
2541:
2538:
2513:
2512:
2497:
2492:
2483:
2475:
2459:
2440:
2435:
2426:
2415:
2396:
2377:
2362:
2357:
2354:
2328:
2323:
2318:
2315:
2292:
2266:
2246:
2219:
2214:
2211:
2185:
2162:
2142:
2121:
2115:
2078:
2054:
2053:
2041:
2017:
2016:
2011:
1988:
1987:
1973:
1965:
1950:
1939:
1918:
1917:
1903:
1895:
1880:
1869:
1851:
1850:
1837:
1832:
1811:
1810:
1795:
1790:
1781:
1773:
1754:
1749:
1740:
1729:
1710:
1699:
1694:
1689:
1686:
1660:
1655:
1650:
1647:
1620:
1615:
1612:
1585:
1580:
1577:
1540:
1534:
1488:
1487:
1485:
1459:
1458:
1456:
1424:
1423:
1406:
1405:
1390:
1375:
1370:
1367:
1335:
1334:
1317:
1316:
1301:
1286:
1281:
1278:
1240:
1235:
1232:
1205:
1200:
1197:
1162:
1157:
1154:
1127:
1122:
1119:
1092:
1087:
1082:
1079:
1057:
1056:
1041:
1036:
1027:
1019:
1000:
995:
986:
975:
956:
945:
940:
935:
932:
908:
899:
878:
872:
838:
818:
806:
787:
772:
121:. This can include gases or solutions of
3509:Bulletin de la Société Chimique de Paris
3176:, meaning "right" (as opposed to left).
2923:) and the differential refractive index
3153:
125:such as sugars, molecules with helical
2530:Using similar math as above we find:
859:The familiar rotation of the axis of
549:-glucose (the biological isomer), is
7:
4211:(6th ed.), Prentice-Hall Inc (1992).
3486:(On structural formulas in space),
3440:Oeuvres complĂštes d'Augustin Fresnel
545:, in solution. In fact one name for
508:light was first observed in 1811 in
4198:, World Scientific, Singapore, 1994
4054:Electrodynamics of Continuous Media
3252:. World Health Organization. 2017.
3012:and its concentration in solution.
1572:Substituting these expressions for
504:The rotation of the orientation of
215:, is the principle of operation of
3229:LibreTexts Chemistry â Polarimetry
2992:
2930:
2900:
2838:
2826:
2797:
2767:
2706:
2683:
2641:
2595:
2463:
2403:
2294:
2271:
2234:{\displaystyle \mathbf {E} _{out}}
2190:
1635:{\displaystyle \mathbf {E} _{LHC}}
1600:{\displaystyle \mathbf {E} _{RHC}}
1255:{\displaystyle \mathbf {E} _{LHC}}
1220:{\displaystyle \mathbf {E} _{RHC}}
1177:{\displaystyle \mathbf {E} _{LHC}}
1142:{\displaystyle \mathbf {E} _{RHC}}
840:
774:
516:. In 1820, the English astronomer
109:. Optical activity occurs only in
25:
4371:NMR spectroscopy of stereoisomers
4181:, 3rd ed., Addison-Wesley, 1998,
1184:are the two circularly polarized
419:CahnâIngoldâPrelog priority rules
66:Optical rotation due to molecules
4409:Diastereomeric recrystallization
3725:Proceedings of the Royal Society
3467:Annales de chimie et de physique
3423:vapeur d'essence de térébenthine
3403:Annales de Chimie et de Physique
3269:from the original on 2022-10-09.
3203:The equivalent French terms are
3063:Comparison to the Faraday effect
2954:spectra are related through the
2731:
2542:
2493:
2436:
2358:
2319:
2215:
1791:
1750:
1690:
1651:
1616:
1581:
1371:
1282:
1236:
1201:
1158:
1123:
1083:
1037:
996:
936:
366:and are based on the compound's
129:such as some proteins, and also
45:for measuring optical rotation.
4196:Beltrami Fields in Chiral Media
3249:The International Pharmacopoeia
2806:{\displaystyle 2\Delta \theta }
2722:relative to the incoming wave:
2280:{\displaystyle -\Delta \theta }
2199:{\displaystyle 2\Delta \theta }
675:. For instance, a metal rod is
4153:10.1103/PhysRevLett.102.023901
4056:. Vol. 8 (2nd ed.).
2909:{\displaystyle \Delta \theta }
2715:{\displaystyle \Delta \theta }
2647:
2625:
2613:
2601:
2579:
2567:
2509:
2389:
2303:{\displaystyle \Delta \theta }
2084:
2071:
2059:
2047:
2034:
2022:
1984:
1981:
1932:
1923:
1911:
1862:
1856:
1847:
1807:
1722:
1558:{\displaystyle e^{-i\omega t}}
1493:
1464:
1435:
1429:
1411:
1402:
1346:
1340:
1322:
1313:
1053:
968:
696:mixture. But when there is an
272:that causes dextrorotation is
1:
3823:10.1103/PhysRevLett.95.227401
2813:(as we used above) given by:
569:, commercially formed by the
4404:Chiral column chromatography
3125:Chirality (electromagnetism)
917:{\displaystyle 2\theta _{0}}
606:Jacobus Henricus van 't Hoff
253:are the optical rotation of
4201:A step by step tutorial on
3577:Journal of Chemical Physics
3288:John Wiley & Sons, Inc.
3071:may also occur through the
2948:optical rotatory dispersion
2130:{\displaystyle \theta _{0}}
887:{\displaystyle \theta _{0}}
472:). For some molecules the (
176:is dominant. For instance,
4492:
4366:Chiral derivatizing agents
4247:enantioselective synthesis
4110:10.1103/PhysRevB.79.035407
3562:10.1103/PhysRevLett.21.342
1502:{\displaystyle {\hat {y}}}
1473:{\displaystyle {\hat {x}}}
1192:direction, we could write
328:-" prefix. The lowercase "
309:
303:
226:
105:are the manifestations of
97:about the optical axis of
32:circularly polarized light
29:
3482:van 't Hoff, J.H. (1874)
3354:, 1st part : 93â134.
3286:(9th ed.). Hoboken:
3160:The first word component
41:Operating principle of a
4292:Supramolecular chirality
3527:Chemical Crystallography
3363:Herschel, J.F.W. (1820)
3075:which involves a static
3001:{\displaystyle \Delta n}
2956:KramersâKronig relations
2939:{\displaystyle \Delta n}
2886:{\displaystyle \lambda }
2776:{\displaystyle \Delta n}
2173:{\displaystyle 2\theta }
849:{\displaystyle \Delta n}
425:of each specific chiral
60:Linearly polarized light
30:Not to be confused with
4133:Physical Review Letters
3948:Applied Physics Letters
3888:Applied Physics Letters
3846:Applied Physics Letters
3803:Physical Review Letters
3768:Applied Physics Letters
3610:Vavilov, S. I. (1950).
3542:Physical Review Letters
3217:Patrick Mailliet et al.
2950:(ORD). ORD spectra and
2254:{\displaystyle \theta }
2150:{\displaystyle \theta }
1642:into the equation for
1270:components as follows:
1114:of the net wave, while
592:) rotates the plane of
217:liquid-crystal displays
3737:10.1098/rspl.1898.0019
3667:10.1364/JOSAA.5.001852
3194:, meaning "left side".
3140:Raman optical activity
3002:
2979:
2940:
2910:
2887:
2863:
2807:
2777:
2752:
2716:
2693:
2654:
2521:
2340:
2304:
2281:
2255:
2235:
2200:
2174:
2151:
2131:
2091:
1993:
1816:
1672:
1636:
1601:
1559:
1509:are unit vectors, and
1503:
1474:
1442:
1353:
1256:
1221:
1178:
1143:
1104:
1065:
918:
888:
850:
823:
722:circular polarizations
659:; this is known as an
518:Sir John F.W. Herschel
501:
493:
433:atom) can be labeled (
423:absolute configuration
368:absolute configuration
312:Absolute configuration
131:chiral liquid crystals
91:circular birefringence
79:
4430:Chiral pool synthesis
4344:Diastereomeric excess
4058:Butterworth-Heinemann
3995:Nature Communications
3503:Le Bel, J.-A. (1874)
3188:comes from the Latin
3120:Chirality (chemistry)
3069:plane of polarization
3003:
2980:
2941:
2911:
2888:
2864:
2808:
2778:
2753:
2717:
2694:
2655:
2522:
2341:
2305:
2282:
2256:
2236:
2201:
2175:
2152:
2132:
2092:
1994:
1817:
1673:
1637:
1602:
1560:
1504:
1475:
1443:
1354:
1257:
1222:
1179:
1144:
1105:
1066:
919:
889:
851:
824:
641:Jagadish Chandra Bose
610:Joseph Achille Le Bel
563:plane of polarization
531:Augustin-Jean Fresnel
499:
487:
417:)- prefixes from the
306:Chirality (chemistry)
255:plane-polarized light
87:polarization rotation
40:
4471:Polarization (waves)
4440:Asymmetric catalysis
4425:Asymmetric induction
4060:. pp. 362â365.
3731:(389â400): 146â152.
3702:10.1364/OL.17.000886
3525:Bunn, C. W. (1945).
3130:Polarization rotator
3067:Rotation of light's
2989:
2969:
2927:
2897:
2877:
2820:
2791:
2764:
2726:
2703:
2667:
2537:
2353:
2314:
2291:
2265:
2245:
2210:
2184:
2161:
2141:
2114:
2010:
1831:
1685:
1646:
1611:
1576:
1533:
1484:
1455:
1366:
1277:
1231:
1196:
1153:
1118:
1078:
931:
898:
871:
837:
771:
713:linear birefringence
512:by French physicist
4338:Enantiomeric excess
4145:2009PhRvL.102b3901Z
4102:2009PhRvB..79c5407P
4007:2012NatCo...3..833R
3960:2016ApPhL.108n1905P
3910:2008ApPhL..93s1911P
3858:2007ApPhL..90v3113P
3815:2005PhRvL..95v7401K
3780:2001ApPhL..78..498S
3694:1992OptL...17..886S
3659:1988JOSAA...5.1852S
3589:1969JChPh..50.1324W
3554:1968PhRvL..21..342W
3461:Pasteur, L. (1850)
3383:Biot, J. B. (1815)
2699:, thus rotated by
759:index of refraction
706:inorganic chemistry
698:enantiomeric excess
619:extrinsic chirality
127:secondary structure
4435:Chiral auxiliaries
4399:Kinetic resolution
4297:Inherent chirality
4282:-symmetric ligands
4016:10.1038/ncomms1805
3326:10.1002/chir.10270
3310:See, for example,
3100:Circular dichroism
2998:
2975:
2952:circular dichroism
2936:
2916:as we have shown.
2906:
2883:
2859:
2803:
2773:
2748:
2712:
2689:
2650:
2517:
2336:
2300:
2277:
2251:
2231:
2196:
2170:
2147:
2127:
2087:
1989:
1812:
1668:
1632:
1597:
1555:
1499:
1470:
1438:
1349:
1262:in terms of their
1252:
1217:
1174:
1139:
1100:
1061:
914:
884:
846:
819:
748:spatial dispersion
598:chemical synthesis
567:Invert sugar syrup
523:Jean Baptiste Biot
506:linearly polarized
502:
494:
350:-" prefixes. The "
300:Chirality prefixes
209:enantiomeric ratio
103:circular dichroism
99:linearly polarized
80:
4458:
4457:
4394:Recrystallization
4386:Chiral resolution
4209:Organic Chemistry
4192:Akhlesh Lakhtakia
4090:Physical Review B
4067:978-0-7506-2634-7
3968:10.1063/1.4944775
3918:10.1063/1.3021082
3866:10.1063/1.2745203
3788:10.1063/1.1342210
3597:10.1063/1.1671194
3494: : 445â454.
3425:), see pp. 72â81.
3283:Organic Chemistry
3219:, page 12 and 15.
3095:Specific rotation
3053:specific rotation
3017:aqueous solutions
3010:specific rotation
2978:{\displaystyle L}
2857:
2616:
2570:
2387:
2383:
2062:
2025:
1926:
1859:
1845:
1720:
1716:
1569:of that product.
1496:
1467:
1432:
1414:
1400:
1396:
1343:
1325:
1311:
1307:
966:
962:
702:organic chemistry
667:identical to its
548:
467:
463:
459:
445:
431:asymmetric carbon
421:characterize the
408:
404:
393:
389:
381:
377:
360:organic compounds
357:
353:
349:
345:
341:
270:chemical compound
52:Unpolarized light
16:(Redirected from
4483:
4361:Optical rotation
4306:Chiral molecules
4271:Planar chirality
4239:
4232:
4225:
4216:
4203:Optical Rotation
4165:
4164:
4128:
4122:
4121:
4087:
4078:
4072:
4071:
4038:
4029:
4028:
4018:
3986:
3980:
3979:
3945:
3936:
3930:
3929:
3903:
3885:
3876:
3870:
3869:
3841:
3835:
3834:
3798:
3792:
3791:
3763:
3757:
3756:
3720:
3714:
3713:
3677:
3671:
3670:
3641:
3635:
3634:
3622:
3616:
3615:
3607:
3601:
3600:
3572:
3566:
3565:
3537:
3531:
3530:
3522:
3516:
3515: : 337â347.
3501:
3495:
3480:
3474:
3459:
3453:
3451:
3435:
3426:
3398:
3392:
3381:
3375:
3361:
3355:
3344:
3338:
3337:
3308:
3302:
3301:
3277:
3271:
3270:
3268:
3245:
3237:
3231:
3226:
3220:
3201:
3195:
3158:
3007:
3005:
3004:
2999:
2984:
2982:
2981:
2976:
2945:
2943:
2942:
2937:
2915:
2913:
2912:
2907:
2892:
2890:
2889:
2884:
2868:
2866:
2865:
2860:
2858:
2853:
2836:
2812:
2810:
2809:
2804:
2782:
2780:
2779:
2774:
2757:
2755:
2754:
2749:
2747:
2746:
2745:
2744:
2734:
2721:
2719:
2718:
2713:
2698:
2696:
2695:
2690:
2679:
2678:
2659:
2657:
2656:
2651:
2637:
2636:
2618:
2617:
2609:
2591:
2590:
2572:
2571:
2563:
2557:
2556:
2545:
2526:
2524:
2523:
2518:
2508:
2507:
2496:
2490:
2489:
2488:
2487:
2470:
2469:
2451:
2450:
2439:
2433:
2432:
2431:
2430:
2410:
2409:
2388:
2379:
2378:
2373:
2372:
2361:
2345:
2343:
2342:
2337:
2335:
2334:
2333:
2332:
2322:
2309:
2307:
2306:
2301:
2286:
2284:
2283:
2278:
2260:
2258:
2257:
2252:
2240:
2238:
2237:
2232:
2230:
2229:
2218:
2205:
2203:
2202:
2197:
2179:
2177:
2176:
2171:
2156:
2154:
2153:
2148:
2136:
2134:
2133:
2128:
2126:
2125:
2096:
2094:
2093:
2088:
2083:
2082:
2064:
2063:
2055:
2046:
2045:
2027:
2026:
2018:
1998:
1996:
1995:
1990:
1980:
1979:
1978:
1977:
1957:
1956:
1955:
1954:
1928:
1927:
1919:
1910:
1909:
1908:
1907:
1887:
1886:
1885:
1884:
1861:
1860:
1852:
1846:
1838:
1821:
1819:
1818:
1813:
1806:
1805:
1794:
1788:
1787:
1786:
1785:
1765:
1764:
1753:
1747:
1746:
1745:
1744:
1721:
1712:
1711:
1706:
1705:
1704:
1703:
1693:
1677:
1675:
1674:
1669:
1667:
1666:
1665:
1664:
1654:
1641:
1639:
1638:
1633:
1631:
1630:
1619:
1606:
1604:
1603:
1598:
1596:
1595:
1584:
1564:
1562:
1561:
1556:
1554:
1553:
1508:
1506:
1505:
1500:
1498:
1497:
1489:
1479:
1477:
1476:
1471:
1469:
1468:
1460:
1447:
1445:
1444:
1439:
1434:
1433:
1425:
1416:
1415:
1407:
1401:
1392:
1391:
1386:
1385:
1374:
1358:
1356:
1355:
1350:
1345:
1344:
1336:
1327:
1326:
1318:
1312:
1303:
1302:
1297:
1296:
1285:
1261:
1259:
1258:
1253:
1251:
1250:
1239:
1226:
1224:
1223:
1218:
1216:
1215:
1204:
1183:
1181:
1180:
1175:
1173:
1172:
1161:
1148:
1146:
1145:
1140:
1138:
1137:
1126:
1109:
1107:
1106:
1101:
1099:
1098:
1097:
1096:
1086:
1070:
1068:
1067:
1062:
1052:
1051:
1040:
1034:
1033:
1032:
1031:
1011:
1010:
999:
993:
992:
991:
990:
967:
958:
957:
952:
951:
950:
949:
939:
923:
921:
920:
915:
913:
912:
893:
891:
890:
885:
883:
882:
855:
853:
852:
847:
828:
826:
825:
820:
817:
816:
798:
797:
752:Faraday rotation
727:refractive index
546:
468:, and most are (
465:
461:
457:
443:
406:
402:
391:
387:
379:
375:
370:relative to (+)-
355:
351:
347:
343:
337:
188:-rotary whereas
137:planes (such as
123:chiral molecules
107:optical activity
85:, also known as
83:Optical rotation
56:Linear polarizer
21:
4491:
4490:
4486:
4485:
4484:
4482:
4481:
4480:
4476:Stereochemistry
4461:
4460:
4459:
4454:
4445:Organocatalysis
4413:
4380:
4349:
4333:Racemic mixture
4301:
4287:Axial chirality
4281:
4254:Chirality types
4249:
4243:
4174:
4172:Further reading
4169:
4168:
4130:
4129:
4125:
4085:
4080:
4079:
4075:
4068:
4050:L.P. Pitaevskii
4040:
4039:
4032:
3988:
3987:
3983:
3943:
3938:
3937:
3933:
3883:
3878:
3877:
3873:
3843:
3842:
3838:
3800:
3799:
3795:
3765:
3764:
3760:
3722:
3721:
3717:
3679:
3678:
3674:
3643:
3642:
3638:
3624:
3623:
3619:
3609:
3608:
3604:
3574:
3573:
3569:
3539:
3538:
3534:
3524:
3523:
3519:
3502:
3498:
3481:
3477:
3460:
3456:
3436:
3429:
3399:
3395:
3382:
3378:
3374: : 43â51.
3362:
3358:
3345:
3341:
3311:
3309:
3305:
3298:
3279:
3278:
3274:
3266:
3260:
3243:
3239:
3238:
3234:
3227:
3223:
3202:
3198:
3166:comes from the
3159:
3155:
3150:
3145:
3110:Geometric phase
3090:Cryptochirality
3085:
3065:
3049:
3026:
2987:
2986:
2967:
2966:
2925:
2924:
2895:
2894:
2875:
2874:
2837:
2818:
2817:
2789:
2788:
2762:
2761:
2736:
2729:
2724:
2723:
2701:
2700:
2670:
2665:
2664:
2628:
2582:
2540:
2535:
2534:
2491:
2479:
2471:
2455:
2434:
2422:
2411:
2392:
2356:
2351:
2350:
2324:
2317:
2312:
2311:
2289:
2288:
2263:
2262:
2243:
2242:
2213:
2208:
2207:
2182:
2181:
2159:
2158:
2139:
2138:
2117:
2112:
2111:
2074:
2037:
2008:
2007:
1969:
1961:
1946:
1935:
1899:
1891:
1876:
1865:
1829:
1828:
1789:
1777:
1769:
1748:
1736:
1725:
1695:
1688:
1683:
1682:
1656:
1649:
1644:
1643:
1614:
1609:
1608:
1579:
1574:
1573:
1536:
1531:
1530:
1482:
1481:
1453:
1452:
1369:
1364:
1363:
1280:
1275:
1274:
1234:
1229:
1228:
1199:
1194:
1193:
1186:basis functions
1156:
1151:
1150:
1121:
1116:
1115:
1088:
1081:
1076:
1075:
1035:
1023:
1015:
994:
982:
971:
941:
934:
929:
928:
904:
896:
895:
874:
869:
868:
835:
834:
802:
783:
769:
768:
653:
482:
374:, which is the
318:
308:
302:
232:
225:
78:
71:linear analyzer
35:
28:
23:
22:
15:
12:
11:
5:
4489:
4487:
4479:
4478:
4473:
4463:
4462:
4456:
4455:
4453:
4452:
4447:
4442:
4437:
4432:
4427:
4421:
4419:
4415:
4414:
4412:
4411:
4406:
4401:
4396:
4390:
4388:
4382:
4381:
4379:
4378:
4373:
4368:
4363:
4357:
4355:
4351:
4350:
4348:
4347:
4341:
4335:
4330:
4325:
4320:
4315:
4309:
4307:
4303:
4302:
4300:
4299:
4294:
4289:
4284:
4279:
4273:
4268:
4263:
4257:
4255:
4251:
4250:
4244:
4242:
4241:
4234:
4227:
4219:
4213:
4212:
4205:
4199:
4189:
4177:Eugene Hecht,
4173:
4170:
4167:
4166:
4123:
4073:
4066:
4030:
3981:
3954:(14): 141905.
3931:
3894:(19): 191911.
3871:
3852:(22): 223113.
3836:
3809:(22): 227401.
3793:
3758:
3715:
3682:Optics Letters
3672:
3636:
3617:
3602:
3567:
3532:
3517:
3496:
3475:
3469:, 3rd series,
3454:
3427:
3405:, 2nd series,
3393:
3376:
3356:
3339:
3303:
3296:
3272:
3258:
3232:
3221:
3196:
3152:
3151:
3149:
3146:
3144:
3143:
3137:
3132:
3127:
3122:
3117:
3112:
3107:
3102:
3097:
3092:
3086:
3084:
3081:
3077:magnetic field
3073:Faraday effect
3064:
3061:
3048:
3045:
3024:
2997:
2994:
2974:
2935:
2932:
2905:
2902:
2882:
2871:
2870:
2856:
2852:
2849:
2846:
2843:
2840:
2834:
2831:
2828:
2825:
2802:
2799:
2796:
2772:
2769:
2743:
2739:
2733:
2711:
2708:
2688:
2685:
2682:
2677:
2673:
2661:
2660:
2649:
2646:
2643:
2640:
2635:
2631:
2627:
2624:
2621:
2615:
2612:
2606:
2603:
2600:
2597:
2594:
2589:
2585:
2581:
2578:
2575:
2569:
2566:
2560:
2555:
2552:
2549:
2544:
2528:
2527:
2516:
2511:
2506:
2503:
2500:
2495:
2486:
2482:
2478:
2474:
2468:
2465:
2462:
2458:
2454:
2449:
2446:
2443:
2438:
2429:
2425:
2421:
2418:
2414:
2408:
2405:
2402:
2399:
2395:
2391:
2386:
2382:
2376:
2371:
2368:
2365:
2360:
2331:
2327:
2321:
2299:
2296:
2276:
2273:
2270:
2250:
2228:
2225:
2222:
2217:
2206:. Let us call
2195:
2192:
2189:
2169:
2166:
2146:
2124:
2120:
2100:
2099:
2098:
2097:
2086:
2081:
2077:
2073:
2070:
2067:
2061:
2058:
2052:
2049:
2044:
2040:
2036:
2033:
2030:
2024:
2021:
2015:
2002:
2001:
2000:
1999:
1986:
1983:
1976:
1972:
1968:
1964:
1960:
1953:
1949:
1945:
1942:
1938:
1934:
1931:
1925:
1922:
1916:
1913:
1906:
1902:
1898:
1894:
1890:
1883:
1879:
1875:
1872:
1868:
1864:
1858:
1855:
1849:
1844:
1841:
1836:
1823:
1822:
1809:
1804:
1801:
1798:
1793:
1784:
1780:
1776:
1772:
1768:
1763:
1760:
1757:
1752:
1743:
1739:
1735:
1732:
1728:
1724:
1719:
1715:
1709:
1702:
1698:
1692:
1663:
1659:
1653:
1629:
1626:
1623:
1618:
1594:
1591:
1588:
1583:
1552:
1549:
1546:
1543:
1539:
1515:imaginary unit
1495:
1492:
1466:
1463:
1449:
1448:
1437:
1431:
1428:
1422:
1419:
1413:
1410:
1404:
1399:
1395:
1389:
1384:
1381:
1378:
1373:
1360:
1359:
1348:
1342:
1339:
1333:
1330:
1324:
1321:
1315:
1310:
1306:
1300:
1295:
1292:
1289:
1284:
1249:
1246:
1243:
1238:
1214:
1211:
1208:
1203:
1171:
1168:
1165:
1160:
1136:
1133:
1130:
1125:
1112:electric field
1095:
1091:
1085:
1072:
1071:
1060:
1055:
1050:
1047:
1044:
1039:
1030:
1026:
1022:
1018:
1014:
1009:
1006:
1003:
998:
989:
985:
981:
978:
974:
970:
965:
961:
955:
948:
944:
938:
911:
907:
903:
881:
877:
845:
842:
831:
830:
815:
812:
809:
805:
801:
796:
793:
790:
786:
782:
779:
776:
731:speed of light
717:phase velocity
652:
649:
630:lithium iodate
626:Sergey Vavilov
514:François Arago
481:
478:
372:glyceraldehyde
304:Main article:
301:
298:
274:dextrorotatory
259:dextrorotation
241:(also spelled
235:Dextrorotation
229:Levo (company)
224:
221:
205:sugar industry
150:dextrorotatory
77:
76:
73:
67:
64:
61:
58:
53:
50:
46:
26:
24:
18:Dextrorotation
14:
13:
10:
9:
6:
4:
3:
2:
4488:
4477:
4474:
4472:
4469:
4468:
4466:
4451:
4448:
4446:
4443:
4441:
4438:
4436:
4433:
4431:
4428:
4426:
4423:
4422:
4420:
4416:
4410:
4407:
4405:
4402:
4400:
4397:
4395:
4392:
4391:
4389:
4387:
4383:
4377:
4374:
4372:
4369:
4367:
4364:
4362:
4359:
4358:
4356:
4352:
4345:
4342:
4339:
4336:
4334:
4331:
4329:
4328:Meso compound
4326:
4324:
4321:
4319:
4316:
4314:
4311:
4310:
4308:
4304:
4298:
4295:
4293:
4290:
4288:
4285:
4283:
4278:
4274:
4272:
4269:
4267:
4264:
4262:
4259:
4258:
4256:
4252:
4248:
4240:
4235:
4233:
4228:
4226:
4221:
4220:
4217:
4210:
4206:
4204:
4200:
4197:
4193:
4190:
4188:
4187:0-201-30425-2
4184:
4180:
4176:
4175:
4171:
4162:
4158:
4154:
4150:
4146:
4142:
4139:(2): 023901.
4138:
4134:
4127:
4124:
4119:
4115:
4111:
4107:
4103:
4099:
4096:(3): 035407.
4095:
4091:
4084:
4077:
4074:
4069:
4063:
4059:
4055:
4051:
4047:
4046:E.M. Lifshitz
4043:
4037:
4035:
4031:
4026:
4022:
4017:
4012:
4008:
4004:
4000:
3996:
3992:
3985:
3982:
3977:
3973:
3969:
3965:
3961:
3957:
3953:
3949:
3942:
3935:
3932:
3927:
3923:
3919:
3915:
3911:
3907:
3902:
3897:
3893:
3889:
3882:
3875:
3872:
3867:
3863:
3859:
3855:
3851:
3847:
3840:
3837:
3832:
3828:
3824:
3820:
3816:
3812:
3808:
3804:
3797:
3794:
3789:
3785:
3781:
3777:
3773:
3769:
3762:
3759:
3754:
3750:
3746:
3742:
3738:
3734:
3730:
3726:
3719:
3716:
3711:
3707:
3703:
3699:
3695:
3691:
3687:
3683:
3676:
3673:
3668:
3664:
3660:
3656:
3652:
3648:
3640:
3637:
3632:
3628:
3621:
3618:
3613:
3606:
3603:
3598:
3594:
3590:
3586:
3582:
3578:
3571:
3568:
3563:
3559:
3555:
3551:
3547:
3543:
3536:
3533:
3528:
3521:
3518:
3514:
3510:
3506:
3500:
3497:
3493:
3489:
3485:
3479:
3476:
3472:
3468:
3464:
3458:
3455:
3450:
3445:
3441:
3434:
3432:
3428:
3424:
3420:
3416:
3412:
3408:
3404:
3397:
3394:
3390:
3386:
3380:
3377:
3373:
3369:
3366:
3360:
3357:
3353:
3349:
3346:Arago (1811)
3343:
3340:
3335:
3331:
3327:
3323:
3319:
3315:
3307:
3304:
3299:
3297:9780471684961
3293:
3290:p. 195.
3289:
3285:
3284:
3276:
3273:
3265:
3261:
3259:9789241550031
3255:
3251:
3250:
3242:
3236:
3233:
3230:
3225:
3222:
3218:
3214:
3213:
3208:
3207:
3200:
3197:
3193:
3192:
3187:
3186:
3181:
3180:
3175:
3174:
3169:
3165:
3164:
3157:
3154:
3147:
3141:
3138:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3116:
3113:
3111:
3108:
3106:
3105:Birefringence
3103:
3101:
3098:
3096:
3093:
3091:
3088:
3087:
3082:
3080:
3078:
3074:
3070:
3062:
3060:
3058:
3054:
3046:
3044:
3042:
3038:
3034:
3030:
3022:
3018:
3013:
3011:
2995:
2972:
2964:
2959:
2957:
2953:
2949:
2933:
2922:
2917:
2903:
2880:
2854:
2850:
2847:
2844:
2841:
2832:
2829:
2823:
2816:
2815:
2814:
2800:
2794:
2786:
2770:
2758:
2741:
2737:
2709:
2686:
2680:
2675:
2671:
2644:
2638:
2633:
2629:
2622:
2619:
2610:
2604:
2598:
2592:
2587:
2583:
2576:
2573:
2564:
2558:
2553:
2550:
2547:
2533:
2532:
2531:
2514:
2504:
2501:
2498:
2484:
2480:
2476:
2472:
2466:
2460:
2456:
2452:
2447:
2444:
2441:
2427:
2423:
2419:
2416:
2412:
2406:
2400:
2397:
2393:
2384:
2380:
2374:
2369:
2366:
2363:
2349:
2348:
2347:
2329:
2325:
2297:
2274:
2268:
2248:
2226:
2223:
2220:
2193:
2187:
2167:
2164:
2144:
2122:
2118:
2109:
2105:
2079:
2075:
2068:
2065:
2056:
2050:
2042:
2038:
2031:
2028:
2019:
2013:
2006:
2005:
2004:
2003:
1974:
1970:
1966:
1962:
1958:
1951:
1947:
1943:
1940:
1936:
1929:
1920:
1914:
1904:
1900:
1896:
1892:
1888:
1881:
1877:
1873:
1870:
1866:
1853:
1842:
1839:
1834:
1827:
1826:
1825:
1824:
1802:
1799:
1796:
1782:
1778:
1774:
1770:
1766:
1761:
1758:
1755:
1741:
1737:
1733:
1730:
1726:
1717:
1713:
1707:
1700:
1696:
1681:
1680:
1679:
1661:
1657:
1627:
1624:
1621:
1592:
1589:
1586:
1570:
1568:
1550:
1547:
1544:
1541:
1537:
1528:
1524:
1520:
1516:
1512:
1490:
1461:
1426:
1420:
1417:
1408:
1397:
1393:
1387:
1382:
1379:
1376:
1362:
1361:
1337:
1331:
1328:
1319:
1308:
1304:
1298:
1293:
1290:
1287:
1273:
1272:
1271:
1269:
1265:
1247:
1244:
1241:
1212:
1209:
1206:
1191:
1187:
1169:
1166:
1163:
1134:
1131:
1128:
1113:
1093:
1089:
1058:
1048:
1045:
1042:
1028:
1024:
1020:
1016:
1012:
1007:
1004:
1001:
987:
983:
979:
976:
972:
963:
959:
953:
946:
942:
927:
926:
925:
909:
905:
901:
879:
875:
866:
865:superposition
862:
857:
843:
813:
810:
807:
803:
799:
794:
791:
788:
784:
780:
777:
767:
766:
765:
763:
760:
755:
753:
749:
744:
739:
736:
733:(in vacuum),
732:
728:
724:
723:
718:
714:
709:
707:
703:
699:
695:
689:
686:
682:
678:
674:
670:
666:
662:
658:
657:stereoisomers
650:
648:
646:
642:
637:
633:
631:
627:
622:
620:
614:
611:
607:
602:
599:
595:
591:
587:
586:tartaric acid
583:
582:Louis Pasteur
578:
576:
572:
568:
564:
561:, causes the
560:
556:
552:
544:
540:
536:
535:birefringence
532:
528:
524:
519:
515:
511:
507:
498:
491:
490:tartaric acid
486:
479:
477:
475:
471:
455:
451:
447:
440:
436:
432:
428:
424:
420:
416:
412:
399:
397:
385:
373:
369:
365:
361:
340:
335:
331:
327:
323:
317:
313:
307:
299:
297:
295:
291:
287:
283:
282:laevorotatory
279:
275:
271:
266:
264:
263:laevorotation
260:
256:
252:
248:
244:
240:
239:laevorotation
236:
230:
222:
220:
218:
214:
210:
206:
202:
197:
195:
191:
187:
183:
179:
175:
171:
167:
163:
159:
155:
151:
146:
144:
143:metamaterials
140:
136:
132:
128:
124:
120:
116:
115:birefringence
112:
108:
104:
100:
96:
92:
88:
84:
74:
72:
68:
65:
62:
59:
57:
54:
51:
48:
47:
44:
39:
33:
19:
4450:Biocatalysis
4360:
4323:Diastereomer
4313:Stereoisomer
4276:
4266:Stereocenter
4245:Concepts in
4208:
4178:
4136:
4132:
4126:
4093:
4089:
4076:
4053:
3998:
3994:
3984:
3951:
3947:
3934:
3891:
3887:
3874:
3849:
3845:
3839:
3806:
3802:
3796:
3771:
3767:
3761:
3728:
3724:
3718:
3685:
3681:
3675:
3653:(11): 1852.
3650:
3646:
3639:
3630:
3627:JETP Letters
3626:
3620:
3611:
3605:
3580:
3576:
3570:
3545:
3541:
3535:
3526:
3520:
3512:
3508:
3499:
3491:
3487:
3478:
3470:
3466:
3457:
3439:
3422:
3414:
3406:
3402:
3396:
3388:
3379:
3371:
3367:
3359:
3351:
3342:
3317:
3313:
3306:
3282:
3275:
3248:
3235:
3224:
3211:
3205:
3199:
3189:
3183:
3177:
3171:
3161:
3156:
3115:Polarization
3066:
3050:
3047:Applications
3041:fused quartz
3014:
2960:
2918:
2872:
2784:
2759:
2662:
2529:
2107:
2103:
2101:
1571:
1566:
1522:
1518:
1510:
1450:
1267:
1263:
1189:
1073:
860:
858:
832:
761:
756:
743:permittivity
740:
734:
720:
710:
690:
684:
676:
669:mirror image
664:
654:
638:
634:
623:
615:
603:
594:polarization
579:
550:
539:polarimeters
503:
473:
469:
453:
449:
438:
434:
427:stereocenter
414:
410:
400:
364:biochemistry
333:
329:
325:
321:
319:
285:
281:
278:dextrorotary
277:
273:
267:
262:
258:
243:levorotation
242:
238:
234:
233:
198:
193:
185:
174:stereoisomer
169:
165:
162:levorotatory
161:
157:
154:dextrorotary
153:
149:
147:
106:
95:polarization
90:
86:
82:
81:
49:Light source
4042:L.D. Landau
3976:10220/40854
3688:(12): 886.
3583:(3): 1324.
3057:polarimeter
1678:we obtain:
529:. In 1822,
384:amino acids
286:laevorotary
201:polarimeter
190:cholesterol
43:polarimeter
4465:Categories
4318:Enantiomer
3774:(4): 498.
3548:(6): 342.
3391:, 190â192.
3320:: S57â64.
3206:dextrogyre
3148:References
3029:optic axis
2963:wavelength
2921:dispersion
661:enantiomer
645:microwaves
632:crystals.
571:hydrolysis
527:turpentine
446:-threonine
339:SMALL CAPS
310:See also:
294:enantiomer
213:polarizers
166:levorotary
69:Rotatable
4418:Reactions
4261:Chirality
4118:119259753
3926:117891131
3901:0807.0523
3417: :
3409: :
3314:Chirality
3035:forms of
3033:amorphous
2993:Δ
2931:Δ
2904:θ
2901:Δ
2881:λ
2855:λ
2851:π
2839:Δ
2830:θ
2827:Δ
2801:θ
2798:Δ
2768:Δ
2738:θ
2710:θ
2707:Δ
2687:θ
2684:Δ
2672:θ
2645:θ
2642:Δ
2630:θ
2623:
2614:^
2599:θ
2596:Δ
2584:θ
2577:
2568:^
2481:θ
2467:θ
2464:Δ
2424:θ
2417:−
2407:θ
2404:Δ
2398:−
2326:θ
2298:θ
2295:Δ
2275:θ
2272:Δ
2269:−
2249:θ
2194:θ
2191:Δ
2168:θ
2145:θ
2119:θ
2076:θ
2069:
2060:^
2039:θ
2032:
2023:^
1971:θ
1959:−
1948:θ
1941:−
1924:^
1901:θ
1878:θ
1871:−
1857:^
1779:θ
1738:θ
1731:−
1697:θ
1658:θ
1567:real part
1548:ω
1542:−
1494:^
1465:^
1430:^
1418:−
1412:^
1341:^
1323:^
1090:θ
1025:θ
984:θ
977:−
943:θ
906:θ
876:θ
841:Δ
800:−
775:Δ
673:chirality
624:In 1950,
604:In 1874,
590:wine lees
580:In 1849,
247:chemistry
4354:Analysis
4161:19257274
4052:(1984).
4025:22588295
3831:16384264
3753:89292757
3710:19794663
3334:12884375
3264:Archived
3212:lévogyre
3083:See also
3039:such as
639:In 1898
559:fructose
551:dextrose
413:)- and (
396:fructose
354:-" and "
346:-" and "
332:-" and "
75:Detector
4141:Bibcode
4098:Bibcode
4003:Bibcode
4001:: 833.
3956:Bibcode
3906:Bibcode
3854:Bibcode
3811:Bibcode
3776:Bibcode
3690:Bibcode
3655:Bibcode
3585:Bibcode
3550:Bibcode
3449:4745976
3446::
3411:372â389
3163:dextro-
1513:is the
1110:is the
694:racemic
575:sucrose
543:glucose
480:History
251:physics
182:camphor
178:sucrose
135:crystal
4185:
4179:Optics
4159:
4116:
4064:
4023:
3924:
3829:
3751:
3745:115973
3743:
3708:
3633:: 264.
3444:Zenodo
3332:
3294:
3256:
3191:laevus
3179:Laevo-
3173:dexter
3037:silica
3021:quartz
2873:where
1527:phasor
1451:where
1074:where
861:linear
833:While
651:Theory
555:dexter
510:quartz
437:) or (
405:- and
316:Aldose
290:chiral
139:quartz
119:fluids
111:chiral
4114:S2CID
4086:(PDF)
3944:(PDF)
3922:S2CID
3896:arXiv
3884:(PDF)
3749:S2CID
3741:JSTOR
3419:63â81
3267:(PDF)
3244:(PDF)
3185:levo-
3170:word
3168:Latin
3142:(ROA)
681:helix
245:) in
223:Forms
141:) or
4346:(de)
4340:(ee)
4183:ISBN
4157:PMID
4062:ISBN
4021:PMID
3827:PMID
3706:PMID
3330:PMID
3292:ISBN
3254:ISBN
3209:and
3023:(SiO
2287:and
2106:and
1607:and
1521:and
1480:and
1266:and
1227:and
1149:and
608:and
401:The
314:and
249:and
237:and
184:are
180:and
4149:doi
4137:102
4106:doi
4011:doi
3972:hdl
3964:doi
3952:108
3914:doi
3862:doi
3819:doi
3784:doi
3733:doi
3698:doi
3663:doi
3593:doi
3558:doi
3322:doi
3182:or
2620:sin
2574:cos
2066:sin
2029:cos
704:or
677:not
665:not
573:of
362:in
284:or
276:or
192:is
164:or
152:or
89:or
4467::
4194:,
4155:.
4147:.
4135:.
4112:.
4104:.
4094:79
4092:.
4088:.
4048:;
4044:;
4033:^
4019:.
4009:.
3997:.
3993:.
3970:.
3962:.
3950:.
3946:.
3920:.
3912:.
3904:.
3892:93
3890:.
3886:.
3860:.
3850:90
3848:.
3825:.
3817:.
3807:95
3805:.
3782:.
3772:78
3770:.
3747:.
3739:.
3729:63
3727:.
3704:.
3696:.
3686:17
3684:.
3661:.
3649:.
3631:29
3629:.
3591:.
3581:50
3579:.
3556:.
3546:21
3544:.
3513:22
3511:,
3490:,
3471:28
3430:^
3415:10
3413:;
3370:,
3328:.
3318:15
3316:.
3262:.
3246:.
2346::
1190:+z
685:is
683:)
452:,3
268:A
168:â
156:â
145:.
4280:2
4277:C
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4224:v
4163:.
4151::
4143::
4120:.
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4100::
4070:.
4027:.
4013::
4005::
3999:3
3978:.
3974::
3966::
3958::
3928:.
3916::
3908::
3898::
3868:.
3864::
3856::
3833:.
3821::
3813::
3790:.
3786::
3778::
3755:.
3735::
3712:.
3700::
3692::
3669:.
3665::
3657::
3651:5
3599:.
3595::
3587::
3564:.
3560::
3552::
3492:9
3407:9
3372:1
3336:.
3324::
3300:.
3025:2
2996:n
2973:L
2934:n
2869:,
2848:2
2845:L
2842:n
2833:=
2824:2
2795:2
2785:L
2771:n
2742:0
2732:E
2681:+
2676:0
2648:)
2639:+
2634:0
2626:(
2611:y
2605:+
2602:)
2593:+
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2580:(
2565:x
2559:=
2554:t
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2510:)
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2375:=
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2188:2
2165:2
2123:0
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2085:)
2080:0
2072:(
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2043:0
2035:(
2020:x
2014:=
1985:)
1982:)
1975:0
1967:i
1963:e
1952:0
1944:i
1937:e
1933:(
1930:i
1921:y
1915:+
1912:)
1905:0
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1848:(
1843:2
1840:1
1835:=
1808:)
1803:C
1800:H
1797:L
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1718:2
1714:2
1708:=
1701:0
1691:E
1662:0
1652:E
1628:C
1625:H
1622:L
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1436:)
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1403:(
1398:2
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1388:=
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954:=
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937:E
910:0
902:2
880:0
844:n
829:.
814:C
811:H
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781:=
778:n
762:n
547:D
492:.
474:R
470:S
466:L
462:L
460:/
458:D
454:S
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411:R
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394:-
392:D
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