Definitions

List of Contents

Introductory Remark
        Before listing short descriptions of the various forms of optical activity, a general comment on the terminology is in place. Two aspects need be distinguished: the underlying optical property inherent to matter and the manifestations of this property in specific optical experiments. For example, a dielectric solid with the property called Linear Dichroism rotates the polarization plane when acting on linearly polarized light but changes the ellipticity when acting on circularly polarized light. An optical property of a material is often referred to by one of its manifestations, which has lead to the use of different synonyms for the same physical property. Some of the synonyms have been indicated in parentheses after the preferred term. We mention in this context Circular Birefringence and Optical Rotation, the latter phenomenon (i.e., the rotation of plane polarized light) being recognized to be a consequence of the former (i.e., the difference in the Refractive Indices for left and right circularly polarized light) by Fresnel.

        An optical medium can be characterized by so-called eigen vectors. These vectors represent polarized light (here, circular or linear) of which the polarization is not altered by interaction with the medium. The eigen vectors can depend on the direction of light propagation. A medium with eigen vectors which differ in absorption gives rise to Dichroism; a difference in the Refraction to Birefringence. The interactions of the eigen vectors with the medium define the eigen values of the medium. The term Linear in expressions like Linear Dichroism and Linear Birefringence refers to media which have eigen vectors corresponding to linearly polarized light. Accordingly, Circular refers media with eigen vectors corresponding to circularly polarized light. In general, the effect of a medium on polarized light can be predicted by: (i) Expansion of the polarized light in the eigen vector basis for the medium. (ii) Calculation of the effect of the medium on the eigen vector components. (iii) Composition of the resulting vectors (including the eigen value factors obtained under (ii)). The construction is illustrated by the Figure. The refractive index (n) has emerged as a basic physical quantity for the description of the interaction between matter and light and from mid 19th century on theories have been advanced to relate this quantity with the electronic structure of matter. Therefore, where possible, we have used terms like Circular Birefringence (preferred term) instead of Optical Rotation (derived term). Descriptions of the derived terms have been included under the preferred term.

List of Descriptions
Birefringence
Circular Birefringence
Circular Dichroism
Cotton-Mouton Effect
Dichroism
Dispersion
Dispersion Relations
Double Absorption
Double Refraction
Faraday Effect
Linear Birefringence
Linear Dichroism
Magnetic Circular Birefringence
Magnetic Circular Dichroism
Magnetic Linear Birefringence
Magnetic Linear Dichroism
Magnetic Optical Rotation
Magnetic Optical Rotatory Dispersion
Natural Circular Birefringence
Natural Circular Dichroism
Optical Activity
Refractive Index
Zeeman Effect

List of Contents

Birefringence (B)
(Synonym: Double Refraction) Birefringence is the dependence of light refraction on light polarization. The refractive index is related to the speed of light (See Refractive Index). A beam of unpolarized light that is incident on a piece of birefringent material is split at the surface into polarized beams propagating along different trajectories with different speeds (called the normal and extraordinary rays). This phenomenon is the origin of the terms Birefringence and Double Refraction.

Circular Birefringence (CB)
(Synonyms: Circular Double Refraction; Optical Rotation; Optical Rotatory Strength; Optical Rotatory Dispersion) Circular Birefringence is the difference in refraction (and the associated speed of light) of left and right circularly polarized light. The effect can been observed in liquids and solutions even if the chromophores are randomly oriented in space. In the latter case, CB reflects the dissymmetry (that is, the lack of mirror symmetry) of the liquid molecules or dissolved chromophores and is only observed for molecules with a three-dimensional structure. CB studies have played an important role in the development of stereochemistry. The polarization plane of linearly polarized light traversing a Circularly Birefringent medium is rotated. The rotation is the result of an increment in the relative phase of the left and right circularly polarized components in which the plane polarized light can be decomposed. The increment (which can be either positive or negative) is caused by differences in the interactions of left and right circularly polarized light with a medium consisting of chiral molecules. The rotation angle is given by

,
where l is the wavelength of the light, l is the path length traversed by the light, and nL and nR are the Refractive Indices for left and right circularly polarized light of wavelength l. This aspect of CB is expressed by the term Optical Rotation. The Optical Rotatory Strength is the material-specific proportionality constant (vCB) occurring in the law
,
where N is the molar concentration of chromophores. The term Optical Rotatory Dispersion is used to describe the dependence of CB on light frequency.

Circular Dichroism (CD)
Circular Dichroism is the difference in the absorption (or emission) of left and right circularly polarized light. Like CB, the effect can already been observed in liquids and solutions in which the chromophores are randomly oriented in space. CD (also called natural CD) reflects the dissymmetry (that is, the lack of mirror symmetry) of the liquid molecules or dissolved chromophores and can only be observed for molecules with a three-dimensional structure (See also: Circular Birefringence)

Cotton-Mouton Effect
The Cotton-Mouton Effect is the combination of Magnetic Linear Birefringence and Magnetic Linear Dichroism of molecular solutions (or colloidal suspensions) caused by the alignment of the molecules (or colloidal particles) induced upon application of a magnetic field (See Linear Birefringence and Linear Dichroism). The Cotton-Mouton effect should not be confused with the intrinsic MLB and MLD effects, which are independent of molecular alignment (SeeMagnetic Linear Birefringence and Magnetic Linear Dichroism).

Dichroism (D)
(Synonym: Double Absorption) In this homepage we are essentially concerned with electric dipole transitions in molecules. With each electronic transition there is associated an electric transition dipole moment, which is a 3-dimensional vector with, in general, complex components. The vector has a definite spatial relationship ("direction") with respect to the nuclear frame of the molecule. The absorption (or emission) of polarized light by the molecule depends on the degree of alignment of the electric radiation field with respect to the electric transition dipole moment. This dependence confers upon the molecule an anisotropy as to its interaction with polarized light. The anisotropy gives rise to Dichroism (also called Natural Dichroism or Double Absorption), which is defined as the effect of there being a difference in the absorption (or emission) of monochromatic light depending on the polarization of the light. Atoms, which are spherically symmetric, do not exhibit any Natural Dichroism without the intervention of symmetry breaking by an applied field. Dichroism of molecular assemblies is related to the Dichroism of the molecular constituents (See Linear Dichroism and Circular Dichroism). In the current definition, Dichroism is an effect that can be observed for monochromatic light. This seems to conflict with the literal meaning of the word "Dichroism = Two-coloredness". The explanation for the termís origin is the following. If one observes a crystal, such as tourmaline, through a linear polarizer, one observes color changes by rotating the polarizer. In other words, the rotation alters the polarized spectrum (i.e., the functional dependence of the transmitted light intensity on frequency). The spectral change is caused by the fact that the absorption difference of the two linearly polarized light components is a function of light frequency. The latter effect is called Dichroic Dispersion and is usually what is meant if the term Dichroism is used.

Dispersion
Dispersion is the dependence of a physical quantity on the frequency of light. The Dispersion of the wavelength of light (l(w)) defines the velocity of light (cí = lw/2p) as a function of color.

Dispersion Relations
A Dispersion Relation expresses the Dispersion of the real part (ní) of the Refractive Index into the imaginary part (n") of the Refractive Index, or vice versa. In the framework of linear response theory, general expressions for the Dispersion Relations (ní(n") and n"(ní)) have been derived by Kramers and Kronig. These relations give a mathematical formulation for the causality principle, viz. that cause precedes effect. It follows that the Dispersion Curves for refraction and absorption are interconvertable quantities and have essentially the same information content. Similar relationships exist for the dispersions in Birefringenceand Dichroism, eliminating the need to do both types of measurement. Dichroic measurements have become the preferred technique for practical reasons.

Double Absorption
(Synonym: Dichroism)

Double Refraction
(Synonym: Birefringence)

Faraday Effect
(Synonym: Magnetic Circular Birefringence)

Linear Birefringence (LB)
(Synonym: Linear Double Refraction) Linear Birefringence is the difference in refraction (and the associated speed of light) of linearly polarized light with orthogonal planes of polarization. The conditions for its occurrence are similar to those described for Linear Dichroism. The polarization plane of linearly polarized light does not change when the polarization plane is parallel to one of anisotropy axes of a Linearly Birefringent medium; only the relative phase of the two orthogonal linearly polarized components is affected (See Introductory Remark).

Linear Dichroism (LD)
Linear Dichroism is the difference in the absorption (or emission) of linearly polarized light beams with orthogonal planes of polarization. Atoms are strictly achroic as a result of their spherical symmetry. A certain degree of anisotropy is required to generate the effect. In general, the electronic transitions in single molecules are Dichroic, with the possible exception of transitions induced by polarized light incident along certain molecular symmetry planes. The effect completely cancels in ensembles of randomly oriented molecules (e.g., chromophores in solution) because with respect to disordered systems all linear polarization planes are equivalent. Linear Dichroism can only be observed in molecular ensembles in which the molecules are to some extent aligned (e.g., in samples with "texture"). The effect is also referred to as Natural Linear Dichroism to emphasize that no applied field is required for the effect to exist. If we consider a thin slab of Dichroic material, the direction along which the chromophores are aligned in the plane of the slab together with its normal define the optical anisotropy axes. Linearly polarized light incident on the slab with a polarization plane parallel to one of the anisotropy axes is diminished in intensity but not altered in polarization (for simplicity, we have assumed here that there is no Birefringence). The two types of polarized light can be considered as the eigen vectors of the material (vectors that are not changed, apart from a constant, by the action of the material) of which the corresponding eigen values are related to the light absorption by the slab. Given the direction of the electric transition dipole with respect to the molecular frame, LD can be used to determine molecular alignment, or vice versa. LD can also be observed from ordered arrays of molecular chromophores in crystals and samples containing molecules that are aligned by an externally applied field (See Cotton-Mouton Effect).

Magnetic Circular Birefringence (MCB)
(Synonyms: Faraday Effect; Magnetic Optical Rotation; Magnetic Optical Rotatory Dispersion (MORD)) Magnetic Linear Birefringence is a kind of Optical Activity that arises upon placing matter in a magnetic field. MCB is defined as the field-induced difference in refraction (and the associated speed of light) of the left and right circularly polarized components of light that is incident parallel to the magnetic field. MCB is a universal effect and does not require any of the prerequisites for natural CB, such as the presence of chiral molecules. MCB leads to the rotation of the polarization plane of linearly polarized light and is therefore also called Magnetic Optical Rotation. The dependence of the rotatory effect on color is referred to as Magnetic Rotatory Dispersion (MORD). The rotatory effect was discovered by Faraday in 1849 and is also called the Faraday Effect.  The discovery played an important role in establishing light as an electro-magnetic phenomenon.

Magnetic Circular Dichroism (MCD)
Magnetic Linear Dichroism is a kind of Optical Activity that arises upon placing matter in a magnetic field. MCD is defined as the field-induced difference in the absorption (or emission) of the left and right circularly polarized components of light that is incident parallel to the magnetic field. MCD is a universal effect and does not require any of the prerequisites for natural CD to occur. The strongest MCD effects have been measured for paramagnetic chromophores. These effects are far more intense than the accompanying natural CD, a property that can be used for selectively probing metal centers in proteins.

Magnetic Linear Birefringence (MLB)
Magnetic Linear Birefringence is a kind of Optical Activity that arises upon placing matter in a magnetic field. The MLB effect is defined as the difference in the refraction (or, equivalently, in the speed) of linearly polarized light beams that are incident normal to the magnetic field and of which the polarization planes are parallel and perpendicular to the applied magnetic field. As for MLD, two effects can be distinguished: intrinsic MLB and orientational MLB (See Magnetic Linear Dichroism).

Magnetic Linear Dichroism (MLD)
Magnetic Linear Dichroism is a kind of optical activity that is induced by placing matter in a magnetic field. The MLD effect is defined as the difference in the absorption (or emission) of linearly polarized light beams that are incident normal to the magnetic field and of which the polarization planes are parallel and perpendicular to the applied magnetic field. Two kinds of MLD can be distinguished. (1) The intrinsic MLD effect, which is a consequence of the Zeeman Effect (the relation between the two effects has been analyzed in some detail in theoretical studies by Voigt in 1902). (2) The orientational MLD effect, which results from orientation of molecules by the magnetic field (also called the Cotton-Mouton Effect). The latter effect resembles Natural Linear Dichroism in that it originates from the preference of molecules to orient themselves along a specified direction in space, but it differs from Natural Linear Dichroism in that the molecules are oriented by an external field and not "spontaneously" by intermolecular interactions. Field-induced orientation originates from interactions of the magnetic field with molecules having either a permanent magnetic moment or an induced magnetic moment. In the latter case, the magnetic interactions result in a torque if the magnetic polarization of the molecule is anisotropic. The average molecular orientation is temperature dependent, an effect described by Langevin. Orientational MLD is found to be stronger than intrinsic MLD in studies of liquid samples (either solutions or pure liquids). As a result, the intrinsic MLD escaped detection, despite great many attempts made by Kerr, Majorana, Meslin, Cotton and Mouton to detect the effect in the period 1900-20. Only if the chromophores are immobilized by freezing the liquid, the orientational effect can be eliminated and the intrinsic MLD measured. Recently, cryogenic conditions in conjunction with instrumental improvements afforded detection of an intrinsic MLD effect of molecular chromophores in frozen solution. The information content of intrinsic MLD differs from that of orientational MLD. While the former effect exclusively depends on chromophore's electronic response to the magnetic field, the latter effect rather reflects its molecular response and is therefore of little use for identification and characterization purposes. Moreover, intrinsic MLD is a universal effect, whereas orientational MLD is not.  Hereafter, we shall use the term MLD to indicate the intrinsic effect.

Magnetic Optical Rotation
(Synonym: Magnetic Circular Birefringence)

Magnetic Optical Rotatory Dispersion (MORD)
(Synonym: Magnetic Circular Birefringence)

Natural Circular Birefringence
(Synonym: Circular Birefringence)

Natural Circular Dichroism
(Synonym: Circular Dichroism) The adjective Natural is often used to indicate that the Dichroism (or Birefringence) in question is not caused by an externally applied field.

Optical Activity
Optical Activity is the effect of light polarization on the interaction of light and matter. This definition includes the various forms of (magnetic) Birefringence and (magnetic) Dichoism listed here.

Refractive Index
The Refractive Index is a material specific complex number, n = ní+in". The real part (ní) relates the speed of light in the material (cí) to the speed of light in vacuum: ní = c/cí; the imaginary part (n") is a measure for the absorption of light. In general, the Refractive Index depends on the light frequency (See Dispersion), the direction of light propagation with respect to the anisotropy axes of the medium, and polarization (See Introductory Remark).

Zeeman Effect
The Zeeman Effect is the splitting of a single unpolarized spectral line into a multiplet of polarized spectral lines occurring upon applying a magnetic field. The effect was discovered in atomic emission spectra of sodium by Zeeman in 1897. The splitting is associated with the alignment of electronic orbits (and spins) by the interaction of the magnetic momenta generated by these periodic electronic motions and a magnetic field. Depending on the direction of observation, the Zeeman spectra show either Magnetic Circular Dichroism or Magnetic Linear Dichroism. The MCD and MLD effects in atomic absorption spectra were detected in a series of studies that started mid 1960th.