Birefringence and Circular Dichroism

Generally speaking, the phenomenon of optical activity can be explained considering that a chiral species interacts in a different manner with the two chiral— namely, circularly polarized—components of linearly polarized light. In particular, the optical rotation arises from the fact that left and right circularly polarized radiations propagate in the optically active medium with different velocities (circular birefringence). In other words, rii (X) in which ni (X) ad mr(A) 

In its absorption spectral region, an optically active sample may absorb the two circularly polarized components of a linearly polarized radiation to different extents. In such a case the species exhibits different absorption coefficients for left- and right-handed light, that is, Sl(A) r( )- This phenomenon is called circular dichroism CD) [3,4], When circular dichroism occurs, the two circularly 

The different absorption experienced by the two circularly polarized components is expressed by means of the ellipticity 0, defined as the angle whose tangent is equal to the ratio between the minor (m) and the major (A/) axes of the ellipse (Fig. 6.4). 

As it will be shown in the next paragraph, the value of ellipticity is related to the absorption difference for the two linearly polarized components, and depends on the wavelength of the radiation. The aim of CD spectroscopy is the measurement of the ellipticity as a function of wavelength. Although this kind of spectroscopy can be carried out in several spectral regions, the most popular case is that of CD in the UV-visible region, which arises from electronic transitions in molecules. Infrared CD spectroscopy, involving vibrational transitions, is less common yet used in several research laboratories. 

Similarly to the isotropic absorption spectrum (i.e., recorded using non-polar-ized light), the circular dichroism spectrum of a chemical species in solution is constituted by bands. There is, however, an important difference between absorption and CD spectra while the former exhibit only positive signals, the latter can show both positive and negative signals, because CD bands are due to absorption differences (Fig. 6.5). 

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This is the form of the scattering matrix for any medium with rotational symmetry even if all the particles are not identical in shape and composition. A collection of optically active spheres is perhaps the simplest example of a particulate medium which is symmetric under all rotations but not under reflection. Mirror asymmetry in a collection of randomly oriented particles can arise either from the shape of the particles (corkscrews, for example) or from optical activity (circular birefringence and circular dichroism). 

This result demonstrates the tendency of an optically active material to rotate the electric vector as it propagates through the sample. Materials possessing this property are normally composed of molecules having chiral symmetry. This effect leads to circular birefringence and circular dichroism, two optical properties that are frequently used in the characterization of biomaterials. 

Noncoaxial Birefringent/Dichroic Element Containing Circular Birefringence and Circular Dichroism... 

Muller T, Wiberg KB, Vaccaro PH (2000) Cavity ring-down polarimetry (CRDP) a new scheme for probing circular birefringence and circular dichroism in the gas phase. J Phys Chem 104 5959-5968... 

A compound is considered optically active if it shows the phenomena of circular birefringence and circular dichroism. These are the manifestations of different refractive indices, /i, and /Ir, and different extinction coefficients, , and Cr, respectively, for left-handed and for right-handed circularly polarized light. Optical activity is therefore closely related to the existence of elliptically and circularly polarized light. 

Circular birefringence , - and circular dichroism e, - Cr can both be measured as a function of the wavelength A or the wave number v. The two quantities are not mutually independent. If /Il(A) - /Ir(A) is known for A = 0 up to A = , values of f,.(A) - Er(A) for A = 0 up to A = < can be derived through a mathematical transformation, and vice versa. In spite of the fact that in practice it is not necessary to have values for the complete infinite interval of A, measurements over a sufficiently large range of values are in general quite difficult, so the transformation is not always possible. 

Figure 5 Schematic diagram of the Cotton effect, illustrating the effects of circular birefringence and circular dichroism within an isolated absorption band.

A medium is said to be circularly dichroic—it absorbs differently according to the state of circular polarization of the light—if kL — kR 0 it is circularly birefringent, which is manifested by optical rotation, if nL — nR = 0. Optical rotation and circular dichroism are not independent phenomena, but are connected by Kramers-Kronig relations ... 

Analogous to the definitions of linear birefringence and linear dichroism following equations (2.15) and (2.21), the form of equation (2.30) suggests the following optical anisotropies for circularly polarized light ... 

The most commonly encountered manifestations of chiroptical phenomena are circular birefringence (also known as optical rotation), optical rotatory dispersion (ORD), and circular dichroism (CD). An explanation as to the nature of circularly and linearly polarized light is provided, and the origins of the various chiroptical effects are discussed. In each instance, a concise summary of the calculations used by workers in the field to report the results of their investigations is provided. 

LFnder the influence of a static electric field liquid crystalline solutions of PBLG become uniaxially oriented and show both linear and circular birefringence and linear and circular dichroism. Accordingly, the measured CD shows a dependence of the microscopic angle, a, that the fast optical axis of the oriented solution makes with respect to the plane of polarization of the polarizer in the CD instrument. When the film is reasonably thin (0.01-0.1 mm thick) or/and only partially oriented (less than 5% orientation), the apparent CD of oriented film of deoxyribonucleic acid is expressed by the equation (50) ... 

Absorbing systems circular dichroism When linearly dichroic dye molecules are dissolved in a cholesteric liquid crystal the medium exhibits circular dichroism because of the helical arrangement of the solute molecules in the structure. The theory developed above can be extended to take into account the effect of absorption by treating the layers as both linearly birefringent and linearly dichroic. Assuming that the principal axes of linear birefringence and linear dichroism are the same, the Jones matrix of any layer with reference to its principal axes is... 

Circular birefringence will induce a differential retardation in the phase of the orthogonal states of circularly polarized light. Circular dichroism, on the other hand, results in anisotropic attenuation of left- and right-circularly polarized light. The Jones matrix of circularly dichroic materials is normally written as ... 

This composite material contains both linear and circular birefringence and dichroism. The orientation of the linear birefringence is at 0 and the orientation of the linear dichroism is at 9". 

The anisotropy itself may be linear or circular, or a combination of both. In linear anisotropy the refractive index depends on the direction of polarised light. It is found in solid polymers under tension and in viscous polymeric liquids during flow (shear and elongation). The refractive index can also depend on the chirality of polarised light in this case one speaks of circular or elliptic anisotropy. Thus the so-called "optical activity" is circular birefringence its extinction analogue is circular dichroism. 

When chirality is involved, information on solid-state structures and supra-molecular properties must be obtained by solid-state circular dichroism (CDf spectroscopy, as certain characteristics may be lost upon dissolution. However extreme care is required to obtain artifact-free solid-state CD spectra. This is because CD spectra in the solid state (except for special homogeneous cases [9,10]) are inevitably accompanied by parasitic signals that originate from thd macroscopic anisotropies of a sample such as LD (linear dichroism) and LB (linear birefringence) [11-16]. We have been working in the field of solid-state chirality for the last 30 years and recently developed a novel universal chiroptical spectrophotometer, UCS J-800KCM, for the measurement of true CD and circular birefringence (CB) spectra in the solid state [17]. 

Birefringence can be produced by mechanical stress exerted on optically isotropic media like glass and cubic crystals. Devices based on this phenomenon are used for polarization modulators. The so called photoelastic modulators (PEM) are widely used for measuring circular dichroism. The mechanical stress in the PEMs is produced by... 

As it is easily derived from Eqs. 6.4-18, the relations are valid also for birefringence and dichroism. As far as optical activity in the UV/VIS range is concerned transformations on this basis have already been widely used for decades to correlate circular-dichroism bands and Cotton effects, i.e. anomalies of the optical rotatory dispersion (Moffit and Moscowitz, 1959 Blout et al., 1967). Another relation is mentioned in the following section. 

The effects of the role of matrix birefringence, photoselection, and rotational diffusion on measuring the circular dichroism of chiral excited triplets embedded in a rigid matrix have been examined. The techniques described in this paper are applied to chiral dimer-like molecules in the binaphthyl and spirobifluorene series. Natural and magnetic circular dichroism spectra of selenofenchone provide evidence for a singlet-triplet component of the n - IT transition. ... 

In the next section we summarize the theoretical background for coupled cluster response theory and discuss certain issues related to their actual implementation. In Sections 3 and 4 we describe the application of quadratic and cubic response in calculations of first and second hyperpolarizabilities. The use of response theory to calculate magneto-optical properties as e.g. the Faraday effect, magnetic circular dichroism, Buckingham effect, Cotton-Mouton effect or Jones birefringence is discussed in Section 5. Finally we give some conclusions and an outlook in Section 6. 

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