Circularly birefringent

Circular dicliroism has been a useful servant to tire biophysical chemist since it allows tire non-invasive detennination of secondary stmcture (a-helices and P-sheets) in dissolved biopolymers. Due to tire dissymmetry of tliese stmctures (containing chiral centres) tliey are biaxial and show circular birefringence. Circular dicliroism is tlie Kramers-Kronig transfonnation of tlie resulting optical rotatory dispersion. The spectral window useful for distinguishing between a-helices and so on lies in tlie region 200-250 nm and hence is masked by certain salts. The metliod as usually applied is only semi-quantitative, since tlie measured optical rotations also depend on tlie exact amino acid sequence. 

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 ... 

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). 

Rotation of the polarization plane (or the axes of the dichroic ellipse) by a small angle a occurs when the phases for the two circular components become different, which requires a difference in the refractive index n (Pearlman and Nguyen 1991). This effect is called circular birefringence. The change of optical rotation with wavelength is called optical rotary dispersion (ORD). 

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. 

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 ... 

The Faraday effect refers to the induction of circular birefringence following the... 

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

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". 

Linear and Circular Birefringence/Dichroic Element in the Limit of Small Anisotropies... 

The pump induced transient polarisation of the medium modifies the polarisation state of a time delayed probe pulse. Phenomenologically, this process can be regarded as a transient pump induced linear or circular birefringence, also called the Specular Optical Kerr Effect (SOKE) and the Specular Inverse Faraday Effect (SIFE) [18], These are cubic non-linear effects and are predicted to exist from symmetry arguments. Both effects consist of coherent and incoherent parts. For the coherent part, the pump drives the coherent electron-hole pair that affects the probe polarisation. The effect depends upon the probe phase relative to that of the electron-hole pair, and hence, that of the pump. For the incoherent part of the SIFE and the SOKE, the relative pump-probe phase is not important, since the probe pulse polarisation is modified by the pump induced sample polarisation that survives after the decoherence of the electron-hole pair. 

For a typical chiral organic compound, such as 2-butanol, the circular birefringence, nL - wR, at A = 589 nm is of the order of 10-7. Even for a very high a = 40° mm-1 at A = 589 nm ( wL - nR 2 X 10 4), linear birefringence, which may arise from residual ordering/aggregation of polymer chains, could easily overwhelm the circular birefringence. 

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. 

Cotton also investigated the use of ellipticity measurements for CD studies. The combination of a linear polarizer and a Fresnel rhomb was used by Cotton to produce polarized light which could vary in its orientation from circular to elliptical. A second linear polarizer was then used to monitor changes in the orientation of the major axis of the ellipse which occurs as a result of the CD. In addition, the apparatus could also be used to measure optical rotation (circular birefringence). The experimental simplicity of this approach relative to his other system allowed more sensitive measurements to be made. This experimental simplicity also served as an impetus for other researchers in the field, and the ellipticity approach dominated the available technology from the time of Cotton s first efforts to the 1960 s, when electronically modulated systems were developed. 

The intrinsic optical rotation (circular birefringence) exhibited by an optically active sample can experimentally complicate the measurement of CD when the measurement is... 

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. 

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... 

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]. 

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) ... 

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. 

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