Birefringence optical

Every transparent material has three refractive indices ny, and nz along the three main axes. A material withwx = ny = nz is called isotropic. At least two of these refractive indices differ in anisotropic materials. The difference between each pair of these refractive indices is called the birefringence A . 

Refractive indices vary according to the polarizability. For example, an alkane has greater polarizability along the chain than perpendicular to it because the electron mobility is greater along the chain. 

Amorphous, nonoriented polymers are not optically birefringent, because their optically anisotropic monomeric units are randomly ordered with respect to one another. A birefringence first occurs when the chains are oriented or placed under strain. Generally, the following relation holds  

each individual phase i contributes to the birefringence according to its volume fraction (f i and birefringence Am. These different phases can, for example, be the amorphous and crystalline phases of partially crystalline polymers, aggregates in block copolymers, fillers, or plasticized regions. 

A form, or shape, birefringence An/is produced when an electric field is distorted at the interface between two phases. In this case each phase must have dimensions of the order of the wavelength of light. 

The value of the refractive index n of light in the anisotropic medium depends on the direction of propagation s and on the direction of the polarisation of the light. For the given relative permittivity tensor ji, the refractive index can be determined from the relation (Born and Wolf 1970 Landau et al. 1987) 

It follows from (10.17) that the refractive index for an isotropic medium is determined by the permittivity constant only 

In the case of an anisotropic system, it is convenient to consider particular cases. Further on, expressions for characteristics of optical birefringence in two typical cases will be shown. 

Methods for the experimental estimation of birefringence can be found in the monograph by Tsvetkov et al. (1964), Janeschitz-Kriegl (1983) and in papers by Lodge and Schrag (1984), Inoue et al. (1991), and Kannon and Kornfield (1994). 

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Biaxial Orientation. Many polymer films require orientation to achieve commercially acceptable performance (10). Orientation may be uniaxial (generally in the machine direction [MD]) or biaxial where the web is stretched or oriented in the two perpendicular planar axes. The biaxial orientation may be balanced or unbalanced depending on use, but most preferably is balanced. Further, this balance of properties may relate particularly to tensile properties, tear properties, optical birefringence, thermal shrinkage, or a combination of properties. A balanced film should be anisotropic, although this is difficult to achieve across the web of a flat oriented film. 

M. Allain, P. Oswald, J. M. di Meglio. Structural defects and phase transition in a lyotropic system optical birefringence and order parameter measurements. Mol Cry St Liq Cryst 7625 161-169, 1988. 

The quantitative assessment of the overall orientation of PET fibers is generally made on the basis of fiber optical anisotropy measurements, i.e., measurements of the optical birefringence of the fiber. The determination of the value of optical birefringence makes it possible to determine the value of Hermans function of orientation based on the equation ... 

Techniques for differentiating between amorphous and crystalline are (i) sharp melting point, (ii) sharp peaks in the solid state infrared fingerprint region, (iii) optical birefringence observed when solid is viewed in a phase contrast microscope and (iv) sharp peaks in the powder X-ray diffraction pattern. 

Banding effects have also been seen in these wormlike micelle materials via optical birefringence [31, 32], although it is not clear that birefringence banding necessarily corresponds to shear banding [33], Of course, the anisotropy of bi-... 

Cao J, Berne BJ (1993) Theory of polarizable liquid crystals optical birefringence. J Chem Phys 99(3) 2213-2220... 

Starch granules, when observed imder polarized light, exhibit an optical birefringence pattern known as a "Maltese cross" (Fig. 5.4), which implies a high degree of molecular order within the granule (Greenwood, 1979). 

Keywords Microphotonics, silicon-on-insulator, integrated optics, birefringence, silicon... 

Figure 13 shows the optical birefringence measured on the (OOl)c and (llO)c faces [19]. According to the indicatrix deformation approach [25], the optical birefringence, An, for the (llO)c face can detect the antiferrodistortive transition, the square of long-range order (P>, and its fluctuation term (SP) in STO by ... 

In the optical Kerr gate experiment6 (Fig. 5), the sample is subjected to a linearly polarized pump beam that induces optical birefringence (and... 

A recent XRD study of CL/DNA complexes has revealed that the addition of linear lambda-phage DNA (48, 502 bp, contour length=16.5 pm) (Raedler et al., 1997) or plasmid DNA (Lin et al., 2000) to binary mixtures of cationic liposomes (mean diameter of 70 nm), consisting of mixtures of neutral lipid DOPC and cationic DOTAP, induces a topological transition from liposomes into collapsed condensates in the form of optically birefringent liquid crystalline (LC) globules with sizes on the order of 1pm. 

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