Birefringence isotropic material

As has been pointed out (63), this is a rather artificial model and, moreover, its application is quite unnecessary. In fact, (a> can be calculated from the refractive index increment (dnjdc), as has extensively been done in the field of light scattering. This procedure is applicable also to the form birefringence effect of coil molecules, as the mean excess polarizability of a coil molecule as a whole is not influenced by the form effect. It is still built up additively of the mean excess polarizabilities of the random links. This reasoning is justified by the low density of links within a coil. In fact, if the coil is replaced by an equivalent ellipsoid consisting of an isotropic material of a refractive index not very much different from that of the solvent, its mean excess polarizability is equal to that of a sphere of equal volume [cf. also Bullough (145)]. 

Electro-optic effects refer to the changes in the refractive index of a material induced by the application of an external electric field, which modulates their optical properties [61, 62], Application of an applied external field induces in an optically isotropic material, like liquids, isotropic thin films, an optical birefringence. The size of this effect is represented by a coefficient B, called Kerr constant. The electric field induced refractive index difference is given by... 

Stress. The application of tensile stress to an isotropic material causes an increase in n normal to the direction of the applied stress and decreases n along the stressed direction. The situation is the exact opposite if a compressive stress is applied. The change of n with applied stress is known as stress birefringence. 

The speed of sound through a medium is a function of applied strain. The relationship is governed by the acoustoelastic coefficient. Stress states with unequal principle stresses (i.e., nonhydrostatic) have the effect of introducing anisotropic acoustic behavior to otherwise isotropic materials. This effect is similar to strain-induced optical birefringence (covered in the next section). The advantage is that ultrasonic birefringence can be measured in optically opaque materials. 

Strain-induced optical birefringence is a rapid and powerful technique for transparent isotropic materials. Not only is it possible for one to see residual strains introduced as a result of processing, but inclusions that are invisible to the naked eye can be seen by their associated strain fields. This technique is extremely fast. The product can be conveyed between two crossed polarizers, allowing a single inspector to inspect the output of a small factory. This technique is capable of resolving stresses of as little as 55 MPa (8 kpsi) in Pyrex glass. 

The optical properties of a birefringent material are shown by a surface called the index ellipsoid or indicatrix. The radial distance from the center to each point on this surface is proportional to the refractive index of light that has its electric displacement D in that radial direction. This is not the refractive index of light that is traveling in that direction. Cross sections of this surface are ellipses. The indicatrix of an isotropic material would be a sphere with circular cross sections. 

Birefringence is a classical method of measurement of orientation. The refractive index represents the slowing of the progress of an electromagnetic wave through a material because of interaction of the wave with polarizable molecules. This problem was first analyzed for isotropic materials (87-89) when the refractive index n was related to the molecular polarizability a through the expression... 

A separate problem for quantitative measurements is that aligned interfaces in optically isotropic materials can also affect the state of polarization. This form birefringence is usually small but inaeases with the density of interfaces and with the difference in the refractive index across the interface. It is difficult to calculate unless the exact stmcture is known. Copolymers or semicrystalline polymers with some phase dimension close to the wavelength of light may be affected. 

Copolymers and blends of BPA-PC and Modified PS. Theoretically, a blend or copolymer of 60 parts BPA-PC (positively birefringent) and 40 parts PS (negatively birefringent) should yield a product free of birefringence (Fig. 25) (207). In spite of modifications to PC to improve the compatibiUty, no blend could be produced which would be optically isotropic and thus suitable as a substrate material. The same holds tme for PC/PS-copolymers (208) in which... 

Tokuoka T., Iwashitnizu Yu., Acoustical birefringence of ultrasonic waves in deformed isotropic elastic materials, Int. J. Solids Structures, 4 (1968), 383—389. 

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