Birefringence phase difference

For the determination of the birefringence effect, polarizer and analyzer are turned by an angle of 45° in their fittings. In this way, the maximum phase difference caused by the total reflection on the mirror device, is added to the phase difference caused by the flowing polymer. This mirror effect, however, can simply be subtracted. It can be calculated with the aid of an exact theory and it can also be measured, when the plate is at rest. For further details the original paper should be inspected (17). 

Figure 4.36. Birefringence phase shift for different values of the internal magnetic anisotropy of the particles. The set of material parameters and meanings of the thin lines are the same as those for Figure 4.34.

Interference between the e-ray and the o-ray, which have travelled with different velocity through the nematic medium, gives rise to the coloured appearance of LCDs operating with plane polarised light. For a wave at normal incidence, the phase difference in radians between the o-ray and the e-ray caused by traversing a birefringent film of thickness d and birefringence An, is referred to as the optical retardation, <5 ... 

Retarders are usually devices which rotate the polarization plane of radiation or convert linearly polarized radiation into a elliptically or circularly polarized one. Their basic physical function consists in decomposing the electric vector of the linearly polarized radiation into two mutually orthogonally polarized components between which a phase difference retardation) is created. Depending on the physical phenomenon that causes the retardation effect practical retarders based on birefringence and total internal reflection are known and used. 

Little is known about infrared refractive indices of organic compounds, and only very few such studies related to liquid crystals are reported. To some extend this is due to the fact that special techniques and even dedicated equipment are required. On the other hand birefringence can be derived from the polarization pattern produced by the phase difference between the ordinary and the extraordinary beam. This experiment had been outlined by Born and Wolf (1980) and was applied to liquid crystals by Wu et al. (1984). The procedure is primarily suitable in transparent regions, for a more comprehensive optical characterization it should be extended to complete ellipsometry (Reins et al., 1993). Results obtained by infrared-spectroscopic ellipsometry are shown in Figs. 4.6-5 and 4.6-6. 

After passage through a birefringent material of thickness e, the two components of linearly polarized light show a phase difference 6 equal to ... 

In all cases of practical importance, the anisotropy of solutions resulting from the combined action of dynamic and electric fields is not high the phase difference of two interfering polarized beams does not exceed 2 ir 10 . Under these conditions, the total birefringence An of the solution and the corresponding orientation angle a can be calculate according to ... 

Figure 1.35 Interaction between plane-polarized light and a birefringent object. Two plane-polarized light waves with a phase difference are generated by the materials. RI, refractive index.

Fig. 9. Drawing showing how a phase difference between Ey and Ez arises in a birefringent material. In this diagram nz > ny...

By contrast with the transmission case, where the phase difference induced by birefringent materials is smooth and progressive, the phase and amplitude changes of the p and s components induced by reflection at a boundary between two materials are discontinuous. Figure 2 shows the effect of these stepwise changes on the polarization of light obliquely incident on a metallic mirror. 

In order to improve the understanding of these systems, Kunieda and coworkers examined the thermotropic behavior of poly(oxyethylene) cholesteryl ethers with different chain lengths, ChFOn, mixed with water at a fixed concentration ( 25 wt%) [32]. This study focused on the different fusion mechanisms that were involved in the solid-liquid phase transition. The soUd-Uquid transition temperature for ChFOn as a function of n is shown in Figure 4.3 (for comparison, the transition temperature for polyethylene glycol is also shown). In both cases, the transition temperature decreased when the chain length was diminished. However, for the cholesterol surfactant, when n < 10, a birefringent phase appeared between... 

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