Optical Anisotropy Birefringence

A consequence of these different refractive indices for the ordinary ray and the extraordinary ray is that the effective birefringence of the medium, A (0), also depends on the propagation direction  

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  

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In the single-domain state, many ferroelectric crystals also exhibit high optical nonlinearity and this, coupled with the large standing optical anisotropies (birefringences) that are often available, makes the ferroelectrics interesting candidates for phase-matched optical second harmonic generation (SHG). 

FIGURE 15.3 Crystal systems. Shown is the shape of the unit cell for each system, the number N of different Bravais lattices in each system, geometrical characteristics of the unit cell, and optical anisotropy (birefringence). Some examples of crystals of various materials are given. 

Optical anisotropy (birefringence, An) Self-organization Ordering (alignment)... 

An optically isotropic liquid crystal (LC) refers to a composite material system whose refractive index is isotropic macroscopically, yet its dielectric constant remains anisotropic microscopically [1]. When such a material is subject to an external electric field, induced birefringence takes place along the electric field direction if the employed LC host has a positive dielectric anisotropy (Ae). This optically isotropic medium is different from a polar Uquid crystal in an isotropic state, such as 5CB (clearing point = 35.4°C) at 50 C. The latter is not switchable because its dielectric anisotropy and optical anisotropy (birefringence) both vanish in the isotropic phase. Blue phase, which exists between cholesteric and isotropic phases, is an example of optically isotropic media. 

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 ... 

It should first be noted that the measurement of emission anisotropy is difficult, and instrumental artefacts such as large cone angles of the incident and/or observation beams, imperfect or misaligned polarizers, re-absorption of fluorescence, optical rotation, birefringence, etc., might be partly responsible for the difference between the fundamental and limiting anisotropies. 

Figure 4.1. Time scales for rotational motions of long DNAs that contribute to the relaxation of the optical anisotropy r(t). Experimental methods used to study these motions in different time ranges are also indicated along with the authors and dates of some early work in each case. FPA, Fluorescence polarization anisotropy (Refs. 15, 18-20, and 87) TPD, transient photodichroism (Refs. 28 and 62) TEB, transient electric birefringence (Refs. 26 and 27) DDLS, depolarized dynamic light scattering (Ref. 116) TED, transient electric dichroism (Refs. 25, 115, and 130) Microscopy, time-resolved fluorescent microscopy (Ref. 176).

If the molecules stand on edge and are oriented by the dipping process, there will exist an optical anisotropy which will manifest itself in dichroism or, if the material is thick enough, in birefringence. On the other hand, if the molecules lie flat, no optical anisotropy will be shown when the material is examined by transmitted light. Thus polarising... 

Particles in different growth stages in the n-butyl acrylate-glycol dimethacrylate system appears in Figure 5. There, no optical anisotropy appears because of the low straining birefringence of acrylates. 

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 polarizability tensor, a, introduced in section 4.1.2, is a measure of the facility of the electron distribution to distortion by an imposed electric field. The structure of the electron distribution will generally be anisotropic, giving rise to intrinsic birefringence. This optical anisotropy reflects the average electron distribution whereas vibrational and rotational modes of the molecules making up a sample will cause the polarizability to fluctuate in time. These modes are discrete, and considering a particular vibrational frequency, vk, the oscillating polarizability can be modeled as... 

The optical measurements presented in the previous chapters can be used to either characterize local, microstractural properties or as probes of bulk responses to orientation processes. In either case, it is normally desirable to make the connection between experimental observables and their molecular or microstractural origins. The particular molecular properties that are probed will naturally depend on the physical interaction between the light and the material. This chapter explores molecular models and theories that describe these interactions and identifies the properties of complex materials that can be extracted from measurements of optical anisotropies. The presentation begins with a discussion of molecular models that are applied to polymeric materials. Using these models, optical phenomena such as birefringence, dichroism, and Rayleigh and Raman scattering are predicted. Models appropriate for particulate systems are also developed. 

Formula (4.370) leads to a simple expression for the macroscopic optical anisotropy. If the Oz axis of the coordinate framework coincides with the applied held direction h, then the uniaxial symmetry condition yields (n2) = (n2) and vx = vy. Hence for the refractive index anisotropy (birefringence) we have... 

Formula (4.371) proves explicitly that the suspension birefringence is an even function of the applied field amplitude. For this reason, in response to the excitation of the frequency go the optical anisotropy Av oscillates with the basic frequency 2co. The higher-rank harmonics induced by the saturation behavior of Av((0) are the multiples of the basic one. It is also clear that besides the oscillatory contribution, the frequency spectrum of Av contains a constant component. 

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