Ordinary beam

A light beam falling normally on the entrance face of the polarizer is split into ordinary and extraordinary beams that propagate together until they reach the oblique face where the ordinary beam experiences total reflection. The extraordinary beam polarized perpendicularly to the optical axis of the crystal enters the second triangle prism and emerges from it with unchanged polarization. The symmetric construction of the polarizers ensures that both sides can be used as a beam entrance. 

Figure 4 An acousto-optic tunable filter [a, tellurium dioxide (Te02) crystal b, incident or input beam c, acoustic transducer d, rf input e, monochromatic light (ordinary beam) f, nonscattered light beam g, monochromatic light (extraordinary beam) h, acoustic wave absorber].

Optical investigations of smetic liquids indicated a behaviour of uniaxial or biaxial crystals depending on the special type of material. They are usually positive birefringent, which means that with transmitted light the ordinary beam has a lower refractive index. The nematic liquid is optically positive. 

In the shortened notation (ooe, eoe,. .. ). the frequencies satisfy the condition wavelength radiation, and the last symbol refers to the shortest-wavelength radiation. Here the ordinary beam, or o-beam is the beam with its polarization normal to the principal plane of the crystal, i. e. the plane containing the wave vector k and the crystallophysical axis Z (or the optical axis, for uniaxial crystals). The extraordinary beam, or e-beam is the beam with its polarization in the principal plane. The third-order term is responsible for the optical Ken-effect. 

For uniaxial crystals, the difference between the refractive indices of the ordinary and extraordinary beams, the birefringence An, is zero along the optical axis (the crystallophysical axis Z) and maximum in a direction normal to this axis. The refractive index for the ordinary beam does not depend on the direction of propagation. However, the refractive index for the extraordinary beam n (6>), is a function of the polar angle 6 between the Z axis and the vector k ... 

If the wave vector k forms an angle 0 0 or 90"" with the optical axis, the wave in the crystal splits into an ordinary beam (refractive index n = 2 = o) where the phase velocity is independent of 9, and an extraordinary wave (refractive index Uq) where and therefore the phase velocity does depend on the direction 6 (Fig. 6.1b). 

A convenient way to attain a very high degree of linear polarization is to use prisms made of the birefringent material calcite (CaCOs). The arrangements in Glan-Taylor and Glan-Thompson polarizers are shown in Fig. 6.46. Both these polarizers consist of a combination of two prisms, in the first type air-spaced, in the second case cemented. The prism angle has been chosen such that the ordinary beam is totally internally reflected and absorbed laterally in the prism, while the extraordinary beam is transmitted into the... 

A nematic liquid crystal with a uniform alignment of the director n behaves like a uniaxial crystal with positive optical anisotropy > <, (where He = i is the refraction index for the extraordinary beam and <, = is the refraction index for the ordinary beam). We can consider the cholesteric structure as a special case of a nematic structure when the director n describes a helix. As is shown in Figure 6.1, the optical anisotropy in CLCs is negative, i.e., rioh > K /i, where tiei, = np and n h = xa are the refractive indices for the extraordinary and ordinary beams, respectively. The index h indicates that the macroscopic optical axis corresponds to the direction of... 

Although an ordinary beam-column element is used to represent a PR connection element for numerical analyses, its stiffness needs to be updated at each iteration since the stiffness representing the partial rigidity depends on 6. This can be accomplished by updating the Young s modulus as ... 

In the crystals described there are one or two directions along which the double refraction does not occur. These directions are referred to as the optical axes of a crystal (in Figure 6.26 and further defined by line MN). Certainly, they are determined by the atomic stracture of a crystal. If the crystal has one such direction it is referred to as a single-axis crystal there are also biaxial crystals with two such directions. Any plane which runs through the crystal s optical axis is referred to as the main section or the main plane. Most interesting is the main section containing the light beam. The plane of the vector E oscillations in an ordinary beam is perpendicular to the main section and in extraordinary beam lies in the main plane. 

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