Positive uniaxial

Zircon belongs to the tetragonal system and is a positive uniaxial. The typical form shows the ill and the 110 planes. The two orientations selected for luminescence polarization study were the (110) plane, parallel to the basal section and the [100] row. In such cases the axis perpendicular to the (110) plane will be called X. The orientation notation is made according to the so-called Porto notation (Porto et al. 1956). The Xi(ZX2)Xi orientation means that the laser light entered parallel to the Xi axis of the crystal and is polarized in the Z direction, while the emission is collected along the Xi axis with X2 polarization. By polarization spectroscopy with a high spectral resolution (less then 0.1 nm) six lines are observed for the Dq- Fi transition of the Eu-II center instead of the maximum three allowed for an unique site (Fig. 5.12). In Z(XX)Z geometry which corresponds to observation of a-polarized luminescence we... 

Fig. 47. Left positive uniaxial indicatrix. Right negative uniaxial indicatrix.

Figure 11. Schematic representation of the refractive index ellipsoid for a positive uniaxial material at frequency w. (Reprinted with permission from Williams, D. J. Atigew. Chem. Int. Ed. Engl 1984,23,690. Copyright VCH Publishers.)...

The direction of the principal axes of the index of refraction tensor n can be described by the indicatrix. For isotropic crystals the indicatrix is a sphere. For positive uniaxial crystals it is a prolate spheroid (ns > n0j) for negative uniaxial crystals it is an oblate spheroid (nol > n,). For orientations away from the principal axis orientations, the extraordinary ray will have a refractive index h - intermediate between nm and ne. 

Figure 4.2. Principal sections of the wave surfaces, o is the point source, o.a. is the optic axis, (a) positive uniaxial liquid crystal, (b) negative uniaxial liquid crystal.

Figure 4.5. Perpendicular incidence on positive uniaxial liquid crystal films, o.a. is the optical axis, (a) rays incident along optical axis, (b) rays incident perpendicular to optical axis.

Figure 4.6. The axis of the positive uniaxial liquid crystal obliques from the surface. The rays AB/CD enter the sample in the direction perpendicular to the surface.

These rules are illustrated in Figure 4.7 showing a principal section of a positive uniaxial wave surface figure. OX is the axis. OS is an ordinary ray of which the vibration direction is at a right angle to the principal section (that is the plane SOX) and at a right angle to the ray. This is represented... 

Figure 4.7. Vibration directions of the ordinary and the extraordinary rays in a positive uniaxial liquid crystal. OX is optic axis.

Cholesteric-nematic phase transition change from negative uniaxiality to positive uniaxiality The electric field is parallel to the helix axis. ... 

Besides, both s tructures posses an optical anisotropy in the spectral range of X a where a i s the "lattice" constant. This is the so called anisotropy of shape described in [4]. Studies of birefringence in 2D PC from macroporous silicon [5] shows it is a positive uniaxial crystal with its optical axis oriented along the pores. The present work is focused on the studies of ID PC from grooved Si. It is expected to be a negative uniaxial crystal whose axis is perpendicular to the Si ribs. 

Fig. 3.17. Conversion charts for a positive uniaxial nematic for different alignments with the same pair of mica sheets, (a) Isotropic or homeotropic sample (n=1.3) between mica sheets with parallel (dashed outer lines) and perpendicular (solid inner line) optical axes. The splitting of the line for parallel alignment is due to the sheets birefringence, which is compensated by crossing the sheets over 7t/2. (b) Planar sample (rie=1.7, no=1.5) with the optical axis parallel to the optical axis of one sheet and perpendicular to the other, (c) Planar sample with the optical axis parallel (dashed outer lines) and perpendicular (inner solid lines) to both optical axes of the sheets.

Observations of the conoscopic images formed in a monochromatic beam converging in the sample are needed to check the uniformity of alignment (Figs 22 and 23). From conoscopic images, evidence has been found for the optically positive uniaxial behavior of... 

With the aid of conoscopic observations, Finkelmann has also proved the positive uniaxial character of comb-like polymers ... 

Both a film and c film can be further divided into positive or negative films depending on the relative values of the extraordinary refractive index tie and the ordinary refractive index Table 8.1 lists aU the types of compensation films and their refractive index relationship. In our analyses, we focus on the uniaxial films. As a general rale, a positive uniaxial film means Tie > no, otherwise, rig < tig for a negative uniaxial film. 

One distinguishes between type-I and type-II phase-matching depending on which of the three waves with coi, C02, C03 = coi C02 propagates as an ordinary or as an extraordinary wave. Type 1 corresponds to (1 e, 2 e, 3- 0) in positive uniaxial crystals and to (1 o, 2 o, 3 e) in negative uniaxial crystals, whereas type II is characterized by (1 o, 2 e, 3 o) for positive and (1 e, 2 o, 3 e) for negative uniaxial crystals [5.220]. Let us now illustrate these general considerations with some specific examples. 

FIGURE 2 Index surfaces for (a) a positive uniaxial crystal and (b) a negative uniaxial crystal [29]. 

Friedel did however understand the layered nature of smectics, firstly through the stepped edges possessed by smectic droplets with a free surface, and secondly through his detailed studies of the optical microscopic textures of thin films of smectic phases. He understood the optical discontinuities, i.e., the defects, of the smectic focal-conic texture and saw the relationship of the black lines delineating ellipses of different eccentricities and their associated hyperbolae in terms of focal-conic domains which may be divided into a series of parallel, curved surfaces known as Dupin cy-clides. He also understood that the optically extinct homeotropic textures of smectics of the type he studied gave positive uniaxial interference figures consistent with systems of layers lying flat to the surface. His microscopic studies demonstrated the immense value of the optical microscope as a precise scientific instrument in studies of all types of liquid crystal phases. 

The use of a single polarizer or analyser is sufficient to vary the defect contrast considerably. As the local ellipsoid of indices is positively uniaxial and the twist is weak, the electric vector of any penetrating wave rotates as the director orientation (Mauguin s condition the wavelength being very small compared to the cholesteric pitch) [66, 67]. 

The nonchiral nematic is optically a positive uniaxial medium. A cholesteric is a nematic with twist. The local structure of a cholesteric is believed to be the same as that of the nematic except that it lacks reflection symmetry. This means that the director and therefore the local extraordinary optic axis is rotating around the helix axis making the cholesteric a negative uniaxial medium with the optic axis coinciding with the twist axis. The question has been asked as to why the nematic with twist could not be biaxial, and attempts have been made to measure a slight biaxiality of the cholesteric phase. In other words, why could the twist not be realized in such a way that the long molecular axis is inclined to the twist axis Why does it have to be perpendicular ... 

The smectic A phase is optically positive uniaxial. The director and the optic axis are in the direction of highest refractive index, ni -/ix= w>0. At the tilting transition... 

Optically, the N phase is positive uniaxial, but it is predicted that where the molecules have a lathlike shape and their rotation along the long axis is also severely sterically hindered, the phase may be positive biaxial. Although the N phase characteristically occurs at a higher temperature than the smectic phase, some cases are known where the smectic phase exists within the tempraature range of the N phase (N-S-N)— although such reentrant phases are rare. ... 

An interesting feature of polymer nematics was discovered in studying the orientation of some polymethacrylate polymers and cross-linked LC elastomers based on polysiloxanes [57]. Most nematic polymers form an optically positive, uniaxial, homeotropic structure under the effect of a mechanical Held such polymers have a positive birefringence (An > 0), like most low-molecular-weight liquid crystals. 

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