Crystals uniaxial

Refractive index, where given for a uniaxial crystal, is for the ordinary (co) ray where given for a biaxial crystal, the index given is for the median ((3) value. Unless otherwise specified, the index is given for the sodium D-line (X = 589.3 m i). 

For, SHG it is desirable to fabricate fibres which allow single mode operation at the fundamental wavelength so that all the launched power is available for conversion. The frequencies for which single mode operation is possible in a step-index uniaxial crystal cored fibre with crystal axis along the fibre axis are given by (30.)... 

When the sample is capable of exhibiting double refraction, the specimen will then appear bright against a dark background. For example, when a uniaxial crystal is placed with the unique c axis horizontal on the stage, it will be alternately dark and bright as the stage is rotated. Furthermore, the crystal will... 

When, however, the uniaxial crystal is mounted with the c axis vertical... 

For biaxial crystals, similar results are obtained as with uniaxial crystals. The exception to this rule is that in monoclinic and triclinic systems, the polarization directions need not be parallel to faces or to the bisectors of face angles. If the prominent faces or edges of an extinguished crystal are not parallel to the axes of the initial polarizer, the extinction is said to be oblique (Fig. 3d). 

Knowledge of the type of extinction permits a determination of the system to which a given crystal belongs. A summary of the extinction characters covering biaxial and uniaxial crystals is provided in Table 3. 

Material like sapphire, which is a uniaxial crystal, does not show nonlinear fluorescence, and direct visualization of filaments is, consequently, not an option. However, the effect of rotation of plane polarization can also be probed in such materials by monitoring the spatial size of the white light disc, and of the spectrum of the super continuum that is produced. Figure 5.3 depicts some typical results obtained with 3 mm long sapphire crystals. The extent of the supercontinuum spectrum is seen to vary as a function of polarization angle. The supercontinuum spectrum has two components [39] symmetric broadening about the incident wavelength that is essentially ascribable to... 

Figure 8.11 Illustration of Mauguin twisted nematic cell, reported in 1911. Substrates are thin mica plates, which are uniaxial with their optic axis parallel to plane of plates. Apparently, uniaxial crystal stmcture of mica produces strong azimuthal anchoring of nematic LCs of Lehmann, such that director is parallel (or perpendicular) to optic axis of mica sheets at both surfaces. Mauguin showed that method of Poincard could be used to explain optics of system if it was assumed that LC sample created layer of material with uniformly rotating optic axis in twisted cells.

Measurements on single crystals of lower symmetry doped with NpO or PuOl" " should remove this uncertainty but no such experiment has been performed so far. However, the distinction between configurations (a) and (b) has been possible in an electron paramagnetic resonance study at 20 K on a single uniaxial crystal of RbU02(N03)3 doped with plutonyl ions. This study conclusively showed that the ground state is H4 with gy = 5.4 and g = 0 28). 

The principal refractive indices of uniaxial crystals are usually symbolized w or nw for the more important of the two, the one which is constant for all orientations, and t or n for the other one. When e is less than w (as in monammonium phosphate) the crystal is described as uniaxial negative when e is greater than co, as in quartz, Si02 (co = 1 544, e = 1 553), the crystal is described as uniaxial positive. 

Fig. 52. Convergent light figures, a. Uniaxial crystal with optic axis parallel (left) and slightly inclined (right) to line of vision. 6. Biaxial crystal with acute bisectrix parallel (left) and inclined (right) to fine of vision.

Pot a fuller discussion of the phenomenon, and a list of the crystal classes which (according to current theories) may exhibit it, see Wooster (1938) and International Tables (1952). Rotation of the plane of polarization, though difficult to observe and measure except in large isotropic and uniaxial crystals, and therefore of rather limited application in identification or structural investigations, is a phenomenon of great interest that has played an important part in the historical development of chemistry and crystallography. 

Optically uniaxial crystals may be tetragonal, hexagonal, or trigonal. If it is possible to recognize a shape characteristic of a particular system this information is useful supplementary evidence but it must be emphasized that the refractive index values by themselves are usually sufficient for identification. 

Crystals, except those belonging to the cubic system, are anisotropic in this respect the force of repulsion varies with the orientation of the crystal with respect to the direction of the field. The graph representing vectorialiy the diamagnetic susceptibility in all directions in a crystal is an ellipsoid, whose orientation with respect to the unit cell is restricted by symmetry in exactly the same way as that of the optical indicatrix. Thus, for uniaxial crystals the magnetic ellipsoid an ellipsoid of revolution whose unique axis coincides with the threefold, fourfold, or sixfold axis of the crystal for orthorhombic crystals the ellipsoid has three unequal axes which necessarily coincide with the three axes of the crystal for monoclinie crystals the only restriction is that one of the principal axes of the magnetic ellipsoid must coincide with the b axis of the crystal while for triclinic crystals the orientation of the ellipsoid is not restricted in any way. 

For the sake of illustration, the determination of the electrooptic coefficient for a uniaxial crystal is described below. Considering the nonlinear uniaxial medium of Figure 11, a D.C. electric field is applied in the z direction. The effect of the electric field is to modify the refractive index in the z direction by an amount proportional to the electric field, the modified ellipsoid is given as... 

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