International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2013 |
International Tables for Crystallography (2013). Vol. D, ch. 1.7, pp. 188-189
Section 1.7.3.1.3. Uniaxial class^{a}Institut Néel CNRS Université Joseph Fourier, 25 rue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France, and ^{b}Laboratoire de Photonique Quantique et Moléculaire, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan, France |
The uniaxial class is characterized by the equality of two principal indices, called ordinary indices (); the other index is called the extraordinary index (). Then, according to (1.7.3.6), the index surface has one umbilicus along the z axis, , called the optic axis, which is along the fold rotation axis of greatest order of the crystal. The two other principal axes are related to the symmetry elements of the orientation class according to the standard conventions (Nye, 1957). The ordinary sheet is spherical i.e. , so an ordinary wave has no walk-off for any direction of propagation in a uniaxial crystal; the extraordinary sheet is ellipsoidal i.e. . The sign of the uniaxial class is defined by the sign of the birefringence . Thus, according to these definitions, () corresponds to () for the positive class () and to () for the negative class (), as shown in Fig. 1.7.3.2.
The ordinary electric field vector is orthogonal to the optic axis (), and also to the extraordinary electric field vector, leading toThis relation is satisfied when ω_{i} and ω_{j} are equal or different and for any direction of propagation ().
According to these results, the coplanarity of the field vectors imposes the condition that the double-refraction angle of the extraordinary wave is in a plane containing the optic axis. Thus, the components of the ordinary and extraordinary unit electric field vectors e^{o} and e^{e} at the circular frequency ω arewith for the positive class and for the negative class. is given byNote that the extraordinary walk-off angle is nil for a propagation along the optic axis () and everywhere in the xy plane ().
References
Nye, J. F. (1957). Physical properties of crystals. Oxford: Clarendon Press.