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. 189-190
Section 1.7.3.1.4. Biaxial 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 |
In a biaxial crystal, the three principal refractive indices are all different. The graphical representations of the index surfaces are given in Fig. 1.7.3.3 for the positive biaxial class () and for the negative one (), both with the usual conventional orientation of the optical frame. If this is not the case, the appropriate permutation of the principal refractive indices is required.
In the orthorhombic system, the three principal axes are fixed by the symmetry; one is fixed in the monoclinic system; and none are fixed in the triclinic system. The index surface of the biaxial class has two umbilici contained in the xz plane, making an angle V with the z axis:The propagation along the optic axes leads to the internal conical refraction effect (Schell & Bloembergen, 1978; Fève et al., 1994).
It is possible to define ordinary and extraordinary waves, but only in the principal planes of the biaxial crystal: the ordinary electric field vector is perpendicular to the z axis and to the extraordinary one. The walk-off properties of the waves are not the same in the plane as in the and planes.
It is impossible to define ordinary and extraordinary waves out of the principal planes of a biaxial crystal: according to (1.7.3.6) and (1.7.3.9), e^{+} and e^{−} have a nonzero projection on the z axis. According to these relations, it appears that e^{+} and e^{−} are not perpendicular, so relation (1.7.3.10) is never verified. The walk-off angles ρ^{+} and ρ^{−} are nonzero, different, and can be calculated from the electric field vectors: or for a positive or a negative optic sign, respectively.
References
Fève, J. P., Boulanger, B. & Marnier, G. (1994). Experimental study of internal and external conical refractions in KTP. Optics Comm. 105, 243–252.Schell, A. J. & Bloembergen, N. (1978). Laser studies of internal conical refraction. I. Quantitative comparison of experimental and theoretical conical intensity distribution in aragonite. J. Opt. Soc. Am. 68, 1093–1106.