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, p. 192
Section 1.7.3.2.2.2. Uniaxial crystals^{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 configurations of polarization in terms of ordinary and extraordinary waves depend on the optic sign of the phasematching direction with the convention given in Section 1.7.3.1: Tables 1.7.3.1 and 1.7.3.2 must be read by substituting (+, −) by (e, o) for a positive crystal and by (o, e) for a negative one.
Because of the symmetry of the index surface, all the phasematching directions for a given type describe a cone with the optic axis as a revolution axis. Note that the previous comment on the anaxial class is valid for a propagation along the optic axis ().
Fig. 1.7.3.4 shows the example of negative uniaxial crystals () like βBaB_{2}O_{4 }(BBO) and KH_{2}PO_{4} (KDP).
From Fig. 1.7.3.4, it clearly appears that the intersection of the sheets is possible only if with for a threewave process and for a fourwave one. The same considerations can be made for the positive sign and for all the other types of phase matching. There are different situations of inequalities allowing zero, one or several types: Table 1.7.3.3 gives the five possible situations for the threewave interactions and Table 1.7.3.4 the 19 situations for the fourwave processes.

