International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 1.7, p. 193

Table 1.7.3.3 

B. Boulangera* and J. Zyssb

aInstitut Néel CNRS Université Joseph Fourier, 25 rue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France, and bLaboratoire de Photonique Quantique et Moléculaire, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan, France
Correspondence e-mail:  benoit.boulanger@grenoble.cnrs.fr

Table 1.7.3.3| top | pdf |
Classes of refractive-index inequalities for collinear phase matching of three-wave interactions in positive and negative uniaxial crystals

Types I, II and III refer to SFG; the types of the corresponding DFG are given in Table 1.7.3.1[link] (Fève et al., 1993[link]).

Positive sign ([n_e> n_o])Negative sign ([n_o> n_e])Types of SFG
[{n_{o3}\over \lambda_3}\,\lt\,{n_{o1}\over \lambda_1}+{n_{e2}\over \lambda_2};{n_{e1}\over\lambda_1}+{n_{o2}\over\lambda_2}] [{n_{o1}\over\lambda_1}+{n_{e2}\over\lambda_2},{n_{e1}\over\lambda_1}+{n_{o2}\over\lambda_2}\,\lt\,{n_{e3}\over\lambda_3}] I, II, III
[{n_{e1}\over\lambda_1}+{n_{o2}\over\lambda_2}\,\lt\,{n_{o3}\over\lambda_3}\,\lt\,{n_{o1}\over \lambda_1}+{n_{e2}\over \lambda_2}] [{n_{o1}\over \lambda_1}+{n_{e2}\over \lambda_2}\,\lt\,{n_{e3}\over\lambda_3}\,\lt\,{n_{e1}\over\lambda_1}+{n_{o2}\over\lambda_2}] I, II
[{n_{o1}\over \lambda_1}+{n_{e2}\over \lambda_2}\,\lt\,{n_{o3}\over \lambda_3}\,\lt\,{n_{e1}\over\lambda_1}+{n_{o2}\over\lambda_2}] [{n_{e1}\over\lambda_1}+{n_{o2}\over\lambda_2}\,\lt\,{n_{e3}\over\lambda_3}\,\lt\,{n_{o1}\over \lambda_1}+{n_{e2}\over \lambda_2}] I, III
[{n_{o1}\over \lambda_1}+{n_{e2}\over \lambda_2}, {n_{e1}\over\lambda_1}+{n_{o2}\over\lambda_2}\,\lt\, {n_{o3}\over \lambda_3}\,\lt\, {n_{e_1}\over\lambda_1}+{n_{e2}\over\lambda_2}] [{n_{o1}\over \lambda_1}+{n_{e2}\over \lambda_2}, {n_{e1}\over\lambda_1}+{n_{o2}\over\lambda_2}\,\lt\, {n_{e3}\over \lambda_3}\,\lt\, {n_{o_1}\over\lambda_1}+{n_{o2}\over\lambda_2}] I
[{n_{e_1}\over\lambda_1}+{n_{e2}\over\lambda_2}\,\lt\,{n_{o3}\over \lambda_3}] [{n_{o_1}\over\lambda_1}+{n_{o2}\over\lambda_2}\,\lt\,{n_{e3}\over \lambda_3}] None