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

International Tables for Crystallography (2013). Vol. D, ch. 1.7, p. 191


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:

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Correspondence between the phase-matching relations, the configurations of polarization and the types according to the sum- and difference-frequency generation processes SFG ([\omega_3=\omega_1+\omega_2]), DFG ([\omega_1=\omega_3-\omega_2]) and DFG ([\omega_2=\omega_3-\omega_1])

[{\bf e}^{\pm}] are the unit electric field vectors relative to the refractive indices [n^{\pm}] in the phase-matching direction (Boulanger & Marnier, 1991[link]).

Phase-matching relationsConfigurations of polarizationTypes of interaction
ω3ω1ω2SFG (ω3)DFG (ω1)DFG (ω2)
[\omega_3n_3^-=\omega_1n_1^+=\omega_2n_2^+] e e+ e+ I II III
[\omega_3n_3^-=\omega_1n_1^-=\omega_2n_2^+] e e e+ II III I
[\omega_3n_3^-=\omega_1n_1^+=\omega_2n_2^-] e e+ e III I II