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

International Tables for Crystallography (2013). Vol. D, ch. 1.7, p. 192


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 SFG ([\omega_4=\omega_1+\omega_2+\omega_3]), DFG ([\omega_1=\omega_4-\omega_2-\omega_3]), DFG ([\omega_2=\omega_4-\omega_1-\omega_3]) and DFG ([\omega_3=\omega_4-\omega_1-\omega_2]) (Boulanger et al., 1993[link])

Phase-matching relationsConfigurations of polarizationTypes of interaction
ω4ω1ω2ω3SFG (ω4)DFG (ω1)DFG (ω2)DFG (ω3)
[\omega_4 n_4^-=\omega_1 n_1^+ +\omega_2 n_2^+ +\omega_3 n_3^+] e e+ e+ e+ I II III IV
[\omega_4n_4^-=\omega_1n_1^-+\omega_2n_2^-+\omega_3n_3^+] e e e e+ II III IV I
[\omega_4n_4^-=\omega_1n_1^-+\omega_2n_2^++\omega_3n_3^-] e e e+ e III IV I II
[\omega_4n_4^-=\omega_1n_1^++\omega_2n_2^-+\omega_3n_3^-] e e+ e e IV I II IV
[\omega_4n_4^-=\omega_1n_1^-+\omega_2n_2^++\omega_3n_3^+] e e e+ e+ V4 V1 V2 V3
[\omega_4n_4^-=\omega_1n_1^++\omega_2n_2^-+\omega_3n_3^+] e e+ e e+ VI4 VI1 VI2 VI3
[\omega_4n_4^-=\omega_1n_1^++\omega_2n_2^++\omega_3n_3^-] e e+ e+ e VII4 VII1 VII2 VII3