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

International Tables for Crystallography (2006). Vol. D, ch. 1.7, p. 181


B. Boulangera* and J. Zyssb

aLaboratoire de Spectrométrie Physique, Université Joseph Fourier, 140 avenue de la Physique, BP 87, 38 402 Saint-Martin-d'Hères, 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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The most common nonlinear effects and the corresponding susceptibility tensors in the frequency domain

ProcessOrder n[-\omega_\sigma; \omega_1,\omega_2,\ldots,\omega_n]K
Linear absorption 1 [-\omega;\omega] 1
Optical rectification 2 [0;-\omega,\omega] 1/2
Linear electro-optic effect 2 [-\omega;\omega,0] 2
Second harmonic generation 2 [-2\omega;\omega,\omega] 1/2
Three-wave mixing 2 [-\omega_3;\omega_1,\omega_2] 1
D.c. Kerr effect 3 [-\omega;\omega,0,0] 3
D.c. induced second harmonic generation 3 [-2\omega;\omega,\omega,0] 3/2
Third harmonic generation 3 [-3\omega;\omega,\omega,\omega] 1/4
Four-wave mixing 3 [-\omega_4;\omega_1,\omega_2,\omega_3] 3/2
Coherent anti-Stokes Raman scattering 3 [-\omega_{\rm as};\omega_p,-\omega_p,-\omega_s] 3/4
Intensity-dependent refractive index 3 [-\omega;\omega,-\omega,\omega] 3/4
nth harmonic generation n [-n\omega;\omega,\omega,\ldots,\omega] [2^{1-n}]