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

International Tables for Crystallography (2013). Vol. D, ch. 1.7, p. 217

Section Phase-matched interaction method

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: Phase-matched interaction method

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The use of phase-matched interactions is suitable for absolute and accurate measurements (Eckardt & Byer, 1991[link]; Boulanger, Fève et al., 1994[link]). The sample studied is usually a slab cut in a phase-matching direction. The effective coefficient is determined from the measurement of the conversion efficiency using the theoretical expressions given by ([link] and ([link] for SHG, and by ([link] for THG, according to the validity of the corresponding approximations. Because of phase matching, the generated harmonic power is not weak and it is measurable with very good accuracy, even with a c.w. conversion efficiency.

Recent experiments have been performed in a KTP crystal cut as a sphere (Boulanger et al., 1997[link], 1998[link]): the absolute magnitudes of the quadratic effective coefficients are measured with an accuracy of 10%, which is comparable with typical experiments on a slab.

For both non-phase-matched and phase-matched techniques, it is important to know the refractive indices and to characterize the spatial, temporal and spectral properties of the pump beam carefully. The considerations developed in Section 1.7.3[link] about effective coefficients and field tensors allow judicious choices of configurations of polarization and directions of propagation for the determination of the absolute value and relative sign of the independent coefficients of tensors χ(2) and χ(3), given in Tables[link] to[link][link][link] for the different crystal point groups.


Boulanger, B., Fève, J. P., Marnier, G., Bonnin, C., Villeval, P. & Zondy, J. J. (1997). Absolute measurement of quadratic nonlinearities from phase-matched second-harmonic-generation in a single crystal cut as a sphere. J. Opt. Soc. Am. B, 14, 1380–1386.
Boulanger, B., Fève, J. P., Marnier, G. & Ménaert, B. (1998). Methodology for nonlinear optical studies: application to the isomorph family KTiOPO4, KTiOAsO4, RbTiOAsO4 and CsTiOAsO4. Pure Appl. Opt. 7, 239–256.
Boulanger, B., Fève, J. P., Marnier, G., Ménaert, B., Cabirol, X., Villeval, P. & Bonnin, C. (1994). Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from second-harmonic-generation measurements. J. Opt. Soc. Am. B, 11(5), 750–757.
Eckardt, R. C. & Byer, R. L. (1991). Measurement of nonlinear optical coefficients by phase-matched harmonic generation. SPIE. Inorganic crystals for optics, electro-optics and frequency conversion, 1561, 119–127.

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