Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.2, p. 741

Section Second-harmonic generation (SHG)

H. Klappera and Th. Hahna Second-harmonic generation (SHG)

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Light waves passing through a noncentrosymmetric crystal induce new waves of twice the incident frequency. This second-harmonic generation is due to the nonlinear optical susceptibility. The second-harmonic coefficients form a third-rank tensor, which is subject to the same symmetry constraints as the piezoelectric tensor (see Section[link]). Thus, only 20 noncentrosymmetric crystals, except those of class 432, can show the second-harmonic effect; cf. Table[link].

Second-harmonic generation is a powerful method of testing crystalline materials for the absence of a symmetry centre. With an appropriate experimental device, very small amounts (less than 10 mg) of powder are sufficient to detect the second-harmonic signals, even for crystals with small deviations from centrosymmetry (Dougherty & Kurtz, 1976[link]).


Dougherty, J. P. & Kurtz, S. K. (1976). A second harmonic analyzer for the detection of non-centrosymmetry. J. Appl. Cryst. 9, 145–158.

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