Section 10.2.4.3. Second-harmonic generation (SHG)

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 10.2.6). Thus, only noncentrosymmetric crystals, except those of class 432, can show the second-harmonic effect; cf. Table 10.2.1.1.

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).