Violations of Kleinman symmetry in nonlinear optics: The forbidden coefficient of α-quartz

The magnitude, sign, and dispersion of the Kleinman forbidden nonlinear optical coefficient d14 for α-quartz has been measured via second harmonic generation. The results, relative to d11 (α-SiO2), are +0.009 and +0.026 for λ0=1.064 μ and 0.532 μ, respectively. The dispersion of the ratio d14/d11 qualitatively agrees with a recent theoretical prediction that d14/d11∝ω2. A microscopic model in terms of bonds and electron lone pairs of symmetry C∞ shows the Si→O bond polarizability β14 to be ten times smaller than the corresponding polarizability found for I→O and Te→O bonds.