Absolute Signs of Second-Harmonic Generation Coefficients of Piezoelectric Crystals

This paper describes the measurement of the absolute signs of the nonlinear optical coefficients $d_{\mathrm{ij}}$ that give rise to second-harmonic generation in piezoelectric crystals. The measurements were made with a repetitively $Q$-switched Nd-yttrium aluminum garnet (Nd-YAG) laser (1.064 μ) and involve relative sign determinations between two crystals followed by a comparison of at least one of them with $d_{14}$ of GaP, which has been shown previously to be positive with respect to the +[111]. To determine the unique directions in the crystals studied, several different methods were used, including: the piezoelectric effect, the pyroelectric effect, the etching behavior, and the electric field aligned spontaneous polarization. The crystals investigated included the following: zinc-blende crystals (ZnSe, ZnTe, and CdTe), wurtzite crystals (ZnO, BeO, CdS, and CdSe), ferroelectric crystals [LiTa${\mathrm{O}}_3$, LiNb${\mathrm{O}}_3$, BaTi${\mathrm{O}}_3$, ${\mathrm{Ba}}_2$Na${\mathrm{Nb}}_5$ ${\mathrm{O}}_{15}$, ${\mathrm{Gd}}_2$ ${\left(\mathrm{M}\mathrm{o}{\mathrm{O}}_4\right)}_3$, and ${\mathrm{Tb}}_2$ ${\left(\mathrm{M}\mathrm{o}{\mathrm{O}}_4\right)}_3$], and several other crystals (LiI${\mathrm{O}}_3$, LiGa${\mathrm{O}}_2$, LiCH${\mathrm{O}}_2$·${\mathrm{H}}_2$O, and quartz). Strong absorption of the second harmonic complicates the interpretation of the experimental results for ZnTe, CdTe, and CdSe. The present results and those of several recent theoretical predictions are in good agreement.