Optical Harmonic Generation in Single Crystal BaTiO3

Second-harmonic generation (SHG) of the Nd-doped CaW${\mathrm{O}}_4$ optical maser beam in ferroelectric BaTi${\mathrm{O}}_3$ has been investigated. Each of the three nonlinear coefficients which determine the magnitude of the SHG have been measured from room temperature to near the Curie temperature. It is found that all three coefficients have the same temperature dependence as the spontaneous ferroelectric polarization. The symmetry of the nonlinear coefficients required for a dispersionless, lossless SHG mechanism, namely, $d_{15}=d_{31}$ for BaTi${\mathrm{O}}_3$, applies over the entire measured temperature range. The effects on SHG due to antiparallel ferroelectric domains are described. The circumstances under which random as well as special antiparallel domain arrays can produce either an enhancement or a degradation of the second-harmonic intensity are discussed. Because of the dependence of SHG on the domain structure, the determination of the nonlinear coefficients requires single-domain crystals. A method for preparing suitable BaTi${\mathrm{O}}_3$ single-domain crystals is described. These crystals are also useful for investigations of the characteristics of ferroelectric domain growth.