Probing domain microstructure in ferroelectric $Bi4Ti3O12$ thin films by optical second harmonic generation

The domain microstructure in an epitaxial thin film of $Bi4Ti3O12$ on a $SrTiO3(001)$ substrate is studied by second harmonic generation measurements. The input polarization dependence of the second harmonic signal exhibits spatial symmetries that reflect the presence of eight different domain variants present in the film. A theoretical model is presented that explains the observed symmetries and extracts quantitative information on the nonlinear optical coefficients of the material and statistics of domain variants present in the film area being probed. The following ratios of nonlinear coefficients and birefringence was determined: $d12/d11=−3.498±0.171,$ $|d26/d12|=0.365±0.010,$ $|d26/d11|=1.273±0.036,$ and $|nb−na|=0.101±0.018$ (at 532 nm).