Optical properties of ferroelectric ${\left({\mathrm{Pb}}_{1-x}{\mathrm{Ba}}_x\right)}_5{\mathrm{Ge}}_3{\mathrm{O}}_{11}$ for $x=0\mathrm{} \mathrm{and} 0.02$

We report accurate measurements of the temperature dependence of the indices of refraction [$n \mathrm{}\left(T\right)\mathrm{}$] in ferroelectric single crystals of ${\left({\mathrm{Pb}}_{1-x}{\mathrm{Ba}}_x\right)}_5{\mathrm{Ge}}_3{\mathrm{O}}_{11}$ for $x=0\mathrm{} \mathrm{and} 0.02$. Above the ferroelectric transition temperature $T_c$, $n \mathrm{}\left(T\right)\mathrm{}$ is linear with temperature. (It had been hoped that the $x=0.02\mathrm{}$ sample would show nonlinear results similar to those observed in BaTi${\mathrm{O}}_3$.) Analyzing $n \mathrm{}\left(T\right)\mathrm{}$ below $T_c$ in terms of the quadratic electro-optic effect, ${\left[\Delta \right(n^{-2\mathrm{}}\left)\right]}_{\mathrm{ij}}=\Sigma {k,l}^{}{g}_{\mathrm{ijkl}}{P}_k{P}_l$, reveals very large $g$ values, 20-100 times larger than those observed in Pb perovskites.