Study on the electro-optic effect in Pb(Zr,Ti)O$_{3}$ (001) film using spectroscopic ellipsometry*

Spectroscopic ellipsometry was applied to study electro-optic effect in lead zirconate titanate$^{ }$(PZT) thin films grown epitaxially on Nb-doped SrTiO$_{3}$(001) substrates by$^{ }$RF magnetron sputtering. Multilayer model analysis was applied$^{ }$to extract the ordinary and extraordinary refractive indices of the PZT thin film with electric$^{ }$field applied along the (001) direction. The effective linear and$^{ }$quadratic coefficients at a wavelength of 632.8 nm were estimated to be -134.6$\times $10$^{-12}$~m/V and 8.5$\times $10$^{-18}$~m$^{2}$/V$^{2}$, respectively, while the individual linear electro-optic$^{ }$coefficients $r_{33}$ and $r_{13}$ were -157.1 and 22 pm/V, respectively. We attributed existence of the linear electro-optic effect in unpoled PZT$^{ }$films to the presence of a built-in polarization$^{ }$and simultaneous poling during ellipsometric measurements.