Quantitative Determination of Sources of the Electro-Optic Effect in LiNbO3and LiTaO3

The electro-optic effect in crystals can be separated into two types of microscopic interaction: an electron-lattice contribution in which the applied field produces a lattice displacement, which in turn modifies the electronic polarizability (or refractive index), and a direct electron-field contribution in which the applied field modifies the electronic polarizability in the absence of lattice displacements. The latter contribution in LiNb${\mathrm{O}}_3$ and LiTa${\mathrm{O}}_3$ can be estimated from second-harmonic-generation experiments by Miller and Savage, and accounts for less than 10% of the refractive-index change. Each polar-lattice optic mode in LiNb${\mathrm{O}}_3$ and LiTa${\mathrm{O}}_3$ ($4A_1+9E$) contributes separately to the electro-optic effect an amount proportional to the product of its Raman-scattering efficiency and infrared oscillator strength. We have measured the absolute scattering efficiencies for LiNb${\mathrm{O}}_3$ and LiTa${\mathrm{O}}_3$. The oscillator strengths for LiNb${\mathrm{O}}_3$ have been measured by Barker and Loudon. We find that the dominant contribution to the electro-optic coefficients $r_{33}$ and $r_{13}$ comes from the lowest-frequency $A_1$ mode; and to $r_{42}$ and $r_{22}$ from the next lowest $E$ mode. These same modes dominate the low-frequency dielectric constant. The absolute values of $r_{13}$, $r_{33}$, $r_{42}$, and $r_{22}$ calculated from the combined Raman, infrared, and second-harmonic-generation data are in excellent agreement with the electro-optic coefficients measured directly by Turner. In addition to the absolute scattering efficiencies for all the transverse and longitudinal modes in LiTa${\mathrm{O}}_3$ and LiNb${\mathrm{O}}_3$, we have also determined the mode frequencies and linewidths, which are important in calculating Raman gain.