Microwave Nonlinearities in Anisotropic Dielectrics and Their Relation to Optical and Electro-Optical Nonlinearities

Abstract

Earlier measurements of the three-frequency microwave nonlinear susceptibility coefficient have been extended to include all of the nonzero tensor components of ${d}_{\mathrm{ijk}}^{ m}(\ensuremath{-}{\ensuremath{\omega}}_{3},{\ensuremath{\omega}}_{2},{\ensuremath{\omega}}_{1})$ of LiNb${\mathrm{O}}_{3}$ and LiTa${\mathrm{O}}_{3}$. These results are interpreted, using the formalism developed by Lax and Nelson, to describe nonlinearities associated with electronic and ionic modes of anisotropic crystalline materials. The linear dispersion parameters for each material are first approximated by a single-electronic and a single-ionic normal mode. Nonlinear elements are then added to this normal-mode model. A macroscopic-bond-charge model is developed. With some simplifying asumptions and knowledge of the optical nonlinear coefficient ${d}_{\mathrm{ijk}}^{ o}$ and the electro-optic coefficient ${d}_{\mathrm{ijk}}^{ \mathrm{eo}}$, a good fit with the measured values of ${d}_{\mathrm{ijk}}^{ m}$ can be obtained. The same parameters used to fit ${d}_{\mathrm{ijk}}^{ m}$ are used to calculate the pyroelectric coefficients for LiNb${\mathrm{O}}_{3}$ and LiTa${\mathrm{O}}_{3}$. In both cases, the correct signs and magnitudes within a factor of 2 of experimental values are obtained.