  An analytical theory is developed for predicting the nonlinear susceptibility
of ionic polarization to continuous electromagnetic waves in both bulk and
strained thin film ferroelectrics. Using a perturbation method for solving the
nonlinear equation of motion for ionic polarization within the framework of
Landau-Ginzburg-Devonshire theory, the full second-order nonlinear
susceptibility tensor is derived as a function of frequency, temperature, and
strain. The theory predicts the coexistence of a significantly enhanced
second-order dielectric susceptibility and a relatively low dielectric loss in
BaTiO3 films with a strain-stabilized monoclinic ferroelectric phase and in a
strained SrTiO3 film near its temperature-driven second-order
ferroelectric-to-paraelectric phase transition. This work establishes a
theoretical framework for predicting and exploiting nonlinear interactions
between THz waves and ferroelectric materials, and more generally, suggests
exciting opportunities to strain-engineer nonlinear dynamical properties of
ferroelectrics beyond the static and quasi-static limits.
