Measurements of Nonlinear Polarization Dynamics in the Tens of Gigahertz

Frequency-dependent linear-permittivity measurements are commonplace in the literature, providing key insights into the structure of dielectric materials. These measurements describe a material's dynamic response to a small applied electric field. However, nonlinear dielectric materials are widely used for their responses to large applied fields, including switching in ferroelectric materials, and field tuning of the permittivity in paraelectric materials. These behaviors are described by nonlinear permittivity. Nonlinear-permittivity measurements are fraught with technical challenges because of the complex electrical coupling between a sample and its environment. Here, we describe a technique for measuring the complex nonlinear permittivity that circumvents many of the difficulties associated with other approaches. We validate this technique by measuring the nonlinear permittivity of a tunable ${Ba}_{0.5}{Sr}_{0.5}{TiO}_3$ thin film up to 40 GHz and comparing our results with a phenomenological model. These measurements provide insight into the dynamics of nonlinear dielectric materials down to picosecond timescales.