FIG. 1.

Schematic picture of nonlinear measurements of thin films. (a) In time-domain measurements, tuning dynamics are characterized by applying a voltage pulse $V_p\left(t\right)$ to a capacitor and measuring the current $I\left(t\right)=V\left(t\right)/Z_{\text{in}}$ that flows as the capacitor charges. This current is related to the change of the polarization with respect to time. (b) We characterize tuning dynamics by exciting a waveguide patterned on a nonlinear material with two microwave frequencies ${\omega }_1$ and ${\omega }_2$, and measuring the waves generated by nonlinear mixing. The complex amplitudes $\hat{a}$ and $\hat{b}$ correspond to the forward (towards the sample) and backward (from the sample) traveling waves, respectively. This method can be extended to much higher frequencies than time-domain measurements.