Millimeter-Wave WGM Resonator-Based Characterization of Continuous and Noncontinuous Ultrathin Cu Films

Abstract

We analyze the experimental data on the evolution of the microwave (MW) response of the whispering gallery mode (WGM) resonator. The focus is on the thickness $d_{f}$ variation of the conducting endplates (CEPs) from $d_{f}$ exceeding skin layer thickness $\delta _{s}$ to $d_{f}\ll \delta _{s}$ down to $d_{f} = 0$ , i.e., with no CEPs. The analysis was performed by comparing the numerical simulation results obtained using COMSOL software with the authors’ experimental data on the response of the Ka -band sapphire WGM resonator. The nonmonotonic change in the WGM resonator response with decreasing thickness $d_{f}$ is explained using the metal–insulator percolation model proposed by Krupka et al. We use a different resonator (quasi-optical) technique and different mode polarization, namely, the HE $_{14~1~\delta }$ mode. The artificially introduced discontinuity of the ultrathin film, resulting in a sharp growth of the ${Q}$ -factor is analogous with the percolation material structure. The revealed effect may be useful for the development of MW devices with dynamically controlled properties of metamaterials.