# High-\(Q\) TeO\({}_{2}\)-Si Hybrid Microring Resonators
## 3 Microring Resonator Characterization  
We used a fiber-chip edge coupling setup, a tunable Agilent 81640A 1510-1640 nm laser, and a fiber probe station to characterize the passive transmission properties of the silicon microring resonators. TE-polarized light from a 1550 nm tunable laser was launched into the chip through the polarization controller and lensed fiber, and the transmitted light across the chip was launched to the output lensed fiber connected to the Agilent power sensor. We observed TE single-mode resonances supported by the microring resonator, as shown in Figure 3a-c. For the TeO\({}_{2}\)-coated silicon microring resonator, we measured a free spectral range (FSR) of 3.7 nm at a wavelength of 1573 nm. The air- and SiO\({}_{2}\)-clad devices were under-coupled over the measured transmission range, while the TeO\({}_{2}\)-clad MRR was under-coupled at shorter wavelengths and became critically coupled above \(\sim\)1600 nm. By fitting the transmission responses of the under-coupled resonator using a Lorentzian function (as indicated in Figure 3d-f), we obtained internal quality factors, \(Q_{i}\), of 2.0 \(\times\) 10\({}^{5}\) at 1542.43 nm, 6.7 \(\times\) 10\({}^{5}\) at 1587.28 nm, and 1.5 \(\times\) 10\({}^{6}\) at 1579.94 nm for the uncoated, SiO\({}_{2}\)-coated, and TeO\({}_{2}\)-coated silicon MRRs, respectively, corresponding to 3.4 dB/cm, 0.97 dB/cm, and 0.42 dB/cm propagation losses in the microring [33]. The results are summarized in Table 1, including the TeO\({}_{2}\) film loss measured by prism coupling on a witness sample, showing low material loss, and fitted external and internal \(Q\) factors for the MRRs with different top claddings. Figure 2: Calculated electric field profile of the fundamental transverse-electric (TE)-polarized mode for (**a**) uncald, (**b**) SiO\({}_{2}\)-clad, and (**c**) TeO\({}_{2}\)-clad silicon microring resonators. (**d**) Calculated fractional optical intensity overlap factors and effective mode areas for the fundamental TE microring mode at 1550 nm wavelength. The total loss in the MRR can be expressed as the losses from the bulk materials, including contributions from the Si, SiO2, and TeO2 linear absorption and Si nonlinear (two-photon) absorption, radiation loss due to waveguide bends, and surface scattering losses related to the waveguide surface roughness and geometry. The bulk loss includes losses from impurities, internal defects, absorption loss due to chemical bonds, and nano- and micro-voids. Because of the high-quality silicon-on-insulator and SiO2 foundry materials, and low TeO2 film loss, we expected the bulk material loss contribution to be negligible. Furthermore, nonlinear optical loss was anticipated to be low due to the low power used in the transmission experiments. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Cladding** & **Cladding** & \begin{tabular}{c} **Film Loss @** \\ **638 nm** \\ **(nm)** \\ \end{tabular} & \begin{tabular}{c} **Film Loss @** \\ **638 nm** \\ **(dB/cm)** \\ \end{tabular} & \begin{tabular}{c} **Extinction** \\ **(dB/cm)** \\ \end{tabular} & \begin{tabular}{c} **External Q** \\ **Ratio (dB)** \\ \end{tabular} & \
\begin{tabular}{c} **Internal Q** \\ **Factor** \\ \end{tabular} &
\begin{tabular}{c} **Propagation** \\ **Loss (dB/cm)** \\ \end{tabular} \\ \hline Uncladded & — & — & — & 1.2 & \(2.8\times 10^{6}\) & \(2.0\times 10^{5}\) & 3.4 \\ SiO2 & 2000 & — & — & 2.8 & \(4.2\times 10^{6}\) & \(6.7\times 10^{5}\) & 0.97 \\ TeO2 & 270 & 0.5 \(\pm\) 0.2 & \(0.1\pm\) 0.1 & 2.8 & \(9.0\times 10^{6}\) & \(1.5\times 10^{6}\) & 0.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measured properties of silicon microring resonators with different cladding materials. Figure 3: Measured TE transmission spectra for (**a**) uncoated, (**b**) SiO2-coated, and (**c**) TeO2-coated silicon microring resonators with a microring–waveguide gap of 1.0 μm.