## 2 Characteristics of Designed Silica Microsphere WGMR for Kerr-OFC
Several techniques can be used to form tapered fiber through thermal heating, for instance, a ceramic tube microheater(s) consisting of a heat-resistant wire that is approximately 22 mm in length and 19 mm inner diameter and placed within the ceramic [30]; another option would be micro burners driven by propane-butane (30% propane and 70% butane) gas flows [23] or by pure hydrogen (H\({}_{2}\)) [31], providing a high-temperature (\(\geq\)1900 \({}^{\circ}\)C) flame. The latter setup was used in our experiments; specifically, a constant hydrogen flow of 50 mL/min from the hydrogen generator (see Figure 2b) was connected to a microburner placed between compact, motorized translation stages. For pure hydrogen generation, we use an in-house-built hydrogen generator (electrolyser) that operates by splitting the water into hydrogen and oxygen through electrolysis. The number of plates for cathode and anode is set to \(\times 11\). Each plate was driven by 12 VDC (30 A) output voltage through an \(11\times\) high-speed Schottky diodes barrier using a (220 V-50 Hz 350 W) power supply unit (PSU). As shown in Figure 2b,f, sets of 11 cathode and 11 anode plates are located in separate tubes (D = 250 mm) where the electrolysis interconnection between them was made by water and potassium hydroxide (KOH) electrolyte through a round tube transition. For the microburner, we used an in-house-built micro torch that consists of 9 cylindrical \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Life Cycle** & **T** & **K** & **FWHM, MHz** & **Q** & **Qintr** & **P\({}_{\text{circ}}\), W** & **L** & **Resulting** \\   Freshly fabricated & 0.13 & 2.1 & 5.2 & 3.7 \(\times\) 10\({}^{7}\) & 1.2 \(\times\) 10\({}^{8}\) & 3327 & 13.8 & yes \\ After 2 months & 0.64 & 9.0 & 15.7 & 1.2 \(\times\) 10\({}^{7}\) & 1.2 \(\times\) 10\({}^{8}\) & 1458 & 6.0 & yes \\ After 3.5 months & 0.62 & 8.4 & 50 & 3.9 \(\times\) 10\({}^{6}\) & 3.6 \(\times\) 10\({}^{7}\) & 455 & 1.9 & no \\ After 4 months & 0.78 & 16.1 & 96 & 2.0 \(\times\) 10\({}^{6}\) & 3.5 \(\times\) 10\({}^{7}\) & 249 & 1.0 & no \\ \hline After 4 months (repaired by Hydrogen flame) & 0.74 & 13.3 & 44 & 4.4 \(\times\) 10\({}^{6}\) & 6.3 \(\times\) 10\({}^{7}\) & 538 & 2.2 & no \\ \hline \end{tabular}
\end{table} 
Table 1: Results of characteristics calculations for 170 μm SiO\({}_{2}\) microsphere resonator versus life cycle. stainless-steel tubes of 0.9 mm inner diameter, allowing us to produce a low and wide flame of ~10 mm along the fiber axis [32]. The fiber position relative to the flame is a critical parameter. Therefore, the microtorch stainless-steel tube position is sprightly adjusted to the fiber's mid-point. To sustain transmission, the tapered fiber needs to be pulled adiabatically while not exceeding the delineation angle [33]. Using a ~7 mm wide hydrogen flame, we produced sub-wavelength nearly adiabatic targets with an overall transmittance higher than 95%, as a very efficient adiabatic transfer from the single mode of the un-tapered fiber to the fundamental mode of the central part of the taper. The burning temperature of the hydrogen flame melted and softened the fiber slowly within the purified fiber section as a result of a tapered thicker section of 18 mm in length. It is important to mention that if the fiber ends are inclined (0.1 mrad) at the place of V-grove fiber holders, a curvature of 5 \(\upmu\)m is intelligently formed in the melted location of the taper when the flame width is 1 mm. The angle exceeding 0.08 mrad is no longer good, as the allowable adiabatic angle is between 0.02 and 0.05 mrad [34]. Due to rapid assembly, a flame wider than 1 mm was used. The mounting of the fiber holders on one optical axis is adjusted under a microscope. The 3-axis X, Y, and Z micro-positioner stages with the built-in piezo controller were used to align the microsphere with the tapered fiber at a location slightly thicker than the taper waist to achieve the critical coupling and to minimize the coupler losses; see Figure 2d,e.