## 2 Characteristics of Designed Silica Microsphere WGMR for Kerr-OFC  
Silica (SiO\({}_{2}\)) microspheres with a diameter of D = 170 \(\upmu\)m used for the Kerr-OFC were fabricated from a standard ITU-T G.652 single-mode telecommunication fiber by the melting method using a specially developed program for a commercially available optical fusion arc splicer, which has been previously demonstrated by authors in [9; 23]. During the manufacturing process, by changing the diameter of the fabricated silica microsphere, we can obtain an OFC with a free spectral range (FSR) ranging from about 200 GHz (sphere D = 320 \(\upmu\)m) [20] up to about 400 GHz (sphere D = 170 \(\upmu\)m) [18] in addition to the possibility of finetuning the coupling conditions between the resonator and tapered fiber, which is not possible for chip-based resonators with integrated waveguides, and therefore can be considered to be a major advantage over other OFC technologies. Silica microsphere resonators also have advantages of fast and simple fabrication using commercially available fusion arc splicers, allowing the fabrication of silica microspheres with user-defined sphere diameter and high-quality factor (Q \(\geq\) 10\({}^{7}\)) in a couple of minutes. Most applications, especially silica microsphere-based Kerr-OFC, require the realization of the highest possible quality factor (so-called Q factor) microsphere resonators. In regular laboratory conditions, the microsphere's Q factor deteriorates within a 1 h time scale in the open environment due to the deposition of nanoscale particles or water vapors to the microsphere surface. The Q factor of the microsphere is determined by several aspects such as intrinsic radiative (curvature) losses, scattering losses on residual surface inhomogeneities, losses introduced by surface contaminants, and material losses [24]. For a more detailed illustration, see Figure 1 where newly fabricated and artificial degradations of the microsphere surface by water vapors are obtained using a scanning electron microscope (SEM, Hitachi S-4800) for 170 \(\upmu\)m silica microsphere resonators. Scanned sphere illustrations with a focused beam of electrons (captured at: 3 kV (accelerating voltage) and 4.0 mm (surface scale) @ \(\times\)400 to 45.0 k times and 2.9 mm @ \(\times\)180 k times) for a particular micro-sphere resonator after 100% humidity exposure (resonator has been in humidity fog for 5 s) are shown in Figure 1a-d. The newly fabricated silica microsphere resonator obtained by SEM (captured at: 3 kV, 4.0 mm @ \(\times\)300 to 50.0 k times) is shown in Figure 1e-h. White dots (see Figure 1f) for evaporated silica (cristobalite) from the arc fusion splicer discharge explain why the maximal Q factor of a newly fabricated microsphere is below 1 \(\times\) 10\({}^{8}\). We can observe that the evaporated silica dust from the arc fusion splicer (see Figure 1g) and nanoscale particles (see Figure 1h) are deposited on the surface of the silica microsphere. It is important to note that, during the experiment, by testing samples of fabricated microspheres, we were able to significantly improve the degraded 4-month-old microsphere (added by water vapor) Q factor from Q = 2.0 \(\times\) 10\({}^{6}\) (96 MHz full width at half maximum (FWHM) of the WGM resonance) to Q = 4.4 \(\times\) 10\({}^{6}\) (44 MHz FWHM of the WGM resonance) using pure hydrogen (H) flame of a micro burner. Note that the Q factor of the newly fabricated microsphere was 3.7 \(\times\) 10\({}^{7}\) (5.2 MHz FWHM of the WGM resonance). The built-up circulating intensity [25] was estimated to be 14 GW/cm\({}^{2}\) exceeding \(\sim\)2.0 GW/cm\({}^{2}\)[26] needed for OFC generation (see Table 1). No OFC was generated when it degraded below 2.0 GW/cm\({}^{2}\). Microresonator with high Q factor can build up a significant internal circulating intensity when pumped with low laser power.