# Microscope-Based Optical Frequency Comb Generator for 200 GHz Spaced WDM Data Transmission System
## 3 Results  
### Microresonator Characteristics  
The simulated spatial distribution of the electric field of the fundamental TE mode at the frequency of about 193.1 THz is shown in Figure 2. For the fundamental TM mode, the spatial distribution of the absolute value of the field is very similar and not depicted here. We solve Equation (1) for different microsphere diameters (\(d=2R\)) to find the optimal one giving FSR of 200 GHz. FSR as a function of the microsphere diameter is plotted in Figure 3 for TE and TM families. These curves for TE and TM modes differ by \(\sim\)10 MHz but almost coincide for the chosen scale in Figure 3.  
Figure 3: FSR as a function of a microsphere diameter for transverse magnetic (TM) and TE modes. Figure 2: The normalized absolute value of the electric field for transverse electric (TE) mode at the eigenfrequency of about 193.1 THz in the equatorial plane (**a**) and in a plane perpendicular to equatorial one (**b**). Furthermore, using Expressions (4) and (5), we calculate dispersion for the optimal microsphere diameter of \(\sim\)328.5 \(\upmu\)m and for comparison for \(d=322\)\(\upmu\)m and for \(d=335\)\(\upmu\)m for which FSR differs by \(\pm\)2% from 200 THz and is 204 and 196 THz, respectively. The frequency-dependent dispersions for TE and TM modes for these diameters are plotted in Figure 4a in the 188-198 THz range. It is seen that curves differ slightly. Figure 4b demonstrates the dispersion of the TE family at a wider frequency range for the diameter of 328.5 \(\upmu\)m. The dispersion is anomalous at 193.1 THz and the zero-dispersion frequency is about 209 THz. The nonlinear Kerr coefficient is about 3.5 (W-km)\({}^{-1}\) at 193.1 THz, and its frequency dependence can be neglected in the C-band. Next, we estimate the influence of thermal effects on shifts of WGM frequencies and FSR for the optimal diameter. Figure 5a,b demonstrate the calculated shift of eigenfrequencies and FSRs as functions of the temperature increase, respectively. For Figure 5, we assume uniform temperature increase distribution. WGM shifts are almost the same for TE and TM mode families, but FSRs differ by \(\sim\)10 MHz. FSR difference occurs due to initial \"cold\" FSR non-equality between TM and TE modes. To understand when such temperature increases can be achieved, we simulate temperature fields at different powers of the heat source. Temperature distributions for the heat powers of 1, 3, and 5 mW are presented in Figure 6a,b, in Figure 6c,d, and in Figure 6e,f, respectively. Figure 6a,c,e show the complete simulated geometry, including the microsphere itself and the fiber stem, but Figure 6b,d,f show an enlarged microsphere. The temperature inside the microsphere is distributed fairly uniformly. For greater clarity, Figure 6g also shows the dependences of the temperature averaged over the  
Figure 4: (**a**) Dispersion as a function of frequency for microspheres with indicated diameters for TE and TM modes. (**b**) Dispersion as a function of frequency for a microsphere with a diameter of 328.5 \(\upmu\)m for TE modes. Figure 5: WGM shift (**a**) and free spectral range (FSR) (**b**) as functions of temperature increase for a microsphere with a diameter of \(\sim\)328.5 \(\upmu\)m.  
sphere, the temperature averaged over the WGM volume, and the maximum temperature on the heat power. Despite the fact that the full nonlinear heat equation was solved, the dependencies of these temperatures on heat power appear to be almost linear for the considered heat power range. After finding the temperature distributions and dependencies of temperature increases on the heat power, we plot the FSR versus the power of the heat source (see Figure 7). We also verified that the change in dispersion curves with increasing temperature is negligible for the considered heat powers of a few mW. Figure 6: Temperature distributions for heat powers: 1 mW (**a**,**b**); 3 mW (**c**,**d**); and 5 mW (**e**,**f**). The temperature increase as a function of heat power (**g**).