## 2 Materials and Methods
### OFC Generation  
The proposed solution to obtain the maximum number of wavelengths is an OFC generation system based on the method in [41], which uses multiple thermally controlled optical microring resonators to shift the frequency of each comb line. Subsequently, these lines are combined using an interleaver to form a single optical comb with a smaller line spacing known as the FSR. Although this methodology requires multiple microring resonators (MRRs), it offers the advantage of having several wavelengths for spectrum assignment, which is crucial in solving this problem. This approach creates flexible WDM grids with different line spacings (12.5 GHz, 50 GHz, 100 GHz, and 200 GHz). We choose silicon nitride MRRs (Si\({}_{3}\)N\({}_{4}\)) because of their ease of fabrication, reproducibility, low optical losses, compatibility with standard CMOS technology, and ability to deterministically generate optical combs [41; 42]. An MRR is a compact, integrated optical device typically fabricated on a silicon substrate. It consists of a ring-like or disk-like waveguide structure that allows light to circulate within it. This circular or looped design enables optical resonance, where specific optical frequencies or wavelengths, become trapped and accumulate within the microresonator (see Figure 2). As light is input into the microresonator through an optical waveguide, it circulates within the closed-loop structure, and, due to the constructive interference of the trapped wavelengths, it intensifies over multiple round trips. This phenomenon generates an optical frequency comb. Designing an MRR to generate frequency combs with a desired free spectral range (FSR) involves careful adjustment of the resonator's radius, as the FSR is inversely proportional to the resonator's radius. A larger radius results in a smaller FSR, while a smaller radius leads to a larger FSR. Managing optical losses through material selection and fabrication techniques is crucial to achieving efficient comb generation and maintaining ahigh Q-factor. Optimizing the coupling factor by tailoring the waveguide designs ensures effective light interaction with the microresonator, collectively allowing precise control over the FSR. We propose two structures based on the approach described in [35] to achieve the desired separation between grid lines. The first structure employs four MRRs with a free spectral range (FSR) of 50 GHz, and their temperature is controlled to shift them by 0 GHz, 12.5 GHz, 25 GHz, and 37.5 GHz. The combination of the wavelengths generated by each MRR using an interleaver results in a final optical comb with a line spacing of 12.5 GHz and four times the number of wavelengths generated by a single MRR. The second structure uses two MRRs with an FSR of 200 GHz, and it utilizes the methodology proposed in [35] to achieve a final line spacing of 100 GHz. The designers should note that the fundamental structures of this design are MRRs with an FSR of 50 GHz and 200 GHz, and they can also use them separately to obtain these FSRs. The scheme for the generation of these combs for the previously proposed line spacings can be observed in Figure 3.  
For this reason, we propose, for the microresonator with a radius of 113 \(\upmu\)m, an anomalous dispersion \(\beta_{2}=-4.7\times 10^{-26}\,[\mathrm{s^{2}m^{-1}}]\), a photon lifetime \(t_{\mathrm{ph}}=\frac{t_{B}}{2\upalpha}=1.37\) ns, a Kerr coefficient \(\gamma=1.09\,[\mathrm{W^{-1}m^{-1}}]\), a loss coefficient \(\alpha=1.61\times 10^{-3}\), and a coupling coefficient \(\theta=3.2\times 10^{-4}\). For the microresonator with a radius of 450 \(\upmu\)m, we propose \(\beta_{2}=-4.7\times 10^{-26}\,[\mathrm{s^{2}m^{-1}}]\), \(t_{ph}=\frac{t_{B}}{2\upalpha}=5.88\) ns, \(\gamma=1.09\,[\mathrm{W^{-1}m^{-1}}]\), \(\alpha=1.7\times 10^{-3}\), and a coupling coefficient \(\theta=2.06\times 10^{-4}\). We select these parameters because they allow us to generate stable optical frequency combs with paths that facilitate reliable generation.