# Generation of Flat Optical Frequency Comb Using Cascaded Electro-Optic Modulators
## 3 Methods and Results
This restriction helped prevent nonlinear distortion and excessive modulation depth caused by high voltage, thereby maintaining the stability of the electro-optic comb. Second, we maintained a constant total input power. In this case, each modulator distributed the power proportionally to avoid uneven optical frequency combs due to power fluctuations. This strategy of keeping the total power constant stabilized the energy distribution of the output spectrum, thereby improving the consistency of each frequency component. By comparing the flatness of these constraints on the optical frequency comb, we could determine the best restriction scheme that balanced minimizing the power fluctuations, reducing the nonlinear distortion, and providing a suitable modulation depth. In the simulation system, the MZM's \(V_{\pi-DC1}=V_{\pi-DC2}=V_{\pi 1}=V_{\pi 2}=3\) V and the extinction ratio was set as 45 dB. The \(V_{\pi-PM}\) of both phase modulators was 3 V. Considering the first restriction condition--that the input of each modulator did not exceed \(2V_{\pi}\)--we conducted calculations for configurations with 33, 31, and 29 comb lines. The results reveal that the flatness for the configuration with 33 comb lines was 3.2496 dB. For the 31-comb-line configuration, the flatness improved to 2.7472 dB. The configuration with 29 comb lines demonstrated an even better flatness of 1.3692 dB. These results indicate that the flatness improved as the number of comb lines decreased. The figure obtained from the simulation, which illustrates these findings, is presented in Figure 3. The flatness verification for 33, 31, and 29 comb lines is displayed from top to bottom. Considering the second restriction condition, we assumed the total input power remained constant. Since the modulation index is proportional to the strength of the input signal, we directly set the square sum of several modulation indices to a fixed value during the optimization process. This approach is equivalent to maintaining a constant total input power. By not constraining each modulator input to a maximum of 2 \(V_{\pi}\), we observed an improvement in the flatness. The flatness of 35 comb lines was measured as 0.7592 dB, while for 33 comb lines, it reached 0.6964 dB. The optimization results were validated through simulation, as shown in Figure 4, which depicts the configurations for 35 and 33 comb lines arranged from top to bottom. Figure 3: Simulation results for the optical frequency comb with the input voltage for each modulator, not exceeding \(2~{}V_{\pi}\). (**a**) The result for 33 comb lines. (**b**) The result for 31 comb lines. (**c**) The result for 29 comb lines. Table 1 presents the optimized parameter values obtained from the neural network. When comparing the above schemes, we obtained the best result of 33 comb lines, with a flatness of 0.5508 dB, and the simulation verification is illustrated in Figure 5.  
To validate the application potential of our generated electro-optic comb in fiber coherent transmission, we conducted an eight-channel, 48-Gbaud, 16-quadrature amplitude modulation (QAM) transmission simulation, whose system link structure is shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \(A_{1}\) & \(A_{2}\) & \(A_{3}\) & DeltaPhi (rad) & Theta (rad) & Flatness (dB) \\ \hline
5.00 & 4.00 & 22.00 & 1.1247 & 1.1310 & 0.6156 \\
5.05 & 5.98 & 21.79 & 1.1288 & 1.0729 & 0.5508 \\
5.00 & 4.00 & 22.00 & 1.1121 & 1.1215 & 0.6534 \\ \hline \end{tabular}
\end{table} 
Table 1: The parameter values optimized by the neural network. Figure 4: Simulation results for the optical frequency comb, where the total input power remained constant. (**a**) The result for 35 comb lines. (**b**) The result for 33 comb lines. After generating the electro-optic comb using the cascaded modulators designed in the previous stage, we used a wavelength division multiplexing (WDM) demultiplexer to divide the spectrum into eight independent optical carriers, each spaced 50 GHz apart.