# Designing a Novel High-Performance FBG-OADM Based on Finite Element and Eigenmode Expansion Methods
## 5 Result and Analysis of the FBG-OADM
Figure 12 details the correlations between the power loss and length of the FBG-OADM, showing that the power loss in the power transmission over the entire FBG-OADM met the review standard for all segment cycles (\(N_{p}\)). Figure 11: Scanning diagram of the optimal FBG-OADM length. Figure 12: Diagram of the relationship between the transmission distance and power loss when the core mode was completely dropped. Figure 10: Scanning diagram of the optimal \(\Lambda_{\text{FBC}}\). To verify that the optimal parameter values were \(\Lambda_{F\text{BG}}\) = 0.5396 \(\upmu\)m and \(N_{P}\) = 18,361, the power transmission along the \(X\)-\(Z\) plane was examined with light inputted via the input port of the FBG-OADM, as shown in Figure 13. The figure shows that the input power was successfully coupled to the drop port of Fiber 2. To further investigate the coupling performance, a 2D power distribution map of the input port, \(z\) = 4955.3991 \(\upmu\)m, and drop port were collected, as shown in Figures 14-16. Figure 14 shows the power distribution map of the input port. Figure 15 displays the 2D power distribution during coupling, showing the perturbation effect of the FBG inducing the core mode to couple to the cladding mode, as well as the cladding mode under the effect of the 2 \(\times\) 2 optical fiber coupler, which facilitated cross-coupling between the two optical fibers. Figure 16 is the power distribution map of the drop port, showing that the cladding mode was subjected to the perturbation effect of the FBG, causing cladding mode to couple to the core mode. Thus, the numerical simulation results in Figures 13-16 confirm the accuracy of the proposed FBG-OADM. To investigate whether the \(-\)3 dB bandwidth of the proposed FBG-OADM satisfied the ITU guidelines, the spectrum of the drop port was plotted, as shown in Figure 17. The figure shows that the FBG-OADM exhibited transmission power of 0 dB in the drop port. In other words, power inputted via the input port was outputted via the drop port with zero power loss, showing that heterodyne and homodyne crosstalk were unlikely to occur in the FBG-OADM. When an OADM drops a signal, power that is not outputted via the drop port of Fiber 2 is restored in the output port in the form of residual power, which creates heterodyne crosstalk with other wavelengths. Similarly, when an OADM adds a signal, power remaining in the output port creates homodyne crosstalk. Figure 18 shows the \(-\)3 dB spectrum of the drop port, indicating that the FBG-OADM demonstrated considerably high bandwidth efficiency. In addition, the FBG-OADM exhibited an FWHM of \(\leq\)0.0375 nm (i.e., \(\leq\)0.0000375 \(\upmu\)m), which is markedly lower than the ITU requirement for DWDMs (FWHM \(<\) 0.4 nm). In this simulation, four Intel Xeon CPUs ([EMAIL_ADDRESS] GHz) and 128 GB memory were used and the computation time was approximately 118 h.  
Figure 16: 2D power distribution map for the output port (\(z=9910.7982\)\(\upmu\)m). \[L_{2}=\Lambda_{FBG}\times N_{P} \tag{3}\]0 Spectrum of the FBG-OADM when the core mode was completely dropped.