# Designing a Novel High-Performance FBG-OADM Based on Finite Element and Eigenmode Expansion Methods
## 6 Conclusions  
The emergence of optical fiber technology in recent years has considerably improved network stability and bandwidth development. OADMs are crucial components for connecting computers in fiber-optic networks. In the past several decades, many types of OADMs have been introduced and used in network systems. Of all the OADMs currently available, the most common one is composed of an FBG and two optical circulators. However, this particular OADM is disadvantageous because of its large size and high-cost, complex production process. The proposed high-performance FBG-OADM model, which was developed on the basis of optical coupling theory, overcomes these shortcomings. The model comprises two SMFs, which are placed side by side so that they work in the same manner as a 2 \(\times\) 2 optical fiber coupler, and two FBGs, which have identical parameters so that they work in the same manner as a mode coupler. To analyze the performance of the FBG-OADM, simulations were performed to predict the performance of the device in a real-world environment. The simulated system comprised an internal part (for simulating the FBG-OADM) and an external part (for simulating the radiation mode absorption). The combination of the FEM and the EEM provided a rigorous yet simple process for designing OADMs and for testing models in an environment that is comparable to the real world. Next, the results were produced in the form of graphs. Concerning the design structure, the FEM was used to obtain solutions for the guided modes in the FBG-OADM and to analyze the modes. Next, the EEM was employed to simulate the guided modes for power transmission simulations. In cyclic components such as the FBG-OADM, because guided modes are identical during a cycle, using the FEM to obtain solutions for the guided modes and using the EEM to simulate power transmission inference during each cycle yielded results representing the simulation results of the overall FBG-OADM. This considerably reduced the memory and computation time requirements for the simulations. When optical signals are inputted into an internal simulation structure, they create both discrete guided modes and continuous radiation modes. However, because continuous radiation modes are considered power loss in real-world environments, they cannot be measured. Therefore, this study designed an external simulation, in which two numerical methods were used to simulate the PRB and PML in order to reduce discrepancies between the simulations and actual performance results. The PRB was used to convert continuous radiation modes into discrete radiation modes, and the PML was used to absorb the power of the discrete radiation modes. The numerical simulations revealed the optimal FBG-OADM cycle (i.e., \(\Lambda_{FBG}\) = 0.5396 \(\upmu\)m) as well as the optimal number of period (i.e., \(N_{P}\) = 18,361). These two parameters were used to develop the high-performance FBG-OADM. The findings are summarized as follows: (1) the orthogonal values between all guided modes satisfied the preset orthogonal value review standard; (2) power loss during transmission in the FEM simulations met the preset power loss review standard; (3) the 2D power  
Figure 18: Spectrum of the FBG-OADM for the \(-3\) dB bandwidth (FWHM). distribution maps of the input and drop ports showed that the FBG-OADM accurately transmitted and dropped signals; (4) the frequency distribution of the drop port showed that at an operating wavelength (\(\lambda\)) of 1550 nm, the power approximated 0 dB, indicating that homodyne and heterodyne crosstalk did not occur; and (5) the FBG-OADM exhibited an FWHM of 0.0375 nm, which is lower than the ITU requirement for DWDMs. These simulation results confirm the feasibility and accuracy of the proposed FBG-OADM, the advantages of which are that it is a miniature-sized all-optical fiber-based multiplexer with a low FWHM and that it can be fabricated through a low-cost and simple manufacturing process.