# Designing a Novel High-Performance FBG-OADM Based on Finite Element and Eigenmode Expansion Methods
## Novel FBG-OADM  
Figure 1 shows the geometric structure of the proposed FBG-OADM [12]. The structure comprises two SMFs placed side by side (Fibers 1 and 2), a 1 \(\upmu\)m thick PML (purple lines), a PRB (yellow lines), a noncoupling area (L\({}_{1}\) and L\({}_{3}\)); a mode-power coupling area (L\({}_{2}\)); an HE\({}_{11}\) core mode (red lines); and a cladding mode (black lines). When the drop wavelength of the FBG-OADM is set to \(\lambda_{1}\) and \(N\) core mode signals with different wavelengths (i.e., \(\lambda_{1},\lambda_{2},\ldots\lambda_{n}\)) are inputted via the input port, core mode signals of all wavelengths (except for that with a wavelength of \(\lambda_{1}\)) are unaffected by the FBG and are outputted directly via the output port. However, the core mode signal with a wavelength of \(\lambda_{1}\) is subjected to perturbation from the FBG and is coupled to the cladding mode propagated along the \(-Z\) direction. Mode theory posits that the power distribution in the core mode exists in the cladding layer in the form of exponential decay (red lines). In other words, the core mode in the figure cannot detect the presence of the surround layer. Thus, the core mode cannot couple Fiber 1 to Fiber 2. Conversely, because the power in the cladding mode can be extended to the surround layer (black lines), the cladding mode can couple Fiber 1 to Fiber 2. Subsequently, the cladding mode in Fiber 2 is subjected to perturbation from the FBG, prompting the coupled core mode to be propagated along the \(Z\) direction and outputted via the drop port, thus completing the signal drop process. Regarding the signal add process, because the proposed FBG-OADM has a symmetric structural design, signal adding works according to the same principle as signal dropping; that is, when a signal is inputted via the add port of Fiber 2, it will be outputted via the output port of Fiber 1, thus completing the signal add process [12]. Compared with a previous long-period fiber grating (LPG) OADM proposed by the author of the present study (in which the LPG-OADM comprised two LPGs and a 2 \(\times\) 2 optical fiber coupler) [7], the present OADM uses FBGs instead of LPGs. Roughly speaking, the overall spectrum of the two OADMs is the product of the spectrums of the two LPGs (or two FBGs) and 2 \(\times\) 2 optical fiber coupler, as shown in Table 1. According to the table, the newly-proposed FBG-OADM features a narrower spectrum, indicating that it can achieve exceptional bandwidth performance (\(-\)3 dB). Figure 1: Side view (\(X\)-\(Z\) plane) of the proposed FBG-OADM. In real-world environments, signals in an optical fiber structure may take the form of one of two mode types: discrete guided modes and continuous radiation modes. However, because continuous radiation modes cannot be measured in real-world environments, they are considered a type of power loss. Moreover, the limitations imposed on numerical simulations by memory and computation time constraints render it impossible to contain continuous radiation modes. To overcome this drawback and, thus, improve the accuracy of simulation results, this study employed a PRB to convert continuous radiation modes into discrete radiation modes. In addition, to enable the converted discrete radiation modes to achieve expected power loss, a PML was incorporated into the surround layer, enabling the propagation constant of the discrete radiation modes to be \(-(\alpha+i\beta)\), where \(\alpha\) is the attenuation constant and \(\beta\) is the phase constant [13; 14]. SMFs were employed as the optical fiber technology in this study. SMFs are a type of fiber in which the solution for the core and the nearly infinite number of solutions for the cladding layer can be identified once the size and constituent materials of the fibers are determined (using PDEs). From a physics perspective, all solutions are referred to as guided modes and each solution corresponds to an equivalent RI.