Designing LPG-OADM Based on a Finite Element Method and an Eigenmode Expansion Method

This study proposes a visual, graphical, and simplistic numerical simulation method for a long period fiber gratings optical add-drop multiplexer (LPG-OADM), as opposed to the well-known traditional mode-coupled theory. This method combines the finite element method and the eigenmode expansion method, where the finite element method is used to solve all existing guided modes. The eigenmode expansion method was used to calculate the energy transfer phenomenon of the guided modes in the LPG-OADM. This study provides a detailed explanation of the key reasons why the periodic structure of the LPG-OADM can achieve significantly superior results for our method compared to those obtained using other numerical methods, such as the finite-difference time-domain and beam propagation methods. All existing numerical simulation methods focus on large-sized periodic components; only the method established in this study has 3-D design and analysis capabilities. This study used actual examples to verify that, under the operating wavelength of λ = 1550 nm, the LPG-OADM designed using this method would have the full-width half-maximum of 0.2846 nm, and an insertion loss and homo-dyne crosstalk of nearly 0. That is, the LPG-OADM designed using this method can reach the ITU specification for the dense wavelength-division multiplexer bandwidth. The primary objective of this study is to use the combination of these two numerical simulation methods in conjunction with a rigorous, simple, and comprehensive design flow to provide a graphical and simplistic simulation technique that reduces the learning time and professional threshold requirements for the design and application of LPG-OADM.