Long-period fiber grating using the finite element method and eigenmode expansion method

Previous studies of long-period fiber grating (LPG) have commonly employed the traditional coupled-mode theory. In this study, however, we propose a visualized, graphical, and simplified numerical simulation method that incorporates the finite element method and eigenmode expansion method. The FEM was employed to solve the existing guided modes in the fiber structure, and the eigenmode expansion method was employed to calculate the power transmissions of the guided modes in the fiber structure. This study provides a detailed explanation of how the periodic structure of optical LPG renders this method significantly superior compared to other numerical methods, such as the finite-difference time-domain method and the beam propagation method. In other words, of all numerical simulation methods that focus on large-scale periodic components, only the method proposed in this study possesses 3D design and analysis capabilities. Additionally, a comparison between the period scan diagram of LPG and the final spectrum diagram showed that the two possessed a certain inverse relationship in the periods or wavelengths of coupling. Therefore, before conducting time-consuming calculations of the fiber grating spectra, this characteristic can be considered to predict the final spectrum. By combining these two numerical simulation methods and adopting a rigorous, simple, and complete design process, this study provides a graphical and simple simulation technique to reduce the required learning time and professional threshold for research and applications of LPG.