Modal Analysis of Planar Waveguides Based on the Immersed Interface Method

Modal analysis of optical waveguides is a basic task in the design advanced waveguide devices and circuits. How to deal with problem electromagnetic heterogeneous interface absorption boundary condition two major difficulties efficient numerical waveguides. Existing high-order accurate finite-difference modal methods have not considered problem, which makes it difficult accurately simulate leakage radiation modes. Based on immersed method perfectly matched layer condition, second- fourth-order accuracy proposed. By using this method, modes single-interface plasmonic waveguide, planar symmetric one-dimensional photonic crystal are analyzed. Numerical experimental results show that convergence rates algorithms consistent expected order for guided, The second-order algorithm provides an ultimate about <inline-formula><tex-math id="M5">\begin{document}$10^{-9}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20230595_M5.jpg"/><graphic xlink:href="14-20230595_M5.png"/></alternatives></inline-formula> relative error effective refractive index, when normalized step size id="M6">\begin{document}$10^{-4}$\end{document}</tex-math><alternatives><graphic xlink:href="14-20230595_M6.jpg"/><graphic xlink:href="14-20230595_M6.png"/></alternatives></inline-formula>. id="M7">\begin{document}$10^{-10}$\end{document}</tex-math><alternatives><graphic xlink:href="14-20230595_M7.jpg"/><graphic xlink:href="14-20230595_M7.png"/></alternatives></inline-formula> id="M8">\begin{document}$10^{-3}$\end{document}</tex-math><alternatives><graphic xlink:href="14-20230595_M8.jpg"/><graphic xlink:href="14-20230595_M8.png"/></alternatives></inline-formula>. Through study field distributions guided cladding we continuity transverse electric mode its first derivative across interface, magnetic discontinuity all can be analyzed precisely. proposed paper used calculate any index profile, only value independent specific functional representation fields. simple tool step-index