Three-dimensional full-wave modeling of plasmonic waveguides using a numerical mode-matching method

Plasmonic waveguide structures pose a significant challenge for numerical electromagnetic modeling due to their large longitudinal extent and the presence of lossy metallic regions. Conventional three-dimensional full-wave discretizations suffer from a rapid growth in degrees of freedom, leading to high computational cost. To address this challenge, this paper develops a numerical mode-matching (NMM) framework for three-dimensional full-wave analysis of plasmonic waveguides, extending the conventional NMM formulation to fully tensorial, anisotropic, and lossy media. The proposed method is based on the combined two-dimensional transverse modal analysis using the mixed finite element (MFEM) method and one-dimensional longitudinal propagation analysis using mode matching. In the transverse direction, an MFEM discretization is employed, and the absorbing boundary condition (ABC) is introduced to truncate the open computational domain. In the longitudinal direction, electromagnetic field propagation and intermodal coupling are described using a mode-expansion scheme combined with reflection-transmission matrices, thereby avoiding fine spatial discretization over the entire three-dimensional domain. Numerical examples demonstrate that the proposed method achieves high accuracy while significantly reducing computational cost compared with conventional full-wave modeling approaches.