3D numerical mode-matching method for a cascaded fiber structure based on photonic crystal fiber

Accurately simulating large-scale and long-distance photonic crystal fiber (PCF) structures remains a significant challenge, as traditional numerical methods often demand excessive computational time and memory resources. This paper introduces a three-dimensional numerical mode matching (3D NMM) method designed to efficiently and accurately model PCF-based cascaded structures. By decomposing the original 3D problem into a two-dimensional (2D) waveguide eigenvalue problem and a one-dimensional analytical solution, the proposed method significantly reduces computational complexity and memory usage. The framework is derived from the governing equations of PCF-based waveguides and incorporates absorbing boundary conditions (ABC) to ensure accurate determination of waveguide eigenmodes and excitation coefficients. Reflection and transmission matrices are employed to model the electromagnetic response along the propagation direction. Numerical simulations demonstrate that the NMM method achieves high accuracy and superior computational efficiency compared to the commercial finite element solver COMSOL. Meanwhile, the convergence analysis of the NMM method validates its performance in simulating large-scale, long-distance PCF-based cascaded structures. Therefore, the proposed method offers a scalable and practical solution for modeling complex PCF systems over extended distances, making it particularly well-suited for the analysis and design of large-scale photonic devices.