An efficient eigenmode restoration and mode matching method for multi‐junctional inhomogeneous waveguiding structures based on the Krylov subspace method

Abstract

Mode matching is a widely used method in various electromagnetic problems due to its dimensional advantages. However, the numerical implementation of mode matching is challenged by its high computational complexity in solving eigenvalue problems. The Lanczos method approximates the original eigenvalue problem in an efficient way and transforms the mode matching into an implicit form. The price of efficiency enhancement is the loss of eigenmode accuracy and behaviour interpretation. Its numerical efficiency is also influenced by block matrix dimensions while solving multi-junctional waveguide structures. This work proposes a novel structure eigenmode restoration algorithm based on the Krylov subspace method. The method takes the conventional explicit mode matching strategy, but the efficiency enhancement for solving eigenmodes is prominent. The overall computational complexity is reduced from the original O(N3) to O(N1.5) without the cost of eigenmode accuracy loss. Numerical benchmark cases verify the proposed method’s accuracy and efficiency. The efficiency advantage is outstanding especially in computational time. Extra discussions about eigenmode selection strategies based on accuracy controlling indicate that the proposed method possesses better flexibility in solving complicated waveguide problems.