Efficient Implicit Mode Matching Method for Complicated Periodic Waveguiding Structures

Mode matching (MM) is a popular method to analyze the multijunction dielectric waveguides. Conventionally, MM is subject to the high complexity of computation of adequate eigenmodes for matching the transverse fields at waveguide junctions. This letter introduces an implicit mode matching (IMM) method to efficiently analyze complicated periodic waveguiding structures with reduced computational and storage complexities. IMM adapts the spectral bi-Lanczos decomposition to avoid the expensive procedure of calculating eigenmodes explicitly. In this IMM, the optimized nonuniform step of bi-Lanczos iterations is leveraged to further reduce the computational complexity in simulating complicated periodic structures. Numerical results validate the feasibility of the proposed method. Moreover, the comparison with rigorous coupled wave analysis is performed to illustrate the application prospect of the proposed method.