Simulation-assisted Formulas for Propagation Constant in Periodic Structures

Simulation-assisted formulas to calculate propagation constant in uniform or periodic structures (FPPS) are deduced and verified through simulations in three types of structures. The FPPS is theoretically rigorous, and its sole precondition is the invariance of the spatial translation of the structure represented by Floquet's theorem. The FPPS uses the field values calculated with a driven-mode solver of a full-wave simulator, and then gives formulas with closed-form solutions for the propagation constants inside both uniform and periodic structures even with strong reflection. Its error comes mainly from inaccurate field values caused by simulation errors. The FPPS has been applied to a variety of typical structures, including uniform waveguides, loss-free and lossy closed periodic structures, and open periodic structures, and compared to the results calculated with exact theoretical formula and eigenmode solvers. The comparison shows the easy-to-use and adaptable nature of the FPPS.