Accurate Full-Wave Bloch Analysis of General 1D-Periodic Open Structures

This paper explores and validates the effectiveness of the multimodal transfer-matrix method (MMTMM) for accurate Bloch analysis of generic one-dimensional (1D) periodic leaky-wave structures. The method offers a systematic methodology for computing the complex wavenumbers of both proper and improper leaky modes by using the multimodal transfer matrix of a single unit cell, which can be obtained with commercial software. The versatility and accuracy of the MMTMM are first validated for rectangular waveguides loaded with periodic slots, where the leaky mode arises as a perturbation of the fundamental waveguide mode. Its applicability is further demonstrated for more complex surface-wave-supporting periodic structures commonly used in leaky-wave antennas, including corrugated surfaces and grounded-dielectric strip gratings. The results are verified against ad hoc solutions using the method of moments. The reliability of the method is demonstrated by the convergence of the solutions from multiple simulations. The MMTMM proves to be an efficient, accurate, and reliable means of obtaining the leakage constant and phase shift of general 1D-periodic open structures.