Multimodal Transfer Matrix Method to Calculate the Dispersion Diagram of Open Structures

We demonstrate that the multimodal transfer-matrix method (MMTMM) can be used to compute the dispersion diagram of general 1- D open periodic structures. To prove this, we analyze corrugated metallic surfaces and strip gratings as benchmark structures that are often utilized in leaky-wave antennas. This method provides a means of obtaining the complex wavenumber of both proper and improper leaky modes based on the multimodal transfer matrix of a single unit cell of the periodic structure, which can be obtained using commercial software. The MMTMM results are verified using the ad hoc method of moments for both structures under study. The applicability and reliability of the proposed method are demonstrated by the convergence of results from various simulations, which vary the number of modes employed in the MMTMM and the simulation parameters. The MMTMM has proved to be an accurate and reliable means for obtaining the leakage constant in general open periodic structures, which avoids the necessity of developing specific ad hoc methods for this purpose.