Dispersion Analysis of Complex Periodic Structures by Full-Wave Solution of Even-Odd-Mode Excitation Problems for Single Unit Cells

Abstract

The Bloch modes of complex periodic structures are computed by superimposing results obtained from even-odd-mode full-wave driven simulations of individual unit cells. In order to emulate the periodic boundary conditions for the Bloch modes, one full-wave simulation is performed with magnetic and one with electric boundary conditions yielding the even-and odd-mode results, respectively. Therefore, the employed full-wave solver does not even need to support periodic boundary conditions. Since the non-periodic boundary conditions can be arbitrary, even open and radiating problems can be analyzed. The excitation of the structures is performed by discrete ports, which are located appropriately in order to excite the desired mode, typically the fundamental mode of the background structure. The found even-and odd-mode impedances deliver directly the complex propagation constant and the Bloch impedance of the periodic structure without any iterative search and under consideration of all electromagnetic interaction effects. This is in contrast to alternative solution methods, which require to solve computationally intensive eigenproblems or many excitation problems. Moreover, this approach allows to determine the field data corresponding to the Bloch mode, where arbitrary real and complex modes can be handled. Numerical results for different classes of problems including 1D and 2D microstrip structures as well as hollow waveguide based unit cells are presented.Index Terms-Composite right/left-handed unit cells, even-odd mode analysis, metamaterials, periodic structures.

On the Computation of the Dispersion Diagram of Symmetric One-Dimensionally Periodic Structures

“…Certainly, the full-wave simulator employed to characterize the macro-cell does take into account all the possible interactions between adjacent cells (which justifies its identification with a cascade of multi-port equivalent networks). This method has several drawbacks such as the intense computational load required to analyze a macro-cell involving many unit cells (as required in many practical problems) [39,41], the appearance of spurious solutions, and the ambiguity of the phase constant outside the first fictitious Brillouin zone imposed by the repetition of the unit cell [39]. These inherent difficulties have motivated the search for approaches that can overcome them, as for example those reported in [39,41].…”

“…This method has several drawbacks such as the intense computational load required to analyze a macro-cell involving many unit cells (as required in many practical problems) [39,41], the appearance of spurious solutions, and the ambiguity of the phase constant outside the first fictitious Brillouin zone imposed by the repetition of the unit cell [39]. These inherent difficulties have motivated the search for approaches that can overcome them, as for example those reported in [39,41]. The procedure given in [39] can solve the drawback related to the appearance of spurious solutions at the expense of increasing the computational load.…”

“…The procedure given in [39] can solve the drawback related to the appearance of spurious solutions at the expense of increasing the computational load. However, the procedure reported in [41] apparently overcomes all the mentioned drawbacks given that it only involves full-wave simulations of a single unit cell (or even half this unit cell under appropriate symmetry conditions) bounded by electric and/or magnetic walls along the direction of periodicity. Unfortunately, the authors of the present work have not been able to reproduce the expected good results of [41] in their own research and have found some reasons to justify this fact.…”

“…In consequence, the development of combined approaches that can take advantage of these features of commercial simulators and can be complemented with a simple in-house post-processing stage is becoming more and more convenient [37][38][39][40]. Some more-simplified approaches involving the simulation of a single unit cell (or even half unit cell) have also been proposed [41]. Thus, the main goal of the present work will be to go over some of these approaches in order to discuss what is the optimized hybrid method that, making use of commercial software, can efficiently provide the dispersion relation of periodic structures.…”

Bloch Analysis of Artificial Lines and Surfaces Exhibiting Glide Symmetry

“…Under the assumption that each corrugation can be replaced by Marcuvitz's closed-form equivalent circuit [28], it was easily shown that the glide symmetry effect is equivalent to simply halving the spatial period. The study in [29], discussing reduced representations of several kinds of higher-symmetric periodic lines proposed in [30], has recently shown that a more correct condition for this conclusion is to neglect interactions due to localized excitation of higher-order waveguide modes.…”