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

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.