Modal Spectrum Shaping and Rotational Unit-Cell Design of Second-Order Symmetric Waveguides

In this work, we will introduce the role of second-order symmetries in modal spectrum shaping, focusing on structures with discrete rotational symmetry, which are notably useful for applications with dual linear and circular polarizations. Relevant examples are provided, as well as a rigorous approach to model the effect that second-order symmetries along with the geometry of the rotational unit cell have on the mode-class monomode bandwidth. Modal spectrum shaping and rotational transversal dispersion diagrams are checked with asymptotic cases and results for regular polygons. Finally, a general workflow for the design of the rotational unit cell is provided.

I. Introduction

Communication systems are subject to an ever-increasing demand for higher bandwidth, with the objective of improving data rates. This is the case for ultrawideband (UWB) applications [1] or fifth- and sixth-generation mobile communications [2]. A common approach for achieving this goal is moving to higher frequencies when the spectrum is available. If this is not the case, for waveguide media, a practical approach is using dual-polarization [3], [4] and/or modifying the cross section of the waveguides, displacing higher-order modes to higher frequencies, for example, using ridge or double-ridge waveguides [5], [6]. Extended bandwidth can also be achieved by controlling the excitation of the problem, specifically the symmetry of its electromagnetic field, so that only the modes belonging to certain classes are generated [7], [8], [9]. Moreover, dual-polarization implicitly demands symmetric devices to guarantee no coupling exists between the two first degenerate modes.