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.