Modal Network Formulation for the Analysis and Design of Mode-Converting Metasurfaces in Cylindrical Waveguides

Modal network theory has proven to be a useful tool in analyzing waveguide discontinuities. Ports of a modal network correspond to waveguide eigenmodes on either side of the discontinuity. In this work, modal network theory is extended beyond conventional/geometrical waveguide discontinuities. We use the modal network formulation to analyze discontinuities resulting from metasurfaces. Specifically, we analyze azimuthally invariant cascaded sheet metasurfaces placed in a cylindrical waveguide excited by ${\text {TM}}_{0n}$ modes. The metasurface comprises multiple radially varying electric admittance sheets separated by dielectric spacers. We derive the modal representation of a single inhomogeneous, electric sheet admittance using two approaches: a conventional numerical integration approach and a discrete Hankel transform (DHT) approach. We show that the DHT approach is more efficient. Subsequently, the modal matrices of cascaded sheet metasurfaces are derived using the DHT. Finally, we propose an optimization-based procedure to synthesize transparent metasurface-based mode converters. The mode converters transform a set of incident modes on one side to another set of desired modes on the opposite side of the metasurface. Two designs are synthesized at 10 GHz: a single-mode converter, and a mode splitter. The designs are verified using the commercial finite element electromagnetic solvers.