A Finite Element formulation for waveguides with first and second order symmetries

This work addresses the efficient analysis of waveguides with rotationally symmetric cross-sections of order
$N$
(also called
$C_{N}$
symmetry), having also additional symmetry planes. These commonly used geometries, called
$C_{N,\nu}$
, which have first and second order symmetries, allow for a finer-grain mode classification and characterization thanks to combining both axial and rotational boundary conditions. A Finite Element Method formulation that takes these properties into account is presented for the first time, having among its advantages the automatic identification of degenerate modes, the ability to predict coupling behaviour and computational domain reduction for efficiency improvement. The formulation has been thoroughly analysed and the most relevant results are presented, justifying its main advantages and limitations.