Proving the Circular Polarization of the Fundamental Modes in Rotationally Symmetric Waveguides

Second-order symmetric waveguides are especially suitable for dual polarization applications, since they present clear, mathematically proven, degeneracy schemes in their spectrum. In this work we will prove that, in second-order rotationally-symmetric waveguides, the fundamental mode presents circular polarization in the circumcenter of the cross-section for any symmetry factor greater than three, and regard-less of its geometry. Moreover we will show that certain mode classes do not carry any power at the circumcenter.