Humblet's Decomposition of the Electromagnetic Angular Moment in Metallic Waveguides

In a seminal paper, Humblet decomposed the angular momentum of a classical electromagnetic field as a sum of three terms: the orbital angular momentum (OAM), the spin, and the more unfamiliar surface angular momentum. In this paper, we present the result of such decomposition for various metallic waveguides. We investigate two hollow metal waveguides with circular and rectangular cross sections, respectively. The waveguides are excited with two TE eigenmodes driven in phase quadrature. As references, two better known modes are also analyzed: a plane, a circularly polarized wave (a TEM mode), and a TE-Bessel beam, both of infinite transverse extent and with no metallic boundaries. Our analysis shows that modes carrying OAM and spin can also propagate in the metallic waveguides, even when the cross section of the waveguide is distinctly non-circular. However, the mode density of orthogonal modes carrying OAM is at most equal to that of the waveguides' eigenmodes.