Analysis of Electromagnetic Angular Momentum in Circular Waveguides

Angular momentum (AM) plays multiple critical roles in wireless communications and detection, whereas waveguides serve as a pivotal propagation environment. The electromagnetic (EM) waves propagating in waveguides carry coupled spin angular momentum (SAM) and orbital angular momentum (OAM), yet the specific OAM mode composition and SAM-OAM coupling relationship have not been fully resolved. Although prior studies have derived average OAM values carried by waveguide eigenmodes, the ambiguity persists due to infinite possible OAM state combinations that yield identical averages. This work addresses two critical gaps: first, it obtains the deterministic decomposition of OAM mode components, and second, it shows the explicit SAM-OAM coupling relationship of EM waves in circular waveguides. By analytically decomposing hybrid eigenmodes into left-handed and right-handed polarized components, this study reveals that each polarization component carries OAM with distinct topological charges. Moreover, consistency is demonstrated among the theory of this study, HFSS simulations, and prior research. As a result, this study establishes a theoretical foundation for angular momentum transmission in circular waveguides, which enables applications in OAM multiplexing and quantum communications.