On the generalized Jordan's lemma with applications in waveguide theory

This paper presents two variants of a generalized Jordan's lemma with applications in waveguide theory. As a main application is considered an asymptotic analysis for open waveguide structures with circular geometry. In particular, the generalized Jordan's lemma can be used to justify that field components can be calculated as the sum of discrete and non-discrete modes, i.e., as the sum of residues and an integral along the branch-cut defined by the transversal wavenumber of the exterior domain. An explicit example regarding the axial symmetric TM0 modes of a single core transmission line, wire, or optical fibre is included to demonstrate the associated asymptotic behavior for a typical open waveguide structure.