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.