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Asymptotic analysis of non‐discrete radiating modes for open waveguide structures
Author(s) -
Nordebo Sven,
Cinar Gökhan,
Gustafsson Stefan,
Ioannidis Andreas,
Nilsson Börje
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2821
Subject(s) - waveguide , mathematics , wavenumber , lemma (botany) , transversal (combinatorics) , mathematical analysis , asymptotic analysis , transverse plane , field (mathematics) , geometry , physics , pure mathematics , optics , ecology , poaceae , structural engineering , biology , engineering
This paper presents an asymptotic analysis of non‐discrete radiating modes with applications in waveguide theory. As a main application, the radiating modes of an open waveguide structure with circular geometry is considered. A generalized Jordan's lemma is used to justify that field components can be calculated as the sum of discrete and non‐discrete modes, that is, as the sum of residues of poles and an integral along the branch‐cut defined by the transversal wavenumber of the exterior domain. An asymptotic expression is derived for field components at large distance along the waveguide and supplemented with rigorous upper and lower error bounds. A numerical example regarding the axial symmetric 0th order transverse magnetic modes of a thin copper wire in water is included to demonstrate that there may be a non‐trivial balance between the contributions from discrete and non‐discrete modes. Copyright © 2013 John Wiley & Sons, Ltd.