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Asymptotics of the far field generated by a modulated point source in a planarly layered electromagnetic waveguide
Author(s) -
BarreraFigueroa Víctor,
Rabinovich Vladimir S.
Publication year - 2014
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.3176
Subject(s) - helmholtz equation , eigenfunction , mathematics , waveguide , mathematical analysis , field (mathematics) , helmholtz free energy , near and far field , dispersion relation , electromagnetic field , eigenvalues and eigenvectors , series (stratigraphy) , basis (linear algebra) , representation (politics) , power (physics) , point source , point (geometry) , physics , quantum mechanics , geometry , pure mathematics , boundary value problem , law , paleontology , politics , political science , biology
In the present work, we analyze the electromagnetic field generated by a modulated point source in a planarly layered waveguide, in the far field region. On the basis of the two‐dimensional stationary phase method, we obtain expressions for the asymptotics of the field at large distance from the source and a large value of the time. The analysis relies on the eigenfunctions and eigenvalues of an auxiliary one‐dimensional spectral problem, which is intimately linked to the Helmholtz equation for inhomogeneous media. In addition, from the spectral parameter power series method [ Math. Meth. Appl. Sci. 2010; 33 (4): 459‐468], we obtain an explicit representation for the dispersion relation of the waveguide, which leads us to the allowed propagation constants and the group velocities for the guided modes. Several examples show the spectral parameter power series approach of the present analysis. Copyright © 2014 John Wiley & Sons, Ltd.