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The dielectric half space as a test bed for transform methods
Author(s) -
Grzesik J. A.,
Lee S. C.
Publication year - 1995
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/95rs01248
Subject(s) - transformation (genetics) , fourier transform , mathematics , mathematical analysis , consistency (knowledge bases) , reflection (computer programming) , laplace transform , electromagnetics , computer science , physics , geometry , biochemistry , chemistry , engineering physics , gene , programming language
The canonical, Fresnel problem, involving normal wave incidence upon a dielectric half space, is rephrased as an elementary Fredholm integral equation conveying the global viewpoint of radiative self‐consistency. This equation is of course well‐known, but we proceed here to exploit its simple features so as to demonstrate the complementary performance of several techniques that are part of the standard mathematical repertoire in electromagnetics. The techniques utilized are (1) mode matching through global self‐consistency; (2) Laplace transformation; and (3) Fourier transformation as reinforced by analyticity arguments of the Wiener‐Hopf type in the transform plane. All three methods naturally succeed in recovering the reflection/transmission solution gotten by the usual procedure of enforcing tangential electric/magnetic field continuity at the dielectric interface. Such benchmark success in so controlled a setting would seem to vindicate the individual power of these independent, popular methods.