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Electromagnetic source transformations and scalarization in stratified gyrotropic media

Patrick De Visschere UGent (2009) PROGRESS IN ELECTROMAGNETICS RESEARCH B. 18. p.165-183
abstract
It is known that with restrictions on the type of the constitutive equations, Maxwell’s equations in non-uniform media can sometimes be reduced to two 2nd order differential equations for 2 scalar quantities only. These results have previously been obtained in two quite different ways, either by a “scalarization of the sources”, where the relevant scalar quantities are essentially vector potential components, and the derivation was limited to isotropic media, or alternatively by using the “scalar Hertz potentials”, and this method has been applied to more general media. In this paper, it is shown that both methods are equivalent for gyrotropic media. We show that the scalarization can be obtained by a combination of transformations between electric and magnetic sources and gauge transformations. It is shown that the method based on the vector potential, which previously used a non-traditional definition of the vector potentials, can also be obtained using the traditional definition provided a proper gauge condition is applied, and this method is then extended from isotropic to gyrotropic media. It is shown that the 2 basic scalar Hertz potentials occurring in the second method are invariant under the source scalarization transformations of the first method and therefore are the natural potentials for obtaining scalarization. Finally, it is shown that both methods are also equivalent with a much older third method based on Hertz vectors.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
potential, electromagnetics, Hertz vector potential, vector potential, scalarization, scalar Hertz potential
journal title
PROGRESS IN ELECTROMAGNETICS RESEARCH B
Progr. Electromagn. Res. B
volume
18
pages
165 - 183
ISSN
1937-6472
language
English
UGent publication?
yes
classification
A2
copyright statement
I have transferred the copyright for this publication to the publisher
id
785279
handle
http://hdl.handle.net/1854/LU-785279
alternative location
http://ceta.mit.edu/pierb/pierb18/09.09070904.pdf
date created
2009-11-19 15:35:49
date last changed
2009-12-02 16:54:01
@article{785279,
  abstract     = {It is known that with restrictions on the type of the constitutive equations, Maxwell{\textquoteright}s equations in non-uniform media can sometimes be reduced to two 2nd order di\unmatched{fb00}erential equations for 2 scalar quantities only. These results have previously been obtained in two quite di\unmatched{fb00}erent ways, either by a {\textquotedblleft}scalarization of the sources{\textquotedblright}, where the relevant scalar quantities are essentially vector potential components, and the derivation was limited to isotropic media, or alternatively by using the {\textquotedblleft}scalar Hertz potentials{\textquotedblright}, and this method has been applied to more general media. In this paper, it is shown that both methods are equivalent for gyrotropic media. We show that the scalarization can be obtained by a combination of transformations between electric and magnetic sources and gauge transformations. It is shown that the method based on the vector potential, which previously used a non-traditional de\unmatched{fb01}nition of the vector potentials, can also be obtained using the traditional de\unmatched{fb01}nition provided a proper gauge condition is applied, and this method is then extended from isotropic to gyrotropic media. It is shown that the 2 basic scalar Hertz potentials occurring in the second method are invariant under the source scalarization transformations of the \unmatched{fb01}rst method and therefore are the natural potentials for obtaining scalarization. Finally, it is shown that both methods are also equivalent with a much older third method based on Hertz vectors.},
  author       = {De Visschere, Patrick},
  issn         = {1937-6472},
  journal      = {PROGRESS IN ELECTROMAGNETICS RESEARCH B},
  keyword      = {potential,electromagnetics,Hertz vector potential,vector potential,scalarization,scalar Hertz potential},
  language     = {eng},
  pages        = {165--183},
  title        = {Electromagnetic source transformations and scalarization in stratified gyrotropic media},
  url          = {http://ceta.mit.edu/pierb/pierb18/09.09070904.pdf},
  volume       = {18},
  year         = {2009},
}

Chicago
De Visschere, Patrick. 2009. “Electromagnetic Source Transformations and Scalarization in Stratified Gyrotropic Media.” Progress in Electromagnetics Research B 18: 165–183.
APA
De Visschere, P. (2009). Electromagnetic source transformations and scalarization in stratified gyrotropic media. PROGRESS IN ELECTROMAGNETICS RESEARCH B, 18, 165–183.
Vancouver
1.
De Visschere P. Electromagnetic source transformations and scalarization in stratified gyrotropic media. PROGRESS IN ELECTROMAGNETICS RESEARCH B. 2009;18:165–83.
MLA
De Visschere, Patrick. “Electromagnetic Source Transformations and Scalarization in Stratified Gyrotropic Media.” PROGRESS IN ELECTROMAGNETICS RESEARCH B 18 (2009): 165–183. Print.