Application of bicomplex (quaternion) algebra to fundamental electromagnetics: A lower order alternative to the Helmholtz equation

Anastassiu, HT; Atlamazoglou, PE; Kaklamani, DI

dc.contributor.author	Anastassiu, HT	en
dc.contributor.author	Atlamazoglou, PE	en
dc.contributor.author	Kaklamani, DI	en
dc.date.accessioned	2014-03-01T01:18:40Z
dc.date.available	2014-03-01T01:18:40Z
dc.date.issued	2003	en
dc.identifier.issn	0018-926X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15147
dc.subject	Analytic solutions	en
dc.subject	Bicomplex algebra	en
dc.subject	Helmholtz equation	en
dc.subject	Inhomogeneous media	en
dc.subject	Quaternions	en
dc.subject	Transverse electric magnetic (TEM) waves	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.classification	Telecommunications	en
dc.subject.other	Algebra	en
dc.subject.other	Electromagnetic wave propagation	en
dc.subject.other	Electromagnetism	en
dc.subject.other	Magnetic field effects	en
dc.subject.other	Vectors	en
dc.subject.other	Transverse electric magnetic (TEM) waves	en
dc.subject.other	Electromagnetic waves	en
dc.title	Application of bicomplex (quaternion) algebra to fundamental electromagnetics: A lower order alternative to the Helmholtz equation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/TAP.2003.810231	en
heal.identifier.secondary	http://dx.doi.org/10.1109/TAP.2003.810231	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	The mathematical concept of bicomplex numbers (quaternions) is introduced in electromagnetics, and is directly applied to the derivation of analytical solutions of Maxwell's equations. It is demonstrated that, with the assistance of a bicomplex vector field, a novel entity combining both the electric and the magnetic fields, the number of unknown quantities is practically reduced by half, whereas the Helmholtz equation is no longer necessary in the development of the final solution. The most important advantage of the technique is revealed in the analysis of electromagnetic propagation through inhomogeneous media, where the coefficients of the (second order) Helmholtz equation are variable, causing severe complications to the solution procedure. Unlike conventional methods, bicomplex algebra invokes merely first order differential equations, solvable even when their coefficients vary, and hence enables the extraction of several closed form solutions, not easily derivable via standard analytical techniques.	en
heal.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC	en
heal.journalName	IEEE Transactions on Antennas and Propagation	en
dc.identifier.doi	10.1109/TAP.2003.810231	en
dc.identifier.isi	ISI:000184769400050	en
dc.identifier.volume	51	en
dc.identifier.issue	8	en
dc.identifier.spage	2130	en
dc.identifier.epage	2136	en