Maxwell's equations in bicomplex (quaternion) form: An alternative to the Helmholtz P.D.E.

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	2014-03-01T02:41:56Z
dc.date.available	2014-03-01T02:41:56Z
dc.date.issued	2001	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/30675
dc.subject	Closed Form Solution	en
dc.subject	Differential Equation	en
dc.subject	Helmholtz Equation	en
dc.subject	Inhomogeneous Media	en
dc.subject	Magnetic Field	en
dc.subject	Second Order Equation	en
dc.subject	Vector Field	en
dc.subject	First Order	en
dc.subject.other	Digital signal processing	en
dc.subject.other	Maxwell equations	en
dc.subject.other	Permittivity	en
dc.subject.other	Vectors	en
dc.subject.other	Bicomplex numbers	en
dc.subject.other	Electromagnetic wave propagation	en
dc.title	Maxwell's equations in bicomplex (quaternion) form: An alternative to the Helmholtz P.D.E.	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1109/DIPED.2001.965025	en
heal.identifier.secondary	http://dx.doi.org/10.1109/DIPED.2001.965025	en
heal.publicationDate	2001	en
heal.abstract	The concept of bicomplex numbers is introduced in Electromagnetics, with direct application to the solution of Maxwell's equations. It is shown that, with the assistance of a bicomplex vector field, defined as a combination of the electric and the magnetic fields, the number of unknown quantities is practically reduced by half, whereas the Helmholtz equation may no longer be necessary in the development of the final solution. Bicomplex, first order differential equations are involved, instead of conventional, complex second order equations, and the solution procedure is greatly simplified. A direct consequence of this observation is the derivation of closed form solutions of the Maxwell's equations for a special class of inhomogeneous media, which cannot be easily extracted from the Helmholtz equation alone.	en
heal.journalName	Proceedings of 6th International Seminar/Workshop on: Direct and Inverse problems of Electromagnetic and Acoustic Wave Theory	en
dc.identifier.doi	10.1109/DIPED.2001.965025	en
dc.identifier.spage	20	en
dc.identifier.epage	24	en