Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By I. V. Lindell

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Differential-form formalism has been often applied, in stead of the more commonplace Gibbsian vector calculus, to express the basic electromagnetic equations in simple and elegant form. However, representing higher-order equations has met with unexpected difficulties, in particular, when dealing with general linear electromagnetic media. In the present study, wave equations involving scalar operators of the fourth order are derived for the electromagnetic two-form and the potential one-form, for the general linear bi-anisotropic medium. This generalizes previous coordinate- free approaches valid for certain special classes of media. The analysis is based on some multivector and dyadic identities derived in the Appendix.

Citation: (See works that cites this article)
I. V. Lindell, "Electromagnetic Wave Equation in Differential-Form Representation," Progress In Electromagnetics Research, Vol. 54, 321-333, 2005.

1. Flanders, H., Differential Forms, Academic Press, New York, 1963.

2. Thirring, W., Classical Field Theory, Springer, New York, 1979.

3. Schutz, B., Geometrical Methods of Mathematical Physics, University Press, Cambridge, 1980.

4. Deschamps, G. A., "Electromagnetics and differential forms," Proc. IEEE, Vol. 69, No. 6, 676-696, 1981.

5. Baldomir, D. and P. Hammond, Geometry of Electromagnetic Systems, Clarendon Press, Oxford, 1996.

6. Warnick, K. F. and D. V. Arnold, "Electromagnetic Green functions using differential forms," J. Electro. Waves Appl., Vol. 10, No. 3, 427-438, 1996.

7. Hehl, F. W. and Yu. W. Obukhov, Foundations of Classical Electrodynamics, Birkhäuser, Boston, 2003.

8. Lindell, I. V., Differential Forms in Electromagnetics, Wiley and IEEE Press, New York, 2004.

9. Lindell, I. V. and K. H. Wallén, "Wave equations for bi-anisotropic media in differential forms," J. Electromag. Waves Appl., Vol. 16, No. 11, 1615-1635, 2002.

10. Lindell, I. V., Methods for Electromagnetic Field Analysis, 2nd ed., University Press, Oxford, 1995.

11. Gibbs, J. W. and E. B. Wilson, Vector Analysis, Dover, New York, 1960.

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