volume | PIER Journals

2005-04-18

Electromagnetic Wave Equation in Differential-Form Representation

Ismo Veikko Lindell

Prof. Ismo Veikko Lindell

Department of Electrical and Communications Engineering

Helsinki University of Technology

Finland

Homepage

Progress In Electromagnetics Research, Vol. 54, 321-333, 2005

doi:10.2528/PIER05021002

Abstract

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.

Download Full Article (288) View Full Article

Citation

Copy Export

Ismo Veikko Lindell, "Electromagnetic Wave Equation in Differential-Form Representation," Progress In Electromagnetics Research, Vol. 54, 321-333, 2005.
doi:10.2528/PIER05021002

References

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

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

3. Schutz, B., Geometrical Methods of Mathematical Physics, University Press, 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, 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, 2003.

8. Lindell, I. V., Differential Forms in Electromagnetics, Wiley and IEEE Press, 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., 1995.

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