Differential Forms - Publications

1. K. Warnick and P. Russer, Green's theorem in electromagnetic field theory, Proceedings of the European Microwave Association, 2006.

2. K. Warnick and P. Russer, Problem Solving in Electromagnetics, Microwave Circuit, and Antenna Design for Communications Engineering, Norwood, MA: Artech House, 2006.

3. Peter Russer, Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering , Artech House, 2 ed., 2006.

   This is a new textbook which covers a broad range of electromagnetic theory and applications using differential forms. The treatment is lucid and complete, and the figures are especially well done.

4. Teaching Electromagnetic Field Theory Using Differential Forms, IEEE Trans. Ed., Vol. 40, No. 1, pp. 53-68, 1997. (ps version)

   This is an elementary introduction to electromagnetics using differential forms. The material is designed to follow the outline of a typical first semester EM theory course. We include simple examples and emphasize graphical representations of differential forms and operations on forms.

5. Electromagnetic Boundary Conditions Using Differential Forms, IEE Proc. H, 142, pp. 326-332, 1995. See also the Figures.

   This paper gives a new formulation for boundary conditions using differential forms. The field intensity and flux density boundary conditions are identical in form, and the boundary conditions have intuitive graphical representations. Some of this paper is devoted to the technical details of twisted forms and can be ignored when using the boundary conditions operationally. See also a more recent paper by Lindell which also derives Huygens' principle as a byproduct of the boundary conditions.

6. Electromagnetic Green Functions Using Differential Forms., J. Elect. Waves Appl., 10, pp. 427-438, 1996.

   Introduction to the use of double forms as a replacement for the dyadic Green function.

7. APS/URSI 1996 Conference Review Paper. Includes anisotropic Green forms briefly.

8. Secondary Dark Rings of Internal Conical Refraction., Phys. Rev. E, Vol. 55, No. 5, pp. 6092-6096, 1997.

   This paper on internal conical refraction by a biaxial medium does not use differential forms, but the results stemmed from the anisotropic Green form viewpoint described in the previous and following papers.

9. Green Forms for Anisotropic, Inhomogeneous Media., Journal of Electromagnetic Waves and Applications, Vol. 11, pp. 1145-1164, 1997.

   Development of Green forms for general anisotropic, inhomogeneous media. The primary result is an integral equation relating the Green form for the electric field to a generalization of the free space scalar Green function.

10. References. Extensive bibliography on differential forms in electromagnetics.

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