A thorough look at the nonuniqueness of the electromagnetic scattering integral equation solutions as compared to the scalar acoustic ones
Article first published online: 22 APR 2003
Copyright 2003 by the American Geophysical Union.
Volume 38, Issue 2, April 2003
How to Cite
2003), A thorough look at the nonuniqueness of the electromagnetic scattering integral equation solutions as compared to the scalar acoustic ones, Radio Sci., 38, 8021, doi:10.1029/2001RS002558, 2.(
- Issue published online: 22 APR 2003
- Article first published online: 22 APR 2003
- Manuscript Accepted: 22 NOV 2002
- Manuscript Revised: 11 JUN 2002
- Manuscript Received: 12 NOV 2001
 It is well-known that solutions of electromagnetic scattering integral equations of the first or second kind (EFIE and MFIE) for perfectly electric or perfectly magnetic conducting scatterers are nonunique for those frequencies which correspond to interior Maxwell resonances of the scatterer; hence, the null spaces of the respective interior problem operators are under concern. In principle, all mathematical facts and proofs regarding this problem and cited in this paper are available from the book by Colton and Kress , yet, these authors mainly concentrate on single and double layer potentials for the scalar acoustic (Dirichlet and Neumann) as well as the magnetic dipole layer ansatz for the perfectly electric conducting (Maxwell) problem and treat the Huygens-type representation, which is more common in the electrical engineering community, not in the same detail. This might be the reason that part of the electrical engineering literature suffers from some confusion regarding the proper null spaces and their physical relevance, in particular, if the electromagnetic problem is considered in 2-D, where it reduces to scalar TM/TE-problems. The present contribution comments on these issues emphasizing that the null spaces of 2-D electromagnetics are the nonphysical null spaces originating from the Huygens-type representation of scalar acoustics.