Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 513953, 18 pages
http://dx.doi.org/10.1155/2014/513953
Research Article

Inverse Diffraction Theory and Computation of Minimum Source Regions of Far Fields

Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115, USA

Received 29 August 2013; Revised 29 October 2013; Accepted 5 November 2013; Published 12 January 2014

Academic Editor: Davide La Torre

Copyright © 2014 Edwin A. Marengo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Kusiak and J. Sylvester, “The scattering support,” Communications on Pure and Applied Mathematics, vol. 56, no. 11, pp. 1525–1548, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. A. D. Yaghjian, T. B. Hansen, and A. J. Devaney, “Minimum source region for a given far-field pattern,” IEEE Transactions on Antennas and Propagation, vol. 45, no. 5, pp. 911–912, 1997. View at Publisher · View at Google Scholar · View at Scopus
  3. A. J. Devaney and E. Wolf, “Multipole expansions and plane wave representations of the electromagnetic field,” Journal of Mathematical Physics, vol. 15, no. 2, pp. 234–244, 1974. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. J. Sylvester, “Notions of support for far fields,” Inverse Problems, vol. 22, no. 4, article 010, pp. 1273–1288, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves, Springer, Berlin, Germany, 1969. View at MathSciNet
  6. T. B. Hansen and A. D. Yaghjian, Plane Wave Theory of Time-Domain Fields: Near-Field Scanning Applications, IEEE Press, Piscataway, NJ, USA, 1999. View at MathSciNet
  7. S. Kusiak and J. Sylvester, “The convex scattering support in a background medium,” SIAM Journal on Mathematical Analysis, vol. 36, no. 4, pp. 1142–1158, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. E. A. Marengo, A. J. Devaney, and R. W. Ziolkowski, “Inverse source problem and minimum-energy sources,” Journal of the Optical Society of America A, vol. 17, no. 1, pp. 34–45, 2000. View at Google Scholar · View at MathSciNet · View at Scopus
  9. A. J. Devaney and G. C. Sherman, “Nonuniqueness in inverse source and scattering problems,” IEEE Transactions on Antennas and Propagation, vol. 30, no. 5, pp. 1034–1037, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. R. Potthast, J. Sylvester, and S. Kusiak, “A “range test” for determining scatterers with unknown physical properties,” Inverse Problems, vol. 19, no. 3, pp. 533–547, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. H. Haddar, S. Kusiak, and J. Sylvester, “The convex back-scattering support,” SIAM Journal on Applied Mathematics, vol. 66, no. 2, pp. 591–615, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. R. Potthast, “A survey on sampling and probe methods for inverse problems,” Inverse Problems, vol. 22, no. 2, pp. R1–R47, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, Elsevier Academic Press, 6th edition, 2005. View at MathSciNet
  14. C. A. Balanis, Advanced Engineering Electromagnetics, John Wiley & Sons, New York, NY, USA, 1989. View at MathSciNet
  15. E. A. Marengo, “A new theory of the generalized optical theorem in anisotropic media,” IEEE Transactions on Antennas and Propagation, vol. 61, no. 4, pp. 2164–2179, 2013. View at Publisher · View at Google Scholar