Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Diffraction of a dipole field by a unidirectionally conducting semi-infinite screen

Author: James Radlow
Journal: Quart. Appl. Math. 17 (1959), 113-127
MSC: Primary 78.00
DOI: https://doi.org/10.1090/qam/106678
MathSciNet review: 106678
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An exact solution is obtained for the diffraction of a dipole field by a unidirectionally conducting semi-infinite plane screen. Double Laplace transforms are applied to Maxwell's equations, and the defining conditions of the unidirectionality lead to an equation between two complex functions of two complex variables. This equation is solved by an extension of the usual function-theoretical method, and we can then express the electro-magnetic field in terms of certain complex triple integrals. These are transformed into real integrals, so that it is possible to discuss the field behavior in the neighborhood of the diffracting edge. The variation of singularity along the edge of the screen is given.

References [Enhancements On Off] (What's this?)

  • [1] G. Toraldo di Francia, Electromagnetic cross section of a small circular disc with unidirectional conductivity, II Nuovo Cimento, Ser. X 3, 1276-84 (1955)
  • [2] S. N. Karp, Forthcoming EM report
  • [3] D. S. Jones, A simplifying technique in the solution of a class of diffraction problems; Quart. J. Math., Oxford, 2nd Ser. 3, 189-96(1952) MR 0051409
  • [4] T. B. A. Senior, The diffraction of a dipole field by a perfectly conducting half-plane, Quart. J. Mech. and Appl. Math. 6, 101-114 (1953) MR 0054518
  • [5] H. M. Macdonald, A class of diffraction problems, Proc. London Math. Soc., Ser. 2 14, 410-427 (1915)
  • [6] R. F. Harrington, Current element near the edge of a conducting half-plane, J. Appl. Phys. 24, 547-550 (1953) MR 0057742
  • [7] G. Doetsch, Theorie und Anwendung der Laplace-Transformation, Dover, New York, 1943, p. 126, Satz 2 MR 0009225
  • [8] Ibid., p. 52, Satz 6
  • [9] G. Toraldo di Francia, Equazioni integrodifferenziali e principio di Babinet per gli schermi piani a conduttivitá unidirezionale, Rendiconti dell'Accademia Nazionale dei Lincei (Classe di Scienze Fisiche, matematiche e naturali) ser. VIII XX, Fasc. 4, 476-480 (1956) MR 0081745
  • [10] G. Toraldo di Francia, On a macroscopic measurement of the spin of electromagnetic radiation, Il Nuovo Cimento, Ser. X 6, 150-167 (1957) MR 0090352
  • [11] J. B. Keller, Diffraction by an aperture, J. Appl. Phys. 28, 426-444 (1957) MR 0101763

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 78.00

Retrieve articles in all journals with MSC: 78.00

Additional Information

DOI: https://doi.org/10.1090/qam/106678
Article copyright: © Copyright 1959 American Mathematical Society

American Mathematical Society