Scattering of a plane electromagnetic wave by a hollow circular cone with thin semi-transparent walls

M A Lyalinov, N Y Zhu, Valery P Smyshlyaev

Research output: Contribution to journalArticle

13 Citations (SciVal)


We study electromagnetic plane wave diffraction by a hollow circular cone with thin walls modelled by the so-called impedance-sheet boundary conditions. By means of Kontorovich-Lebedev integral representations for the Debye potentials and a 'partial' separation of variables, the problem is reduced to coupled functional difference (FD) equations for the relevant spectral functions. For a circular cone, the FD equations are then further reduced to integral equations, which are subsequently shown to be Fredholm-type equations via a semi-inversion by use of Dixon's resolvent. We then solve the integral equations numerically using an appropriate quadrature method. Certain useful further integral representations for the solution of 'Watson-Bessel' and Sommerfeld types are developed, which gives a theoretical basis for subsequent calculation of the far-field (high-frequency) asymptotics for the diffracted field. Based on this asymptotics, the radar cross section in the domain, which is free from both the reflected and the surface waves, has been computed numerically.
Original languageEnglish
Pages (from-to)676-719
Number of pages44
JournalIMA Journal of Applied Mathematics
Issue number5
Publication statusPublished - Oct 2010


  • numerical evaluation of the vertex diffracted wave
  • the far-field asymptotics
  • semi-transparent cone
  • functional difference equations
  • diffraction


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