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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on January 24, 2008
The Quarterly Journal of Mechanics and Applied Mathematics 2008 61(2):219-239; doi:10.1093/qjmam/hbm029
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Q. Jl Mech. Appl. Math, Vol. 61. No. 2 © The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Electromagnetic fields in the presence of an infinite dielectric wedge: the phased line source excitation case

M. A. Salem{dagger} and A. H. Kamel

( New Jersey Institute of Technology, Newark, NJ 07102, USA and Advanced Industrial, Technological and Engineering Center, PO Box 433, Heliopolis Center, Cairo 11757, Egypt )

{dagger} < ms2.718{at}gmail.com>

Received 6 August 2007. Revise 27 November 2007. Accepted 29 November 2007.


  Abstract

Electromagnetic fields, excited by an electric phased line source in the presence of an infinite dielectric wedge, are determined by application of the Kontorovich–Lebedev transform. The Maxwell's equations together with the conditions of continuity of the tangential field components at the material interfaces are formulated as a vector boundary-value problem. By representing the field components as Kontorovich–Lebedev integrals, the problem is reduced to a system of singular integral equations for the unknown spectral functions. We construct numerical solutions to those equations that permit fields evaluation for values of the wedge refractive index, not necessarily close to unity, and for arbitrary positioned source and observer. Numerical results showing the influence of a wedge presence on the directivity of a phased line source are presented and verified through finite-difference frequency-domain simulations.


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