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Abstract
Electromagnetic fields excited by a 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. This system of singular integral equations is
solved either by perturbation procedure, where the solution is
obtained in the form of a Neumann series in powers of 1−N−2 ; or
by application of a collocation scheme of matrices inversion. The
constructed numerical solutions permit fields evaluation for values
of the wedge refractive index, not necessarily close to unity and for
arbitrary positioned source and observer. Asymptotic
approximations for the near and far fields inside and outside the
dielectric wedge are derived. 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. Variations to the canonical problem
in form of excitation by unphased line source for the dielectric and
the meta-material wedge have been presented. Formulations for the
dipole excitation and the moving source have been provided.