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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. |