The Diffraction of Waves By a Penetrable Ribbon

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Abstract
The exact solution of the diffraction of waves by a dielectric ribbon or by an elliptical dielectric cylinder is obtained. Results are given in terms of Mathieu and modified Mathieu functions. It is found that each expansion coefficient of the scattered or transmitted wave is coupled to all coefficients of the series expansion for the incident wave, except when the elliptical cylinder degenerates to a circular one. Both polarizations of the incident wave are considered: one with the incident electric vector in the axial direction and the other with the incident magnetic vector in the axial direction. It is noted that the technique used in this paper to satisfy the boundary conditions may be applied to similar types of problems; such as the plasma‐coated ribbon radiator and the corresponding acoustical problems.

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