The azimuthal current induced by an H-polarized plane wave with an arbitrary angle of incidence on an infinite cylinder with an infinite axial slot is considered. A system of dual series equations is derived from the modal expansions of the tangential field components by enforcing the electromagnetic boundary conditions. This dual series system is then solved for the modal coefficients with techniques borrowed from the Riemann-Hilbert problem of complex variable theory. The resulting infinite system of linear equations for the modal coefficients can be handled in an efficient manner. A comparison of the generalized dual series solution with a purely numerical method of moments solution based upon vector and scalar potentials is made. In contrast to this method of moments solution, it explicitly contains the behavior of the solution near the aperture rim and can generate the current values in a shadow region for small to large ratios of cylinder radius to wavelength without additional special considerations.
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