n -Series Problems and the Coupling of Electromagnetic Waves to Apertures: A Riemann–Hilbert Approach

An effective approach to the solution of a large class of mixed boundary value problems (those reducible to an n-series problem) is developed. The method is based on the deduction of the equivalent Riemann-Hilbert problem and its solution. This generalized n-series approach leads to analytical descriptions of the coupling of electromagnetic waves through apertures in canonical structures into open or enclosed regions. In particular, it is applied to the canonical problem of plane wave coupling to an infinite circular cylinder with multiple infinite axial slots. Numerical results for currents induced by an H-polarized plane wave on a circular cylinder with a single slit are given.