"Modeling a Non-Planar Aperture with Cylindrical Symmetry Based on the Exact Solution of the Helmholtz Equation"

"The paper considers a general mathematical formulation of the problem of calculating the electromagnetic field radiated from a closed surface in the form of a straight circular cylinder, generally of unlimited height. The frequency domain analysis based on the Helmholtz wave equation was carried out, which made it possible to formulate the corresponding boundary value problem for any cartesian component of the field. Using the separation of variables method, a solution was obtained in the form of an eigenfunction decomposition that satisfies the asymptotic radiation conditions and is valid for any physically realizable field distribution on the boundary of the calculation volume. An alternative method for calculating spectral characteristics is also discussed, based on calculating the Fourier transform of the primitive impulse response of the cylindrical aperture. An example with specified numerical values is analyzed and the calculation results obtained by the two methods are compared."