The aperture admittance of a circumferential slot in a circular cylinder

A circumferential slot in an infinitely long cylinder when fed with a tangential electric field is considered. Parseval's theorem, in which Fourier integrals appear, is used to express the aperture admittance as the integral from zero to infinity of an infinite series. Recognizing that the first two terms of this infinite series have a nonintegrable singularity when the variable of integration w is equal to the wavenumber k, the authors distort slightly the contour of integration to avoid k. The terms of the infinite series are then approximated when w is close to k. A combination of numerical and analytical schemes employing both large and small argument approximations of Hankel functions is used to perform the integration. It has been found that these integration schemes work very well, and a simple and fast algorithm has resulted.>