Theory of Axially Slitted Circular and Elliptic Cylinder Antennas

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Abstract
A method proposed by Sommerfeld for solving boundary value problems involving discontinous surfaces has been applied to the general case of a plane electromagnetic wave of arbitrary direction of incidence and polarization diffracting about one or more sections of perfecting conducting circular and elliptic cylinders of infinite length. The solution is in series form, where the series coefficients are independent for the special case of slots of infinitesimal width (slits). Radiation from the slitted cylinder is restricted to discrete right circular cones about the cylinder axis, each cone corresponding to an ordinary wave‐guide mode in the cylinder, while slots of finite width radiate over a continuous range of conical angles. For slots of small but finite width, the relative pattern in the cone α=α0 about a circular cylinder of radius a is the same as in a plane normal to the axis of a cylinder of radius a sinα0; patterns of the slotted elliptic cylinder are similarly related, where the analog of radius is distance between foci. Conical patterns are shown for the principal TE and TM waveguide modes in circular cylinders containing one and two diametrically opposed axial slits.

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