Electromagnetic radiation from a cylindrically capped bi-wedge

Abstract
The cylindricalLy capped bi-wedge is an arrangement of two perfectly conducting wedges, apex to apex and exactly opposing; it is truncated by a cylinder whose axis is the apex of the biwedge. A line source at the apex excites this geometry. To find the radiation properties of this configuration the corresponding boundary-value problem is solved. Truncating the bi-wedge by a cylinder defines two regions-the interior and the exterior. The fields in the interior and exterior region are given by appropriate series expansions which are solutions to Maxwell's equations. A relationship between the coefficients of the two fields is obtained when thoe fields are matched across the aperture. A set of infinite simultaneous equations is generated. These can be solved for the coefficients to which special summation techniques have been applied to make a truncation of the infinite matrix valid. The radiated field of a bi-wedge is then expressed as a series with unknown coefficients. These can now be calculated by solving a set of finite simultaneous equations. A bi-wedge in the resonance region was chosen to illustrate this procedure. The computations forka = \pi/2were performed and the far-field radiation patterns plotted for various wedge angles. The limiting cases of the Rayleigh region, the thin bi-wedge, and the bi-wedge when the angle\theta_{0}approaches\pi/2are then analyzed. It is found that for the thin and the very thick bi-wedge the matrix decouples, and the field can be given exactly for these two limiting cases. Furthermore, it was found that the simple formulas of the two limiting cases could be extended to give usable results for other angles, thereby avoiding a solution of the infinite matrix.

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