A further study of the patterns of single slots on circular conducting cylinders

The azimuthal patterns of both axial and circumferential slots on circular conducting cylinders have been carefully calculated in both magnitude and phase and some experimental checks have been obtained. The calculated patterns show that in the semicircle over which the slot is optically visible, the magnitude, and particularly the phase, of the patterns, are very similar to those, of a similarly situated slot in an infinite ground plane. This conclusion has significant implications in the design of an antenna involving several slots on a cylinder. On the semicircle over which the slot is optically invisible, and partioularly near the mid-point of this range, the pattern is very well represented by
E_{\pi} \cos \nu_{1} (\pi-\phi)
where
E_{\pi}
is the value of the pattern at
\phi=\pi
(the point opposite the slot) and
\nu_{1}
is complex. Thus the field of either one of the rear quadrants resembles the voltage of an open-circuited lossy transmission line. The implications of the above-noted form of the field pattern behind the slot led to the consideration of an expression for the field which is quite different from the usual one originally employed. By an exact transformation of the usual expression it is possible to show that the far field is given by the expansion
\Sigma\min{m = 1} A_{m} \cos \nu_{m}(\pi-\phi)
, where
\nu_{m}
is complex. Near
\phi=\pi
, the first term of this series is dominant, and the results of this approach agree with those noted above. The procedure and its significance are quite closely related to the problem of electromagnetic wave propagation over a sphere, which has been of considerable interest for some time. The various aspects of the cylindrical problem are discussed in some detail.