Remarkable relation between TCS and directivity through narrow slots in thin conducting screen

This study presents the relation between transmission cross section (TCS) and directivity (D) of a narrow slot in an infinitesimally thin and perfectly conducting screen. Although TCS is recognized to increase proportionally with increasing D according to 2Dλ2/4π, this paper shows that TCS is not proportional to D in the imperfect transmission. The resonant transmission (RT) factor defined by D, 0 ≤ KRT ≤ 1, was used to explain the transmission quality related to TCS and D. The perfect-RT (KRT = 1) occurs at the first resonance slot length as a perfect parallel resonance and leads to perfect transmission. In this perfect-RT, TCS is equal to 2Dλ2/4π. However, the imperfect-RT (KRT < 1) occurs at the second resonance slot length and thereafter as an imperfect resonance and leads to imperfect transmission. In this case, TCSs are not equal to 2Dλ2/4π due to the imperfect resonance caused by the stored reactive power.