On the admitting area of slender antennas

The incident power (also the "available" or "admitted" power) may be trivially defined in the case of large scatterers or receiving aperture antennas. being the integral of the incident Poynting vector over the physical aperture of the scatterer. Such a definition is implicitly included, e.g., in the IEEE standard [1], where the aperture efficiency is defined as the ratio between the received and incident powers. This, however, does not apply to small or slender scatterers. For this purpose, we suggest a definition based on a near field version of the Optical Theorem [2]. The Optical Theorem is a form of the Poynting Theorem when the field is decomposed into an incident plane wave and scattered constituents, and can be represented either in raw terms (2) as noted, e.g., in [3], or the more popular far-field version (9) that is a direct consequence of (2) [4, pp. 421], [5, pp. 453]. The near filed formulation of the Optical Theorem is juxtaposed with the far field formulation in (12), makes it possible to suggest a universal definition for the admitting area.