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Several fundamental questions about the operation of receiving antennas are addressed, such as ldquoWhy does a receiving antenna scatter an incident field?rdquo and ldquoUnder what conditions does a receive antenna capture all of the available incident power?rdquo A new method is described by which the received power can be maximized for an arbitrary receiving antenna. The technique is first illustrated for two-dimensional infinite receiving arrays of electric and/or magnetic dipole elements, which result in simple plane waves for the scattered (re-radiated) fields. Optimal results (for maximum received power) are derived for several cases, and it is established that half the available incident power may be received by an array of electric (or magnetic) elements in free space, and that all available incident power may be received by an array that combines electric and magnetic elements, or one that incorporates a ground plane. Next, an arbitrary finite three-dimensional antenna enclosed by a mathematical spherical surface is treated using spherical vector wave functions. It is shown that half the available incident power can be received by such an antenna consisting of either TM or TE only elements, while all available incident power can be received when both TM and TE elements are used. It is also shown that the absorption efficiency for any optimal arbitrary antenna is 50%.