Polarization of Maximum Gain Antennas

Several aspects of the polarization of maximum gain arbitrary directional antennas are discussed. Starting with a general expansion of the fields radiated by an arbitrary antenna into spherical harmonics, each with two orthogonal electric sources and two orthogonal magnetic sources, it is shown that the maximum gain of a circularly polarized antenna is identical to the maximum gain achieved for the linearly polarized case. In addition, it is shown that the co- and cross-polarizations for a linearly polarized maximum gain antenna are consistent with Ludwig´s third definition. This analysis also leads to the result that the cross-polarization field is identically zero for linearly or circularly polarized maximum gain antennas.