A spectral Green's function approach is developed here to analyze Fabry-Perot antennas for the generation of circular polarization. The structure consists of a single cavity, created between a partially reflective surface and a high impedance surface, fed by a low directive linearly polarized source. The elements in the antenna are characterized by tensor impedances. This frame allows to conceive a circularly polarized antenna supporting a single hybrid leaky-wave mode. By means of a residue analysis, it is demonstrated that the use of a single hybrid leaky mode is sufficient to generate circular polarization. The tool is validated by an antenna design matched over a relative bandwidth of 28.5% with an axial ratio lower than 3 dB.
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