Bessel beams can be generated at microwaves by means of compact, planar devices based on Fabry-Perot cavity leaky-wave resonators. Most designs are based on the excitation of a single transverse magnetic/electric (TM/TE) leaky mode by means of a vertical electric/magnetic dipole source. In this work, we analyze the important case of a horizontal magnetic dipole which excites both TM and TE modes, developing an original theoretical framework suitable for resonant radiators. Analytical expressions are provided for the dominant leaky-wave aperture field. The near-field distribution is then evaluated through an accurate numerical integration of the radiating currents, and validated through full-wave simulations for the relevant case of a Bessel-beam launcher when excited by a waveguide-fed slot. Different designs are presented and analyzed in order to obtain TM, TE, and hybrid polarization, finding in all …