Resonant Bessel-beam launchers (BBLs)are radiating devices constituted by a cylindrical metallic cavity with a partially reflecting sheet (PRS) on top. Millimeter-wave resonant BBLs typically exhibit transverse magnetic (TM) polarization due to the use of coaxial probes as feeders and homogenized metasurfaces as PRS. Launchers showing either a purely transverse electric (TE) or a hybrid (quasi-TE) polarization have recently been proposed for realizing wireless power transfer (WPT) links in the radiative near-field region at millimeter waves. The former are obtained by means of a radial slot array as a feeder and a homogenized metasurface as a PRS. The latter are obtained by using a loop antenna as a feeder and an annular strip grating in the homogenization limit as radiating aperture. In this work, based on an original semi-analytical model, such a metasurface is demonstrated to show a dichroic behavior. This interpretation explains the improvement in terms of polarization purity with respect to more nondichroic conventional homogenized metasurfaces. The behavior of the annular strip grating under a pure TM polarization is tested with a coaxial feeder, whereas its behavior under a pure TE polarization is tested by means of the radial slot array feeder. Results confirm the validity of the proposed analysis, which is finally exploited to evaluate the WPT performance.