2025ApJ...988..164W

Frequency-dependent polarization properties provide crucial insights into the radiation mechanisms and magnetic environments of fast radio bursts (FRBs). We explore an analytical solution of radiative transfer of the polarization properties of FRBs as a strong incoming wave propagates in a homogeneous magnetized plasma. The cases of a thermal plasma are studied in detail. The rotational axis of the polarization spectrum undergoes precession with frequency on the Poincaré sphere when the medium has both strong Faraday rotation and conversion. Such precession on the Poincaré sphere could occur in hot or cold plasma with a strong magnetic field component perpendicular to the line of sight. Significant absorption can exist in a dense plasma medium, which may give rise to a highly circularly polarized outgoing wave. We apply the analytical solution with the mixing Faraday case to fit the observations of frequency-dependent Stokes parameters for FRB 20180301A and FRB 20201124A. The analytical solution offers a more physical description of FRBs' magnetic environment properties than the empirical “generalized Faraday rotation” method commonly adopted in the literature. The frequency-dependent Stokes parameters may be associated with reversing rotation measures or the presence of a persistent radio source around an FRB.