Unusual intra-burst variations of polarization states in FRB 20210912A and FRB 20230708A : Effects of plasma birefringence?

Fast radio bursts (FRBs) are highly energetic events of short-duration intense radio emission, the origin of which remains elusive till date. Polarization of the FRB signals carry information about the emission source as well as the magneto-ionic media the signal passes through before reaching terrestrial radio telescopes. Currently known FRBs show a diverse range of polarization, sometimes with complex features, making it challenging to describe them in a unified model. FRB 20230708A and FRB 20210912A are two bright and highly polarized (apparently) one-off FRBs detected in the Commensal Real-time ASKAP Fast Transients (CRAFT) survey with the Australian Square Kilometre Array Pathfinder (ASKAP) that exhibit time-dependent conversion between linear and circular polarizations as well as intra-burst (apparent) variation of Faraday rotation measure. We investigate the intra-burst temporal evolution of the polarization state of radio emission in these two events using the Poincar\'e sphere representation and find that the trajectories of the polarization state are well described by great circles on the Poincar\'e sphere. These polarization features may be signatures of a transition between two partially coherent orthogonal polarization modes or propagation through a birefringent medium. We find that the observed variations of the polarization states of these two FRBs are qualitatively consistent with a magnetospheric origin of the bursts and the effects of propagation through a birefringent medium with linearly polarized modes located close to the emission source -- likely in the outer magnetosphere or near-wind region of a neutron star.