Effect of nonlinear electrodynamics on polarization distribution around black holes

We have investigated the polarized images of synchrotron emission from a magnetically charged, spherically symmetric regular Bronnikov black hole (in general relativity coupled to nonlinear electrodynamics) and the singular Reissner-Nordstr"om black hole (in general relativity coupled to Maxwell electrodynamics). By taking into account the fact that, within the framework of nonlinear electrodynamics, the propagation of the light ray is governed not by the null geodesics of the original spacetime, but rather by the null geodesics associated with the effective metric, we have examined synchrotron radiation characteristics near these black holes at different inclination angles. Our calculations reveal that intensity differences between these two black holes are significant, especially at high values of magnetic charges and large tilt angles. Polarization quantities, such as the electric vector polarization angle and normalized intensity difference ($\mathrm{\ensuremath{\Delta}}I/I$) show similar trends, driven by lensing, Doppler effects, and redshift, offering insights into black hole metrics.