Plasma lensing with magnetic field and a small correction to the Faraday rotation measurement

Plasma lensing displays interesting characteristics that set it apart from gravitational lensing. The magnetized medium induces birefringence in the two polarization modes. As the lensing deflection grows stronger, e.g. when images form near the critical curve, the geometric delay of the signal can cause rotation in linear polarization, in addition to Faraday rotation. This rotation has a frequency dependence to the power of four. We study the geometric rotation of the lensed image in a Gaussian density model and find that it is necessary to take into account the geometric rotation when estimating magnetized media, especially in the underdense lens. At frequencies of ~1 GHz or lower, the geometric rotation can dominate. We simulate the flux of lensed images and find that when the image forms near the lensing critical curve, the birefringence can convert the linear polarization and un-polarization pulse into a circular mode. The lensing magnification has the potential to increase the probability of detecting such events.