The polarisation of strongly lensed point-like radio sources

Aims. The magnetised medium induces birefringence, splitting the light into two distinct wave modes. The differing propagation speeds of the two modes result in different trajectories. Strong gravitational lensing amplifies the birefringence and introduces an additional geometric rotation on top of the Faraday rotation. We aim to compare the geometric rotation with the Faraday rotation. Methods. We constructed the lens equation for massive objects in a magnetised plasma environment and calculated the time-delay difference between the two modes using two toy examples. We presented that in the strong-lensed radio sources, birefringence causes geometric rotation, which is a non-negligible effect, even with a weak magnetic field. Results. In both examples, the geometric delay causes a comparable or stronger rotation than the Faraday rotation and shows a similar dependence on the wavelength of the signal. For a point lens with a strong magnetic field, the two wave modes exhibit distinct behaviours. The polarisation of lensed sources can provide additional insights into the magnetic field and plasma environment.