Strong gravitational lensing for photons coupled to Weyl tensor in a regular phantom black hole

We study strong gravitational lensing for photons coupled to Weyl tensor in a regular phantom black hole spacetime. It is generally accepted that photons with different polarizations have different trajectories which yields a phenomenon of birefringence. As a result, there are two sets of relativistic images on each side of the object, this is quite different from the uncoupled case in which there is only one set of images. Nevertheless, we focus our attention on the relativistic images on one side of the object and investigate the difference between them by discussing how the coupling constant and phantom hair affect the difference of photon sphere radius, minimum impact parameter and deflection angle. After that, we find that the closer the light gets to the black hole, the larger the deflection angle will be. Then, we investigate the difference in angular image position and relative magnitudes of the first relativistic image between the two types of polarized photons, and find that the two images for different polarizations will separate further and be distinguished more easily in the cases that the phantom hair decreases or the absolute value of the coupling constant increases. Furthermore, the image is brighter when it seats closer to the optical axis.