Gravitational Lensing of Charged Ayon-Beato-Garcia Black Holes and Nonlinear Effects of Maxwell Fields

Nonsingular Ayon-Beato-Garcia (ABG) spherically symmetric static black hole (BH) with charge to mass ratio q = g/2m is metric solution of Born Infeld nonlinear Maxwell-Einstein theory. Central region of the BH behaves as (anti-)de Sitter for (|q| > 1) |q| < 1. In the case where |q| = 1, the BH central region behaves as Minkowski flat metric. Nonlinear Electromagnetic (NEM) fields counterpart causes deviation of light geodesics and so light rays will be forced to move on from effective metric. In this paper we study weak and strong gravitational lensing of light rays by seeking effects of NEM fields counterpart on image locations and corresponding magnification. We set our calculations to experimentally observed Sgr A* BH. In short we obtained the following: for large distances, the NEM counterpart is negligible and it reduces to linear Maxwell fields. The NEM field enlarges radius of the BH photon sphere linearly by raising |q| > 1 but decreases by raising |q| <= 1. Sign of deflection angle of bending light rays is changed in presence of NEM effects with respect to ones obtained in absence of NEM fields. Absolute value of deflection angle rises by increasing |q| -> 1. Image locations in weak deflection limit (WDL) decrease (increases) by raising 0 < |q| < 1 in presence (absence) of NEM fields. By raising the closest distance of the bending light rays image locations in WDL change from left (right) to right (left) in absence (presence) of NEM fields. In WDL, radius of Einstein rings and corresponding magnification centroid become larger (smaller) in presence (absence) of NEM fields. Angular separation called s between the innermost and outermost relativistic images increases (decreases) by increasing 0 < |q| < 1 in absence (presence) of NEM fields. Corresponding magnification r decreases (increases) by raising 0 < |q| < 1 in absence (presence) of NEM fields.