  We study the geodesics of charged black holes in polynomial Maxwell
Lagrangians, a subclass of models within the nonlinear electrodynamics (NLED).
Specifically, we consider black holes in Kruglov, power-law, and
Ayon-Beato-Garcia models. Our exploration on the corresponding null bound
states reveals that photon can orbit the extremal black holes in stable radii
outside the corresponding horizon. The reason behind this is the well-known
theorem that a photon in a NLED background propagates along its own {\it
effective} geometry. This nonlinearity is able to shift the local minimum of
the effective potential away from its corresponding outer horizon. For the null
scattering states we obtain corrections to the weak deflection angle off the
black holes. We rule out the power-law model to be physical since its
deflection angle does not reduce to the Schwarzschild in the limit of the
vanishing charge.
