Bending of electromagnetic wave in an ultra-strong magnetic field
  We consider the bending of light by nonlinear electrodynamics when the magnetic field $B$ exceeds the critical value $B_{\rm c}$. Using the index of refraction derived from the analytic series representation in one-loop effective action of QED, we found the trajectory and the bending angle of light in geometric optics. The angle bent by ultra-strong magnetic field of magnetar was estimated and compared with the gravitational bending. The result may be useful in studying the lensing, birefringence, and other nonlinear quantum electrodynamic effects above $B_{\rm c}$. 
Jin Young Kim
hep-ph astro-ph.HE