Scharnhorst effect for a general two-parameter Lagrangian density

We discuss how the propagation of electromagnetic fields described by a general two-parameter Lagrangian, which contains the Euler-Heisenberg effective Lagrangian and the Born-Infeld Lagrangian as particular cases, is affected by a pair of parallel plates that impose boundary conditions in the quantized field. We consider three differents setups, namely: (i) two perfectly conducting plates; (ii) two infinitely permeable plates and (iii) a pair of plates in which one of them is a perfect conductor and the other has an infinite magnetic permeability.