  We construct a non-linear electrodynamics arising from the spontaneous
Lorentz symmetry breaking triggered by a non-zero vacuum expectation value of
the electromagnetic field strength, instead of the electromagnetic potential.
The expansion of the corresponding action in terms of the physical photon
excitations is naturally written in terms of generalized permeabilities, in a
manner similar to when the polarization is expanded in terms of the
susceptibilities when studying non-linear effects in standard optics. The new
version of the Goldstone theorem is investigated and implies that the lowest
order permeability, been the analogous of the mass matrix in the standard case,
has zero modes. These are interpreted as the corresponding Goldstone modes of
the model and they are explicitly constructed for one of the two choices of
vacua that the theory admits. Further iterations of the method employed to
obtain such theorem yield relationships among the generalized permeabilities.
Some preliminary results regarding the splitting of the two degrees of freedom
of the model into Goldstone and non-Goldstone modes are presented.
