The properties of the modified Maxwell electrodynamics (ModMax) are
investigated in the presence of an external and uniform electromagnetic field.
We expand the non-linear theory around an electromagnetic background up to
second order in the propagating fields to obtain the permittivity and
permeability tensors, the dispersion relations, the group velocity and the
refractive index of the wave as functions of the uniform electric and magnetic
fields. The case in which these background fields are perpendicular is
analyzed. The birefringence phenomenon is discussed where the parameter of the
non-linear theory has a fundamental role. We calculate the difference of the
refractive indices as function of the ModMax parameter, and of the electric and
magnetic fields. Finally, we compute the interaction energy for an axionic
ModMax electrodynamics in the presence of an external magnetic background
fields, within the framework of the gauge-invariant, but path-dependent
variables formalism. Our results show that the interaction energy contains a
linear term leading to the confinement of static probe charges.Comment: 10 pages, 2 figure