  By using Bianchi I type of homogenous and anisotropic background metric
having cylindrical symmetry in $x$ direction of a local cartesian coordinates
system, we solve metric field equations for a non-minimally coupled
Einstein-Maxwell gravity. To do so we choose long wavelength EM waves where
spatial dependence of the waves are negligible at the expansion duration.
Motivation of this work is study directional effects of the EM vector potential
on anisotropy trajectory of the space time expansion scale factor. This problem
is checked just for de Sitter inflationary epoch because of its importance in
the expansion of the universe. By applying the dynamical system approach we
investigate stability nature of the cosmic system in two different cases: (a)
direction of the EM vector potential is parallel to $x$ direction of the
spacetime and (b) it is perpendicular to $x$ direction. We obtained at stable
critical points for some of obtained inflationary solutions the EM waves behave
as dark energy in cases $a$ and $b$ where the anisotropy is negligible by
expanding of the universe while there are some stable critical points with
inflationary stable solutions in case $b$ for which the EM waves behave as
baryonic visible matter with non-vanishing anisotropy.
