  We carry out a thorough analysis on a class of cosmological spacetimes which
admit three space-like Killing vectors of Bianchi class B and contain
electromagnetic fields. Using dynamical system analysis, we show that a family
of vacuum plane-wave solutions of the Einstein-Maxwell equations is the stable
attractor for expanding universes. Phase dynamics are investigated in detail
for particular symmetric models. We integrate the system exactly for some
special cases to confirm the qualitative features. Some of the obtained
solutions have not been presented previously to the best of our knowledge.
Finally, based on those solutions, we discuss the relation between those
homogeneous models and perturbations of open FLRW universes. We argue that the
vacuum plane-wave modes correspond to a certain long-wavelength limit of
electromagnetic perturbations.
