  The light propagation of a probe field pulse in a four-level double-lambda
type system driven by laser fields that form a closed interaction loop is
studied. Due to the finite frequency width of the probe pulse, a
time-independent analysis relying on the multiphoton resonance assumption is
insufficient. Thus we apply a Floquet decomposition of the equations of motion
to solve the time-dependent problem beyond the multiphoton resonance condition.
We find that the various Floquet components can be interpreted in terms of
different scattering processes, and that the medium response oscillating in
phase with the probe field in general is not phase-dependent. The phase
dependence arises from a scattering of the coupling fields into the probe field
mode at a frequency which in general differs from the probe field frequency. We
thus conclude that in particular for short pulses with a large frequency width,
inducing a closed loop interaction contour may not be advantageous, since
otherwise the phase-dependent medium response may lead to a distortion of the
pulse shape. Finally, using our time-dependent analysis, we demonstrate that
both the closed-loop and the non-closed loop configuration allow for sub- and
superluminal light propagation with small absorption or even gain. Further, we
identify one of the coupling field Rabi frequencies as a control parameter that
allows to conveniently switch between sub- and superluminal light propagation.
