  Slow light propagation is an important phenomenon in quantum optics. Here, we
theoretically study the properties of slow light in a simple optomechanical
system considering an effect of non-rotating wave approximation (NRWA) that was
ignored in previous related works. With the NRWA effect, the ultraslow light
can be easily achieved at the window of optomechanically induced transparency,
especially in unresolved sideband regime. From the theoretical results, we find
the upper bound of the time delay is exactly the mechanical ringdown time which
can last for \textit{several minutes} (mHz linewidth) in recent experiments.
Additionally, the interesting phenomena of the perfect optomechanically induced
transmission and absorption are studied in the system with the NRWA effect. We
believe the results can be used to control optical transmission in modern
optical networks.
