  We study the optical transmission characteristics of pump-probe driven
spinning optomechanical ring resonators coupled in a series configuration.
After performing the steady-state analysis valid for an arbitrary number of
resonators, as an example, we discuss the two-resonator problem in detail.
Therein, we focus on how changing the optical Sagnac effect due to same or
opposite spinning directions of resonators can lead to enhanced, non-reciprocal
and delayed probe light transmission. This work can help in devising spin
degree of freedom based novel devices of manipulating light propagation in
quantum networks and quantum communication technologies.
