  Strong coupling in optomechanical systems is the basic condition for
observing many quantum phenomena such as optomechanical squeezing and
entanglement. Normal-mode splitting (NMS) is the most evident signature of
strong coupling systems. Here we show the NMS in the spectra of the movable
mirror and the output field in an optomechanical system can be flexibly
engineered by a combination of optical parametric amplifier (OPA) and coherent
feedback (CF). Moreover, the NMS could be enhanced by optimizing the parameters
such as input optical power, OPA gain and phase, CF strength in terms of
amplitude reflectivity of beam splitter.
