The phenomenon of nonreciprocity arises from the disruption of time reversal symmetry, enabling the one-way transfer of signals through specific channels. In the framework of cavity optomechanics, this symmetry breaking is attributed to a nonuniform radiation pressure force resulting from the interaction between light and matter. This study investigates a hybrid cavity optomechanical system (COMS) comprising two optical modes, directly coupled to each other via photon hopping interaction and indirectly via a common mechanical excitation in the form of a movable mirror, and an additional parallel metallic plate that induces a dynamical Casimir force (DCF) interaction between the plates. The two optical cavities are driven by two strong laser fields, accompanied by two weak probe classical fields from each port. The primary focus lies in exploring the nonreciprocal behavior of the light field across ports one and two, strongly manipulated by the DCF. The DCF plays a pivotal role in providing extra degrees of flexibility and manipulation in controlling the nonreciprocal signal transmission by modifying the resonance conditions of the fields within the hybrid COMS and is responsible for the amplification and swapping of information between the two ports.
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