We theoretically investigate second-order sideband generation (SSG) and tunable slow-fast light propagation via strong nonlinear coupling among photons, phonons, and excitons in two coupled microcavities, consisting of an active (gain) cavity and a passive (loss) cavity that contains a quantum well and an optical parametric amplifier (OPA). By solving the Heisenberg-Langevin equations perturbatively, we obtain analytical expressions for the optical transmission and SSG efficiency. We found that the OPA significantly enhances both the transmission and the sideband generation efficiency. The enhancement becomes stronger in the active-passive configuration than in the passive-passive case and is further reinforced in the exciton-photon strong-coupling regime. Numerical analysis of higher-order sidebands further reveals substantial amplification induced by the OPA, strong exciton-photon coupling, and intercavity tunneling. In addition, by tuning system parameters, a controllable transition between slow and fast light is achieved in the output field, which could be utilized for an all-optical switching mechanism. These findings highlight the potential of coupled exciton-optomechanical cavities for tunable nonlinear frequency conversion and light-propagation control, with possible applications in optical switching, frequency comb generation, and quantum information technologies.

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• Coherent control
• Optomechanics
• Quantum optics