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We theoretically study a strongly-driven optomechanical system which consistsof a passive optical cavity and an active mechanical resonator. When theoptomechanical coupling strength is varied, phase transitions, which aresimilar those observed in $\mathcal{PT}$-symmetric systems, are observed. Weshow that the optical transmission can be controlled by changing the gain ofthe mechanical resonator and loss of the optical cavity mode. Especially, wefind that: (i) for balanced gain and loss, optical amplification and absorptioncan be tuned by changing the optomechanical coupling strength through a controlfield; (ii) for unbalanced gain and loss, even with a tiny mechanical gain,both optomechanically-induced transparency and anomalous dispersion can beobserved around a critical point, which exhibits an ultra-long group delay. Thetime delay $\tau$ can be optimized by regulating the optomechanical couplingstrength through the control field and improved up to several orders ofmagnitude ($\tau\sim2$ $\mathrm{ms}$) compared to that of conventionaloptomechanical systems ($\tau\sim1$ $\mu\mathrm{s}$). The presence ofmechanical gain makes the group delay more robust to environmentalperturbations. Our proposal provides a powerful platform to control lighttransport using a $\mathcal{PT}$-symmetric-like optomechanical system.

Controllable optical response by modifying the gain and loss of a mechanical resonator and cavity mode in an optomechanical system