| Summary: | We investigate the optical amplification of the output field and fast-slow light effect in a three-mode cavity optomechanical system without rotating wave approximation and discuss two ways of realizing the optical amplification effect. Resorting to the Coulomb coupling between the nanomechanical resonators, the asymmetric double optomechanically induced amplification effect can be achieved by utilizing the counterrotating term. Moreover, we find a remarkable optical amplification effect and observe the prominent fast-slow light effect at the singular point since the introduction of mechanical gain. Meanwhile, the transmission rate of the output field is increased by four orders of magnitude and the group delay time can reach in the order of <inline-formula><math display="inline"><semantics><mrow><msup><mn>10</mn><mn>5</mn></msup><mspace width="3.33333pt"/><mi mathvariant="sans-serif">μ</mi><mi mathvariant="normal">s</mi></mrow></semantics></math></inline-formula>. Our work is of great significance for the potential applications of optomechanically induced amplification in quantum information processing and quantum precision measurement.
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