We present a detailed study of a three-mode-coupling cavity optomechanical system where one mechanical mode and two optical whispering-gallery modes are coupled together. We extend the earlier investigation of regular optomechanically induced transparency (OMIT) [Science 330, 1520 (2010)] in a more general case. A complete analytical description of the present system is obtained, and quantitative analyses of the Fano-shape OMIT spectrum are provided. It is clearly shown that a sharp and asymmetric Fano-shape OMIT lineshape, which is decided by the phase difference between the probe field and the mechanical driving, can be observed from the probe output. (C) 2018 Optical Society of America
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