Electromagnetically induced transparency has great theoretical and experimental importance in many physics subjects, such as atomic physics, quantum optics, and more recent cavity optomechanics. Optical delay is the most prominent feature of electromagnetically induced transparency, and in cavity optomechanics optical delay is limited by mechanical dissipation rate of sideband-resolved mechanical modes. Here we demonstrate a cascaded optical transparency scheme by leveraging the parametric phonon-phonon coupling in a multimode optomechanical system, where a low damping mechanical mode in the unresolved-sideband regime is made to couple to an intermediate, high frequency mechanical mode in the resolved-sideband regime of an optical cavity. Extended optical delay and higher transmission, as well as optical advancing are demonstrated. These results provide a route to realize ultra-long optical delay, indicating a significant step toward integrated classical and quantum information storage devices.
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