Abstract
Optical cavity combining a mechanical degree of freedom provides a unique platform to implement information transmission and processing via optomechanical effects, and introduces a strong link between nanophotonics and nanomechanics. Here, we study the optical property of a cascaded optomechanical array, which consists of two or more optomechanical systems. We find that the steady states of the optomechanical array have algebraic duality symmetry for the case of two identical optomechanical resonators, which is exactly the embodiment of the spatial symmetry and leads to symmetric optical transmission. Breaking of the algebraic duality symmetry gives rise to different behaviors between the forward and the backward transmission, which can be remarkable under low input power. Our results may have potential application for achieving high precision measurement and on-chip manipulation of light propagation.
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