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Exceptional points enhancing second-order sideband generation in a whispering-gallery-mode microresonator optomechanical system coupled with nanoparticles

We theoretically investigate the second-order sideband generation (SSG) in a whispering-gallery-mode (WGM) microresonator optomechanical system, in which the WGM microresonator couples with two nanoparticles. The nanoparticles can induce the optical coupling of the clockwise (CW) and the counterclockwise (CCW) WGM fields. And by continuously adjusting the relative phase angle between two nanoparticles, two eigenmodes of the optomechanical system coalesce and the so-called exceptional points (EPs) emerge periodically. It is shown that in the WGM microresonator optomechanical system coupled with nanoparticles in the second-order sideband can be generated due to the nonlinear optomechanical interactions, modulated periodically by the relative phase angle between two nanoparticles, and enhanced significantly at the EPs. Particularly, considering the frequency shift caused by the nanoparticles at the EPs, the generation and absorption of the second-order sideband can be flexibly realized. These results may have potential applications for high precision measurements and the manipulation of light propagation in optical cavities.