▎ 摘　　要

It has been demonstrated that acoustic plasmon resonances (APRs) with mode sizes of a few nanometers and large momentums can be excited at nanogaps between graphene and metal surfaces by the far-field coupling. Here, we consider a graphene-dielectric-metal hybrid-structure (GDMHS) for excited APRs by the far-field, analyze the physical process of the formation of the APRs, and analytically present a simplified model to pre-dict APR wavelengths for greatly improving the efficiency of experiments using spectrometers. Furthermore, we show that the GDMHS can function as a plasmon ruler to resolve ultrasmall changes of dimensions or materials in the nanogaps by tracing spectral shifts with extremely high sensitivities. Both analytical and numerical in-vestigations prove that a sub-femometer (sub-fm) resolution for probing changes in the thickness of the dielectric spacer is reached by monitoring spectral shifts of the lowest-order APR mode, which is tens to hundreds of times higher than the previously reported results at the same structural scale. Moreover, the smallest detectable change in the refractive index (RI) of the dielectric spacer is on the order of 10-6 RI unit (RIU) when APRs are used to sense material changes of the spacer. Impressively, such APR sensors can be actively tuned over a broad fre-quency band of interest by adjusting the chemical potential of graphene. Besides sensing applications with ultra-high sensitivity, the APR modes also demonstrate the tremendous potential in enhanced infrared molecule spectroscopy and exploring strong light-matter interactions at the deep sub-wavelength nanoscale.