Multiple Sharp Fano Resonances in a Deep-Subwavelength Spherical Hyperbolic Metamaterial Cavity.

We theoretically study the multiple sharp Fano resonances produced by the near-field coupling between the multipolar narrow plasmonic whispering-gallery modes (WGMs) and the broad-sphere plasmon modes supported by a deep-subwavelength spherical hyperbolic metamaterial (HMM) cavity, which is constructed by five alternating silver/dielectric layers wrapping a dielectric nanosphere core. We find that the linewidths of WGMs-induced Fano resonances are as narrow as 7.4-21.7 nm due to the highly localized feature of the electric fields. The near-field coupling strength determined by the resonant energy difference between WGMs and corresponding sphere plasmon modes can lead to the formation of the symmetric-, asymmetric-, and typical Fano lineshapes in the far-field extinction efficiency spectrum. The deep-subwavelength feature of the proposed HMM cavity is verified by the large ratio (~5.5) of the longest resonant wavelength of WGM1,1 (1202.1 nm) to the cavity size (diameter: 220 nm). In addition, the resonant wavelengths of multiple Fano resonances can be easily tuned by adjusting the structural/material parameters (the dielectric core radius, the thickness and refractive index of the dielectric layers) of the HMM cavity. The narrow linewidth, multiple, and tunability of the observed Fano resonances, together with the deep-subwavelength feature of the proposed HMM cavity may create potential applications in nanosensors and nanolasers.