Fluorescence Triggered by Radioactive β Decay in Optimized Hyperbolic Cavities

Luminescence arising from $\ensuremath{\beta}$ decay of radiotracers has attracted much interest recently as a viable in vivo imaging technique. The emitted Cerenkov radiation can be directly detected by high-sensitivity cameras or used to excite highly efficient fluorescent dyes. Here we investigate the enhancement of visible and infrared emission driven by $\ensuremath{\beta}$ decay of radioisotopes in the presence of a hyperbolic nanocavity. By means of a transfer-matrix approach, we obtain quasianalytic expressions for the fluorescence-enhancement factor at the dielectric core of the metalodielectric cavity, and report a 100-fold amplification in periodic structures. A particle-swarm optimization of the layered shell geometry reveals that enhancement of up to $10\phantom{\rule{0.1em}{0ex}}000$-fold is possible because of the hybridization and spectral overlap of whispering-gallery and localized-plasmon modes. Our findings may find application in nuclear-optical medical imaging, as they provide a strategy for the use of highly energetic gamma rays, Cerenkov luminescence, and visible and near-infrared fluorescence through the same nanotracer.