Illuminating Mie Voids: An Analytical Model for Nanophotonics

High Resolution Image Download MS PowerPoint Slide Mie voids, low-refractive-index cavities in high-refractive-index substrates, have emerged as a compelling alternative to traditional dielectric nanoparticles. Unlike solid resonators, the electromagnetic modes of Mie voids are inherently accessible, facilitating direct interaction with 2D materials, quantum emitters, analytes, and nanoparticles. Despite their potential, the design of these structures has relied largely on computationally intensive numerical simulations that obscure the underlying physics. In this work, we present an analytical waveguide model that treats Mie voids as cylindrical cavities characterized by an effective refractive index. Our theory decouples the transverse mode profile from the longitudinal standing-wave resonance, providing a clear physical intuition for the interplay between void radius and depth. We validate our analytical expressions against full-wave numerical simulations and experimental data from single Mie voids and demonstrate that the model accurately predicts the near-field distributions, far-field reflectance, and structural color under an optical microscope. Furthermore, we apply the model to sensing scenarios, including the refractometric monitoring of liquid analytes and the identification of individual nanoplastic particles (PS, PMMA, and PET) based on their distinct refractive indices. Changes in the local environment and the capture of nanoparticles induce spectral and chromatic shifts that are predicted quantitatively by our analytical model. This framework offers a rigorous yet intuitive toolkit for the rapid design and optimization of Mie void metasurfaces, high-resolution images, and light-matter-interaction platforms.