Narwhal-shaped Wavefunctions Enabling Three-dimensional Sub-diffraction-limited Dielectric Photonics

Abstract: Field localization, characterized by mode volume, is central to optics, photonics, and all light-matter interactions. Smaller mode volumes amplify the electric field per photon, enhancing spontaneous emission, strengthening nonlinear optical effects, and enabling strong coupling in cavity quantum electrodynamics. However, in lossless dielectric systems, the diffraction limit has long been considered an unbreakable barrier to light confinement. Here, we uncover a novel class of wavefunctions - narwhal-shaped wavefunctions - and reveal their pivotal role in enabling extreme light confinement in lossless dielectrics across all spatial dimensions. Through rigorous theoretical analysis, simulations, and experimental validation, we propose and realize a three-dimensional singular cavity supported by these wavefunctions, achieving an ultra-small mode volume of 5x10^-7 lambda^3 (lambda: free-space wavelength). Our findings open new frontiers for unprecedented control over light-matter interactions at the smallest possible scales.