Singulonics: narwhal-shaped wavefunctions for sub-diffraction-limited nanophotonics and imaging

Abstract The diffraction limit, rooted in the wave nature of light and formalized by the Heisenberg uncertainty principle, imposes a fundamental constraint on optical resolution and device miniaturization. The recent discovery of the singular dispersion equation in dielectric media provides a rigorous, lossless framework for overcoming this barrier. Here, we demonstrate that achieving such confinement necessarily involves a new class of optical eigenmodes—narwhal-shaped wavefunctions—which emerge from the singular dispersion equation and uniquely combine global Gaussian decay with local power-law enhancement. These wavefunctions enable full-space field localization beyond conventional limits. Guided by this principle, we design and experimentally realize a three-dimensional sub-diffraction-limited cavity that supports narwhal-shaped wavefunctions, achieving an ultrasmall mode volume of 5 × 10 −7 λ 3 . We term this class of systems singulonic, and define the emerging field of singulonics as a new nanophotonic paradigm—establishing a platform for confining and manipulating light at deep-subwavelength scales without dissipation, enabled by the singular dispersion equation. Building on this extreme confinement, we introduce singular field microscopy: a near-field imaging technique that employs singulonic eigenmodes as intrinsically localized, background-free light sources. This enables optical imaging at a spatial resolution of λ /1000, making atomic-scale optical microscopy possible. Our findings open new frontiers for unprecedented control over light–matter interactions at the smallest possible scales.