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

Wen-Zhi Mao; Hong-Yi Luan; Ren-Min Ma

doi:10.1186/s43593-025-00104-x

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

eLight Vol. 5, (2025)

Research Article | Updated：2025-12-01

- Singulonics: narwhal-shaped wavefunctions for sub-diffraction-limited nanophotonics and imaging
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- DOI：10.1186/s43593-025-00104-x
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- Received：10 August 2025，
  
  Revised：2025-08-23，
  
  Accepted：27 August 2025，
  
  Published Online：01 October 2025，
  
  Published：2025-12
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Wen-Zhi Mao, Hong-Yi Luan, Ren-Min Ma. Singulonics: narwhal-shaped wavefunctions for sub-diffraction-limited nanophotonics and imaging[J]. eLight, 2025, 5.
DOI：

Wen-Zhi Mao, Hong-Yi Luan, Ren-Min Ma. Singulonics: narwhal-shaped wavefunctions for sub-diffraction-limited nanophotonics and imaging[J]. eLight, 2025, 5. DOI： 10.1186/s43593-025-00104-x.

摘要

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

. 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

/1000

making at

omic-scale optical microscopy possible. Our findings open new frontiers for unprecedented control over light–matter interactions at the smallest possible scales.

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