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  • Perspective
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Sub-diffraction confinement in dielectrics with narwhal wavefunctions

Nature Reviews Physics volume 8, pages 240–252 (2026)Cite this article

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Abstract

The ability to confine light below the diffraction limit — coherently and without loss — has long been considered unattainable in transparent dielectrics. This limitation steered nanophotonics towards plasmonics, in which subwavelength confinement can be achieved at the expense of material absorption. Singular nanophotonics, also called singulonics, is an emerging regime in nanophotonics, which can overcome the trade-off between confinement and loss by leveraging the singular dispersion equation in lossless dielectric media, giving rise to highly localized singular modes, called narwhal wavefunctions. This framework establishes a rigorous, lossless pathway to sub-diffraction confinement, grounded in Maxwell’s equations and governed by the interplay between spatial and momentum uncertainties. This Perspective presents the theoretical foundations and experimental realizations of singular nanophotonics, contrasts it with conventional plasmonic and dielectric approaches and explores its broad implications and challenges.

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Fig. 1: Dispersion equation of dielectric, plasmonic and singulonic modes.
Fig. 2: Boundary-condition enhancement versus narwhal-wavefunction confinement.
Fig. 3: Quality factor versus inverse of the mode volume with representative optical cavities.
Fig. 4: Field localization enabled by momentum-space mode locking.
Fig. 5: Singular dispersion as a unifying mechanism for atomic-scale photonic applications.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (grant nos 12225402, 12450005, 62321004 and 92250302), the National Key R&D Program of China (grant no. 2022YFA1404700) and the New Cornerstone Science Foundation through the XPLORER PRIZE. K.L.T. acknowledges support for this research by the General Secretariat for Research and Technology and the Hellenic Foundation for Research and Innovation (HFRI) under Grant no. 4509. K.L.T.’s part was also carried out within the framework of the National Recovery and Resilience Plan Greece 2.0, funded by the European Union — Next Generation EU (Implementation body: HFRI) under Grant no. 16909.

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Authors and Affiliations

  1. State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing, China

    Ren-Min Ma  (马仁敏), Hong-Yi Luan  (栾弘义), Wen-Zhi Mao  (毛文志) & Yun-Hao Ouyang  (欧阳云浩)

  2. Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu, China

    Ren-Min Ma  (马仁敏)

  3. National Biomedical Imaging Center, Peking University, Beijing, China

    Ren-Min Ma  (马仁敏)

  4. Section of Condensed Matter Physics, National and Kapodistrian University of Athens, Panepistimioupolis, Athens, Greece

    Kosmas L. Tsakmakidis

  5. Beijing Key Laboratory of Advanced Micro- and Nanoscale Light Source Materials and Devices, Peking University, Beijing, China

    Ren-Min Ma  (马仁敏)

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  1. Ren-Min Ma  (马仁敏)
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R.-M.M. drafted the manuscript. All authors discussed and revised the manuscript.

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Correspondence to Ren-Min Ma  (马仁敏).

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Ma, RM., Tsakmakidis, K.L., Luan, HY. et al. Sub-diffraction confinement in dielectrics with narwhal wavefunctions. Nat Rev Phys 8, 240–252 (2026). https://doi.org/10.1038/s42254-026-00924-x

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