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 2025年5卷

Research Article | Updated：2025-12-01

- Singulonics: narwhal-shaped wavefunctions for sub-diffraction-limited nanophotonics and imaging
- Singulonics: narwhal-shaped wavefunctions for sub-diffraction-limited nanophotonics and imaging
- Affiliations：
- Author bio：
- Funds：
  
  National Natural Science Foundation of China
- DOI：10.1186/s43593-025-00104-x
  中图分类号：
- 收稿：2025-08-10，
  
  修回：2025-08-23，
  
  录用：2025-08-27，
  
  网络出版：2025-10-01，
  
  纸质出版：2025-12
- Accepted：
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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.

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

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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references

P.A.M. Dirac , The quantum theory of the emission and absorption of radiation . Proc. R. Soc. Lond. A 114 , 243 ( 1927 ). http://doi.org/10.1098/rspa.1927.0039 http://doi.org/10.1098/rspa.1927.0039

E.M. Purcell , Spontaneous emission probabilities at radio frequencies . Phys. Rev. 69 , 681 ( 1946 ).

K.J. Vahala , Optical microcavities . Nature 424 , 839 ( 2003 ). http://doi.org/10.1038/nature01939 http://doi.org/10.1038/nature01939

S. Haroche , Nobel lecture: controlling photons in a box and exploring the quantum to classical boundary . Rev. Mod. Phys. 85 , 1083 ( 2013 ). http://doi.org/10.1103/RevModPhys.85.1083 http://doi.org/10.1103/RevModPhys.85.1083

A.F. Kockum , A. Miranowicz , S. De Liberato , S. Savasta , F. Nori , Ultrastrong coupling between light and matter . Nat. Rev. Phys. 1 , 19 ( 2019 ). http://doi.org/10.1038/s42254-018-0006-2 http://doi.org/10.1038/s42254-018-0006-2

P. Forn-Díaz , L. Lamata , E. Rico , J. Kono , E. Solano , Ultrastrong coupling regimes of light–matter interaction . Rev. Mod. Phys. 91 ,( 2019 ). http://doi.org/10.1103/RevModPhys.91.025005 http://doi.org/10.1103/RevModPhys.91.025005

W.L. Barnes , A. Dereux , T.W. Ebbesen , Surface plasmon subwavelength optics . Nature 424 , 824 ( 2003 ). http://doi.org/10.1038/nature01937 http://doi.org/10.1038/nature01937

E. Ozbay , Plasmonics: merging photonics and electronics at nanoscale dimensions . Science 311 , 189 ( 2006 ). http://doi.org/10.1126/science.1114849 http://doi.org/10.1126/science.1114849

J.N. Anker , W.P. Hall , O. Lyandres , N.C. Shah , J. Zhao , R.P. Van Duyne , Biosensing with plasmonic nanosensors . Nat. Mater. 7 , 442 ( 2008 ). http://doi.org/10.1038/nmat2162 http://doi.org/10.1038/nmat2162

J.A. Schuller , E.S. Barnard , W. Cai , Y.C. Jun , J.S. White , M.L. Brongersma , Plasmonics for extreme light concentration and manipulation . Nat. Mater. 9 , 193 ( 2010 ). http://doi.org/10.1038/nmat2630 http://doi.org/10.1038/nmat2630

H.A. Atwater , A. Polman , Plasmonics for improved photovoltaic devices . Nat. Mater. 9 , 205 ( 2010 ). http://doi.org/10.1038/nmat2629 http://doi.org/10.1038/nmat2629

D.K. Gramotnev , S.I. Bozhevolnyi , Plasmonics beyond the diffraction limit . Nat. Photon. 4 , 83 ( 2010 ). http://doi.org/10.1038/nphoton.2009.282 http://doi.org/10.1038/nphoton.2009.282

Y. Liu , X. Zhang , Metamaterials: a new frontier of science and technology . Chem. Soc. Rev. 40 , 2494 ( 2011 ). http://doi.org/10.1039/c0cs00184h http://doi.org/10.1039/c0cs00184h

O. Hess , J.B. Pendry , S.A. Maier , R.F. Oulton , J.M. Hamm , K.L. Tsakmakidis , Active nanoplasmonic metamaterials . Nat. Mater. 11 , 573 ( 2012 ). http://doi.org/10.1038/nmat3356 http://doi.org/10.1038/nmat3356

M. Kauranen , A.V. Zayats , Nonlinear plasmonics . Nat. Photonics 6 , 737 ( 2012 ). http://doi.org/10.1038/nphoton.2012.244 http://doi.org/10.1038/nphoton.2012.244

M.S. Tame , K.R. McEnery , ŞK Özdemir , J. Lee , S.A. Maier , M.S. Kim , Quantum plasmonics . Nat. Phys. 9 , 329 ( 2013 ). http://doi.org/10.1038/nphys2615 http://doi.org/10.1038/nphys2615

J.B. Khurgin , How to deal with the loss in plasmonics and metamaterials . Nat. Nanotechnol. 10 , 2 ( 2015 ). http://doi.org/10.1038/nnano.2014.310 http://doi.org/10.1038/nnano.2014.310

K.L. Tsakmakidis , O. Hess , R.W. Boyd , X. Zhang , Ultraslow waves on the nanoscale . Science 358 ,( 2017 ). http://doi.org/10.1126/science.aan5196 http://doi.org/10.1126/science.aan5196

R.M. Ma , R.F. Oulton , Applications of nanolasers . Nat. Nanotechnol. 14 , 12 ( 2019 ). http://doi.org/10.1038/s41565-018-0320-y http://doi.org/10.1038/s41565-018-0320-y

J.J. Baumberg , J. Aizpurua , M.H. Mikkelsen , D.R. Smith , Extreme nanophotonics from ultrathin metallic gaps . Nat. Mater. 18 , 668 ( 2019 ). http://doi.org/10.1038/s41563-019-0290-y http://doi.org/10.1038/s41563-019-0290-y

T. Wu , M. Gurioli , P. Lalanne , Nanoscale light confinement: the Q’s and V’s . ACS Photonics 8 , 1522 ( 2021 ). http://doi.org/10.1021/acsphotonics.1c00336 http://doi.org/10.1021/acsphotonics.1c00336

Y.H. Ouyang , H.Y. Luan , Z.W. Zhao , W.Z. Mao , R.M. Ma , Singular dielectric nanolaser with atomic-scale field localization . Nature 632 , 287 ( 2024 ). http://doi.org/10.1038/s41586-024-07674-9 http://doi.org/10.1038/s41586-024-07674-9

Y. Zhang , M. Lončar , Submicrometer diameter micropillar cavities with high quality factor and ultrasmall mode volume . Opt. Lett. 34 , 902 ( 2009 ). http://doi.org/10.1364/OL.34.000902 http://doi.org/10.1364/OL.34.000902

S. Hu , S.M. Weiss , Design of photonic crystal cavities for extreme light concentration . ACS Photonics 3 , 1647 ( 2016 ). http://doi.org/10.1021/acsphotonics.6b00219 http://doi.org/10.1021/acsphotonics.6b00219

H. Choi , M. Heuck , D. Englund , Self-similar nanocavity design with ultrasmall mode volume for single-photon nonlinearities . Phys. Rev. Lett. 118 ,( 2017 ). http://doi.org/10.1103/PhysRevLett.118.223605 http://doi.org/10.1103/PhysRevLett.118.223605

S. Hu , M. Khater , R. Salas-Montiel , E. Kratschmer , S. Engelmann , W.M.J. Green , S.M. Weiss , Experimental realization of deep-subwavelength confinement in dielectric optical resonators . Sci. Adv. 4 ,( 2018 ). http://doi.org/10.1126/sciadv.aat2355 http://doi.org/10.1126/sciadv.aat2355

M. Albrechtsen , B. Vosoughi Lahijani , R.E. Christiansen , V.T.H. Nguyen , L.N. Casses , S.E. Hansen , N. Stenger , O. Sigmund , H. Jansen , J. Mørk , S. Stobbe , Nanometer-scale photon confinement in topology-optimized dielectric cavities . Nat. Commun. 13 ,( 2022 ). http://doi.org/10.1038/s41467-022-33874-w http://doi.org/10.1038/s41467-022-33874-w

A.N. Babar , T.A.S. Weis , K. Tsoukalas , S. Kadkhodazadeh , G. Arregui , B. Vosoughi Lahijani , S. Stobbe , Self-assembled photonic cavities with atomic-scale confinement . Nature 624 , 57 ( 2023 ). http://doi.org/10.1038/s41586-023-06736-8 http://doi.org/10.1038/s41586-023-06736-8

R.M. Ma , Nanolaser technology with atomic-scale field localization . Nat. Rev. Electr. Eng. 1 , 632 ( 2024 ). http://doi.org/10.1038/s44287-024-00101-1 http://doi.org/10.1038/s44287-024-00101-1

J.B. Pendry , L. Martin-Moreno , F.J. Garcia-Vidal , Mimicking surface plasmons with structured surfaces . Science 305 , 847 ( 2004 ). http://doi.org/10.1126/science.1098999 http://doi.org/10.1126/science.1098999

N. Fang , H. Lee , C. Sun , X. Zhang , Sub-diffraction-limited optical imaging with a silver superlens . Science 308 , 534 ( 2005 ). http://doi.org/10.1126/science.1108759 http://doi.org/10.1126/science.1108759

K.L. Tsakmakidis , A.D. Boardman , O. Hess , ‘Trapped rainbow’ storage of light in metamaterials . Nature 450 , 397 ( 2007 ). http://doi.org/10.1038/nature06285 http://doi.org/10.1038/nature06285

R.F. Oulton , V.J. Sorger , T. Zentgraf , R.M. Ma , C. Gladden , L. Dai , G. Bartal , X. Zhang , Plasmon lasers at deep subwavelength scale . Nature 461 , 629 ( 2009 ). http://doi.org/10.1038/nature08364 http://doi.org/10.1038/nature08364

A.E. Miroshnichenko , S. Flach , Y.S. Kivshar , Fano resonances in nanoscale structures . Rev. Mod. Phys. 82 , 2257 ( 2010 ). http://doi.org/10.1103/RevModPhys.82.2257 http://doi.org/10.1103/RevModPhys.82.2257

A.I. Kuznetsov , A.E. Miroshnichenko , M.L. Brongersma , Y.S. Kivshar , B. Luk’yanchuk , Optically resonant dielectric nanostructures . Science 354 ,( 2016 ). http://doi.org/10.1126/science.aag2472 http://doi.org/10.1126/science.aag2472

L. Feng , R. El-Ganainy , L. Ge , Non-hermitian photonics based on parity–time symmetry . Nat. Photonics 11 , 752 ( 2017 ). http://doi.org/10.1038/s41566-017-0031-1 http://doi.org/10.1038/s41566-017-0031-1

T. Ozawa , H.M. Price , A. Amo , N. Goldman , M. Hafezi , L. Lu , M.C. Rechtsman , D. Schuster , J. Simon , O. Zilberberg , I. Carusotto , Topological photonics . Rev. Mod. Phys. 91 ,( 2019 ). http://doi.org/10.1103/RevModPhys.91.015006 http://doi.org/10.1103/RevModPhys.91.015006

H.Z. Chen , T. Liu , H.Y. Luan , R.J. Liu , X.Y. Wang , X.F. Zhu , Y.B. Li , Z.M. Gu , S.J. Liang , H. Gao , L. Lu , L. Ge , S. Zhang , J. Zhu , R.M. Ma , Revealing the missing dimension at an exceptional point . Nat. Phys. 16 , 571 ( 2020 ). http://doi.org/10.1038/s41567-020-0807-y http://doi.org/10.1038/s41567-020-0807-y

X.R. Mao , Z.K. Shao , H.Y. Luan , S.L. Wang , R.M. Ma , Magic-angle lasers in nanostructured moiré superlattice . Nat. Nanotechnol. 16 , 1099 ( 2021 ). http://doi.org/10.1038/s41565-021-00956-7 http://doi.org/10.1038/s41565-021-00956-7

C. Wang , Z. Fu , W. Mao , J. Qie , A.D. Stone , L. Yang , Non-hermitian optics and photonics: from classical to quantum . Adv. Opt. Photon. 15 , 442 ( 2023 ). http://doi.org/10.1364/AOP.475477 http://doi.org/10.1364/AOP.475477

H.Y. Luan , Y.H. Ouyang , Z.W. Zhao , W.Z. Mao , R.M. Ma , Reconfigurable moiré nanolaser arrays with phase synchronization . Nature 624 , 282 ( 2023 ). http://doi.org/10.1038/s41586-023-06789-9 http://doi.org/10.1038/s41586-023-06789-9

R.M. Ma , H.Y. Luan , Z.W. Zhao , W.Z. Mao , S.L. Wang , Y.H. Ouyang , Z.K. Shao , Twisted lattice nanocavity with theoretical quality factor exceeding 200 billion . Fundam. Res. 3 , 537 ( 2023 ). http://doi.org/10.1016/j.fmre.2022.11.004 http://doi.org/10.1016/j.fmre.2022.11.004

S.T. Ha , Q. Li , J.K.W. Yang , H.V. Demir , M.L. Brongersma , A.I. Kuznetsov , Optoelectronic metadevices . Science 386 ,( 2024 ). http://doi.org/10.1126/science.adm7442 http://doi.org/10.1126/science.adm7442

J.M. Raimond , M. Brune , S. Haroche , Manipulating quantum entanglement with atoms and photons in a cavity . Rev. Mod. Phys. 73 , 565 ( 2001 ). http://doi.org/10.1103/RevModPhys.73.565 http://doi.org/10.1103/RevModPhys.73.565

S. Gleyzes , S. Kuhr , C. Guerlin , J. Bernu , S. Deléglise , U.B. Hoff , M. Brune , J.-M. Raimond , S. Haroche , Quantum jumps of light recording the birth and death of a photon in a cavity . Nature 446 , 297 ( 2007 ). http://doi.org/10.1038/nature05589 http://doi.org/10.1038/nature05589

C.-Y. Lu , J.-W. Pan , Quantum-dot single-photon sources for the quantum internet . Nat. Nanotechnol. 16 , 1294 ( 2021 ). http://doi.org/10.1038/s41565-021-01033-9 http://doi.org/10.1038/s41565-021-01033-9

J.B. Khurgin , G. Sun , Comparative analysis of spasers, vertical-cavity surface-emitting lasers and surface-plasmon-emitting diodes . Nat. Photonics 8 , 468 ( 2014 ). http://doi.org/10.1038/nphoton.2014.94 http://doi.org/10.1038/nphoton.2014.94

J.B. Khurgin , Ultimate limit of field confinement by surface plasmon polaritons . Faraday Discuss. 178 , 109 ( 2015 ). http://doi.org/10.1039/C4FD00193A http://doi.org/10.1039/C4FD00193A

B. Hecht , B. Sick , U.P. Wild , V. Deckert , R. Zenobi , O.J.F. Martin , D.W. Pohl , Scanning near-field optical microscopy with aperture probes: fundamentals and applications . J. Chem. Phys. 112 , 7761 ( 2000 ). http://doi.org/10.1063/1.481382 http://doi.org/10.1063/1.481382

X. Chen , D. Hu , R. Mescall , G. You , D.N. Basov , Q. Dai , M. Liu , Modern scattering-type scanning near-field optical microscopy for advanced material research . Adv. Mater. 31 ,( 2019 ). http://doi.org/10.1002/adma.201804774 http://doi.org/10.1002/adma.201804774

R. Hillenbrand , Y. Abate , M. Liu , X. Chen , D.N. Basov , Visible-to-THz near-field nanoscopy . Nat. Rev. Mater. 10 , 285 ( 2025 ). http://doi.org/10.1038/s41578-024-00761-3 http://doi.org/10.1038/s41578-024-00761-3

Z. Zhao , V. Kravtsov , Z. Wang , Z. Zhou , L. Dou , D. Huang , Z. Wang , X. Cheng , M.B. Raschke , T. Jiang , Applications of ultrafast nano-spectroscopy and nano-imaging with tip-based microscopy . eLight ( 2025 ). http://doi.org/10.1186/s43593-024-00079-1 http://doi.org/10.1186/s43593-024-00079-1

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