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Disorder-assisted real–momentum topological photonic crystal

Nature volume 639, pages 602–608 (2025)Cite this article

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Abstract

Topological defects and disorder counteract each other1,2,3,4,5. Intuitively, disorder is considered detrimental, requiring efforts to mitigate its effects in conventional topological photonics6,7,8,9. We propose a counter-intuitive approach that exploits a real–momentum topological photonic crystal that harnesses real-space disorder to generate a Pancharatnam–Berry phase10,11, without disrupting the momentum-space singularity originating from bound states in the continuum12. This methodology allows flat optical devices to encode spatial information or even extra topological charge in real space while preserving the topology of bound states in the continuum in momentum space with inherent alignment. Here, as a proof of concept, we demonstrate the simultaneous and independent generation of a real-space broadband vortex or a holographic image alongside resonant momentum-space vortex beams with a narrow bandwidth, which cannot be achieved with conventional methods. Such engineered disorder contributes to vast intrinsic freedoms without adding extra dimensions or compromising the optical flatness13,14. Our findings of real–momentum duality not only lay the foundation for disorder engineering in topological photonics but also open new avenues for optical wavefront shaping, encryption and communications.

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Fig. 1: Disorder-assisted real–momentum topological PhC.
Fig. 2: Robustness of momentum topology against disorder on notch geometries and rotation angles.
Fig. 3: Amplitude-modulated PB phase in real space for various rotation angles.
Fig. 4: Experiments on real–momentum vortex generation and topology duality.
Fig. 5: Experimental demonstration of real-space holography and momentum-space vortex with a single real–momentum topological PhC.

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Data availability

The data supporting the findings of this study are available in the article and the Supplementary Information.

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Acknowledgements

Q.S. acknowledges funding support from the National Natural Science Foundation of China (grant nos. 12474388 and 12204264) and the Shenzhen Science and Technology Innovation Commission (grant no. JCYJ20230807111706014). This work is also funded by the Basic Research Program of Jiangsu (grant no. BK20243029). H.Q., Z.Z. and R.F. acknowledge funding support from the Swiss State Secretariat for Education, Research and Innovation (contract no. MB22.00028). C.-W.Q. acknowledges support from the Ministry of Education in Singapore (grant nos. A-8002152-00-00 and A-8002458-00-00) and a Competitive Research Program Award from the NRF, Prime Minister’s Office, Singapore (grant nos. NRF-CRP22-2019-0006 and NRF-CRP26-2021-0004). H.Q. and Z.S. thank H. Yang for help with instrumentation.

Author information

Author notes

  1. These authors contributed equally: Haoye Qin, Zengping Su, Zhe Zhang

Authors and Affiliations

  1. Institute of Materials Research (IMR), Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China

    Haoye Qin, Zengping Su, Wenjing Lv, Zijin Yang, Xinyue Gao, Bo Li & Qinghua Song

  2. Laboratory of Wave Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Haoye Qin, Zhe Zhang & Romain Fleury

  3. School of Materials Science and Engineering, Tsinghua University, Beijing, China

    Zengping Su, Wenjing Lv, Zijin Yang & Ji Zhou

  4. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

    Weijin Chen, Heng Wei & Cheng-Wei Qiu

  5. Institute of Precision Optical Engineering, School of Physics Science and Engineering, Tongji University, Shanghai, China

    Yuzhi Shi

  6. Suzhou Laboratory, Suzhou, China

    Bo Li & Qinghua Song

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Contributions

H.Q., R.F. and Q.S. conceived the project. H.Q. carried out the numerical simulations. H.Q. and Z.S. fabricated the samples and conducted the measurements. H.Q., Z.Z., Z.S. and W.L. analysed the results and performed the visualizations. Z.Y., W.C., X.G. and H.W. provided technical support. H.Q., Z.Z., W.L. and Q.S. wrote the manuscript. H.Q., Z.Y., W.C., R.F., C.-W.Q., Y.S., B.L., J.Z. and Q.S. revised the manuscript. R.F., C.-W.Q. and Q.S. supervised the entire project. All authors discussed the results and commented on the article.

Corresponding authors

Correspondence to Romain Fleury, Cheng-Wei Qiu or Qinghua Song.

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Nature thanks Alex Krasnok, Gianluca Ruffato and Lei Shi for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

This file contains Supplementary Figs. 1–29 and Notes 1–8.

Supplementary Video 1

Wavelength-engineered real–momentum topology duality.

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Qin, H., Su, Z., Zhang, Z. et al. Disorder-assisted real–momentum topological photonic crystal. Nature 639, 602–608 (2025). https://doi.org/10.1038/s41586-025-08632-9

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