Full-space inverse-designed meta-optics for complex vector field shaping of intracavity landscapes

Mingfeng Xu; Di Sang; Mingbo Pu; Ping Gao; Bowen Zhao; Yuhan Zheng; Qingji Zeng; Lianwei Chen; Fei Zhang; Yinghui Guo; Xiong Li; Xiaoliang Ma; Yunqi Fu; Xiangang Luo

doi:10.1038/s41377-026-02258-w

Your Location：

Home >

Browse articles >

Full-space inverse-designed meta-optics for complex vector field shaping of intracavity landscapes

Original Articles

- Full-space inverse-designed meta-optics for complex vector field shaping of intracavity landscapes
- Light: Science & Applications Vol. 15, Issue 6, Pages: 2067-2077(2026)
- Affiliations：
  
  1.State Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu 610209, China
  2.Research Center on Vector Optical Fields, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
  3.College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
  4.College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China
- Author bio：
  
  Mingbo Pu (pmb@ioe.ac.cn)
  Xiangang Luo (lxg@ioe.ac.cn)
- Funds：
- DOI：10.1038/s41377-026-02258-w
  CLC：
- Received：09 November 2025，
  
  Revised：2026-02-20，
  
  Accepted：27 February 2026，
  
  Online First：03 April 2026，
  
  Published：30 June 2026
- Accepted：
Scan QR Code
Xu, M. F. et al. Full-space inverse-designed meta-optics for complex vector field shaping of intracavity landscapes. Light: Science & Applications, 15, 2067-2077 (2026).
DOI：

Xu, M. F. et al. Full-space inverse-designed meta-optics for complex vector field shaping of intracavity landscapes. Light: Science & Applications, 15, 2067-2077 (2026). DOI： 10.1038/s41377-026-02258-w.

摘要

Abstract

The sophisticated shaping of electromagnetic field landscapes

both outside and inside optical cavities

has long been an important goal of optics and photonics

with broad applications in near-field imaging

lithography

and laser science. Despite extensive progress in far-field shaping of extracavity landscapes

achieving accurate tailoring of three-dimensional intracavity fields has remained elusive. Here

we propose full-space adjoint-enabled freeform meta-optics for complex

on-demand vector field shaping of intracavity landscapes. In contrast with conventional semi-space adjoint approaches

the full-space adjoint strategy allows for efficient full-wave optimization of vector fields at the subwavelength scale

overcoming strong multiple scattering and interference intrinsic to enclosed cavity boundaries. We experimentally demonstrate tailored plasmonic cavity landscapes with a freeform metasurface mask

realizing a fivefold enhancement in imaging fidelity without sacrificing optical super-resolution performance. Our work significantly broadens the scope of freeform meta-optics and may open new avenues for applications in nanophotonics

topological photonics

and quantum optics.

关键词

Keywords

references

Cheben, P. et al. Subwavelength integrated photonics. Nature 560 , 565–572 (2018)..

Wei, S. B. et al. Toward broadband, dynamic structuring of a complex plasmonic field. Sci. Adv. 4 , eaao0533 (2018)..

Ginis, V. et al. Remote structuring of near-field landscapes. Science 369 , 436–440 (2020)..

Wu, S. F. et al. Monolayer semiconductor nanocavity lasers with ultralow thresholds. Nature 520 , 69–72 (2015)..

Shaltout, A. M. et al. Ultrathin and multicolour optical caviti es with embedded metasurfaces. Nat. Commun. 9 , 2673 (2018)..

Baßler, N. S. et al. Metasurface-based hybrid optical cavities for chiral sensing. Phys. Rev. Lett. 132 , 043602 (2024)..

Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91 , 015006 (2019)..

Smirnova, D. et al. Nonlinear topological photonics. Appl. Phys. Rev. 7 , 021306 (2020)..

Lodahl, P., Mahmoodian, S. & Stobbe, S. Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87 , 347–400 (2015)..

Jensen, J. S. & Sigmund, O. Topology optimization for nano-photonics. Laser Photonics Rev. 5 , 308–321 (2011)..

Molesky, S. et al. Inverse design in nanophotonics. Nat. Photonics 12 , 659–670 (2018)..

Jensen, J. S. & Sigmund, O. Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends. Appl. Phys. Lett. 84 , 2022–2024 (2004)..

Riishede, J. & Sigmund, O. Inverse design of dispersion compensating optical fiber using topology optimization. J. Opt. Soc. Am. B 25 , 88–97 (2008)..

Yang, K. Y. et al. Inverse-designed non-reciprocal pulse router for chip-based LiDAR. Nat. Photonics 14 , 369–374 (2020)..

Lin, Z. N. et al. Cavity-enhanced second-harmonic generation vianonlinear-overlap optimization. Optica 3 , 233–238 (2016)..

Christiansen, R. E., Wang, F. W. & Sigmund, O. Topological insulators by topology optimization. Phys. Rev. Lett. 122 , 234502 (2019)..

Sitawarin, C. et al. Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion [Invited ] . Photonics Res . 6 , B82-B89 (2018)..

Wang, Q. Q. Forward and adjoint sensitivity computation of chaotic dynamical systems. J. Comput. Phys. 235 , 1–13 (2013)..

Blonigan, P. J. & Wang, Q. Q. Least squares shadowing sensitivity analysis of a modified Kuramoto-Sivashinsky equation. Chaos Solit. Fractals 64 , 16–25 (2014)..

Elsawy, M. M. R. et al. Numerical optimization methods for metasurfaces. Laser Photonics Rev. 14 , 1900445 (2020)..

Li, Z. Y. et al. Empowering metasurfaces with inverse design: Principles and applications. ACS Photonics 9 , 2178–2192 (2022)..

Ji, W. Y. et al. Recent advances in metasurface design and quantum optics applications with machine learning, physics-informed neural networks, and topology optimization methods. Light Sci. Appl. 12 , 169 (2023)..

Zhou, Y. et al. Large-area, high-numerical-aperture, freeform metasurfaces. Laser Photonics Rev. 18 , 2300988 (2024)..

Sell, D. et al. Large-angle, multifunctional metagratings based on freeform multimode geometries. Nano Lett. 17 , 3752–3757 (2017)..

Phan, T. et al. High-efficiency, large-area, topology-optimized metasurfaces. Light Sci. Appl. 8 , 48 (2019)..

Xu, M. F. et al. Topology-optimized catenary-like metasurface for wide-angle and high-efficiency deflection: from a discrete to continuous geometric phase. Opt. Express 29 , 10181–10191 (2021)..

Zhou, Y. et al. Multiresonant nonlocal metasurfaces. Nano Lett. 23 , 6768–6775 (2023)..

Lin, Z. N. et al. Topology optimization of freeform large-area metasurfaces. Opt. Express 27 , 15765–15775 (2019)..

Chung, H. & Miller, O. D. High-NA achromatic metalenses by inverse design. Opt. Express 28 , 6945–6965 (2020)..

Mansouree, M. et al. Large-scale parametrized metasurface design using adjoint optimization. ACS Photonics 8 , 455–463 (2021)..

Li, Z. Y. et al. Inverse design enables large-scale high-performance meta-optics reshaping virtual reality. Nat. Commun. 13 , 2409 (2022)..

Sang, D. et al. Toward high-efficiency ultrahigh numerical aperture freeform metalens: From vector diffraction theory to t opology optimization. Laser Photonics Rev. 16 , 2200265 (2022)..

Zheng, Y. H. et al. Designing high-efficiency extended depth-of-focus metalens via topology-shape optimization. Nanophotonics 11 , 2967–2975 (2022)..

Ha, Y. L. et al. Physics-data-driven intelligent optimization for large-aperture metalenses. Opto-Electron. Adv. 6 , 230133 (2023)..

Li, S. Y., Lin, H. C. & Hsu, C. W. High-efficiency high-numerical-aperture metalens designed by maximizing the efficiency limit. Optica 11 , 454–459 (2024)..

Shi, Z. J. et al. Continuous angle-tunable birefringence with freeform metasurfaces for arbitrary polarization conversion. Sci. Adv. 6 , eaba3367 (2020)..

Wang, S. et al. Metasurface-based solid Poincaré sphere polarizer. Phys. Rev. Lett. 130 , 123801 (2023)..

Chen, T. Q. et al. Freeform metasurface-assisted waveguide coupler for guided wave polarization manipulation and spin-orbit angular momentum conversion. ACS Photonics 11 , 1051–1059 (2024)..

Chen, Y. Q. et al. Topology optimization-based inverse design of plasmonic nanodimer with maximum near-field enhancement. Adv. Funct. Mater. 30 , 2000642 (2020)..

Zhao, Y. G. et al. Fast topology optimization for near-field focusing all-dielectric metasurfaces using the discrete dipole approximation. ACS Nano 16 , 18951–18958 (2022)..

Nam, S. H. et al. Photolithographic realization of target nanostructures in 3D space by inverse design of phase modulation. Sci. Adv. 8 , eabm6310 (2022)..

Xu, M. F. et al. Emerging long-range order from a freeform disordered metasurface. Adv. Mater. 34 , 2108709 (2022)..

Cordaro, A. et al. Solving integral equations in free space with inverse-designed ultrathin optical metagratings. Nat. Nanotechnol. 18 , 365–372 (2023)..

Mann, S. A., Goh, H. & Alù, A. Inverse design of nonlinear polaritonic metasurfaces for second harmonic generation. ACS Photonics 10 , 993–1000 (2023)..

Willets , K. A. et al. Super-resolution imaging and plasmonics. Chem. Rev. 117 , 7538–7582 (2017)..

Hong, F. & Blaikie, R. Plasmonic lithography: Recent progress. Adv. Opt. Mater. 7 , 1801653 (2019)..

Luo, X. G. & Ishihara, T. Surface plasmon resonant interference nanolithography technique. Appl. Phys. Lett. 84 , 4780–4782 (2004)..

Fang, N. et al. Sub-diffraction-limited optical imaging with a silver superlens. Science 308 , 534–537 (2005)..

Zhang, X. & Liu, Z. W. Superlenses to overcome the diffraction limit. Nat. Mater. 7 , 435–441 (2008)..

Luo, X. G. Principles of electromagnetic waves in metasurfaces. Sci. China Phys. Mech. Astron. 58 , 594201 (2015)..

Xu, T. et al. Localizing surface plasmons with a metal-cladding superlens for projecting deep-subwavelength patterns. Appl. Phys. B 97 , 175–179 (2009)..

Yang, X. F. et al. Breaking the feature s izes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer. Opt. Express 17 , 21560–21565 (2009)..

Gao, P. et al. Enhancing aspect profile of half-pitch 32 nm and 22 nm lithography with plasmonic cavity lens. Appl. Phys. Lett. 106 , 093110 (2015)..

Liu, H. et al. High contrast superlens lithography engineered byloss reduction. Adv. Funct. Mater. 22 , 3777–3783 (2012)..

Chen, X. et al. Large-area high aspect ratio plasmonic interference lithography utilizing a single high-k mode. ACS Nano 10 , 4039–4045 (2016)..

Luo, Y. F. et al. Proximity correction and resolution enhancement of plasmonic lens lithography far beyond the near field diffraction limit. RSC Adv. 7 , 12366–12373 (2017)..

Guan, F. X. et al. Overcoming losses in superlenses with synthetic waves of complex frequency. Science 381 , 766–771 (2023)..

Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85 , 3966–3969 (2000)..

Pendry, J. B. & Ramakrishna, S. A. Refining the perfect lens. Phys. B: Condens. Matter 338 , 329–332 (2003)..

Luo, J. et al. Fabrication of anisotropically arrayed nano-slots metasurfaces using reflective plasmonic lithography. Nanoscale 7 , 18805–18812 (2015)..

Liu, L. Q. et al. Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography. Adv. Opt. Mater. 5 , 1700429 (2017)..

Wong, A. K.-K. Optical imaging in projection microlithography (SPIE Press, 2005).

Yeh, P. & Hendry, M. Optical waves in layered media. Phys. Today 43 , 77–78 (1990)..

Zhan, T. R. et al. Transfer matrix method for optics in graphene layers. J. Phys. Condens. Matter 25 , 215301 (2013)..

Ma, X. & Arce, G. R. Computational Lithography . (Hoboken: John Wiley & Sons, 2010).

Dainese, P . et al. Shape optimization for high efficiency metasurfaces: theory and implementation. Light Sci. Appl. 13 , 300 (2024)..

Shen, Y. J., Wong, N. & Lam, E. Y. Level-set-based inverse lithography for photomask synthesis. Opt. Express 17 , 23690–23701 (2009)..

Ma, X., Li, Y. Q. & Dong, L. S. Mask optimization approaches in optical lithography based on a vector imaging model. J. Opt. Soc. Am. A 29 , 1300–1312 (2012)..

Ma, X. et al. Nonlinear compressive inverse lithography aided by low-rank regularization. Opt. Express 27 , 29992–30008 (2019)..

Chung, H. et al. Inverse design of high-NA metalens for maskless lithography. Nanophotonics 12 , 2371–2381 (2023)..

Yang, Y. M. et al. All-dielectric metasurface analogue of electromagnetically induced transparency. Nat. Commun. 5 , 5753 (2014)..

Ma, W. et al. Deep learning for the design of photonic structures. Nat. Photonics 15 , 77–90 (2021)..

Ma, T. et al. Benchmarking deep learning-based models on nanophotonic inverse design problems. Opto-Electron. Sci. 1 , 210012 (2022)..

Ma, T. G., Wang, H. Z. & Guo, L. J. OptoGPT: a foundation model for inverse design in optical multilayer thin film structures. Opto-Electron. Adv. 7 , 240062(2024)..

Liu, M. Z. et al. Multifunctional metasurfaces enabled by simultaneous and independent control of phase and amplitude for orthogonal polarization states. Light Sci. Appl. 10 , 107 (2021)..

Song, M. W. et al. Versatile full-colour nanopainting enabled by a pixelated plasmonic metasurface. Nat. Nanotechnol. 18 , 71–78 (2023)..

Clark, L., Roberts, A. & Wesemann, L. Neural reparameterization for nonlocal metasurface topology optimization. APL Photonics 10 , 100803 (2025)..

Hammond, A. M. et al. Unifying and accelerating level-set and density-based topology optimization by subpixel-smoothed projection. Opt. Express 33 , 33620–33642 (2025)..

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

Compact and programmable large-scale optical processor in free space

Single-shot, reference-less computational wavefront sensing for complex optical fields

Editors at the frontier: exploring advanced optical engineering in the UK

Integrated optomechanical ultrasonic sensors with nano-Pascal-level sensitivity

High-dimensional multiplexing through vortex electromagnetic wave manipulation by space-time-coding metasurfaces

Related Author

No data

Related Institution

No data

⁰