Abstract
The orbital angular momentum is a fundamental degree of freedom of light wavefronts, currently exploited in applications where information capacity is a key requirement, such as optical communication, super-resolution imaging and high-dimensional quantum computing. However, generating orbital angular momentum beams requires spatio-temporally coherent light sources (lasers or supercontinuum sources), because incoherent light would smear out the doughnut features of orbital angular momentum beams, forming polychromatic or obscured orbital angular momentum beams instead. Here we show generation of coloured orbital angular momentum beams using incoherent white light. Spatio-temporal coherence is achieved by miniaturizing spiral phase plates and integrating them with structural colour filters, three-dimensionally printed at the nanoscale. Our scheme can in principle generate multiple helical eigenstates and combine colour information into orbital angular momentum beams independently. These three-dimensional optical elements encoded with colour and orbital angular momentum information substantially increase the number of combinations for optical anti-counterfeiting and photonic lock–key devices in a pairwise fashion.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The data that support the figures and other findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.
Code availability
The code used for the photonic tally design and characterization is available from the corresponding authors upon reasonable request.
References
Nye, J. F., Berry, M. V. & Frank, F. C. Dislocations in wave trains. Proc. R. Soc. Lond. A 336, 165–190 (1974).
Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992).
Yan, Y. et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing. Nat. Commun. 5, 4876 (2014).
Lei, T. et al. Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings. Light Sci. Appl. 4, e257 (2015).
Molina-Terriza, G., Torres, J. P. & Torner, L. Twisted photons. Nat. Phys. 3, 305–310 (2007).
Gwosch, K. C. et al. MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells. Nat. Methods 17, 217–224 (2020).
Li, L. et al. Metalens-array-based high-dimensional and multiphoton quantum source. Science 368, 1487–1490 (2020).
Lee, J. C. T., Alexander, S. J., Kevan, S. D., Roy, S. & McMorran, B. J. Laguerre–Gauss and Hermite–Gauss soft X-ray states generated using diffractive optics. Nat. Photon. 13, 205–209 (2019).
Fang, X., Ren, H. & Gu, M. Orbital angular momentum holography for high-security encryption. Nat. Photon. 14, 102–108 (2020).
Ren, H. et al. Complex-amplitude metasurface-based orbital angular momentum holography in momentum space. Nat. Nanotechnol. 15, 948–955 (2020).
Ouyang, X. et al. Synthetic helical dichroism for six-dimensional optical orbital angular momentum multiplexing. Nat. Photon. 15, 901–907 (2021).
Ni, J. et al. Multidimensional phase singularities in nanophotonics. Science 374, eabj0039 (2021).
Beijersbergen, M. W., Coerwinkel, R. P. C., Kristensen, M. & Woerdman, J. P. Helical-wavefront laser beams produced with a spiral phaseplate. Opt. Commun. 112, 321–327 (1994).
Sroor, H. et al. High-purity orbital angular momentum states from a visible metasurface laser. Nat. Photon. 14, 498–503 (2020).
Cai, X. et al. Integrated compact optical vortex beam emitters. Science 338, 363–366 (2012).
Miao, P. et al. Orbital angular momentum microlaser. Science 353, 464–467 (2016).
Zhang, Z. et al. Tunable topological charge vortex microlaser. Science 368, 760–763 (2020).
Devlin, R. C., Ambrosio, A., Rubin, N. A., Mueller, J. P. B. & Capasso, F. Arbitrary spin-to-orbital angular momentum conversion of light. Science 358, 896–901 (2017).
Genevet, P., Lin, J., Kats, M. A. & Capasso, F. Holographic detection of the orbital angular momentum of light with plasmonic photodiodes. Nat. Commun. 3, 1278 (2012).
Huang, K. et al. Spiniform phase-encoded metagratings entangling arbitrary rational-order orbital angular momentum. Light Sci. Appl. 7, 17156 (2018).
Zhen, B., Hsu, C. W., Lu, L., Stone, A. D. & Soljačić, M. Topological nature of optical bound states in the continuum. Phys. Rev. Lett. 113, 257401 (2014).
Chen, W., Chen, Y. & Liu, W. Singularities and Poincare indices of electromagnetic multipoles. Phys. Rev. Lett. 122, 153907 (2019).
Wang, B. et al. Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum. Nat. Photon. 14, 623–628 (2020).
Huang, C. et al. Ultrafast control of vortex microlasers. Science 367, 1018–1021 (2020).
Berkhout, G. C. G., Lavery, M. P. J., Courtial, J., Beijersbergen, M. W. & Padgett, M. J. Efficient sorting of orbital angular momentum states of light. Phys. Rev. Lett. 105, 153601 (2010).
Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photon. 6, 488–496 (2012).
Mirhosseini, M., Malik, M., Shi, Z. & Boyd, R. W. Efficient separation of the orbital angular momentum eigenstates of light. Nat. Commun. 4, 2781 (2013).
Ren, H., Li, X., Zhang, Q. & Gu, M. On-chip noninterference angular momentum multiplexing of broadband light. Science 352, 805–809 (2016).
Jin, Z. et al. Phyllotaxis-inspired nanosieves with multiplexed orbital angular momentum. eLight 1, 5 (2021).
Zhang, J. et al. Mode-division multiplexed transmission of wavelength-division multiplexing signals over a 100-km single-span orbital angular momentum fiber. Photon. Res. 8, 1236–1242 (2020).
Fang, J. et al. Spin-dependent optical geometric transformation for cylindrical vector beam multiplexing communication. ACS Photon. 5, 3478–3484 (2018).
Jung, C. et al. Metasurface-driven optically variable devices. Chem. Rev. 121, 13013–13050 (2021).
Ozaki, M., Kato, J.-i & Kawata, S. Surface-plasmon holography with white-light illumination. Science 332, 218–220 (2011).
Joo, W.-J. et al. Metasurface-driven Oled displays beyond 10,000 pixels per inch. Science 370, 459–463 (2020).
Remmersmann, C., Stürwald, S., Kemper, B., Langehanenberg, P. & von Bally, G. Phase noise optimization in temporal phase-shifting digital holography with partial coherence light sources and its application in quantitative cell imaging. Appl. Opt. 48, 1463–1472 (2009).
León-Rodríguez, M., Rodríguez-Vera, R., Rayas, J. A. & Calixto, S. High topographical accuracy by optical shot noise reduction in digital holographic microscopy. J. Opt. Soc. Am. A 29, 498–506 (2012).
Lavery, M. P. J., Barnett, S. M., Speirits, F. C. & Padgett, M. J. Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body. Optica 1, 1–4 (2014).
Ren, H. et al. An achromatic metafiber for focusing and imaging across the entire telecommunication range. Nat. Commun. 13, 4183 (2022).
Shi, Z. et al. Single-layer metasurface with controllable multiwavelength functions. Nano Lett. 18, 2420–2427 (2018).
Kotlyar, V. V., Kovalev, A. A., Nalimov, A. G. & Stafeev, S. S. Topological charge of multi-color optical vortices. Photonics 9, 145 (2022).
Berry, M. V. & Liu, W. No general relation between phase vortices and orbital angular momentum. J. Phys. A 55, 374001 (2022).
Arppe, R. & Sørensen, T. J. Physical unclonable functions generated through chemical methods for anti-counterfeiting. Nat. Rev. Chem. 1, 0031 (2017).
Sahoo, S. K., Tang, D. & Dang, C. Single-shot multispectral imaging with a monochromatic camera. Optica 4, 1209–1213 (2017).
Wang, H. et al. Full color and grayscale painting with 3D printed low-index nanopillars. Nano Lett. 21, 4721–4729 (2021).
Wang, H. et al. Optical fireworks based on multifocal three-dimensional color prints. ACS Nano 15, 10185–10193 (2021).
Geday, M. A., Caño-García, M., Otón, J. M. & Quintana, X. Adaptive spiral diffractive lenses—lenses with a twist. Adv. Opt. Mater. 8, 2001199 (2020).
Nair, S. P., Trisno, J., Wang, H. & Yang, J. K. W. 3D printed fiber sockets for plug and play micro-optics. Int. J. Extrem. Manuf. 3, 015301 (2020).
Dong, Z. et al. Schrodinger’s red pixel by quasi-bound-states-in-the-continuum. Sci. Adv. 8, eabm4512 (2022).
Acknowledgements
J.K.W.Y. acknowledges funding support from the National Research Foundation (NRF) of Singapore under its Competitive Research Programme award (NRF-CRP20-2017-0004) and NRF Investigatorship Award (NRF-NRFI06-2020-0005). C.-W.Q. acknowledges financial support from the NRF, Prime Minister’s Office, Singapore under the Competitive Research Program Award (NRF-CRP26-2021-0063). C.-W.Q. is also supported by a grant (A-0005947-16-00) from the Advanced Research and Technology Innovation Centre at the National University of Singapore. M.G. acknowledges the support from the Science and Technology Commission of Shanghai Municipality (grant no. 21DZ1100500) and the Shanghai Frontiers Science Center Program (2021–2025 no. 20).
Author information
Authors and Affiliations
Contributions
Hongtao Wang, J.K.W.Y. and C.-W.Q. conceived the idea of CVBs and a photonic tally pair. Hongtao Wang performed the design, numerical simulation, fabrication and characterization of the photonic tally pair with assistance from Hao Wang and drafted the paper. All the authors contributed to the data analysis and paper revision. J.K.W.Y. and C.-W.Q. supervised the whole project.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Nanotechnology thanks Dong Jianji and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Supplementary Notes 1–4, Figs. 1–15 and captions for Videos 1–8.
Supplementary Video 1
Fabrication of CVB units.
Supplementary Video 2
Observation method for CVB units and photonic tallies.
Supplementary Video 3
Photonic tally pair I.
Supplementary Video 4
Photonic tally pair II.
Supplementary Video 5
Photonic tally pair III.
Supplementary Video 6
Photonic tally pair IV.
Supplementary Video 7
Photonic tally pair V, Tetris-like blocks with the same colours.
Supplementary Video 8
Photonic tally pair VI, Tetris-like blocks with different colours.
Source data
Source Data Fig. 2
Measured spectra of Fig. 2f.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Wang, H., Wang, H., Ruan, Q. et al. Coloured vortex beams with incoherent white light illumination. Nat. Nanotechnol. 18, 264–272 (2023). https://doi.org/10.1038/s41565-023-01319-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41565-023-01319-0
This article is cited by
-
Arbitrary engineering of spatial caustics with 3D-printed metasurfaces
Nature Communications (2024)
-
Multiplexed manipulation of orbital angular momentum and wavelength in metasurfaces based on arbitrary complex-amplitude control
Light: Science & Applications (2024)
-
Efficient conversion of acoustic vortex using extremely anisotropic metasurface
Frontiers of Physics (2024)
-
Twisted light gets a splash of colour
Nature Nanotechnology (2023)
-
Pick and place process for uniform shrinking of 3D printed micro- and nano-architected materials
Nature Communications (2023)