Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Revealing the invariance of vectorial structured light in complex media

Nature Photonics volume 16, pages 538–546 (2022)Cite this article

Subjects

A Publisher Correction to this article was published on 25 July 2022

This article has been updated

Abstract

Optical aberrations place fundamental limits on the achievable resolution with focusing and imaging. In the context of structured light, optical imperfections and misalignments and perturbing media such as turbulent air, underwater and optical fibre distort the amplitude and phase of the light’s spatial pattern. Here we show that polarization inhomogeneity that defines vectorial structured light is immune to all such perturbations, provided they are unitary. As an example, we study the robustness of vector vortex beams propagating through highly aberrated systems, demonstrating that the inhomogeneous nature of polarization remains unaltered even as the medium itself changes. The unitary nature of the channel allows us to undo this change through a simple lossless operation. This approach paves the way to the versatile application of vectorial structured light, even through non-ideal optical systems, crucial in applications such as imaging and optical communication across noisy channels.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Vectorial light through a tilted lens.
Fig. 2: Impact of scattering across multiple subspaces.
Fig. 3: Unitary channel mapping and its inversion.
Fig. 4: Choice of measurement basis.
Fig. 5: Unravelling turbulence.
Fig. 6: Real-world channels.

Similar content being viewed by others

Data availability

The code used to reproduce the results is available at https://doi.org/10.5281/zenodo.6502858.

Code availability

The code used to reproduce the results is available at https://doi.org/10.5281/zenodo.6502858.

Change history

References

  1. Forbes, A., de Oliveira, M. & Dennis, M. R. Structured light. Nat. Photon. 15, 253–262 (2021).

    Article  ADS  Google Scholar 

  2. Shen, Y., Hou, Y., Papasimakis, N. & Zheludev, N. I. Supertoroidal light pulses as electromagnetic skyrmions propagating in free space. Nat. Commun. 12, 5891 (2021).

    Article  ADS  Google Scholar 

  3. Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020).

    Article  ADS  Google Scholar 

  4. Larocque, H. et al. Reconstructing the topology of optical polarization knots. Nat. Phys. 14, 1079–1082 (2018).

    Article  Google Scholar 

  5. Galvez, E. J., Rojec, B. L., Kumar, V. & Viswanathan, N. K. Generation of isolated asymmetric umbilics in light’s polarization. Phys. Rev. A 89, 031801 (2014).

    Article  ADS  Google Scholar 

  6. Zdagkas, A. et al. Observation of toroidal pulses of light. Preprint at https://arxiv.org/abs/2102.03636 (2021).

  7. Keren-Zur, S., Tal, M., Fleischer, S., Mittleman, D. M. & Ellenbogen, T. Generation of spatiotemporally tailored terahertz wavepackets by nonlinear metasurfaces. Nat. Commun. 10, 1778 (2019).

    Article  ADS  Google Scholar 

  8. Bauer, T. et al. Observation of optical polarization Möbius strips. Science 347, 964–966 (2015).

    Article  ADS  Google Scholar 

  9. Brown, T. G. Unconventional polarization states: beam propagation, focusing, and imaging. Prog. Opt. 56, 81–129 (2011).

    Article  ADS  Google Scholar 

  10. Wang, J., Castellucci, F. & Franke-Arnold, S. Vectorial light–matter interaction: exploring spatially structured complex light fields. AVS Quantum Sci. 2, 031702 (2020).

    Article  ADS  Google Scholar 

  11. Otte, E., Alpmann, C. & Denz, C. Polarization singularity explosions in tailored light fields. Laser Photonics Rev. 12, 1700200 (2018).

    Article  ADS  Google Scholar 

  12. Rosales-Guzmán, C., Ndagano, B. & Forbes, A. A review of complex vector light fields and their applications. J. Opt. 20, 123001 (2018).

    Article  ADS  Google Scholar 

  13. Forbes, A. & Nape, I. Quantum mechanics with patterns of light: progress in high dimensional and multidimensional entanglement with structured light. AVS Quantum Sci. 1, 011701 (2019).

    Article  ADS  Google Scholar 

  14. Sederberg, S. et al. Vectorized optoelectronic control and metrology in a semiconductor. Nat. Photon. 14, 680–685 (2020).

    Article  ADS  Google Scholar 

  15. Fang, Y. et al. Photoelectronic mapping of the spin–orbit interaction of intense light fields. Nat. Photon. 15, 115–120 (2021).

    Article  ADS  Google Scholar 

  16. El Ketara, M., Kobayashi, H. & Brasselet, E. Sensitive vectorial optomechanical footprint of light in soft condensed matter. Nat. Photon. 15, 121–124 (2021).

    Article  ADS  Google Scholar 

  17. Hawley, R. D., Cork, J., Radwell, N. & Franke-Arnold, S. Passive broadband full Stokes polarimeter using a Fresnel cone. Sci. Rep. 9, 2688 (2019).

  18. Fang, L., Wan, Z., Forbes, A. & Wang, J. Vectorial Doppler metrology. Nat. Commun. 12, 4186 (2021).

    Article  ADS  Google Scholar 

  19. Curcio, V., Alemán-Castañeda, L. A., Brown, T. G., Brasselet, S. & Alonso, M. A. Birefringent Fourier filtering for single molecule coordinate and height super-resolution imaging with dithering and orientation. Nat. Commun. 11, 5307 (2020).

    Article  ADS  Google Scholar 

  20. Milione, G. et al. 4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer. Opt. Lett. 40, 1980–1983 (2015).

    Article  ADS  Google Scholar 

  21. Zhang, J. et al. Fiber vector eigenmode multiplexing based high capacity transmission over 5-km FMF with Kramers-Kronig receiver. J. Lightw. Technol. 39, 4932–4938 (2021).

  22. Zhu, Z. et al. Compensation-free high-dimensional free-space optical communication using turbulence-resilient vector beams. Nat. Commun. 12, 1666 (2021).

    Article  ADS  Google Scholar 

  23. Zhao, Y. & Wang, J. High-base vector beam encoding/decoding for visible-light communications. Opt. Lett. 40, 4843–4846 (2015).

    Article  ADS  Google Scholar 

  24. Radwell, N., Hawley, R., Götte, J. & Franke-Arnold, S. Achromatic vector vortex beams from a glass cone. Nat. Commun. 7, 10564 (2016).

    Article  ADS  Google Scholar 

  25. Beckley, A. M., Brown, T. G. & Alonso, M. A. Full Poincaré beams. Opt. Express 18, 10777–10785 (2010).

    Article  ADS  Google Scholar 

  26. He, C. et al. Complex vectorial optics through gradient index lens cascades. Nat. Commun. 10, 4264 (2019).

    Article  ADS  Google Scholar 

  27. Rosales-Guzmán, C. et al. Polarisation-insensitive generation of complex vector modes from a digital micromirror device. Sci. Rep. 10, 10434 (2020).

  28. Chen, J. et al. Compact vectorial optical field generator based on a 10-megapixel resolution liquid crystal spatial light modulator. Opt. Commun. 495, 127112 (2021).

  29. Wu, H.-J. et al. Vectorial nonlinear optics: type-II second-harmonic generation driven by spin-orbit-coupled fields. Phys. Rev. A 100, 053840 (2019).

    Article  ADS  Google Scholar 

  30. Tang, Y. et al. Harmonic spin–orbit angular momentum cascade in nonlinear optical crystals. Nat. Photon. 14, 658–662 (2020).

    Article  ADS  Google Scholar 

  31. Marrucci, L., Manzo, C. & Paparo, D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 96, 163905 (2006).

    Article  ADS  Google Scholar 

  32. Nassiri, M. G. & Brasselet, E. Multispectral management of the photon orbital angular momentum. Phys. Rev. Lett. 121, 213901 (2018).

    Article  ADS  Google Scholar 

  33. Devlin, R. C., Ambrosio, A., Rubin, N. A., Mueller, J. B. & Capasso, F. Arbitrary spin-to–orbital angular momentum conversion of light. Science 358, 896–901 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. Forbes, A. Structured light from lasers. Laser Photonics Rev. 13, 1900140 (2019).

    Article  ADS  Google Scholar 

  35. Beckley, A. M., Brown, T. G. & Alonso, M. A. Full Poincaré beams II: partial polarization. Opt. Express 20, 9357–9362 (2012).

    Article  ADS  Google Scholar 

  36. Ma, Z. & Ramachandran, S. Propagation stability in optical fibers: role of path memory and angular momentum. Nanophotonics 10, 209–224 (2020).

  37. Biss, D. P. & Brown, T. Primary aberrations in focused radially polarized vortex beams. Opt. Express 12, 384–393 (2004).

    Article  ADS  Google Scholar 

  38. Youngworth, K. S. & Brown, T. G. Focusing of high numerical aperture cylindrical-vector beams. Opt. Express 7, 77–87 (2000).

    Article  ADS  Google Scholar 

  39. Mamani, S. et al. Transmission of classically entangled beams through mouse brain tissue. J. Biophotonics 11, e201800096 (2018).

  40. Gianani, I. et al. Transmission of vector vortex beams in dispersive media. Adv. Photon. 2, 036003 (2020).

    Article  ADS  Google Scholar 

  41. Biton, N., Kupferman, J. & Arnon, S. OAM light propagation through tissue. Sci. Rep. 11, 2407 (2021).

  42. Suprano, A. et al. Propagation of structured light through tissue-mimicking phantoms. Opt. Express 28, 35427–35437 (2020).

    Article  ADS  Google Scholar 

  43. Cox, M. A. et al. Structured light in turbulence. IEEE J. Sel. Topics Quantum Electron. 27, 1–21 (2020).

  44. Gu, Y., Korotkova, O. & Gbur, G. Scintillation of nonuniformly polarized beams in atmospheric turbulence. Opt. Letters 34, 2261–2263 (2009).

    Article  ADS  Google Scholar 

  45. Cheng, W., Haus, J. W. & Zhan, Q. Propagation of vector vortex beams through a turbulent atmosphere. Opt. Express 17, 17829–17836 (2009).

    Article  ADS  Google Scholar 

  46. Cai, Y., Lin, Q., Eyyuboğlu, H. T. & Baykal, Y. Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere. Opt. Express 16, 7665–7673 (2008).

    Article  ADS  Google Scholar 

  47. Ji-Xiong, P., Tao, W., Hui-Chuan, L. & Cheng-Liang, L. Propagation of cylindrical vector beams in a turbulent atmosphere. Chinese Phys. B 19, 089201 (2010).

    Article  ADS  Google Scholar 

  48. Wang, T. & Pu, J. Propagation of non-uniformly polarized beams in a turbulent atmosphere. Opt. Commun. 281, 3617–3622 (2008).

    Article  ADS  Google Scholar 

  49. Cox, M. A., Rosales-Guzmán, C., Lavery, M. P. J., Versfeld, D. J. & Forbes, A. On the resilience of scalar and vector vortex modes in turbulence. Opt. Express 24, 18105–18113 (2016).

    Article  ADS  Google Scholar 

  50. Lochab, P., Senthilkumaran, P. & Khare, K. Designer vector beams maintaining a robust intensity profile on propagation through turbulence. Phys. Rev. A 98, 023831 (2018).

    Article  ADS  Google Scholar 

  51. Hufnagel, F. et al. Investigation of underwater quantum channels in a 30 meter flume tank using structured photons. New J. Phys. 22, 093074 (2020).

    Article  ADS  Google Scholar 

  52. Bouchard, F. et al. Quantum cryptography with twisted photons through an outdoor underwater channel. Opt. Express 26, 22563–22573 (2018).

    Article  ADS  Google Scholar 

  53. Ren, Y. et al. Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications. Sci. Rep. 6, 33306 (2016).

    Article  ADS  Google Scholar 

  54. Spreeuw, R. J. C. A classical analogy of entanglement. Found. Phys. 28, 361–374 (1998).

    Article  MathSciNet  Google Scholar 

  55. Forbes, A., Aiello, A. & Ndagano, B. Classically entangled light. Prog. Opt. 64, 99–153 (2019).

    Google Scholar 

  56. Kagalwala, K. H., Di Giuseppe, G., Abouraddy, A. F. & Saleh, B. E. Bell’s measure in classical optical coherence. Nat. Photon. 7, 72–78 (2013).

    Article  ADS  Google Scholar 

  57. Qian, X.-F. & Eberly, J. Entanglement and classical polarization states. Opt. Lett. 36, 4110–4112 (2011).

    Article  ADS  Google Scholar 

  58. Reyes, S. M., Nolan, D. A., Shi, L. & Alfano, R. R. Special classes of optical vector vortex beams are Majorana-like photons. Opt. Commun. 464, 125425 (2020).

    Article  Google Scholar 

  59. McLaren, M., Konrad, T. & Forbes, A. Measuring the nonseparability of vector vortex beams. Phys. Rev. A 92, 023833 (2015).

    Article  ADS  Google Scholar 

  60. Jiang, M., Luo, S. & Fu, S. Channel-state duality. Phys. Rev. A 87, 022310 (2013).

    Article  ADS  Google Scholar 

  61. Konrad, T. et al. Evolution equation for quantum entanglement. Nat. Phys. 4, 99–102 (2008).

    Article  Google Scholar 

  62. Valencia, N. H., Goel, S., McCutcheon, W., Defienne, H. & Malik, M. Unscrambling entanglement through a complex medium. Nat. Phys. 16, 1112–1116 (2020).

    Article  Google Scholar 

  63. Ndagano, B. et al. Characterizing quantum channels with non-separable states of classical light. Nat. Phys. 13, 397–402 (2017).

    Article  Google Scholar 

  64. Zhan, Q. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1, 1–57 (2009).

    Article  Google Scholar 

  65. Mamani, S. et al. Hybrid generation and analysis of vector vortex beams. Appl. Opt. 56, 2171–2175 (2017).

    Article  ADS  Google Scholar 

  66. Vaity, P., Banerji, J. & Singh, R. Measuring the topological charge of an optical vortex by using a tilted convex lens. Phys. Lett. A 377, 1154–1156 (2013).

    Article  ADS  Google Scholar 

  67. Milione, G., Sztul, H., Nolan, D. & Alfano, R. Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light. Phys. Rev. Lett. 107, 053601 (2011).

    Article  ADS  Google Scholar 

  68. Holleczek, A., Aiello, A., Gabriel, C., Marquardt, C. & Leuchs, G. Classical and quantum properties of cylindrically polarized states of light. Opt. Express 19, 9714–9736 (2011).

    Article  ADS  Google Scholar 

  69. He, C., Antonello, J. & Booth, M. J. Vectorial adaptive optics. Preprint at https://arxiv.org/abs/2110.02606 (2021).

  70. Hu, Q., He, C. & Booth, M. J. Arbitrary complex retarders using a sequence of spatial light modulators as the basis for adaptive polarisation compensation. J. Opt. 23, 065602 (2021).

    Article  ADS  Google Scholar 

  71. de Oliveira, A., da Silva, N. R., de Araújo, R. M., Ribeiro, P. S. & Walborn, S. Quantum optical description of phase conjugation of vector vortex beams in stimulated parametric down-conversion. Phys. Rev. Appl. 14, 024048 (2020).

    Article  ADS  Google Scholar 

  72. Selyem, A., Rosales-Guzmán, C., Croke, S., Forbes, A. & Franke-Arnold, S. Basis-independent tomography and nonseparability witnesses of pure complex vectorial light fields by Stokes projections. Phys. Rev. A 100, 063842 (2019).

    Article  ADS  Google Scholar 

  73. Padgett, M. J. & Courtial, J. Poincaré-sphere equivalent for light beams containing orbital angular momentum. Opt. Lett. 24, 430–432 (1999).

    Article  ADS  Google Scholar 

  74. He, C., He, H., Chang, J., Chen, B., Ma, H. & Booth, M. J. Polarisation optics for biomedical and clinical applications: a review. Light Sci. Appl. 10, 194 (2021).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

A.F. thanks the NRF-CSIR Rental Pool Programme.

Author information

Author notes

  1. These authors contributed equally: Isaac Nape, Keshaan Singh.

Authors and Affiliations

  1. School of Physics, University of the Witwatersrand, Wits, South Africa

    Isaac Nape, Keshaan Singh, Asher Klug, Wagner Buono, Ané Kritzinger, Angela Dudley & Andrew Forbes

  2. Centro de Investigaciones en Óptica, León, Mexico

    Carmelo Rosales-Guzman

  3. Wang Da-Heng Collaborative Innovation Center for Quantum Manipulation and Control, Harbin University of Science and Technology, Harbin, China

    Carmelo Rosales-Guzman

  4. School of Physics and Astronomy, University of Glasgow, Glasgow, Scotland

    Amy McWilliam & Sonja Franke-Arnold

  5. Department of Chemistry, University of Pretoria, Pretoria, South Africa

    Ané Kritzinger & Patricia Forbes

Authors
  1. Isaac Nape
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Keshaan Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Asher Klug
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wagner Buono
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Carmelo Rosales-Guzman
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Amy McWilliam
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Sonja Franke-Arnold
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Ané Kritzinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Patricia Forbes
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Angela Dudley
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Andrew Forbes
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

I.N., W.B., A. Klug, A.M., K.S., C.R.-G. and A. Kritzinger performed the experiments. All the authors contributed to the data analysis and writing of the manuscript. A.F. supervised the project.

Corresponding author

Correspondence to Andrew Forbes.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Shawn Sederberg 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 Tables 1–5, Figs. 1–11 and Sections I–XII.

Rights and permissions

Springer Nature or its licensor 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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nape, I., Singh, K., Klug, A. et al. Revealing the invariance of vectorial structured light in complex media. Nat. Photon. 16, 538–546 (2022). https://doi.org/10.1038/s41566-022-01023-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-022-01023-w

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing