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.

Metasurface optics for on-demand polarization transformations along the optical path

Abstract

Polarization plays a key role in science; hence its versatile manipulation is crucial. Existing polarization optics, however, can only manipulate polarization in a single transverse plane. Here we demonstrate a new class of polarizers and wave plates—based on metasurfaces—that can impart an arbitrarily chosen polarization response along the propagation direction, regardless of the incident polarization. The underlying mechanism relies on transforming an incident waveform into an ensemble of pencil-like beams with different polarization states that beat along the optical axis thereby changing the resulting polarization at will, locally, as light propagates. Remarkably, using form-birefringent metasurfaces in combination with matrix-based holography enables the desired propagation-dependent polarization response to be enacted without a priori knowledge of the incident polarization—a behaviour that would require three polarization-sensitive holograms if implemented otherwise. Our work expands the use of polarization in the design of multifunctional metasurfaces and may find application in tunable structured light, optically switchable devices and versatile light–matter interactions.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: The concept of longitudinally variable polarization elements.
Fig. 2: Device implementation and characterization.
Fig. 3: Longitudinally variable analyser.
Fig. 4: z-Dependent HWP.
Fig. 5: z-dependent QWP.

Data availability

All key data generated and analysed are included in this paper and its Supplementary Information. Additional datasets that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

Code availability

The codes and simulation files that support the plots and data analysis within this paper are available from the corresponding author on reasonable request.

References

  1. 1.

    Goldstein, D. H. & Collett, E. Polarized Light 3 (Taylor and Francis, 2003).

  2. 2.

    Scully, M. O. & Zubairy, M. S. Quantum optics. Am. J. Phys. 67, 648–648 (1999).

    ADS  Google Scholar 

  3. 3.

    Demos, S. G. & Alfano, R. R. Optical polarization imaging. Appl. Opt. 36, 150–155 (1997).

    ADS  Google Scholar 

  4. 4.

    Holliman, N. S., Dodgson, N. A., Favalora, G. E. & Pockett, L. Three-dimensional displays: a review and applications analysis. IEEE Trans. Broadcast. 57, 362–371 (2011).

    Google Scholar 

  5. 5.

    Tyo, J. S., Goldstein, D. L., Chenault, D. B. & Shaw, J. A. Review of passive imaging polarimetry for remote sensing applications. Appl. Opt. 45, 5453–5469 (2006).

    ADS  Google Scholar 

  6. 6.

    Bomzon, Z., Biener, G., Kleiner, V. & Hasman, E. Space-variant pancharatnam–berry phase optical elements with computer-generated subwavelength gratings. Opt. Lett. 27, 1141–1143 (2002).

    ADS  Google Scholar 

  7. 7.

    Yin, X., Ye, Z., Rho, J., Wang, Y. & Zhang, X. Photonic spin hall effect at metasurfaces. Science 339, 1405–1407 (2013).

    ADS  Google Scholar 

  8. 8.

    Ling, X. et al. Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence. Light Sci. Appl. 4, e290 (2015).

    Google Scholar 

  9. 9.

    Balthasar Mueller, J. P., Rubin, N. A., Devlin, R. C., Groever, B. & Capasso, F. Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization. Phys. Rev. Lett. 118, 113901 (2017).

    ADS  Google Scholar 

  10. 10.

    Arbabi, A., Horie, Y., Bagheri, M. & Faraon, A. Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol. 10, 937–943 (2015).

    Google Scholar 

  11. 11.

    Kruk, S. et al. Invited article: broadband highly efficient dielectric metadevices for polarization control. APL Photon. 1, 030801 (2016).

    ADS  Google Scholar 

  12. 12.

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

    ADS  Google Scholar 

  13. 13.

    Intaravanne, Y. & Chen, X. Recent advances in optical metasurfaces for polarization detection and engineered polarization profiles. Nanophotonics 9, 0479 (2020).

  14. 14.

    Davis, J. A. et al. Diffraction gratings generating orders with selective states of polarization. Opt. Express 24, 907–917 (2016).

    ADS  Google Scholar 

  15. 15.

    Rubin, N. A. et al. Polarization state generation and measurement with a single metasurface. Opt. Express 26, 21455–21478 (2018).

    ADS  Google Scholar 

  16. 16.

    Deng, Z.-L. et al. Diatomic metasurface for vectorial holography. Nano Lett. 18, 2885–2892 (2018).

    ADS  Google Scholar 

  17. 17.

    Rubin, N. A. et al. Matrix fourier optics enables a compact full-stokes polarization camera. Science 365, eaax1839 (2019).

    ADS  Google Scholar 

  18. 18.

    Pfeiffer, C. & Grbic, A. Controlling vector bessel beams with metasurfaces. Phys. Rev. Applied 2, 044012 (2014).

    ADS  Google Scholar 

  19. 19.

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

    Google Scholar 

  20. 20.

    Naidoo, D. et al. Controlled generation of higher-order poincaré sphere beams from a laser. Nat. Photon. 10, 327–332 (2016).

    ADS  Google Scholar 

  21. 21.

    Nieminen, T. A., Heckenberg, N. R. & Rubinsztein-Dunlop, H. Forces in optical tweezers with radially and azimuthally polarized trapping beams. Opt. Lett. 33, 122–124 (2008).

    ADS  Google Scholar 

  22. 22.

    Shvedov, V., Davoyan, A. R., Hnatovsky, C., Engheta, N. & Krolikowski, W. A long-range polarization-controlled optical tractor beam. Nat. Photon. 8, 846–850 (2014).

    ADS  Google Scholar 

  23. 23.

    Hnatovsky, C., Shvedov, V. G., Shostka, N., Rode, A. V. & Krolikowski, W. Polarization-dependent ablation of silicon using tightly focused femtosecond laser vortex pulses. Opt. Lett. 37, 226–228 (2012).

    ADS  Google Scholar 

  24. 24.

    Milione, G., Nguyen, T. A., Leach, J., Nolan, D. A. & Alfano, R. R. Using the nonseparability of vector beams to encode information for optical communication. Opt. Lett. 40, 4887–4890 (2015).

    ADS  Google Scholar 

  25. 25.

    Xie, X., Chen, Y., Yang, K. & Zhou, J. Harnessing the point-spread function for high-resolution far-field optical microscopy. Phys. Rev. Lett. 113, 263901 (2014).

    ADS  Google Scholar 

  26. 26.

    Bryant, D. M. & Mostov, K. E. From cells to organs: building polarized tissue. Nat. Rev. Mol. Cell Biol. 9, 887–901 (2008).

    Google Scholar 

  27. 27.

    Moreno, I., Davis, J. A., Sánchez-López, M. M., Badham, K. & Cottrell, D. M. Nondiffracting bessel beams with polarization state that varies with propagation distance. Opt. Lett. 40, 5451–5454 (2015).

    ADS  Google Scholar 

  28. 28.

    Fu, S., Zhang, S. & Gao, C. Bessel beams with spatial oscillating polarization. Sci. Rep. 6, 30765(2016).

    ADS  Google Scholar 

  29. 29.

    Li, P. et al. Generation and self-healing of vector bessel-gauss beams with variant state of polarizations upon propagation. Opt. Express 25, 5821–5831 (2017).

    ADS  Google Scholar 

  30. 30.

    Chen, R.-P., Chen, Z., Gao, Y., Ding, J. & He, S. Flexible manipulation of the polarization conversions in a structured vector field in free space. Laser Photon. Rev. 11, 1700165 (2017).

    ADS  Google Scholar 

  31. 31.

    Corato-Zanarella, M., Dorrah, A. H., Zamboni-Rached, M. & Mojahedi, M. Arbitrary control of polarization and intensity profiles of diffraction-attenuation-resistant beams along the propagation direction. Phys. Rev. Appl. 9, 024013 (2018).

    ADS  Google Scholar 

  32. 32.

    Otte, E., Rosales-Guzmán, C., Ndagano, B., Denz, C. & Forbes, A. Entanglement beating in free space through spin–orbit coupling. Light Sci. Appl. 7, 18009 (2018).

    ADS  Google Scholar 

  33. 33.

    Li, P. et al. Three-dimensional modulations on the states of polarization of light fields. Chin. Phys. B 27, 114201 (2018).

    ADS  Google Scholar 

  34. 34.

    Hu, Q., Dai, Y., He, C. & Booth, M. J. Arbitrary vectorial state conversion using liquid crystal spatial light modulators. Opt. Commun. 459, 125028 (2020).

    Google Scholar 

  35. 35.

    Fatemi, F. K. Cylindrical vector beams for rapid polarization-dependent measurements in atomic systems. Opt. Express 19, 25143–25150 (2011).

    ADS  Google Scholar 

  36. 36.

    Tang, Y. & Cohen, A. E. Optical chirality and its interaction with matter. Phys. Rev. Lett. 104, 163901 (2010).

    ADS  Google Scholar 

  37. 37.

    Santhosh, K., Bitton, O., Chuntonov, L. & Haran, G. Vacuum Rabi splitting in a plasmonic cavity at the single quantum emitter limit. Nat. Commun. 7, 11823 (2016).

    ADS  Google Scholar 

  38. 38.

    Jones, R. C. A new calculus for the treatment of optical systems. I. Description and discussion of the calculus. J. Opt. Soc. Am. 31, 488–493 (1941).

    ADS  MATH  Google Scholar 

  39. 39.

    Durnin, J. Exact solutions for nondiffracting beams. I. The scalar theory. J. Opt. Soc. Am. A 4, 651–654 (1987).

    ADS  Google Scholar 

  40. 40.

    McGloin, D. & Dholakia, K. Bessel beams: diffraction in a new light. Contemporary Phys. 46, 15–28 (2005).

    ADS  Google Scholar 

  41. 41.

    Goodman, J. Introduction to Fourier Optics (W. H. Freeman, 2005).

  42. 42.

    Zamboni-Rached, M. Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency bessel beams: frozen waves. Optics Express 12, 4001–4006 (2004).

    ADS  Google Scholar 

  43. 43.

    Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).

    Google Scholar 

  44. 44.

    Devlin, R. C., Khorasaninejad, M., Chen, W. T., Oh, J. & Capasso, F. Broadband high-efficiency dielectric metasurfaces for the visible spectrum. Proc. Natl Acad. Sci. USA 113, 10473–10478 (2016).

    ADS  Google Scholar 

  45. 45.

    Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45–57 (1984).

    ADS  MathSciNet  MATH  Google Scholar 

  46. 46.

    Zhu, A. Y. et al. Giant intrinsic chiro-optical activity in planar dielectric nanostructures. Light Sci. Appl. 7, 17158–17158 (2018).

    Google Scholar 

  47. 47.

    Fienup, J. R. Phase retrieval algorithms: a comparison. Appl. Opt. 21, 2758–2769 (1982).

    ADS  Google Scholar 

  48. 48.

    Hsueh, C. K. & Sawchuk, A. A. Computer-generated double-phase holograms. Appl. Opt. 17, 3874–3883 (1978).

    ADS  Google Scholar 

  49. 49.

    Mendoza-Yero, O., Mínguez-Vega, G. & Lancis, J. Encoding complex fields by using a phase-only optical element. Opt. Lett. 39, 1740–1743 (2014).

    ADS  Google Scholar 

  50. 50.

    Aleksanyan, A. & Brasselet, E. Spin–orbit photonic interaction engineering of bessel beams. Optica 3, 167–174 (2016).

    ADS  Google Scholar 

Download references

Acknowledgements

We thank W.-T. Chen and X. Yin, both of Harvard University, for their helpful discussions. A.H.D. acknowledges the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant no. PDF-533013-2019. N.A.R. acknowledges support from the National Science Foundation Graduate Research Fellowship Program (GRFP) under grant no. DGE1144152. This work was performed in part at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation under NSF award no. 1541959. CNS is part of Harvard University. Additionally, financial support from the Office of Naval Research (ONR) MURI program, under grant no. N00014-20-1-2450, and from the Air Force Office of Scientific Research (AFOSR), grant no. FA95550-19-1-0135, is acknowledged.

Author information

Affiliations

Authors

Contributions

A.H.D. and N.A.R. developed the theoretical framework and fabricated the devices. A.Z. helped formulate the dual matrix holography theory. A.H.D. designed and measured the devices and analysed the data. M.T. contributed to the fabrication and characterization of the devices. A.H.D., N.A.R. and F.C. wrote the manuscript. F.C. supervised the project.

Corresponding author

Correspondence to Federico Capasso.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Photonics thanks Philippe St-Jean and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–11 and Notes 1–9.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Dorrah, A.H., Rubin, N.A., Zaidi, A. et al. Metasurface optics for on-demand polarization transformations along the optical path. Nat. Photonics 15, 287–296 (2021). https://doi.org/10.1038/s41566-020-00750-2

Download citation

Further reading

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