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:

Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum

Nature Photonics volume 14, pages 623–628 (2020)Cite this article

Subjects

Abstract

Optical vortices, beams with spiral wavefronts and screw phase dislocations, have been attracting increasing interest in various fields. Here, we theoretically propose and experimentally realize an easy approach to generating optical vortices. We leverage the inherent momentum-space topological vortex-like response of polarization (strong polarization anisotropy) around bound states in the continuum of two-dimensional periodic structures, for example photonic crystal slabs, to induce Pancharatnam–Berry phases and spin–orbit interaction in the beams. This new class of optical vortex generators operates in momentum space, meaning that the structure is almost homogeneous without a real-space centre. In principle, any even-order optical vortex that is a diffraction-resistant high-order quasi-Bessel beam can be achieved at any desired working wavelength. The proposed approach expands the application of bound states in the continuum and topological photonics.

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: Concept of the proposed OV generation method.
Fig. 2: Simulated band structure and polarization distribution of the designed C4v structure.
Fig. 3: Experimental set-up and measured results of the fabricated four-fold symmetric sample.
Fig. 4: Results of the fabricated six-fold symmetric sample generating a higher-order OV.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. 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).

    ADS  Google Scholar 

  2. Bliokh, K. Y. Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect. Phys. Rev. Lett. 97, 043901 (2006).

    ADS  Google Scholar 

  3. Dennis, M. R., O’Holleran, K. & Padgett, M. J. in Progress in Optics Vol. 53 (ed. Wolf, E.) 293–363 (Elsevier, 2009).

  4. Fürhapter, S., Jesacher, A., Bernet, S. & Ritsch-Marte, M. Spiral interferometry. Opt. Lett. 30, 1953–1955 (2005).

    ADS  Google Scholar 

  5. Grier, D. G. A revolution in optical manipulation. Nature 424, 810–816 (2003).

    ADS  Google Scholar 

  6. Padgett, M. & Bowman, R. Tweezers with a twist. Nat. Photon. 5, 343–348 (2011).

    ADS  Google Scholar 

  7. Walker, G., Arnold, A. S. & Franke-Arnold, S. Trans-spectral orbital angular momentum transfer via four-wave mixing in Rb vapor. Phys. Rev. Lett. 108, 243601 (2012).

    ADS  Google Scholar 

  8. Willner, A. E. et al. Optical communications using orbital angular momentum beams. Adv. Opt. Photon. 7, 66–106 (2015).

    Google Scholar 

  9. Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001).

    ADS  Google Scholar 

  10. 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 

  11. Tamburini, F., Mari, E., Thidé, B., Barbieri, C. & Romanato, F. Experimental verification of photon angular momentum and vorticity with radio techniques. Appl. Phys. Lett. 99, 204102 (2011).

    ADS  Google Scholar 

  12. Karimi, E. et al. Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface. Light Sci. Appl. 3, e167 (2014).

    MathSciNet  Google Scholar 

  13. Lin, D., Fan, P., Hasman, E. & Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014).

    ADS  Google Scholar 

  14. Miao, P. et al. Orbital angular momentum microlaser. Science 353, 464–467 (2016).

    ADS  Google Scholar 

  15. Beijersbergen, M., Coerwinkel, R., Kristensen, M. & Woerdman, J. Helical-wavefront laser beams produced with a spiral phaseplate. Opt. Commun. 112, 321–327 (1994).

    ADS  Google Scholar 

  16. Bai, Q., Tennant, A. & Allen, B. Experimental circular phased array for generating OAM radio beams. Electron. Lett. 50, 1414–1415 (2014).

    ADS  Google Scholar 

  17. Kildishev, A. V., Boltasseva, A. & Shalaev, V. M. Planar photonics with metasurfaces. Science 339, 1232009 (2013).

    Google Scholar 

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

    ADS  Google Scholar 

  19. Berry, M. The adiabatic phase and Pancharatnam’s phase for polarized light. J. Mod. Opt. 34, 1401–1407 (1987).

    ADS  MathSciNet  MATH  Google Scholar 

  20. 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).

    ADS  Google Scholar 

  21. Zhang, Y. et al. Observation of polarization vortices in momentum space. Phys. Rev. Lett. 120, 186103 (2018).

    ADS  Google Scholar 

  22. Doeleman, H. M., Monticone, F., den Hollander, W., Alù, A. & Koenderink, A. F. Experimental observation of a polarization vortex at an optical bound state in the continuum. Nat. Photon. 12, 397–401 (2018).

    ADS  Google Scholar 

  23. Chen, W., Chen, Y. & Liu, W. Singularities and Poincaré indices of electromagnetic multipoles. Phys. Rev. Lett. 122, 153907 (2019).

    ADS  Google Scholar 

  24. Durnin, J., Miceli, J. J. & Eberly, J. H. Diffraction-free beams. Phys. Rev. Lett. 58, 1499–1501 (1987).

    ADS  Google Scholar 

  25. Sadrieva, Z., Frizyuk, K., Petrov, M., Kivshar, Y. & Bogdanov, A. Multipolar origin of bound states in the continuum. Phys. Rev. B 100, 115303 (2019).

    ADS  Google Scholar 

  26. Sadreev, A. F., Bulgakov, E. N. & Rotter, I. Bound states in the continuum in open quantum billiards with a variable shape. Phys. Rev. B 73, 235342 (2006).

    ADS  Google Scholar 

  27. Bulgakov, E. N. & Sadreev, A. F. Bound states in the continuum in photonic waveguides inspired by defects. Phys. Rev. B 78, 075105 (2008).

    ADS  Google Scholar 

  28. Molina, M. I., Miroshnichenko, A. E. & Kivshar, Y. S. Surface bound states in the continuum. Phys. Rev. Lett. 108, 070401 (2012).

    ADS  Google Scholar 

  29. Hsu, C. W. et al. Observation of trapped light within the radiation continuum. Nature 499, 188–191 (2013).

    ADS  Google Scholar 

  30. Bulgakov, E. N. & Sadreev, A. F. Bloch bound states in the radiation continuum in a periodic array of dielectric rods. Phys. Rev. A 90, 053801 (2014).

    ADS  Google Scholar 

  31. Yang, Y., Peng, C., Liang, Y., Li, Z. & Noda, S. Analytical perspective for bound states in the continuum in photonic crystal slabs. Phys. Rev. Lett. 113, 037401 (2014).

    ADS  Google Scholar 

  32. Gomis-Bresco, J., Artigas, D. & Torner, L. Anisotropy-induced photonic bound states in the continuum. Nat. Photon. 11, 232–236 (2017).

    ADS  Google Scholar 

  33. Guo, Y., Xiao, M. & Fan, S. Topologically protected complete polarization conversion. Phys. Rev. Lett. 119, 167401 (2017).

    ADS  Google Scholar 

  34. Jin, J. et al. Topologically enabled ultrahigh-Q guided resonances robust to out-of-plane scattering. Nature 574, 501–504 (2019).

    ADS  Google Scholar 

  35. Koshelev, K., Lepeshov, S., Liu, M., Bogdanov, A. & Kivshar, Y. Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum. Phys. Rev. Lett. 121, 193903 (2018).

    ADS  Google Scholar 

  36. Cerjan, A., Hsu, C. W. & Rechtsman, M. C. Bound states in the continuum through environmental design. Phys. Rev. Lett. 123, 023902 (2019).

    ADS  Google Scholar 

  37. Hasman, E., Biener, G., Niv, A. & Kleiner, V. in Progress in Optics Vol. 47 (ed. Wolf, E.) 215–289 (Elsevier, 2005).

  38. Kodigala, A. et al. Lasing action from photonic bound states in continuum. Nature 541, 196–199 (2017).

    ADS  Google Scholar 

  39. Bahari, B. et al. Integrated and steerable vortex lasers using bound states in continuum. Preprint at https://arxiv.org/abs/1707.00181 (2017).

  40. Ha, S. T. et al. Directional lasing in resonant semiconductor nanoantenna arrays. Nat. Nanotechnol. 13, 1042–1047 (2018).

    ADS  Google Scholar 

  41. Bliokh, K. Y., Rodríguez-Fortuño, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nat. Photon. 9, 796–808 (2015).

    ADS  Google Scholar 

  42. Adachi, H., Akahoshi, S. & Miyakawa, K. Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light. Phys. Rev. A 75, 063409 (2007).

    ADS  Google Scholar 

  43. Zhao, Y., Edgar, J. S., Jeffries, G. D. M., McGloin, D. & Chiu, D. T. Spin-to-orbital angular momentum conversion in a strongly focused optical beam. Phys. Rev. Lett. 99, 073901 (2007).

    ADS  Google Scholar 

  44. Monteiro, P. B., Neto, P. A. M. & Nussenzveig, H. M. Angular momentum of focused beams: beyond the paraxial approximation. Phys. Rev. A 79, 033830 (2009).

    ADS  Google Scholar 

  45. Brasselet, E., Murazawa, N., Misawa, H. & Juodkazis, S. Optical vortices from liquid crystal droplets. Phys. Rev. Lett. 103, 103903 (2009).

    ADS  Google Scholar 

  46. Bliokh, K. Y. et al. Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems. Opt. Express 19, 26132–26149 (2011).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  48. Huang, L. et al. Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity. Light Sci. Appl. 2, e70 (2013).

    Google Scholar 

  49. Lin, J. et al. Polarization-controlled tunable directional coupling of surface plasmon polaritons. Science 340, 331–334 (2013).

    ADS  Google Scholar 

  50. Shitrit, N. et al. Spin-optical metamaterial route to spin-controlled photonics. Science 340, 724–726 (2013).

    ADS  MathSciNet  MATH  Google Scholar 

  51. Rafayelyan, M., Tkachenko, G. & Brasselet, E. Reflective spin–orbit geometric phase from chiral anisotropic optical media. Phys. Rev. Lett. 116, 253902 (2016).

    ADS  Google Scholar 

  52. Carlon Zambon, N. et al. Optically controlling the emission chirality of microlasers. Nat. Photon. 13, 283–288 (2019).

    ADS  Google Scholar 

Download references

Acknowledgements

We thank C. T. Chan and H. Yin for discussions. The work was supported by the China National Key Basic Research Program (2016YFA0301103, 2016YFA0302000 and 2018YFA0306201) and the National Science Foundation of China (11774063, 11727811, 91750102 and 91963212). L.S. was further supported by the Science and Technology Commission of Shanghai Municipality (19XD1434600, 2019SHZDZX01 and 19DZ2253000).

Author information

Author notes

  1. These authors contributed equally: Bo Wang, Wenzhe Liu, Maoxiong Zhao.

Authors and Affiliations

  1. State Key Laboratory of Surface Physics, Key Laboratory of Micro- and Nano-Photonic Structures (Ministry of Education) and Department of Physics, Fudan University, Shanghai, China

    Bo Wang, Wenzhe Liu, Maoxiong Zhao, Jiajun Wang, Yiwen Zhang, Ang Chen, Fang Guan, Xiaohan Liu, Lei Shi & Jian Zi

  2. Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China

    Xiaohan Liu, Lei Shi & Jian Zi

  3. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China

    Jian Zi

Authors
  1. Bo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenzhe Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maoxiong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiajun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yiwen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Fang Guan
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Xiaohan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Lei Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Jian Zi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

W.L., L.S. and J.Z. conceived the basic idea for this work. W.L. gave the theoretical explanation. B.W. and W.L. designed the structures, carried out the finite-element method and the finite-difference time-domain method simulations and analysed the simulated and measured data. B.W. and J.W. performed the sample fabrications. B.W., M.Z. and J.W. performed the optical measurements. M.Z. and Y.Z. constructed the measurement system. L.S. and J.Z. supervised the research and the development of the manuscript. W.L. wrote the draft of the manuscript, and all authors took part in the discussion and revision and approved the final copy of the manuscript.

Corresponding authors

Correspondence to Wenzhe Liu, Lei Shi or Jian Zi.

Ethics declarations

Competing interests

The authors declare no competing interests.

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 Figs. 1–10 and discussions.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, B., Liu, W., Zhao, M. et al. Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum. Nat. Photonics 14, 623–628 (2020). https://doi.org/10.1038/s41566-020-0658-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-020-0658-1

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