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.

Guiding light via geometric phases

Abstract

All known methods for transverse confinement and guidance of light rely on modification of the refractive index, that is, on the scalar properties of electromagnetic radiation1,2,3,4,5,6,7,8,9,10,11. Here, we disclose the concept of a dielectric waveguide that exploits vectorial spin–orbit interactions of light and the resulting geometric phases12,13,14,15,16,17. The approach relies on the use of anisotropic media with an optic axis that lies orthogonal to the propagation direction but is spatially modulated, so that the refractive index remains constant everywhere. A spin-controlled cumulative phase distortion is imposed on the beam, balancing diffraction for a specific polarization. As well as theoretical analysis, we present an experimental demonstration of the guidance using a series of discrete geometric-phase lenses made from liquid crystal. Our findings show that geometric phases may determine the optical guiding behaviour well beyond a Rayleigh length, paving the way to a new class of photonic devices. The concept is applicable to the whole electromagnetic spectrum.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Geometric phase.
Figure 2: Concept of the geometric-phase waveguide.
Figure 3: Theory and simulations.
Figure 4: Apparatus.
Figure 5: Experiment.

References

  1. Snyder, A. W. & Love, J. D. Optical Waveguide Theory (Chapman & Hall, 1983).

    Google Scholar 

  2. Yeh, P. & Yariv, A. Bragg reflection waveguides. Opt. Commun. 19, 427–430 (1976).

    ADS  Article  Google Scholar 

  3. Joannopoulos, J. D., Villeneuve, P. R. & Fan, S. H. Photonic crystals: putting a new twist on light. Nature 386, 143–149 (1997).

    ADS  Article  Google Scholar 

  4. Knight, J. C. Photonic crystal fibres. Nature 424, 847–851 (2003).

    ADS  Article  Google Scholar 

  5. Russell, P. Photonic crystal fibers. Science 299, 358–362 (2003).

    ADS  Article  Google Scholar 

  6. Almeida, V. R., Xu, Q., Barrios, C. A. & Lipson, M. Guiding and confining light in void nanostructure. Opt. Lett. 29, 1209–1211 (2004).

    ADS  Article  Google Scholar 

  7. Weeber, J. C., Lacroute, Y. & Dereux, A. Optical near-field distributions of surface plasmon waveguide modes. Phys. Rev. B 68, 115401 (2003).

    ADS  Article  Google Scholar 

  8. Yariv, A., Xu, Y., Lee, R. K. & Scherer, A. Coupled-resonator optical waveguide: a proposal and analysis. Opt. Lett. 24, 711–713 (1999).

    ADS  Article  Google Scholar 

  9. Lin, Q. & Fan, S. Light guiding by effective gauge field for photons. Phys. Rev. X 4, 031031 (2014).

    Google Scholar 

  10. Cohen, O., Freedman, B., Fleischer, J. W., Segev, M. & Christodoulides, D. N. Grating-mediated waveguiding. Phys. Rev. Lett. 93, 103902 (2004).

    ADS  Article  Google Scholar 

  11. Alberucci, A., Marrucci, L. & Assanto, G. Light confinement via periodic modulation of the refractive index. New J. Phys. 15, 083013 (2013).

    ADS  Article  Google Scholar 

  12. Bliokh, K. Y., Rodriguez-Fortuno, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nature Photon. 9, 796–808 (2015).

    ADS  Article  Google Scholar 

  13. Cardano, F. & Marrucci, L. Spin–orbit photonics. Nature Photon. 9, 776–778 (2015).

    ADS  Article  Google Scholar 

  14. Chiao, R. Y. & Wu, Y. S. Manifestations of Berry's topological phase for the photon. Phys. Rev. Lett. 57, 933 (1986).

    ADS  Article  Google Scholar 

  15. Haldane, F. D. M. Path dependence of the geometric rotation of polarization in optical fibers. Opt. Lett. 11, 730–732 (1986).

    ADS  Article  Google Scholar 

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

    ADS  MathSciNet  Article  Google Scholar 

  17. Bhandari, R. Polarization of light and topological phases. Phys. Rep. 281, 1–64 (1997).

    ADS  Article  Google Scholar 

  18. Peccianti, M., Conti, C., Assanto, G., De Luca, A. & Umeton, C. Routing of anisotropic spatial solitons and modulational instability in liquid crystals. Nature 432, 733–737 (2004).

    ADS  Article  Google Scholar 

  19. Bomzon, Z., Kleiner, V. & Hasman, E. Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings. Opt. Lett. 26, 1424–1426 (2001).

    ADS  Article  Google Scholar 

  20. Marrucci, L., Manzo, C. & Paparo, D. Pancharatnam–Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation. Appl. Phys. Lett. 88, 221102 (2006).

    ADS  Article  Google Scholar 

  21. Slussarenko, S. et al. Tunable liquid crystal q-plates with arbitrary topological charge. Opt. Express 19, 4085–4090 (2011).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  24. Pancharatnam, S. Generalized theory of interference, and its applications. Proc. Indian Acad. Sci. A 44, 247–262 (1956).

    MathSciNet  Article  Google Scholar 

  25. Liberman, V. S. & Zel'dovich, B. Y. Spin–orbit interaction of a photon in an inhomogeneous medium. Phys. Rev. A 46, 5199–5207 (1992).

    ADS  Article  Google Scholar 

  26. Bliokh, K. Y. & Bliokh, Y. P. Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect. Phys. Rev. E 70, 026605 (2004).

    ADS  Article  Google Scholar 

  27. Lin, C., Cohen, L. G. & Kogelnik, H. Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3–1.7-μm spectral region. Opt. Lett. 5, 476–478 (1980).

    ADS  Article  Google Scholar 

  28. Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. S. Interactions between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939 (1962).

    ADS  Article  Google Scholar 

  29. Hasman, E., Kleiner, V., Biener, G. & Niv, A. Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics. Appl. Phys. Lett. 82, 328–330 (2003).

    ADS  Article  Google Scholar 

  30. Roux, F. S. Geometric phase lens. J. Opt. Soc. Am. A 23, 476–482 (2006).

    ADS  Article  Google Scholar 

  31. Berry, M. Pancharatnam, virtuoso of the Poincaré sphere: an appreciation. Curr. Sci. 67, 220–223 (1994).

    Google Scholar 

  32. Oskooi, A. F. et al. MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method. Comput. Phys. Commun. 181, 687–702 (2010).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  34. Nersisyan, S., Tabiryan, N., Steeves, D. M. & Kimball, B. R. Fabrication of liquid crystal polymer axial waveplates for UV-IR wavelengths. Opt. Express 17, 11926–11934 (2009).

    ADS  Article  Google Scholar 

  35. Alexeyev, C. N. Circular array of anisotropic fibers: a discrete analog of a q plate. Phys. Rev. A 86, 063830 (2012).

    ADS  Article  Google Scholar 

  36. Chigrinov, V. G., Kozenkov, V. M. & Kwok, H. S. Photoalignment of Liquid Crystalline Materials: Physics and Applications (Wiley, 2008).

    Book  Google Scholar 

  37. Piccirillo, B., D'Ambrosio, V., Slussarenko, S., Marrucci, L. & Santamato, E. Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate. Appl. Phys. Lett. 97, 241104 (2010).

    ADS  Article  Google Scholar 

  38. Sun, H. Thin lens equation for a real laser beam with weak lens aperture truncation. Opt. Eng. 37, 2906–2913 (1998).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

The work in Naples was supported by the 7th Framework Programme of the European Commission, within the Future Emerging Technologies programme, under grant no. 255914 (PHORBITECH), and by the European Research Council (ERC), under grant no. 694683 (PHOSPhOR). A.A. and G.A. thank the Academy of Finland for financial support through FiDiPro grant no. 282858. C.P.J. gratefully acknowledges Fundação para a Ciência e a Tecnologia, POPH-QREN and FSE (FCT, Portugal) for fellowship no. SFRH/BPD/77524/2011.

Author information

Authors and Affiliations

Authors

Contributions

This work was jointly conceived by A.A., C.P.J., G.A. and L.M. S.S. designed and carried out the experiment, with the help and supervision of B.P., E.S. and L.M. A.A. and C.P.J. developed the theory and performed the numerical simulations, with the help and supervision of L.M. and G.A. All authors discussed the results and contributed to the manuscript.

Corresponding authors

Correspondence to Gaetano Assanto or Lorenzo Marrucci.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1153 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Slussarenko, S., Alberucci, A., Jisha, C. et al. Guiding light via geometric phases. Nature Photon 10, 571–575 (2016). https://doi.org/10.1038/nphoton.2016.138

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2016.138

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