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Guiding light via geometric phases

Nature Photonics volume 10, pages 571–575 (2016)Cite this article

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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.

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

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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).

    Article  ADS  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  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).

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  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

Author notes

  1. Sergei Slussarenko and Alessandro Alberucci: These authors contributed equally to this work

Authors and Affiliations

  1. Dipartimento di Fisica, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo, via Cintia, Napoli, 80126, Italy

    Sergei Slussarenko, Bruno Piccirillo, Enrico Santamato & Lorenzo Marrucci

  2. Centre for Quantum Dynamics and Centre for Quantum Computation and Communication Technology, Griffith University, Brisbane, 4111, Queensland, Australia

    Sergei Slussarenko

  3. Nonlinear Optics and OptoElectronics Lab, University Roma Tre, Rome, I-00146, Italy

    Alessandro Alberucci & Gaetano Assanto

  4. Department of Physics, Optics Lab, Tampere University of Technology, Tampere, FI-33101, Finland

    Alessandro Alberucci & Gaetano Assanto

  5. Centro de Física do Porto, Faculdade de Ciências, Universidade do Porto, Porto, 4169-007, Portugal

    Chandroth P. Jisha

  6. Consiglio Nazionale delle Ricerche, Institute for Complex Systems (ISC), Via dei Taurini 19, Rome, 00185, Italy

    Gaetano Assanto

  7. Consiglio Nazionale delle Ricerche, Institute of Applied Science & Intelligent Systems (ISASI), Via Campi Flegrei 34, Pozzuoli (NA), 80078, Italy

    Lorenzo Marrucci

Authors
  1. Sergei Slussarenko
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  4. Bruno Piccirillo
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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.

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The authors declare no competing financial interests.

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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

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