Trapping light by mimicking gravitational lensing

Journal name:
Nature Photonics
Year published:
Published online


One of the most fascinating predictions of the theory of general relativity is the effect of gravitational lensing, the bending of light in close proximity to massive stellar objects. Recently, artificial optical materials have been proposed to study the various aspects of curved spacetimes, including light trapping and Hawking radiation. However, the development of experimental ‘toy’ models that simulate gravitational lensing in curved spacetimes remains a challenge, especially for visible light. Here, by utilizing a microstructured optical waveguide around a microsphere, we propose to mimic curved spacetimes caused by gravity, with high precision. We experimentally demonstrate both far-field gravitational lensing effects and the critical phenomenon in close proximity to the photon sphere of astrophysical objects under hydrostatic equilibrium. The proposed microstructured waveguide can be used as an omnidirectional absorber, with potential light harvesting and microcavity applications.

At a glance


  1. Analogue of light deflection in a gravitational field and microstructured optical waveguide.
    Figure 1: Analogue of light deflection in a gravitational field and microstructured optical waveguide.

    a, Depiction of light deflection by the gravitational field of a massive stellar object. b, Schematic view of the microstructured optical waveguide formed around a microsphere and used to emulate the deflection of light by a gravitational field. In the experimental set-up, a grating is drilled across a 50-nm-thick silver layer, which is then used to couple the incident laser light into the waveguide. Red arrows denote the incident laser beam.

  2. Structural and optical measurements of the sample.
    Figure 2: Structural and optical measurements of the sample.

    a, Interference pattern around the microsphere illuminated by white (top) and blue (bottom) light. b, Surface profile of the PMMA layer measured with AFM. c, The effective refractive index of the microstructured waveguide is extracted, showing a strong power-law dependence with radial distance from the microsphere. d, A particular example of light bending in close proximity to the microsphere. The incident beam is coupled into the waveguide using a diffraction grating drilled into the metal layer.

  3. Scattered field intensity around the microsphere.
    Figure 3: Scattered field intensity around the microsphere.

    a,b, Scattered field intensity observed in the experiment (a) and calculated using a full-wave finite-difference frequency-domain (FDFD) electromagnetic code (b). In the calculations, the effective refractive index is extracted from the experimental data. From top to bottom, the incident beam impact parameter is gradually decreased, resulting in a strong increase in beam deflection from the original path. At critical impact parameters (bottom two images), the light rays approach the photon sphere with a fraction of the incident energy scattered away from the microsphere, while the rest is captured around the microsphere.

  4. Deflection angles.
    Figure 4: Deflection angles.

    Deflection angles measured in the experiment (symbols) and calculated (red and blue lines) based on equation (3). Because of the final width of the incident light beam, two deflection angles θ1 and θ2, corresponding to the edges of the beam (at 1/e intensity), can be extracted unambiguously. The beam envelope is then represented by two points of closest approach rt1 and rt2, corresponding to the two deflection angles shown in the inset and calculated using equation (2). For the purpose of presentation we depict the deflection angles as a function of the geometrical average between the two turning distances: . Error bars due to the experiment are also included. The experimental data closely match the theory for all measured cases. A singularity in the deflection angle is observed for rt2  a = 28.5 µm, corresponding to the photon sphere of our system.


  1. Dyson, F. W., Eddington, A. S. & Davidson, C. A determination of the deflection of light by the Sun's gravitational field, from observations made at the total eclipse of May 29, 1919. Phil. Trans. R. Soc. Lond. A 220, 291333 (1920).
  2. Kramer, M. et al. Tests of general relativity from timing the double pulsar. Science 314, 97102 (2006).
  3. Hafele, J. C. & Keating, R. E. Around-the-world atomic clocks: predicted relativistic time gains. Science 177, 166168 (1972).
  4. Bennett, C. L. Cosmology from start to finish. Nature 440, 11261131 (2006).
  5. Everitt, C. W. F. et al. Gravity probe B: final results of a space experiment to test general relativity. Phys. Rev. Lett. 106, 221101 (2011).
  6. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 17801782 (2006).
  7. Leonhardt, U. Optical conformal mapping. Science 312, 17771780 (2006).
  8. Shalaev, V. M. Transforming light. Science 322, 384386 (2008).
  9. Li, J. & Pendry, J. B. Hiding under the carpet: a new strategy for cloaking. Phys. Rev. Lett. 101, 203901 (2008).
  10. Lai, Y. et al. Illusion optics: the optical transformation of an object into another object. Phys. Rev. Lett. 102, 253902 (2009).
  11. Chen, H., Chan, C. T. & Sheng, P. Transformation optics and metamaterials. Nature Mater. 9, 387396 (2010).
  12. Leonhardt, U. & Philbin, T. G. General relativity in electrical engineering. New J. Phys. 8, 247 (2006).
  13. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977980 (2006).
  14. Cai, W., Chettiar, U. K., Kildishev, A. V. & Shalaev, V. M. Optical cloaking with metamaterials. Nature Photon. 1, 224227 (2007).
  15. Alù, A. & Engheta, N. Multifrequency optical invisibility cloak with layered plasmonic shells. Phys. Rev. Lett. 100, 113901 (2008).
  16. Valentine, J. et al. An optical cloak made of dielectrics. Nature Mater. 8, 568571 (2009).
  17. Gabrielli, L. H., Cardenas, J., Poitras, C. B. & Lipson, M. Silicon nanostructure cloak operating at optical frequencies. Nature Photon. 3, 461463 (2009).
  18. Smolyaninov, I. I., Smolyaninova, V. N., Kildishev, A. V. & Shalaev, V. M. Anisotropic metamaterials emulated by tapered waveguides: application to optical cloaking. Phys. Rev. Lett. 102, 213901 (2009).
  19. Ergin, T. et al. Three-dimensional invisibility cloak at optical wavelengths. Science 328, 337339 (2010).
  20. Rahm, M., Roberts, D. A., Pendry, J. B. & Smith, D. R. Transformation-optical design of adaptive beam bends and beam expanders. Opt. Express 16, 1155511567 (2008).
  21. Ma, Y. G., Ong, C. K., Tyc, T. & Leonhardt, U. An omnidirectional retroreflector based on the transmutation of dielectric singularities. Nature Mater. 8, 639642 (2009).
  22. Cheng, Q., Cui, T. J., Jiang, W. X. & Cai, B. G. An omnidirectional electromagnetic absorber made of metamaterials. New J. Phys. 12, 063006 (2010).
  23. Zentgraf, T. et al. Plasmonic Luneburg and Eaton lenses. Nature Nanotech. 6, 151155 (2011).
  24. Leonhardt, U. & Piwnicki, P. Optics of nonuniformly moving media. Phys. Rev. A 60, 43014312 (1999).
  25. Genov, D. A., Zhang, S. & Zhang, X. Mimicking celestial mechanics in metamaterials. Nature Phys. 5, 687692 (2009).
  26. Narimanov, E. E. & Kildishev, A. V. Optical black hole: broadband omnidirectional light absorber. Appl. Phys. Lett. 95, 041106 (2009).
  27. Chen, H., Miao, R.-X. & Li, M. Transformation optics that mimics the system outside a Schwarzschild black hole. Opt. Express 18, 1518315188 (2010).
  28. Genov, D. A. Optical black-hole analogues. Nature Photon. 5, 7678 (2011).
  29. Smolyaninov, I. I. & Narimanov, E. E. Metric signature transitions in optical metamaterials. Phys. Rev. Lett. 105, 067402 (2010).
  30. Greenleaf, A., Kurylev, Y., Lassas, M. & Uhlmann, G. Electromagnetic wormholes and virtual magnetic monopoles from metamaterials. Phys. Rev. Lett. 99, 183901 (2007).
  31. Mackay, T. G. & Lakhtakia, A. Towards a metamaterial simulation of a spinning cosmic string. Phys. Lett. A 374, 23052308 (2010).
  32. Smolyaninov, I. I. & Hung, Y.-J. Modeling of time with metamaterials. J. Opt. Soc. Am. B 28, 15911595 (2011).
  33. Ginis, V., Tassin, P., Craps, B. & Veretennicoff, I. Frequency converter implementing an optical analogue of the cosmological redshift. Opt. Express 18, 53505355 (2010).
  34. Philbin, T. G. et al. Fiber-optical analog of the event horizon. Science 319, 13671370 (2008).
  35. Belgiorno, F. et al. Hawking radiation from ultrashort laser pulse filaments. Phys. Rev. Lett. 105, 203901 (2010).
  36. Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (W. H. Freeman, 1973).
  37. De Felice, F. On the gravitational field acting as an optical medium. Gen. Relativ. Gravit. 2, 347357 (1971).

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Author information


  1. National Laboratory of Solid State Microstructures & Department of Physics, National Center of Microstructures and Quantum Manipulation, Nanjing University, Nanjing 210093, China

    • C. Sheng,
    • H. Liu,
    • Y. Wang &
    • S. N. Zhu
  2. College of Engineering and Science, Louisiana Tech University, Ruston, Louisiana 71270, USA

    • D. A. Genov


C.S., H.L., Y.W. and S.N.Z. proposed and carried out the experiment. D.A.G. contributed to the experimental characterization and interpretation, and proposed and developed the theory. D.A.G., C.S. and H.L. co-wrote the manuscript.

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