Subwavelength Focussing in Metamaterials Using Far Field Time Reversal

  • Mathias Fink
  • Fabrice Lemoult
  • Julien de Rosny
  • Arnaud Tourin
  • Geoffroy LeroseyEmail author
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 166)


Time reversal is a physical concept that allows focussing of waves both spatially and temporally regardless of the complexity of the propagation medium. Time reversal mirrors have been demonstrated first in acoustics, then with electromagnetic waves, and are being intensively studied in many fields ranging from underwater communications to sensing.

In this chapter we review the principles of time reversal and in particular its ability to focus waves in complex media. We show that this focussing effect depends on the complexity of the propagation medium rather than on the time reversal mirror itself. A modal approach is utilized to explain the results and grasp the physical mechanisms underlying the concept.

A particular focus is given to the possibility of overcoming the diffraction barrier from the far field using time reversal. With this aim, we return to the first proof of concept of this original approach. Those results are explained in terms of the coherent excitation of subwavelength modes. In particular, we show that a finite size medium consisting of coupled subwavelength resonators, which we call a resonant metalens, supports modes which radiate spatial information of the near field of a source efficiently in the far field. We show that such a process, due to reversibility, enables us to beat the diffraction limit using far field time reversal, and especially that this result occurs due to the inherent broadband nature of time reversal. We then generalize the concept to other types of media, and finally show experimentally that it is also valid for acoustic waves, demonstrating deep subwavelength focal spots obtained within an array of soda cans.


Focal Spot Time Reversal Diffraction Limit Helmholtz Resonator Collapse Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Aulbach, J., et al.: Control of light transmission through opaque scattering media in space and time. Phys. Rev. Lett. 106, 103901 (2011) CrossRefGoogle Scholar
  2. 2.
    Bartal, G., Lerosey, G., Zhang, X.: Subwavelength dynamic focusing in plasmonic nanostructures using time reversal. Phys. Rev. B 79, 201103 (2009) CrossRefGoogle Scholar
  3. 3.
    Belov, P.A., Hao, Y., Sudhakaran, S.: Subwavelength microwave imaging using an array of parallel conducting wires as a lens. Phys. Rev. B 73, 33108 (2006) CrossRefGoogle Scholar
  4. 4.
    Betzig, E., Trautman, J.: Near-field optics: Microscopy, spectroscopy, and surface modification beyond the diffraction limit. Science 257, 189–195 (1992) CrossRefGoogle Scholar
  5. 5.
    Carminati, R., et al.: Theory of the electromagnetic time reversal cavity. Opt. Lett. 32, 3107–3109 (2007) CrossRefGoogle Scholar
  6. 6.
    Carminati, R., Nieto-Vesperinas, M., Greffet, J.J.: Reciprocity of evanescent electromagnetic waves. J. Opt. Soc. Am. A 15, 706–712 (1998) CrossRefGoogle Scholar
  7. 7.
    Cassereau, D., Fink, M.: Time-reversal of ultrasonic fields—Part III: Theory of the closed time reversal cavity. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 579 (1992) CrossRefGoogle Scholar
  8. 8.
    Christensen, J., et al.: Collimation of sound assisted by acoustic surface waves. Nat. Phys. 3, 851–852 (2007) CrossRefGoogle Scholar
  9. 9.
    Dehong, L., et al.: Electromagnetic time-reversal imaging of a target in a cluttered environment. IEEE Trans. Antennas Propag. 53, 3058 (2005) CrossRefGoogle Scholar
  10. 10.
    Derode, A., Roux, P., Fink, M.: Robust acoustic time reversal with high-order multiple scattering. Phys. Rev. Lett. 75, 4206–4209 (1995) CrossRefGoogle Scholar
  11. 11.
    Derode, A., Tourin, A., Fink, M.: Random multiple scattering of ultrasound. II. Is time reversal a self-averaging process? Phys. Rev. E 64, 036606 (2001) CrossRefGoogle Scholar
  12. 12.
    Derode, A., et al.: Taking advantage of multiple scattering to communicate with time-reversal antennas. Phys. Rev. Lett. 90, 014301 (2003) CrossRefGoogle Scholar
  13. 13.
    de Rosny, J., Fink, M.: Overcoming the diffraction limit in wave physics using a time-reversal mirror and a novel acoustic sink. Phys. Rev. Lett. 89, 124301 (2002) CrossRefGoogle Scholar
  14. 14.
    de Rosny, J., Fink, M.: Focusing properties of near-field time reversal. Phys. Rev. A 76, 065801 (2007) CrossRefGoogle Scholar
  15. 15.
    de Rosny, J., Lerosey, G., Fink, M.: Theory of electromagnetic time reversal mirrors. IEEE Trans. Antennas Propag. 58, 3139–3149 (2010) CrossRefGoogle Scholar
  16. 16.
    Draeger, C., Fink, M.: One-channel time reversal of elastic waves in a chaotic 2D-silicon cavity. Phys. Rev. Lett. 79, 407–410 (1997) CrossRefGoogle Scholar
  17. 17.
    Fang, N., et al.: Ultrasonic metamaterials with. Negative modulus. Nat. Mater. 5, 452 (2006) CrossRefGoogle Scholar
  18. 18.
    Fink, M.: Time reversed acoustics. Phys. Today 50, 34–40 (1997) CrossRefGoogle Scholar
  19. 19.
    Fink, M., et al.: Time reversed acoustics. Rep. Prog. Phys. 63, 1933 (2000) CrossRefGoogle Scholar
  20. 20.
    Fink, M., Montaldo, G., Tanter, M.: Time reversal acoustics in biomedical engineering. Annu. Rev. Biomed. Eng. 5, 465 (2003) CrossRefGoogle Scholar
  21. 21.
    Fink, M., et al.: Time reversal in metamaterials. C. R. Phys. 10, 447 (2009) CrossRefGoogle Scholar
  22. 22.
    Goodman, J.: Introduction to Fourier Optics. Roberts & Company, Greenwood Village (2005) Google Scholar
  23. 23.
    Goos, F., Hänchen, H.: Ann. Phys. 436, 333 (1947) CrossRefGoogle Scholar
  24. 24.
    Guo, B., Xu, L., Li, J.: Time reversal based microwave hyperthermia treatment of Breast. In: Proc. Conf. Cancer, Signal, Systems and Computers 29th Asilomar, vol. 290 (2005) Google Scholar
  25. 25.
    Ing, R.K., et al.: In solid localization of finger impacts using acoustic time-reversal process. Appl. Phys. Lett. 87, 204104 (2005) CrossRefGoogle Scholar
  26. 26.
    Katz, O., Small, E., Bromberg, Y.: Focusing and compression of ultrashort pulses through scattering media. Nat. Photonics 5, 372–377 (2011) CrossRefGoogle Scholar
  27. 27.
    Kosmas, P., Rappaport, C.M.: Time reversal with the FDTD method for microwave breast cancer detection. IEEE Trans. Microw. Theory Tech. 53, 2317 (2005) CrossRefGoogle Scholar
  28. 28.
    Kuperman, W.A., et al.: Phase conjugation in the ocean: Experimental demonstration of an acoustic time-reversal mirror. J. Acoust. Soc. Am. 103, 25–40 (1998) CrossRefGoogle Scholar
  29. 29.
    Lemoult, F., et al.: Manipulating spatiotemporal degrees of freedom of waves in random media. Phys. Rev. Lett. 103, 173902 (2009) CrossRefGoogle Scholar
  30. 30.
    Lemoult, F., et al.: Resonant metalenses for breaking the diffraction barrier. Phys. Rev. Lett. 104, 203901 (2010) CrossRefGoogle Scholar
  31. 31.
    Lemoult, F., Lerosey, G., Fink, M.: Revisiting the wire medium: An ideal resonant metalens. Waves in Random and Complex Media 21, 591–613 (2011) CrossRefGoogle Scholar
  32. 32.
    Lemoult, F., Lerosey, G., Fink, M.: Far field subwavelength imaging and focusing using a wire medium based resonant metalens. Waves Random Complex Media 21, 614–627 (2011) CrossRefGoogle Scholar
  33. 33.
    Lemoult, F., Fink, M., Lerosey, G.: Acoustic resonators for far field control of sound on a subwavelength scale. Phys. Rev. Lett. 107, 064301 (2011) CrossRefGoogle Scholar
  34. 34.
    Lerosey, G.: Ph.D. thesis, Université Paris VII (2006) Google Scholar
  35. 35.
    Lerosey, G., et al.: Time reversal of electromagnetic waves. Phys. Rev. Lett. 92, 193904 (2004) CrossRefGoogle Scholar
  36. 36.
    Lerosey, G., et al.: Time reversal of electromagnetic waves and telecommunication. Radio Sci. 40, RS6S12 (2005) CrossRefGoogle Scholar
  37. 37.
    Lerosey, G., et al.: Time reversal of wideband microwaves. Appl. Phys. Lett. 88, 154101 (2006) CrossRefGoogle Scholar
  38. 38.
    Lerosey, G., et al.: Focusing beyond the diffraction limit with far-field time reversal. Science 315, 1120–1122 (2007) CrossRefGoogle Scholar
  39. 39.
    Lewis, A., et al.: Development of a 500Å resolution microscope. Ultramicroscopy 13, 227–231 (1984) CrossRefGoogle Scholar
  40. 40.
    Lezec, H.J., et al.: Beaming light from a subwavelength aperture. Science 297, 820 (2002) CrossRefGoogle Scholar
  41. 41.
    Liu, Z., et al.: Locally resonant sonic materials. Science 289, 1734 (2000) CrossRefGoogle Scholar
  42. 42.
    Mc Phedran, R.C., et al.: Density of states functions for photonic crystals. Phys. Rev. E 69, 016609 (2004) CrossRefGoogle Scholar
  43. 43.
    Montaldo, G., Tanter, M., Fink, M.: Real time inverse filter focusing through iterative time reversal. J. Acoust. Soc. Am. 115, 768–775 (2004) CrossRefGoogle Scholar
  44. 44.
    Pohl, D.W., Denk, W., Lanz, M.: Optical stethoscope: Image recording with resolution λ/20. Appl. Phys. Lett. 44, 651–653 (1984) CrossRefGoogle Scholar
  45. 45.
    Popoff, S.M., et al.: Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media. Phys. Rev. Lett. 104, 100601 (2010) CrossRefGoogle Scholar
  46. 46.
    Popoff, S., et al.: Image transmission through an opaque material. Nat. Commun. 1, 81 (2010). doi: 10.1038/ncomms1078 CrossRefGoogle Scholar
  47. 47.
    Purcell, E.: Spontaneous transition probabilities in radio-frequency spectroscopy. Phys. Rev. 69, 681 (1946) CrossRefGoogle Scholar
  48. 48.
    Qiu, R.C., et al.: Time reversal with MISO for ultrawideband communications: Experimental results. IEEE Antennas Wirel. Propag. Lett. 5, 269 (2006) CrossRefGoogle Scholar
  49. 49.
    Sarychev, A., Shalaev, V.: Electrodynamics of Metamaterials. World Scientific, London (2007) CrossRefGoogle Scholar
  50. 50.
    Sentenac, A., Chaumet, P.: Subdiffraction light focusing on a grating substrate. Phys. Rev. Lett. 101, 013901 (2008) CrossRefGoogle Scholar
  51. 51.
    Shvets, G., et al.: Guiding, focusing, and sensing on the subwavelength scale using metallic wire arrays. Phys. Rev. Lett. 99, 53903 (2007) CrossRefGoogle Scholar
  52. 52.
    Smith, D.R., et al.: Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000) CrossRefGoogle Scholar
  53. 53.
    Strohmer, T., et al.: Application of time-reversal with MMSE equalizer to UWB communications. In: Proc. GLOBECOM ’04 IEEE, vol. 5, p. 3123 (2005) Google Scholar
  54. 54.
    Synge, E.: A suggested method for extending microscopic resolution into the ultra-microscopic region. Philos. Mag. 6, 356–362 (1928) Google Scholar
  55. 55.
    Tanter, M., Thomas, J.L., Fink, M.: Time reversal and the inverse filter. J. Acoust. Soc. Am. 108, 223–234 (2000) CrossRefGoogle Scholar
  56. 56.
    Tourin, A., et al.: Time reversal telecommunications in complex environments. C. R. Phys. 7, 816 (2006) CrossRefGoogle Scholar
  57. 57.
    Vellekoop, I.M., Mosk, A.P: Focusing coherent light through opaque strongly scattering media. Opt. Lett. 32, 2309–2311 (2007) CrossRefGoogle Scholar
  58. 58.
    Vellekoop, I.M., Lagendijk, A., Mosk, A.P.: Exploiting disorder for perfect focusing. Nat. Photonics 4, 320–322 (2010) CrossRefGoogle Scholar
  59. 59.
    von Helmholtz, H.: On the Sensations of Tone as a Physiological Basis for the Theory of Music. Longmans, Green, New York (1885) Google Scholar
  60. 60.
    Yang, S., et al.: Focusing of sound in a 3D phononic crystal. Phys. Rev. Lett. 93, 024301 (2004) CrossRefGoogle Scholar
  61. 61.
    Yang, Z., et al.: Membrane-type acoustic metamaterial with negative dynamic mass. Phys. Rev. Lett. 101, 204301 (2008) CrossRefGoogle Scholar
  62. 62.
    Yavuz, M.E., Texeira, F.L.: Space-frequency ultrawideband time reversal imaging. IEEE Trans. Geosci. Remote Sens. 46, 1115 (2008) CrossRefGoogle Scholar
  63. 63.
    Zenhausern, F., Martin, Y., Wickramasinghe, H.: Scanning interferometric apertureless microscopy. Science 269, 1083–1085 (1995) CrossRefGoogle Scholar
  64. 64.
    Zhang, S., et al.: Focusing ultrasound with an acoustic metamaterial network. Phys. Rev. Lett. 102, 194301 (2009) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Mathias Fink
    • 1
  • Fabrice Lemoult
    • 1
  • Julien de Rosny
    • 1
  • Arnaud Tourin
    • 1
  • Geoffroy Lerosey
    • 1
    Email author
  1. 1.Institut LangevinESPCI ParisTech – CNRSParisFrance

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