Skip to main content
SpringerLink
Log in

Subwavelength Focussing in Metamaterials Using Far Field Time Reversal

  • Chapter
Acoustic Metamaterials

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 166))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aulbach, J., et al.: Control of light transmission through opaque scattering media in space and time. Phys. Rev. Lett. 106, 103901 (2011)

    Article  Google Scholar 

  2. Bartal, G., Lerosey, G., Zhang, X.: Subwavelength dynamic focusing in plasmonic nanostructures using time reversal. Phys. Rev. B 79, 201103 (2009)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  4. Betzig, E., Trautman, J.: Near-field optics: Microscopy, spectroscopy, and surface modification beyond the diffraction limit. Science 257, 189–195 (1992)

    Article  CAS  Google Scholar 

  5. Carminati, R., et al.: Theory of the electromagnetic time reversal cavity. Opt. Lett. 32, 3107–3109 (2007)

    Article  CAS  Google Scholar 

  6. Carminati, R., Nieto-Vesperinas, M., Greffet, J.J.: Reciprocity of evanescent electromagnetic waves. J. Opt. Soc. Am. A 15, 706–712 (1998)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  8. Christensen, J., et al.: Collimation of sound assisted by acoustic surface waves. Nat. Phys. 3, 851–852 (2007)

    Article  CAS  Google Scholar 

  9. Dehong, L., et al.: Electromagnetic time-reversal imaging of a target in a cluttered environment. IEEE Trans. Antennas Propag. 53, 3058 (2005)

    Article  Google Scholar 

  10. Derode, A., Roux, P., Fink, M.: Robust acoustic time reversal with high-order multiple scattering. Phys. Rev. Lett. 75, 4206–4209 (1995)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  12. Derode, A., et al.: Taking advantage of multiple scattering to communicate with time-reversal antennas. Phys. Rev. Lett. 90, 014301 (2003)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  14. de Rosny, J., Fink, M.: Focusing properties of near-field time reversal. Phys. Rev. A 76, 065801 (2007)

    Article  Google Scholar 

  15. de Rosny, J., Lerosey, G., Fink, M.: Theory of electromagnetic time reversal mirrors. IEEE Trans. Antennas Propag. 58, 3139–3149 (2010)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  17. Fang, N., et al.: Ultrasonic metamaterials with. Negative modulus. Nat. Mater. 5, 452 (2006)

    Article  CAS  Google Scholar 

  18. Fink, M.: Time reversed acoustics. Phys. Today 50, 34–40 (1997)

    Article  Google Scholar 

  19. Fink, M., et al.: Time reversed acoustics. Rep. Prog. Phys. 63, 1933 (2000)

    Article  Google Scholar 

  20. Fink, M., Montaldo, G., Tanter, M.: Time reversal acoustics in biomedical engineering. Annu. Rev. Biomed. Eng. 5, 465 (2003)

    Article  CAS  Google Scholar 

  21. Fink, M., et al.: Time reversal in metamaterials. C. R. Phys. 10, 447 (2009)

    Article  CAS  Google Scholar 

  22. Goodman, J.: Introduction to Fourier Optics. Roberts & Company, Greenwood Village (2005)

    Google Scholar 

  23. Goos, F., Hänchen, H.: Ann. Phys. 436, 333 (1947)

    Article  Google Scholar 

  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. Ing, R.K., et al.: In solid localization of finger impacts using acoustic time-reversal process. Appl. Phys. Lett. 87, 204104 (2005)

    Article  Google Scholar 

  26. Katz, O., Small, E., Bromberg, Y.: Focusing and compression of ultrashort pulses through scattering media. Nat. Photonics 5, 372–377 (2011)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  29. Lemoult, F., et al.: Manipulating spatiotemporal degrees of freedom of waves in random media. Phys. Rev. Lett. 103, 173902 (2009)

    Article  Google Scholar 

  30. Lemoult, F., et al.: Resonant metalenses for breaking the diffraction barrier. Phys. Rev. Lett. 104, 203901 (2010)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  34. Lerosey, G.: Ph.D. thesis, Université Paris VII (2006)

    Google Scholar 

  35. Lerosey, G., et al.: Time reversal of electromagnetic waves. Phys. Rev. Lett. 92, 193904 (2004)

    Article  CAS  Google Scholar 

  36. Lerosey, G., et al.: Time reversal of electromagnetic waves and telecommunication. Radio Sci. 40, RS6S12 (2005)

    Article  Google Scholar 

  37. Lerosey, G., et al.: Time reversal of wideband microwaves. Appl. Phys. Lett. 88, 154101 (2006)

    Article  Google Scholar 

  38. Lerosey, G., et al.: Focusing beyond the diffraction limit with far-field time reversal. Science 315, 1120–1122 (2007)

    Article  CAS  Google Scholar 

  39. Lewis, A., et al.: Development of a 500Å resolution microscope. Ultramicroscopy 13, 227–231 (1984)

    Article  Google Scholar 

  40. Lezec, H.J., et al.: Beaming light from a subwavelength aperture. Science 297, 820 (2002)

    Article  CAS  Google Scholar 

  41. Liu, Z., et al.: Locally resonant sonic materials. Science 289, 1734 (2000)

    Article  CAS  Google Scholar 

  42. Mc Phedran, R.C., et al.: Density of states functions for photonic crystals. Phys. Rev. E 69, 016609 (2004)

    Article  Google Scholar 

  43. Montaldo, G., Tanter, M., Fink, M.: Real time inverse filter focusing through iterative time reversal. J. Acoust. Soc. Am. 115, 768–775 (2004)

    Article  Google Scholar 

  44. Pohl, D.W., Denk, W., Lanz, M.: Optical stethoscope: Image recording with resolution λ/20. Appl. Phys. Lett. 44, 651–653 (1984)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  46. Popoff, S., et al.: Image transmission through an opaque material. Nat. Commun. 1, 81 (2010). doi:10.1038/ncomms1078

    Article  Google Scholar 

  47. Purcell, E.: Spontaneous transition probabilities in radio-frequency spectroscopy. Phys. Rev. 69, 681 (1946)

    Article  Google Scholar 

  48. Qiu, R.C., et al.: Time reversal with MISO for ultrawideband communications: Experimental results. IEEE Antennas Wirel. Propag. Lett. 5, 269 (2006)

    Article  Google Scholar 

  49. Sarychev, A., Shalaev, V.: Electrodynamics of Metamaterials. World Scientific, London (2007)

    Book  Google Scholar 

  50. Sentenac, A., Chaumet, P.: Subdiffraction light focusing on a grating substrate. Phys. Rev. Lett. 101, 013901 (2008)

    Article  Google Scholar 

  51. Shvets, G., et al.: Guiding, focusing, and sensing on the subwavelength scale using metallic wire arrays. Phys. Rev. Lett. 99, 53903 (2007)

    Article  CAS  Google Scholar 

  52. Smith, D.R., et al.: Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000)

    Article  CAS  Google Scholar 

  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. Synge, E.: A suggested method for extending microscopic resolution into the ultra-microscopic region. Philos. Mag. 6, 356–362 (1928)

    CAS  Google Scholar 

  55. Tanter, M., Thomas, J.L., Fink, M.: Time reversal and the inverse filter. J. Acoust. Soc. Am. 108, 223–234 (2000)

    Article  CAS  Google Scholar 

  56. Tourin, A., et al.: Time reversal telecommunications in complex environments. C. R. Phys. 7, 816 (2006)

    Article  CAS  Google Scholar 

  57. Vellekoop, I.M., Mosk, A.P: Focusing coherent light through opaque strongly scattering media. Opt. Lett. 32, 2309–2311 (2007)

    Article  CAS  Google Scholar 

  58. Vellekoop, I.M., Lagendijk, A., Mosk, A.P.: Exploiting disorder for perfect focusing. Nat. Photonics 4, 320–322 (2010)

    Article  CAS  Google Scholar 

  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. Yang, S., et al.: Focusing of sound in a 3D phononic crystal. Phys. Rev. Lett. 93, 024301 (2004)

    Article  Google Scholar 

  61. Yang, Z., et al.: Membrane-type acoustic metamaterial with negative dynamic mass. Phys. Rev. Lett. 101, 204301 (2008)

    Article  CAS  Google Scholar 

  62. Yavuz, M.E., Texeira, F.L.: Space-frequency ultrawideband time reversal imaging. IEEE Trans. Geosci. Remote Sens. 46, 1115 (2008)

    Article  Google Scholar 

  63. Zenhausern, F., Martin, Y., Wickramasinghe, H.: Scanning interferometric apertureless microscopy. Science 269, 1083–1085 (1995)

    Article  CAS  Google Scholar 

  64. Zhang, S., et al.: Focusing ultrasound with an acoustic metamaterial network. Phys. Rev. Lett. 102, 194301 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut Langevin, ESPCI ParisTech – CNRS, 10 rue Vauquelin, 75005, Paris, France

    Mathias Fink, Fabrice Lemoult, Julien de Rosny, Arnaud Tourin & Geoffroy Lerosey

Authors
  1. Mathias Fink
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabrice Lemoult
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Julien de Rosny
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arnaud Tourin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Geoffroy Lerosey
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Geoffroy Lerosey .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Imperial College, South Kensington Campus, London, SW7 2BZ, United Kingdom

    Richard V. Craster

  2. Institut Fresnel CNRS, Rue du Coteau 71, Marseille, 13770, France

    Sébastien Guenneau

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Fink, M., Lemoult, F., de Rosny, J., Tourin, A., Lerosey, G. (2013). Subwavelength Focussing in Metamaterials Using Far Field Time Reversal. In: Craster, R., Guenneau, S. (eds) Acoustic Metamaterials. Springer Series in Materials Science, vol 166. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4813-2_6

Download citation

Publish with us

Policies and ethics

Search

Navigation