Letter | Published:

Subwavelength anti-diffracting beams propagating over more than 1,000 Rayleigh lengths

Nature Photonics volume 9, pages 228232 (2015) | Download Citation

Abstract

Propagating light beams with widths down to and below the optical wavelength require bulky large-aperture lenses and remain focused only for micrometric distances1,2. Here, we report the observation of light beams that violate this localization/depth-of-focus law by shrinking as they propagate, allowing resolution to be maintained and increased over macroscopic propagation lengths. In nanodisordered ferroelectrics3,4 we observe a non-paraxial propagation of a sub-micrometre-sized beam for over 1,000 diffraction lengths, the narrowest visible beam reported to date5,6,7,8. This unprecedented effect is caused by the nonlinear response of a dipolar glass, which transforms the leading optical wave equation into a Klein–Gordon-type equation that describes a massive particle field9. Our findings open the way to high-resolution optics over large depths of focus, and a route to merging bulk optics into nanodevices.

Access optionsAccess options

References

  1. 1.

    , & Diffraction-unlimited three-dimensional optical nanoscopy with opposing lenses. Nature Photon. 3, 381–387 (2009).

  2. 2.

    , & Plasmonics for near-field nano-imaging and superlensing. Nature Photon. 3, 388–394 (2009).

  3. 3.

    & Dielectric relaxation in relaxor ferroelectrics. J. Adv. Dielectrics 2, 1241010 (2012).

  4. 4.

    & Lead-free relaxor ferroelectrics. J. Am. Ceram. Soc. 95, 1–26 (2012).

  5. 5.

    & Spatial Solitons (Springer-Verlag, 2001).

  6. 6.

    & Soliton Driven Photonics (Kluwer Academic, 2001).

  7. 7.

    & Optical Solitons (Academic Press, 2003).

  8. 8.

    , & Optical spatial solitons: historical overview and recent advances. Rep. Prog. Phys. 75, 086401 (2012).

  9. 9.

    Quantum Field theory (Wiley, 1984).

  10. 10.

    & Principles of Optics 7th edn (Cambridge Univ. Press, 1999).

  11. 11.

    , & Subwavelength optical spatial solitons and three-dimensional localization in disordered ferroelectrics: towards metamaterials of nonlinear origin. Phys. Rev. A 84, 043809 (2011).

  12. 12.

    Quantum Electronics (Wiley, 1988).

  13. 13.

    Laser Electronics (Prentice Hall, 1981).

  14. 14.

    Glass transition in amorphous polymers a phenomenological study. Adv. Polym. Sci. 3, 394–508 (1963).

  15. 15.

    , , & Scale-free optics and diffractionless waves in nanodisordered ferroelectrics. Nature Photon. 5, 39–42 (2011).

  16. 16.

    & Crossover (or Kovacs) effect in an aging molecular liquid. Phys. Rev. Lett. 92, 045504 (2004).

  17. 17.

    & Thermodynamics of the Glassy State (Taylor & Francis, 2008).

  18. 18.

    et al. Subwavelength light focusing using random nanoparticles. Nature Photon. 7, 454–458 (2013).

  19. 19.

    The electrodynamics of substances with simultaneously negative values of ε and μ. Sov. Phys. Usp. 10, 509–514 (1968).

  20. 20.

    Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000).

  21. 21.

    , , & Sub-diffraction-limited optical imaging with a silver superlens. Science 308, 534–537 (2005).

  22. 22.

    Optical negative-index metamaterials. Nature Photon. 1, 41–48 (2007).

  23. 23.

    , & Nonlinear electric metamaterials. Appl. Phys. Lett. 95, 084102 (2009).

  24. 24.

    et al. Self-collimating phenomena in photonic crystals. Appl. Phys. Lett. 74, 1212–1214 (1999).

  25. 25.

    , , & Diffraction management. Phys. Rev. Lett. 85, 1863–1866 (2000).

  26. 26.

    , , , & Elimination, reversal and directional bias of optical diffraction. Nature Phys. 5, 665–668 (2009).

  27. 27.

    , , , & Nonlinear optical diffraction effects and solitons due to anisotropic charge-diffusion-based self-interaction. Phys. Rev. Lett. 82, 1664–1667 (1999).

  28. 28.

    & Nonlinear Photonics and Novel Optical Phenomena Vol. 170 (eds Chen, Z. & Morandotti, R.) Ch. 8 (Springer-Verlag, 2012).

  29. 29.

    , , & Programming scale-free optics in disordered ferroelectrics. Opt. Lett. 37, 2355–2357 (2012).

  30. 30.

    , , & Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time. Opt. Express 20, 27382–27387 (2012).

  31. 31.

    , & Characterization of a new photorefractive material: K1−yLyT1−xNx. Opt. Lett. 17, 713–715 (1992).

  32. 32.

    , & Confinement kinetics in a KTN:Cu crystal: experiment and theory. Phys. Rev. B 73, 104104 (2006).

  33. 33.

    , , , & Aging in K1−xLixTaO3: a domain growth interpretation. Phys. Rev. Lett. 81, 4987–4990 (1998).

Download references

Acknowledgements

The research leading to these results was supported by funding from the Italian Ministry of Research (MIUR) through the ‘Futuro in Ricerca’ FIRB grant PHOCOS-RBFR08E7VA and from the European Research Council under the European Community Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 201766. Partial funding was received through the SMARTCONFOCAL project of the Regione Lazio and through the PRIN 2012BFNWZ2 and Sapienza 2013PHOTOANDERSON projects. A.J.A. acknowledges support from the Peter Brojde Center for Innovative Engineering.

Author information

Affiliations

  1. Physics Department, University of Rome Sapienza, Rome 00185, Italy

    • Eugenio DelRe
    • , Fabrizio Di Mei
    • , Jacopo Parravicini
    •  & Claudio Conti
  2. Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, Rome 00161, Italy

    • Fabrizio Di Mei
  3. Physics Department, University of Pavia, Pavia 27100, Italy

    • Gianbattista Parravicini
  4. Applied Physics Department, Hebrew University of Jerusalem, Jerusalem 91904, Israel

    • Aharon J. Agranat
  5. Institute for Complex Systems, National Research Council (ISC-CNR), Via dei Taurini 19, Rome 00185, Italy

    • Claudio Conti

Authors

  1. Search for Eugenio DelRe in:

  2. Search for Fabrizio Di Mei in:

  3. Search for Jacopo Parravicini in:

  4. Search for Gianbattista Parravicini in:

  5. Search for Aharon J. Agranat in:

  6. Search for Claudio Conti in:

Contributions

E.D. and C.C. conceived and developed the experiments and theory. R.A. designed and fabricated the KTN:Li samples and participated in the analysis and interpretation of results. F.D. and J.P. carried out the experiments and data analysis. G.P. carried out the dielectric characterization of the material.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Eugenio DelRe.

Supplementary information

PDF files

  1. 1.

    Supplementary information

    Supplementary information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nphoton.2015.21

Further reading

Newsletter Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing