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Photon transport enhanced by transverse Anderson localization in disordered superlattices

Nature Physics volume 11, pages 268–274 (2015)Cite this article

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Abstract

Controlling the flow of light at subwavelength scales provides access to functionalities such as negative or zero index of refraction, transformation optics, cloaking, metamaterials and slow light, but diffraction effects severely restrict our ability to control light on such scales. Here we report the photon transport and collimation enhanced by transverse Anderson localization in chip-scale dispersion-engineered anisotropic media. We demonstrate a photonic crystal superlattice structure in which diffraction is nearly completely arrested by cascaded resonant tunnelling through transverse guided resonances. By modifying the geometry of more than 4,000 scatterers in the superlattices we add structural disorder controllably and uncover the mechanism of disorder-induced transverse localization. Arrested spatial divergence is captured in the power-law scaling, along with exponential asymmetric mode profiles and enhanced collimation bandwidths for increasing disorder. With increasing disorder, we observe the crossover from cascaded guided resonances into the transverse localization regime, beyond both the ballistic and diffusive transport of photons.

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Figure 1: Ordered and disordered superlattices.
Figure 2: Numerical dispersive-propagation maps for the ordered and disordered superlattices.
Figure 3: Dispersive propagation of the ordered and disordered superlattices.
Figure 4: High-resolution far-field infrared scattering images illustrating photon transport in the disordered superlattices.
Figure 5: Disorder-induced enhanced photon transport at the onset of transverse localization.
Figure 6: Photon transport enhanced by transverse localization.

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References

  1. Luk’yanchuk, B. et al. The Fano resonance in plasmonic nanostructures and metamaterials. Nature Mater. 9, 707–715 (2010).

    Article  ADS  Google Scholar 

  2. Chatterjee, R. et al. Achieving subdiffraction imaging through bound surface states in negative-refraction photonic crystals in the near-infrared range. Phys. Rev. Lett. 100, 187401 (2008).

    Article  ADS  Google Scholar 

  3. Kocaman, S. et al. Observations of zero-order bandgaps in negative-index photonic crystal superlattices at the near-infrared. Phys. Rev. Lett. 102, 203905 (2009).

    Article  ADS  Google Scholar 

  4. Veselago, V. G. The electrodynamics of substances with simultaneously negative values of ɛ and μ. Usp. Fiz. Nauk 92, 517–526 (1964); Sov. Phys. Usp. 10, 509 (1968)

  5. Leonhardt, U. Optical conformal mapping. Science 312, 1777–1780 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  6. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  7. Rakich, P. T. et al. Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal. Nature Mater. 5, 93–96 (2006).

    Article  ADS  Google Scholar 

  8. Mocella, V. et al. Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial. Phys. Rev. Lett. 102, 133902 (2009).

    Article  ADS  Google Scholar 

  9. Arlandis, J. et al. Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals. Phys. Rev. Lett. 108, 037401 (2012).

    Article  ADS  Google Scholar 

  10. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

    Article  ADS  Google Scholar 

  11. Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).

    Article  ADS  Google Scholar 

  12. John, S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987).

    Article  ADS  Google Scholar 

  13. John, S. Confined Electrons and Photons Vol. 340, 523–584 (NATO ASI Series B, 1995).

    Book  Google Scholar 

  14. Wang, J. & Genack, A. Z. Transport through modes in random media. Nature 471, 345–348 (2011).

    Article  ADS  Google Scholar 

  15. Levi, L., Krivolapov, Y., Fishman, S. & Segev, M. Hyper-transport of light and stochastic acceleration by evolving disorder. Nature Phys. 8, 912–917 (2012).

    Article  ADS  Google Scholar 

  16. Levi, L. et al. Disorder-enhanced transport in photonic quasicrystals. Science 332, 1541–1544 (2011).

    Article  ADS  Google Scholar 

  17. Burresi, M. et al. Weak localization of light in superdiffusive random systems. Phys. Rev. Lett. 108, 110604 (2012).

    Article  ADS  Google Scholar 

  18. Conti, C. & Fratalocchi, A. Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals. Nature Phys. 4, 794–798 (2008).

    Article  ADS  Google Scholar 

  19. Karbasi, S. et al. Image transport through a disordered optical fibre mediated by transverse Anderson localization. Nature Commun. 5, 3362 (2014).

    Article  ADS  Google Scholar 

  20. Asatryan, A. A. et al. Suppression of Anderson localization in disordered metamaterials. Phys. Rev. Lett. 99, 193902 (2007).

    Article  ADS  Google Scholar 

  21. De Raedt, H., Lagendijk, A. & de Vries, P. Transverse localization of light. Phys. Rev. Lett. 62, 47–50 (1989).

    Article  ADS  Google Scholar 

  22. Mott, N. F. Metal–Insulator Transitions (Taylor and Francis, 1974).

    Google Scholar 

  23. Lahini, Y. et al. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008).

    Article  ADS  Google Scholar 

  24. Savona, V. Electromagnetic modes of a disordered photonic crystal. Phys. Rev. B 83, 085301 (2011).

    Article  ADS  Google Scholar 

  25. Patterson, M. et al. Disorder-induced coherent scattering in slow-light photonic crystal waveguides. Phys. Rev. Lett. 102, 253903 (2009).

    Article  ADS  Google Scholar 

  26. Bliokh, Y. P., Freilikher, V. & Nori, F. Ballistic charge transport in graphene and light propagation in periodic dielectric structures with metamaterials: A comparative study. Phys. Rev. B 87, 245134 (2013).

    Article  ADS  Google Scholar 

  27. Ponomarenko, L. A. et al. Tunable metal–insulator transition in double-layer graphene heterostructures. Nature Phys. 7, 958–961 (2011).

    Article  ADS  Google Scholar 

  28. Esaki, L. & Tsu, R. Superlattice and negative differential conductivity in semiconductors. IBM J. Res. Dev. 14, 61–65 (1970).

    Article  Google Scholar 

  29. Ohtomo, A. & Hwang, H. Y. A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface. Nature 427, 423–426 (2004).

    Article  ADS  Google Scholar 

  30. Billy, J. et al. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 891–894 (2008).

    Article  ADS  Google Scholar 

  31. Roati, G. et al. Anderson localization of a non-interacting Bose–Einstein condensate. Nature 453, 895–898 (2008).

    Article  ADS  Google Scholar 

  32. Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge discussions with M. Weinstein, S. Kocaman and C-T. Chen. We also thank S-N. Chiu for the data analysis. This work is supported by the Office of Naval Research under M. F. Shlesinger (N00014-14-1-0041) and the Studying Abroad Scholarship by the Department of Education in Taiwan. This work is also supported by NSF Division of Materials Research (1108176) and EPSRC EP/G030502/1. The electron-beam lithography carried out at the Brookhaven National Laboratory is supported by the US Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886. The authors acknowledge the use of the UCL Legion High Performance Computing Facility (Legion@UCL) and associated support services in the completion of this work.

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Authors and Affiliations

  1. Optical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science and Engineering, Mechanical Engineering, Columbia University, New York, New York 10027, USA

    P. Hsieh, J. F. McMillan & C. W. Wong

  2. Quantumstone Research Inc., Taipei 114, Taiwan

    P. Hsieh, C. Chung & M. Tsai

  3. Center for Micro/Nano Science and Technology and Advanced Optoelectronic Technology Center, National Cheng Kung University, Tainan 701, Taiwan

    C. Chung

  4. Center for Measurement Standards, Industrial Technology Research Institute, Hsinchu 300, Taiwan

    M. Tsai

  5. Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA

    M. Lu

  6. Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, UK,

    N. C. Panoiu

  7. Thomas Young Centre, London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London WC1H 0AH, UK,

    N. C. Panoiu

  8. Mesoscopic Optics and Quantum Electronics Laboratory, University of California, Los Angeles, California 90095, USA

    C. W. Wong

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Contributions

P.H., N.C.P. and C.W.W. conceived the project. P.H. designed the photonic superlattices and performed numerical simulations, sample nanofabrication, measurements and image analysis. C.C. and M.L. performed the electron-beam lithography, and C.C. carried out focused ion beam imaging. J.F.M. performed the far-field and group velocity measurements. M.T. prepared the NSOM probes. N.C.P. designed the photonic superlattices and performed the theoretical analysis and FDTD numerical simulations. P.H., N.C.P. and C.W.W. wrote the manuscript, which all authors discussed.

Corresponding authors

Correspondence to P. Hsieh, N. C. Panoiu or C. W. Wong.

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The authors declare no competing financial interests.

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Hsieh, P., Chung, C., McMillan, J. et al. Photon transport enhanced by transverse Anderson localization in disordered superlattices. Nature Phys 11, 268–274 (2015). https://doi.org/10.1038/nphys3211

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