Triggering extreme events at the nanoscale in photonic seas

Abstract

Hurricanes, tsunamis, rogue waves and tornadoes are rare natural phenomena that embed an exceptionally large amount of energy, which appears and quickly disappears in a probabilistic fashion. This makes them difficult to predict and hard to generate on demand. Here we demonstrate that we can trigger the onset of rare events akin to rogue waves controllably, and systematically use their generation to break the diffraction limit of light propagation. We illustrate this phenomenon in the case of a random field, where energy oscillates among incoherent degrees of freedom. Despite the low energy carried by each wave, we illustrate how to control a mechanism of spontaneous synchronization, which constructively builds up the spectral energy available in the whole bandwidth of the field into giant structures, whose statistics is predictable. The larger the frequency bandwidth of the random field, the larger the amplitude of rare events that are built up by this mechanism. Our system is composed of an integrated optical resonator, realized on a photonic crystal chip. Through near-field imaging experiments, we record confined rogue waves characterized by a spatial localization of 206 nm and with an ultrashort duration of 163 fs at a wavelength of 1.55 μm. Such localized energy patterns are formed in a deterministic dielectric structure that does not require nonlinear properties.

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Figure 1: Classical and diluted random walks of photons.
Figure 2: Photonic crystal resonator.
Figure 3: FDTD analysis of ultrafast subwavelength light localization
Figure 4: Summary of NSOM experimental results and comparison with theory.

References

  1. 1

    Oulton, R. F. et al. Plasmon lasers at deep subwavelength scale. Nature 461, 629–632 (2009).

    ADS  Article  Google Scholar 

  2. 2

    Chen, J. et al. Optical nano-imaging of gate-tunable graphene plasmons. Nature 487, 77–81 (2012).

    ADS  Article  Google Scholar 

  3. 3

    Gramotnev, D. K. & Bozhevolnyi, S. I. Plasmonics beyond the diffraction limit. Nature Photon. 4, 83–91 (2010).

    ADS  Article  Google Scholar 

  4. 4

    Lerman, G. M., Yanai, A. & Levy, U. Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light. Nano Lett. 9, 2139–2143 (2009).

    ADS  Article  Google Scholar 

  5. 5

    Zhang, X. & Liu, Z. Superlenses to overcome the diffraction limit. Nature Mater. 7, 435–441 (2008).

    ADS  Article  Google Scholar 

  6. 6

    Schuller, J. A. et al. Plasmonics for extreme light concentration and manipulation. Nature Mater. 9, 192–204 (2010).

    ADS  Google Scholar 

  7. 7

    Polman, A. & Atwater, H. A. Photonic design principles for ultrahigh-efficiency photovoltaics. Nature Mater. 11, 174–177 (2012).

    ADS  Article  Google Scholar 

  8. 8

    Nishijima, Y., Rosa, L. & Juodkazis, S. Surface plasmon resonances in periodic and random patterns of gold nano-disks for broadband light harvesting. Opt. Express 20, 11466–11477 (2012).

    ADS  Article  Google Scholar 

  9. 9

    Rogers, E. T. F. et al. A super-oscillatory lens optical microscope for subwavelength imaging. Nature Mater. 11, 432–435 (2012).

    ADS  Article  Google Scholar 

  10. 10

    Kao, T. S., Rogers, E. T. F., Ou, J. Y. & Zheludev, N. I. Digitally addressable focusing of light into a subwavelength hot spot. Nano Lett. 12, 2728–2731 (2012).

    ADS  Article  Google Scholar 

  11. 11

    Choi, Y. et al. Overcoming the diffraction limit using multiple light scattering in a highly disordered medium. Phys. Rev. Lett. 107, 023902 (2011).

    ADS  Article  Google Scholar 

  12. 12

    Vellekoop, I., Lagendijk, A. & Mosk, A. Exploiting disorder for perfect focusing. Nature Photon. 4, 320–322 (2010).

    Article  Google Scholar 

  13. 13

    Katz, O., Small, E., Bromberg, Y. & Silberberg, Y. Focusing and compression of ultrashort pulses through scattering media. Nature Photon. 5, 372–377 (2011).

    ADS  Article  Google Scholar 

  14. 14

    Krauss, G. et al. Synthesis of a single cycle of light with compact erbium-doped fibre technology. Nature Photon. 4, 33–36 (2010).

    ADS  Article  Google Scholar 

  15. 15

    Oktem, B., Ülgüdür, C. & Ilday, F. O. Soliton–similariton fibre laser. Nature Photon. 4, 307–311 (2010).

    Article  Google Scholar 

  16. 16

    Onorato, M., Osborne, A. R., Serio, M. & Bertone, S. Freak waves in random oceanic sea states. Phys. Rev. Lett. 86, 5831–5834 (2001).

    ADS  Article  Google Scholar 

  17. 17

    Ganshin, A. N., Efimov, V. B., Kolmakov, G. V., Mezhov-Deglin, L. P. & McClintock, P. V. E. Observation of an inverse energy cascade in developed acoustic turbulence in superfluid helium. Phys. Rev. Lett. 101, 065303 (2008).

    ADS  Article  Google Scholar 

  18. 18

    Höhmann, R., Kuhl, U., Stöckmann, H-J., Kaplan, L. & Heller, E. J. Freak waves in the linear regime: A microwave study. Phys. Rev. Lett. 104, 093901 (2010).

    ADS  Article  Google Scholar 

  19. 19

    Solli, D. R., Ropers, C., Koonath, P. & Jalali, B. Optical rogue waves. Nature 450, 1054–1057 (2007).

    ADS  Article  Google Scholar 

  20. 20

    Dudley, J. M., Genty, G. & Eggleton, B. J. Harnessing and control of optical rogue waves in supercontinuum generation. Opt. Express 16, 3644–3651 (2008).

    ADS  Article  Google Scholar 

  21. 21

    Kasparian, J., Béjot, P., Wolf, J-P. & Dudley, J. M. Optical rogue wave statistics in laser filamentation. Opt. Express 17, 12070–12075 (2009).

    ADS  Article  Google Scholar 

  22. 22

    Bosco, A. K. D., Wolfersberger, D. & Sciamanna, M. Extreme events in time-delayed nonlinear optics. Opt. Lett. 38, 703–705 (2013).

    ADS  Article  Google Scholar 

  23. 23

    Marsal, N., Caullet, V., Wolfersberger, D. & Sciamanna, M. Spatial rogue waves in a photorefractive pattern-forming system. Opt. Lett. 39, 3690–3693 (2014).

    ADS  Article  Google Scholar 

  24. 24

    Picozzi, A. et al. Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics. Phys. Rep. 504, 1–132 (2014).

    ADS  MathSciNet  Article  Google Scholar 

  25. 25

    Hammani, K., Kibler, B., Finot, C. & Picozzi, A. Emergence of rogue waves from optical turbulence. Phys. Lett. A 374, 3585–3589 (2010).

    ADS  Article  Google Scholar 

  26. 26

    Onorato, M., Residori, S., Bortolozzo, U., Montina, A. & Arecchi, F. Rogue waves and their generating mechanisms in different physical contexts. Phys. Rep. 528, 47–89 (2013).

    ADS  MathSciNet  Article  Google Scholar 

  27. 27

    Bonatto, C. et al. Deterministic optical rogue waves. Phys. Rev. Lett. 107, 053901 (2011).

    ADS  Article  Google Scholar 

  28. 28

    Baronio, F., Degasperis, A., Conforti, M. & Wabnitz, S. Solutions of the vector nonlinear Schrödinger equations: Evidence for deterministic rogue waves. Phys. Rev. Lett. 109, 044102 (2012).

    ADS  Article  Google Scholar 

  29. 29

    Stöckmann, H. J. Quantum Chaos: An Introduction (Cambridge Univ. Press, 2007).

    Google Scholar 

  30. 30

    Sandtke, M. et al. Novel instrument for surface plasmon polariton tracking in space and time. Rev. Sci. Instrum. 79, 013704 (2008).

    ADS  Article  Google Scholar 

  31. 31

    Berry, M. V. A note on superoscillations associated with bessel beams. J. Opt. 15, 044006 (2013).

    ADS  Article  Google Scholar 

  32. 32

    Liu, C. et al. Enhanced energy storage in chaotic optical resonators. Nature Photon. 7, 473–478 (2013).

    ADS  Article  Google Scholar 

  33. 33

    Dysthe, K., Krogstad, H. E. & Müller, P. Oceanic rogue waves. Annu. Rev. Fluid Mech. 40, 287–310 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  34. 34

    Redding, B., Liew, S. F., Sarma, R. & Cao, H. Compact spectrometer based on a disordered photonic chip. Nature Photon. 7, 746–751 (2013).

    ADS  Article  Google Scholar 

  35. 35

    Cohen, S. D., de S. Cavalcante, H. L. D. & Gauthier, D. J. Subwavelength position sensing using nonlinear feedback and wave chaos. Phys. Rev. Lett. 107, 254103 (2011).

    ADS  Article  Google Scholar 

  36. 36

    Conti, C., Leonetti, M., Fratalocchi, A., Angelani, L. & Ruocco, G. Condensation in disordered lasers: Theory, simulations, and experiments. Phys. Rev. Lett. 101, 143901 (2008).

    ADS  Article  Google Scholar 

  37. 37

    Cahill, B. G. & Lewis, A. W. Resource Variability and Extreme Wave Conditions at the Atlantic Marine Energy Test Site 17–19 (4th International Conference on Ocean Energy (ICOE), 2011).

    Google Scholar 

  38. 38

    Vergeles, S. & Turitsyn, S. K. Optical rogue waves in telecommunication data streams. Phys. Rev. A 83, 061801 (2011).

    ADS  Article  Google Scholar 

  39. 39

    Hauer, J., Demeure, C. & Scharf, L. Initial results in Prony analysis of power system response signals. IEEE Trans. Power Syst. 5, 80–89 (1990).

    ADS  Article  Google Scholar 

  40. 40

    Tijhuis, A. G. Electromagnetic Inverse Profiling, Theory and Numerical Implementation (VNU Science Press, 1987).

    Google Scholar 

  41. 41

    Falco, A. D., Krauss, T. F. & Fratalocchi, A. Lifetime statistics of quantum chaos studied by a multiscale analysis. Appl. Phys. Lett. 100, 184101 (2012).

    ADS  Article  Google Scholar 

  42. 42

    Rotenberg, N. & Kuipers, L. Mapping nanoscale light fields. Nature Photon. 8, 919–926 (2014).

    ADS  Article  Google Scholar 

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Acknowledgements

For the computer time, we used the resources of the KAUST Supercomputing Laboratory and the Red Dragon cluster of the Primalight group. This work is part of the research program of Kaust ‘Optics and plasmonics for efficient energy harvesting’ and the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO). This work is supported by Kaust (Award No. CRG-1-2012-FRA-005), by NanoNextNL of the Dutch ministry EL&I and 130 partners and by the EU FET project ‘SPANGL4Q’.

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A.F. initiated the work and developed the theoretical model for the controlled formation of rogue waves. C.L. performed FDTD simulations. R.E.C.v.d.W., N.R., and L.K. realized NSOM measurements. A.D.F fabricated samples used in experiments. All authors contributed equally in the analysis and interpretation of experimental results. All authors contributed to writing the manuscript.

Corresponding author

Correspondence to A. Fratalocchi.

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The authors declare no competing financial interests.

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Liu, C., van der Wel, R., Rotenberg, N. et al. Triggering extreme events at the nanoscale in photonic seas. Nature Phys 11, 358–363 (2015). https://doi.org/10.1038/nphys3263

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