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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Oulton, R. F. et al. Plasmon lasers at deep subwavelength scale. Nature 461, 629–632 (2009).
Chen, J. et al. Optical nano-imaging of gate-tunable graphene plasmons. Nature 487, 77–81 (2012).
Gramotnev, D. K. & Bozhevolnyi, S. I. Plasmonics beyond the diffraction limit. Nature Photon. 4, 83–91 (2010).
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).
Zhang, X. & Liu, Z. Superlenses to overcome the diffraction limit. Nature Mater. 7, 435–441 (2008).
Schuller, J. A. et al. Plasmonics for extreme light concentration and manipulation. Nature Mater. 9, 192–204 (2010).
Polman, A. & Atwater, H. A. Photonic design principles for ultrahigh-efficiency photovoltaics. Nature Mater. 11, 174–177 (2012).
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).
Rogers, E. T. F. et al. A super-oscillatory lens optical microscope for subwavelength imaging. Nature Mater. 11, 432–435 (2012).
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).
Choi, Y. et al. Overcoming the diffraction limit using multiple light scattering in a highly disordered medium. Phys. Rev. Lett. 107, 023902 (2011).
Vellekoop, I., Lagendijk, A. & Mosk, A. Exploiting disorder for perfect focusing. Nature Photon. 4, 320–322 (2010).
Katz, O., Small, E., Bromberg, Y. & Silberberg, Y. Focusing and compression of ultrashort pulses through scattering media. Nature Photon. 5, 372–377 (2011).
Krauss, G. et al. Synthesis of a single cycle of light with compact erbium-doped fibre technology. Nature Photon. 4, 33–36 (2010).
Oktem, B., Ülgüdür, C. & Ilday, F. O. Soliton–similariton fibre laser. Nature Photon. 4, 307–311 (2010).
Onorato, M., Osborne, A. R., Serio, M. & Bertone, S. Freak waves in random oceanic sea states. Phys. Rev. Lett. 86, 5831–5834 (2001).
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).
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).
Solli, D. R., Ropers, C., Koonath, P. & Jalali, B. Optical rogue waves. Nature 450, 1054–1057 (2007).
Dudley, J. M., Genty, G. & Eggleton, B. J. Harnessing and control of optical rogue waves in supercontinuum generation. Opt. Express 16, 3644–3651 (2008).
Kasparian, J., Béjot, P., Wolf, J-P. & Dudley, J. M. Optical rogue wave statistics in laser filamentation. Opt. Express 17, 12070–12075 (2009).
Bosco, A. K. D., Wolfersberger, D. & Sciamanna, M. Extreme events in time-delayed nonlinear optics. Opt. Lett. 38, 703–705 (2013).
Marsal, N., Caullet, V., Wolfersberger, D. & Sciamanna, M. Spatial rogue waves in a photorefractive pattern-forming system. Opt. Lett. 39, 3690–3693 (2014).
Picozzi, A. et al. Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics. Phys. Rep. 504, 1–132 (2014).
Hammani, K., Kibler, B., Finot, C. & Picozzi, A. Emergence of rogue waves from optical turbulence. Phys. Lett. A 374, 3585–3589 (2010).
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).
Bonatto, C. et al. Deterministic optical rogue waves. Phys. Rev. Lett. 107, 053901 (2011).
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).
Stöckmann, H. J. Quantum Chaos: An Introduction (Cambridge Univ. Press, 2007).
Sandtke, M. et al. Novel instrument for surface plasmon polariton tracking in space and time. Rev. Sci. Instrum. 79, 013704 (2008).
Berry, M. V. A note on superoscillations associated with bessel beams. J. Opt. 15, 044006 (2013).
Liu, C. et al. Enhanced energy storage in chaotic optical resonators. Nature Photon. 7, 473–478 (2013).
Dysthe, K., Krogstad, H. E. & Müller, P. Oceanic rogue waves. Annu. Rev. Fluid Mech. 40, 287–310 (2008).
Redding, B., Liew, S. F., Sarma, R. & Cao, H. Compact spectrometer based on a disordered photonic chip. Nature Photon. 7, 746–751 (2013).
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).
Conti, C., Leonetti, M., Fratalocchi, A., Angelani, L. & Ruocco, G. Condensation in disordered lasers: Theory, simulations, and experiments. Phys. Rev. Lett. 101, 143901 (2008).
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).
Vergeles, S. & Turitsyn, S. K. Optical rogue waves in telecommunication data streams. Phys. Rev. A 83, 061801 (2011).
Hauer, J., Demeure, C. & Scharf, L. Initial results in Prony analysis of power system response signals. IEEE Trans. Power Syst. 5, 80–89 (1990).
Tijhuis, A. G. Electromagnetic Inverse Profiling, Theory and Numerical Implementation (VNU Science Press, 1987).
Falco, A. D., Krauss, T. F. & Fratalocchi, A. Lifetime statistics of quantum chaos studied by a multiscale analysis. Appl. Phys. Lett. 100, 184101 (2012).
Rotenberg, N. & Kuipers, L. Mapping nanoscale light fields. Nature Photon. 8, 919–926 (2014).
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’.
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