Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Dissipative self-organization in optical space

Nature Photonics volume 12, pages 739–743 (2018)Cite this article

Subjects

Abstract

The complex behaviours of schools of fish1 and swarms of bacteria2,3 can be emulated in soft-matter systems that assemble into flocks4,5 and active nematics6, respectively. These artificial structures emerge far from thermodynamic equilibrium through the process of dissipative self-organization, in which many-body interactions coordinate energy dissipation. The development of such active matter has deepened our understanding of living systems. Yet, the application of dissipative self-organization has been restricted to soft-matter systems, whose elements organize through their respective motions. Here, we demonstrate dissipative self-organization in solid-state photonics. Our structure consists of a random array of Fabry–Pérot resonators that are externally driven and interact coherently through thermo-optical feedback. At sufficient optical driving power, the system undergoes a phase transition into a robustly organized non-equilibrium state that actively partitions energy dissipation, while displaying resiliency to perturbations and collective memory7,8. Self-organizing photonics opens possibilities for developing scalable architectures and life-like networks for brain-inspired computation9,10.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Self-organization of optical phase.
Fig. 2: Phase transition to the organized steady state.
Fig. 3: Resilience to thermal perturbation.
Fig. 4: Collective memory effects and hidden states.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Katz, Y., Tunstrøm, K., Ioannou, C. C., Huepe, C. & Couzin, I. D. Inferring the structure and dynamics of interactions in schooling fish. Proc. Natl Acad. Sci. USA 108, 18720–18725 (2011).

    Article  ADS  Google Scholar 

  2. Wu, X.-L. & Libchaber, A. Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84, 3017–3020 (2000).

    Article  ADS  Google Scholar 

  3. Dombrowski, C., Cisneros, L., Chatkaew, S., Goldstein, R. E. & Kessler, J. O. Self-concentration and large-scale coherence in bacterial dynamics. Phys. Rev. Lett. 93, 098103 (2004).

    Article  ADS  Google Scholar 

  4. Narayan, V., Ramaswamy, S. & Menon, N. Long-lived giant number fluctuations in a swarming granular nematic. Science 317, 105–108 (2007).

    Article  ADS  Google Scholar 

  5. Bricard, A., Caussin, J.-B., Desreumaux, N., Dauchot, O. & Bartolo, D. Emergence of macroscopic directed motion in populations of motile colloids. Nature 503, 95–98 (2013).

    Article  ADS  Google Scholar 

  6. Sanchez, T., Chen, D. T. N., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).

    Article  ADS  Google Scholar 

  7. England, J. L. Dissipative adaptation in driven self-assembly. Nat. Nanotech. 10, 919–923 (2015).

    Article  ADS  Google Scholar 

  8. Perunov, N., Marsland, R. A. & England, J. L. Statistical physics of adaptation. Phys. Rev. X 6, 021036 (2016).

    Google Scholar 

  9. Yu, S., Wu, Y., Jeyasingh, R., Kuzum, D. & Wong, H. S. P. An electronic synapse device based on metal oxide resistive switching memory for neuromorphic computation. IEEE Trans. Electron. Devices 58, 2729–2737 (2011).

    Article  ADS  Google Scholar 

  10. Wang, Z. et al. Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing. Nat. Mater. 16, 101–108 (2017).

    Article  ADS  Google Scholar 

  11. Fialkowski, M. et al. Principles and implementations of dissipative (dynamic) self-assembly. J. Phys. Chem. B 110, 2482–2496 (2006).

    Article  Google Scholar 

  12. Mora, T. et al. Local equilibrium in bird flocks. Nat. Phys. 12, 1153–1157 (2016).

    Article  Google Scholar 

  13. Whitesides, G. M. & Grzybowski, B. Self-assembly at all scales. Science 295, 2418–2421 (2002).

    Article  ADS  Google Scholar 

  14. Beatus, T., Tlusty, T. & Bar-Ziv, R. Phonons in a one-dimensional microfluidic crystal. Nat. Phys. 2, 743–748 (2006).

    Article  Google Scholar 

  15. Boekhoven, J. et al. Dissipative self-assembly of a molecular gelator by using a chemical fuel. Angew. Chem. Int. Ed. 122, 4935–4938 (2010).

    Article  Google Scholar 

  16. Maiti, S., Fortunati, I., Ferrante, C., Scrimin, P. & Prins, L. J. Dissipative self-assembly of vesicular nanoreactors. Nat. Chem. 8, 725–731 (2016).

    Article  Google Scholar 

  17. Kondepudi, D., Kay, B. & Dixon, J. End-directed evolution and the emergence of energy-seeking behavior in a complex system. Phys. Rev. E 91, 050902 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  18. Snezhko, A. & Aranson, I. S. Magnetic manipulation of self-assembled colloidal asters. Nat. Mater. 10, 698–703 (2011).

    Article  ADS  Google Scholar 

  19. Martinez-Pedrero, F., Ortiz-Ambriz, A., Pagonabarraga, I. & Tierno, P. Colloidal microworms propelling via a cooperative hydrodynamic conveyor belt. Phys. Rev. Lett. 115, 138301 (2015).

    Article  ADS  Google Scholar 

  20. Souslov, A., Zuiden, B. C., van Bartolo, D. & Vitelli, V. Topological sound in active-liquid metamaterials. Nat. Phys. 13, 1091–1094 (2017).

    Article  Google Scholar 

  21. Bachelard, N. et al. Emergence of an enslaved phononic bandgap in a non-equilibrium pseudo-crystal. Nat. Mater. 16, 808–813 (2017).

    Article  ADS  Google Scholar 

  22. Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).

    Article  ADS  Google Scholar 

  23. Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).

    Article  ADS  Google Scholar 

  24. Yariv, A. & Yeh, P. Photonics: Optical Electronics in Modern Communications. (Oxford Univ. Press, Oxford, 2006).

  25. Espinola, R. L., Tsai, M. C., Yardley, J. T. & Osgood, R. M. Fast and low-power thermooptic switch on thin silicon-on-insulator. IEEE Photon. Technol. Lett. 15, 1366–1368 (2003).

    Article  ADS  Google Scholar 

  26. Zhang, M., Shah, S., Cardenas, J. & Lipson, M. Synchronization and phase noise reduction in micromechanical oscillator arrays coupled through light. Phys. Rev. Lett. 115, 163902 (2015).

    Article  ADS  Google Scholar 

  27. Heinrich, G., Ludwig, M., Qian, J., Kubala, B. & Marquardt, F. Collective dynamics in optomechanical arrays. Phys. Rev. Lett. 107, 043603 (2011).

    Article  ADS  Google Scholar 

  28. Leonetti, M., Conti, C. & Lopez, C. The mode-locking transition of random lasers. Nat. Photon. 5, 615–617 (2011).

    Article  ADS  Google Scholar 

  29. Tretiakov, K. V., Bishop, K. J. M. & Grzybowski, B. A. The dependence between forces and dissipation rates mediating dynamic self-assembly. Soft Matter 5, 1279–1284 (2009).

    Article  ADS  Google Scholar 

  30. Snezhko, A., Aranson, I. S. & Kwok, W.-K. Structure formation in electromagnetically driven granular media. Phys. Rev. Lett. 94, 108002 (2005).

    Article  ADS  Google Scholar 

  31. Osterman, N. et al. Field-induced self-assembly of suspended colloidal membranes. Phys. Rev. Lett. 103, 228301 (2009).

    Article  ADS  Google Scholar 

  32. Uspal, W. E. & Doyle, P. S. Self-organizing microfluidic crystals. Soft Matter 10, 5177–5191 (2014).

    Article  ADS  Google Scholar 

  33. Morin, A., Desreumaux, N., Caussin, J.-B. & Bartolo, D. Distortion and destruction of colloidal flocks in disordered environments. Nat. Phys. 13, 63–67 (2017).

    Article  Google Scholar 

  34. Snezhko, A., Aranson, I. S. & Kwok, W.-K. Surface wave assisted self-assembly of multidomain magnetic structures. Phys. Rev. Lett. 96, 078701 (2006).

    Article  ADS  Google Scholar 

  35. Timonen, J. V. I., Latikka, M., Leibler, L., Ras, R. H. A. & Ikkala, O. Switchable static and dynamic self-assembly of magnetic droplets on superhydrophobic surfaces. Science 341, 253–257 (2013).

    Article  ADS  Google Scholar 

  36. Morin, A. & Bartolo, D. Flowing active liquids in a pipe: hysteretic response of polar flocks to external fields. Phys. Rev. X 8, 021037 (2018).

    Google Scholar 

  37. Maier, S. A. & Atwater, H. A. Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures. J. Appl. Phys. 98, 011101 (2005).

    Article  ADS  Google Scholar 

  38. Mookherjea, S., Park, J. S., Yang, S.-H. & Bandaru, P. R. Localization in silicon nanophotonic slow-light waveguides. Nat. Photon. 2, 90–93 (2008).

    Article  ADS  Google Scholar 

  39. Carmon, T., Yang, L. & Vahala, K. J. Dynamical thermal behavior and thermal self-stability of microcavities. Opt. Express 12, 4742–4750 (2004).

    Article  ADS  Google Scholar 

  40. Green, M. A. Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients. Sol. Energy Mater. Sol. Cells 92, 1305–1310 (2008).

    Article  Google Scholar 

  41. Hölke, A. & Henderson, H. T. Ultra-deep anisotropic etching of (110) silicon. J. Micromech. Microeng. 9, 51 (1999).

    Article  ADS  Google Scholar 

  42. Lipson, A. & Yeatman, E. M. Low-loss one-dimensional photonic bandgap filter in (110) silicon. Opt. Lett. 31, 395–397 (2006).

    Article  ADS  Google Scholar 

  43. Fu, C. J. & Zhang, Z. M. Nanoscale radiation heat transfer for silicon at different doping levels. Int. J. Heat Mass Transf. 49, 1703–1718 (2006).

    Article  Google Scholar 

  44. Yamada, S., Song, B.-S., Asano, T. & Noda, S. Experimental investigation of thermo-optic effects in SiC and Si photonic crystal nanocavities. Opt. Lett. 36, 3981–3983 (2011).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Laboratory Directed Research and Development Program (Non-Equilibrium Metamaterials,18-174) of Lawrence Berkeley National Laboratory under US Department of Energy contract no. DE-AC02-05CH11231 for theory and optical design and measurement. Sample fabrication at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231. Support was also provided by the King Abdullah University of Science and Technology Office of Sponsored Research (OSR) (award OSR-2016-CRG5-2950-03) for data analysis.

Author information

Author notes

  1. These authors contributed equally: Chad Ropp, Nicolas Bachelard.

Authors and Affiliations

  1. NSF Nanoscale Science and Engineering Center, University of California, Berkeley, CA, USA

    Chad Ropp, Nicolas Bachelard, David Barth, Yuan Wang & Xiang Zhang

  2. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Yuan Wang & Xiang Zhang

  3. University of Hong Kong, Hong Kong, China

    Xiang Zhang

Authors
  1. Chad Ropp
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nicolas Bachelard
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David Barth
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

C.R. and N.B. designed and conducted experiments and performed the theoretical investigation. C.R. and D.B. performed sample fabrication. X.Z. and Y.W. guided the research. All authors contributed to writing the manuscript.

Corresponding author

Correspondence to Xiang Zhang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains Supplementary Figures 1–10.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ropp, C., Bachelard, N., Barth, D. et al. Dissipative self-organization in optical space. Nature Photon 12, 739–743 (2018). https://doi.org/10.1038/s41566-018-0278-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-018-0278-1

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

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