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.

Interaction and co-assembly of optical and topological solitons

Abstract

Solitons attract a great deal of interest in many fields, ranging from optics to fluid mechanics, cosmology, particle physics and condensed matter. However, solitons of these very different types rarely coexist and interact with each other. Here we develop a system that hosts optical solitons coexisting with topological solitonic structures localized in the molecular alignment field of a soft birefringent medium. We experimentally demonstrate and theoretically explain optomechanical interactions between such optical and topological solitons, mediated by the local transfer of momentum between light and matter and the nonlocal orientational elasticity of the liquid-crystal phase used in our system. We show that the delicate balance arising from these different contributions to the optomechanical force enables facile dynamical control and spatial localization of topological solitons. Our findings reveal unusual solitonic tractor beams and emergent light–matter self-patterning phenomena that could aid in creating new breeds of nonlinear photonic materials and devices.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Host system with coexisting topological and optical solitons.
Fig. 2: Properties of spin–orbit solitons.
Fig. 3: Spin–orbit soliton interactions with torons.
Fig. 4: Properties of bouncing solitons.
Fig. 5: Bouncing optical soliton interactions with torons.

Data availability

All data and postprocessing scripts are available from the Zenodo repository (https://doi.org/10.5281/zenodo.6394431). Polarized optical microscopy simulations were performed using the open-source software Nemaktis (https://github.com/warthan07/Nemaktis and https://doi.org/10.5281/zenodo.4695959).

References

  1. Guo, B., Pang, X.-F., Wang, Y.-F. & Liu, N. Solitons (De Gruyter, 2018).

  2. Korteweg, D. J. & De Vries, G. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Lond. Edinb. Dubl. Philos. Mag. J. Sci. 39, 422–443 (1895).

    MathSciNet  MATH  Article  Google Scholar 

  3. Philbin, T. G. et al. Fiber-optical analog of the event horizon. Science 319, 1367–1370 (2008).

    ADS  Article  Google Scholar 

  4. Lautrup, B., Appali, R., Jackson, A. & Heimburgb, T. The stability of solitons in biomembranes and nerves. Eur. Phys. J. E 34, 57 (2011).

    Article  Google Scholar 

  5. Skyrme, T. H. R. Particle states of a quantized meson field. Proc. R. Soc. Lond. A 262, 237–245 (1961).

    ADS  MathSciNet  MATH  Article  Google Scholar 

  6. Frieman, J. A., Olinto, A. V., Gleiser, M. & Alcock, C. Cosmic evolution of nontopological solitons. Phys. Rev. D 40, 3241–3251 (1989).

    ADS  Article  Google Scholar 

  7. Shnir, Y. M. Gravitating Hopfions. J. Exp. Theor. Phys. 121, 991–997 (2015).

    ADS  Article  Google Scholar 

  8. Shnir, Y. M. Topological and Non-Topological Solitons in Scalar Field Theories (Cambridge Univ. Press, 2018).

  9. Chen, Z., Segev, M. & Christodoulides, D. N. Optical spatial solitons: historical overview and recent advances. Rep. Prog. Phys. 75, 086401 (2012).

    ADS  Article  Google Scholar 

  10. Stegeman, G. I. & Segev, M. Optical spatial solitons and their interactions: universality and diversity. Science 286, 1518–1523 (1999).

    Article  Google Scholar 

  11. Conti, C., Peccianti, M. & Assanto, G. Observation of optical spatial solitons in a highly nonlocal medium. Phys. Rev. Lett. 92, 113902 (2004).

    ADS  Article  Google Scholar 

  12. Assanto, G. (ed.) Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals (Wiley, 2013).

  13. Assanto, G. & Smyth, N. F. Self-confined light waves in nematic liquid crystals. Physica D 402, 132182 (2020).

    MathSciNet  Article  Google Scholar 

  14. Peccianti, M., Conti, C., Assanto, G., De Luca, A. & Umeton, C. Routing of anisotropic spatial solitons and modulational instability in liquid crystals. Nature 432, 733–737 (2004).

    ADS  Article  Google Scholar 

  15. Peccianti, M., Dyadyusha, A., Kaczmarek, M. & Assanto, G. Tunable refraction and reflection of self-confined light beams. Nat. Phys. 2, 737–742 (2006).

    Article  Google Scholar 

  16. Peccianti, M., Assanto, G., Dyadyusha, A. & Kaczmarek, M. Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media. Phys. Rev. Lett. 98, 113902 (2007).

    ADS  Article  Google Scholar 

  17. Piccardi, A., Assanto, G., Lucchetti, L. & Simoni, F. All-optical steering of soliton waveguides in dye-doped liquid crystals. Appl. Phys. Lett. 93, 171104 (2008).

    ADS  Article  Google Scholar 

  18. Izdebskaya, Y. V., Desyatnikov, A. S. & Kivshar, Y. S. Self-induced mode transformation in nonlocal nonlinear media. Phys. Rev. Lett. 111, 123902 (2013).

    ADS  Article  Google Scholar 

  19. Alberucci, A., Piccardi, A., Kravets, N., Buchnev, O. & Assanto, G. Soliton enhancement of spontaneous symmetry breaking. Optica 2, 783–789 (2015).

    ADS  Article  Google Scholar 

  20. Kravets, N. et al. Bistability with optical beams propagating in a reorientational medium. Phys. Rev. Lett. 113, 023901 (2014).

    ADS  Article  Google Scholar 

  21. Perumbilavil, S. et al. Beaming random lasers with soliton control. Nat. Commun. 9, 3863 (2018).

    ADS  Article  Google Scholar 

  22. Fratalocchi, A., Assanto, G., Brzdąkiewicz, K. A. & Karpierz, M. A. Discrete light propagation and self-trapping in liquid crystals. Opt. Express 13, 1808–1815 (2005).

    ADS  Article  Google Scholar 

  23. Henninot, J., Debailleul, M. & Warenghem, M. Tunable non-locality of thermal non-linearity in dye doped nematic liquid crystal. Mol. Cryst. Liq. Cryst. 375, 631–640 (2002).

    Article  Google Scholar 

  24. Piccardi, A., Alberucci, A., Tabiryan, N. & Assanto, G. Dark nematicons. Opt. Lett. 36, 1356–1358 (2011).

    ADS  Article  Google Scholar 

  25. Karpierz, M. A. Solitary waves in liquid crystalline waveguides. Phys. Rev. E 66, 036603 (2002).

    ADS  Article  Google Scholar 

  26. Jisha, C. P., Alberucci, A., Beeckman, J. & Nolte, S. Self-trapping of light using the Pancharatnam–Berry phase. Phys. Rev. X 9, 021051 (2019).

    Google Scholar 

  27. Assanto, G. & Smyth, N. F. Spin-optical solitons in liquid crystals. Phys. Rev. A 102, 033501 (2020).

    ADS  Article  Google Scholar 

  28. Laudyn, U. A., Kwasny, M. & Karpierz, M. A. Nematicons in chiral nematic liquid crystals. Appl. Phys. Lett. 94, 091110 (2009).

    ADS  Article  Google Scholar 

  29. Poy, G., Hess, A. J., Smalyukh, I. I. & Žumer, S. Chirality-enhanced periodic self-focusing of light in soft birefringent media. Phys. Rev. Lett. 125, 077801 (2020).

    ADS  Article  Google Scholar 

  30. Lam, L. & Prost, J. (eds) Solitons in Liquid Crystals (Springer, 2012).

  31. Smalyukh, I. I. Review: knots and other new topological effects in liquid crystals and colloids. Rep. Prog. Phys. 83, 106601 (2020).

    ADS  MathSciNet  Article  Google Scholar 

  32. Smalyukh, I. I., Lansac, Y., Clark, N. A. & Trivedi, R. P. Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids. Nat. Mater. 9, 139–145 (2010).

    ADS  Article  Google Scholar 

  33. Ackerman, P. J. & Smalyukh, I. I. Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions. Phys. Rev. X 7, 011006 (2017).

    Google Scholar 

  34. Oswald, P., Baudry, J. & Pirkl, S. Static and dynamic properties of cholesteric fingers in electric field. Phys. Rep. 337, 67–96 (2000).

    ADS  Article  Google Scholar 

  35. Ackerman, P. J. et al. Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities. Sci. Rep. 2, 414 (2012).

    Article  Google Scholar 

  36. Loussert, C. & Brasselet, E. Multiple chiral topological states in liquid crystals from unstructured light beams. Appl. Phys. Lett. 104, 051911 (2014).

    ADS  Article  Google Scholar 

  37. Hu, C. & Whinnery, J. R. Losses of a nematic liquid-crystal optical waveguide. J. Opt. Soc. Am. 64, 1424–1432 (1974).

    ADS  Article  Google Scholar 

  38. Karpierz, M. A., Sierakowski, M., Świłło, M. & Woliński, T. Self focusing in liquid crystalline waveguides. Mole. Cryst. Liq. Cryst. A 320, 157–163 (1998).

    Article  Google Scholar 

  39. Kwasny, M. et al. Self-guided beams in low-birefringence nematic liquid crystals. Phys. Rev. A 86, 013824 (2012).

    ADS  Article  Google Scholar 

  40. Hess, A. J., Poy, G., Tai, J.-S. B., Žumer, S. & Smalyukh, I. I. Control of light by topological solitons in soft chiral birefringent media. Phys. Rev. X 10, 031042 (2020).

    Google Scholar 

  41. Chen, J., Ng, J., Lin, Z. & Chan, C. Optical pulling force. Nat. Photonics 5, 531–534 (2011).

    ADS  Article  Google Scholar 

  42. Sohn, H. R. & Smalyukh, I. I. Electrically powered motions of toron crystallites in chiral liquid crystals. Proc. Natl. Acad. Sci. USA 117, 6437–6445 (2020).

  43. Sohn, H. R., Liu, C. D. & Smalyukh, I. I. Schools of skyrmions with electrically tunable elastic interactions. Nat. Commun. 10, 4744 (2019).

    ADS  Article  Google Scholar 

  44. Sohn, H. R., Liu, C. D., Wang, Y. & Smalyukh, I. I. Light-controlled skyrmions and torons as reconfigurable particles. Opt. Express 27, 29055–29068 (2019).

    ADS  Article  Google Scholar 

  45. Minardi, S. et al. Three-dimensional light bullets in arrays of waveguides. Phys. Rev. Lett. 105, 263901 (2010).

    ADS  Article  Google Scholar 

  46. Tai, J.-S. B. & Smalyukh, I. I. Three-dimensional crystals of adaptive knots. Science 365, 1449–1453 (2019).

    ADS  Article  Google Scholar 

  47. Giomi, L., Kos, Ž., Ravnik, M. & Sengupta, A. Cross-talk between topological defects in different fields revealed by nematic microfluidics. Proc. Natl. Acad. Sci. USA 114, E5771–E5777 (2017).

  48. Everts, J. C. & Ravnik, M. Complex electric double layers in charged topological colloids. Sci. Rep. 8, 14119 (2018).

    ADS  Article  Google Scholar 

  49. Aplinc, J., Pusovnik, A. & Ravnik, M. Designed self-assembly of metamaterial split-ring colloidal particles in nematic liquid crystals. Soft Matter 15, 5585–5595 (2019).

    ADS  Article  Google Scholar 

  50. Fert, A., Reyren, N. & Cros, V. Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 17031 (2017).

    ADS  Article  Google Scholar 

  51. Pandey, M. et al. Self-assembly of skyrmion-dressed chiral nematic colloids with tangential anchoring. Phys. Rev. E 89, 060502 (2014).

    ADS  Article  Google Scholar 

  52. Pandey, M. et al. Topology and self-assembly of defect-colloidal superstructure in confined chiral nematic liquid crystals. Phys. Rev. E 91, 012501 (2015).

    ADS  Article  Google Scholar 

  53. Evans, J. S., Ackerman, P. J., Broer, D. J., van de Lagemaat, J. & Smalyukh, I. I. Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles. Phys. Rev. E 87, 032503 (2013).

    ADS  Article  Google Scholar 

  54. Peccianti, M., Fratalocchi, A. & Assanto, G. Transverse dynamics of nematicons. Opt. Express 12, 6524–6529 (2004).

    ADS  Article  Google Scholar 

  55. Alberucci, A., Peccianti, M. & Assanto, G. Nonlinear bouncing of nonlocal spatial solitons at the boundaries. Opt. Lett. 32, 2795–2797 (2007).

    ADS  Article  Google Scholar 

  56. Alberucci, A. et al. Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal. Phys. Rev. A 79, 043816 (2009).

    ADS  Article  Google Scholar 

  57. Harris, C. R. et al. Array programming with NumPy. Nature 585, 357–362 (2020).

    ADS  Article  Google Scholar 

  58. Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).

    Article  Google Scholar 

  59. Nieminen, T. A. et al. Optical tweezers: theory and modelling. J. Quant. Spectrosc. Radiat. Transf. 146, 59–80 (2014).

    ADS  Article  Google Scholar 

  60. Poy, G. & Žumer, S. Physics-based multistep beam propagation in inhomogeneous birefringent media. Opt. Express 28, 24327–24342 (2020).

    ADS  Article  Google Scholar 

  61. Piccirillo, B. & Santamato, E. Light angular momentum flux and forces in birefringent inhomogeneous media. Phys. Rev. E 69, 056613 (2004).

    ADS  Article  Google Scholar 

  62. Poy, G. & Žumer, S. Ray-based optical visualisation of complex birefringent structures including energy transport. Soft Matter 15, 3659–3670 (2019).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

Experimental research at CU-Boulder was supported by the National Science Foundation through grant DMR-1810513 (A.J.H., A.J.S., M.P. and I.I.S.). G.P. and S.Ž. acknowledge funding from the ARSS (Javna Agencija za Raziskovalno Dejavnost RS) through grant P1-0099 and from the European Union’s Horizon 2020 programme through the Marie Sklodowska-Curie grant agreement no. 834256 and COST European Topology Interdisciplinary Action (EUTOPIA CA17139). A.J.H. thanks the United States’ Office of Science Graduate Student Research (SCGSR) Fellowship for partial project support. A.J.H. also thanks the United States’ National Renewable Energy Laboratory and its Technology Transfer Office for remuneration from the Technology Licensing and Commercialization Fellowship while data were analysed and the manuscript was written. I.I.S. also acknowledges the hospitality of the Chirality Research Center (CResCent) at the University of Hiroshima, Japan, during his sabbatical stay, where he was partly working on this article. We thank P. Ackerman, Y. Yuan, T. Lee and H. Mundoor for discussions.

Author information

Authors and Affiliations

Authors

Contributions

A.J.H., A.J.S. and M.P. performed the experiments. A.J.H. built the experimental setup and oversaw the systematic collection of experimental data. A.J.H. and G.P. analysed the data. G.P. wrote postprocessing scripts to analyse experimental toron trajectories, designed the theoretical framework and realized numerical simulations to explain the experimental findings. G.P., A.J.H., S.Ž. and I.I.S. wrote the paper, with feedback from all authors. I.I.S. conceived the project and initiated the collaboration. S.Ž. supervised the theoretical research and I.I.S. supervised the experimental research.

Corresponding author

Correspondence to Ivan I. Smalyukh.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Alexander Szameit and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Sections 1–4 and Figs. 1–6.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Poy, G., Hess, A.J., Seracuse, A.J. et al. Interaction and co-assembly of optical and topological solitons. Nat. Photon. 16, 454–461 (2022). https://doi.org/10.1038/s41566-022-01002-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-022-01002-1

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