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.

  • Article
  • Published:

Coherent control of chaotic optical microcavity with reflectionless scattering modes

Nature Physics volume 20, pages 109–115 (2024)Cite this article

Subjects

Abstract

Non-Hermitian wave engineering has attracted a surge of interest in photonics in recent years. Prominent non-Hermitian phenomena include coherent perfect absorption and its generalization, reflectionless scattering modes, in which electromagnetic scattering at the input ports is suppressed due to critical coupling with the power leaked to output ports, and interference phenomena. These concepts are ideally suited to enable real-time dynamic control over absorption, scattering and radiation. Nonetheless, reflectionless scattering modes have not been observed in complex photonic platforms involving open systems and multiple inputs. Here we demonstrate the emergence of reflectionless scattering modes in a chaotic photonic microcavity involving over a thousand optical modes. We model the optical fields in a silicon stadium microcavity within a quasi-normal mode expansion, which is able to capture a dense family of reflection zeros at the input ports, associated with reflectionless scattering modes. We observe non-Hermitian degeneracies of reflectionless scattering modes in the telecommunication wavelength band, enabling efficient dynamic control over light radiation from the cavity.

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: Simulations of RSMs in a chaotic optical microresonator.
Fig. 2: Experimental set-up and chaotic optical microresonator system.
Fig. 3: Experimental results for chaotic RSMs.
Fig. 4: Experimental measurement of emission field intensities.
Fig. 5: Experimental results of the degeneracy of chaotic RSMs.

Similar content being viewed by others

Data availability

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

Code availability

The codes and the in-house software used in this work are available upon request to the corresponding authors.

References

  1. El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).

    Article  Google Scholar 

  2. Bergholtz, E. J., Budich, J. C. & Kunst, F. K. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93, 015005 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  3. Özdemir, K., Rotter, S., Nori, F. & Yang, L. Parity–time symmetry and exceptional points in photonics. Nat. Mater. 18, 783–798 (2019).

    Article  ADS  Google Scholar 

  4. Bender, C. M. & Boettcher, S. Real spectra in non-Hermitian Hamiltonians having P T symmetry. Phys. Rev. Lett. 80, 5243 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  5. Miri, M. A. & Alù, A. Exceptional points in optics and photonics. Science 363, eaar7709 (2019).

    Article  MathSciNet  Google Scholar 

  6. Wang, C. et al. Electromagnetically induced transparency at a chiral exceptional point. Nat. Phys. 16, 334–340 (2020).

    Article  ADS  Google Scholar 

  7. Chong, Y. D., Ge, L., Cao, H. & Stone, A. D. Coherent perfect absorbers: time-reversed lasers. Phys. Rev. Lett. 105, 053901 (2010).

    Article  ADS  Google Scholar 

  8. Wan, W. et al. Time-reversed lasing and interferometric control of absorption. Science 331, 889–892 (2011).

    Article  ADS  Google Scholar 

  9. Pichler, K. et al. Random anti-lasing through coherent perfect absorption in a disordered medium. Nature 567, 351–355 (2019).

    Article  ADS  Google Scholar 

  10. Imani, F. M., Smith, D. R. & del Hougne, P. Perfect absorption in a disordered medium with programmable meta-atom inclusions. Adv. Funct. Mater. 30, 2005310 (2020).

    Article  Google Scholar 

  11. Sol, J., Alhulaymi, A., Stone, A. D. & del Hougne, P. Reflectionless programmable signal routers. Sci. Adv. 9, eadf0323 (2023).

    Article  Google Scholar 

  12. Baranov, D. G., Krasnok, A., Shegai, T., Alù, A. & Chong, Y. Coherent perfect absorbers: linear control of light with light. Nat. Rev. Mater. 2, 17064 (2017).

    Article  ADS  Google Scholar 

  13. Stone, A. D., Sweeney, W. R., Hsu, C. W., Wisal, K. & Wang, Z. Reflectionless excitation of arbitrary photonic structures: a general theory. Nanophotonics 10, 343–360 (2021).

    Article  Google Scholar 

  14. Wang, C., Sweeney, W. R., Stone, A. D. & Yang, L. Coherent perfect absorption at an exceptional point. Science 373, 1261–1265 (2021).

    Article  ADS  Google Scholar 

  15. Müllers, A. et al. Coherent perfect absorption of nonlinear matter waves. Sci. Adv. 4, eaat6539 (2018).

    Article  ADS  Google Scholar 

  16. Roger, T. et al. Coherent perfect absorption in deeply subwavelength films in the single-photon regime. Nat. Commun. 6, 7031 (2015).

    Article  ADS  Google Scholar 

  17. Sun, Y., Tan, W., Li, H. Q., Li, J. & Chen, H. Experimental demonstration of a coherent perfect absorber with pt phase transition. Phys. Rev. Lett. 112, 143903 (2014).

    Article  ADS  Google Scholar 

  18. Slobodkin, Y. et al. Massively degenerate coherent perfect absorber for arbitrary wavefronts. Science 377, 995–998 (2022).

    Article  ADS  Google Scholar 

  19. Soleymani, S. et al. Chiral and degenerate perfect absorption on exceptional surfaces. Nat. Commun. 13, 599 (2022).

    Article  ADS  Google Scholar 

  20. Derode, A., Tourin, A. & Fink, M. Random multiple scattering of ultrasound. I. Coherent and ballistic waves. Phys. Rev. E 64, 036605 (2001).

    Article  ADS  Google Scholar 

  21. Mosk, A. P., Lagendijk, A., Lerosey, G. & Fink, M. Controlling waves in space and time for imaging and focusing in complex media. Nat. Photon. 6, 283–292 (2012).

    Article  ADS  Google Scholar 

  22. del Hougne, P., Lemoult, F., Fink, M. & Lerosey, G. Spatiotemporal wave front shaping in a microwave cavity. Phys. Rev. Lett. 117, 134302 (2016).

    Article  ADS  Google Scholar 

  23. Rotter, S. & Gigan, S. Light fields in complex media: mesoscopic scattering meets wave control. Rev. Mod. Phys. 89, 015005 (2017).

    Article  ADS  Google Scholar 

  24. Chen, L., Kottos, T. & Anlage, S. M. Perfect absorption in complex scattering systems with or without hidden symmetries. Nat. Commun. 11, 5826 (2020).

    Article  ADS  Google Scholar 

  25. Li, H., Suwunnarat, S., Fleischmann, R., Schanz, H. & Kottos, T. Random matrix theory approach to chaotic coherent perfect absorbers. Phys. Rev. Lett. 118, 044101 (2017).

    Article  ADS  Google Scholar 

  26. Choi, Y., Hahn, C., Yoon, J. W., Song, S. H. & Berini, P. Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points. Nat. Commun. 8, 14154 (2017).

    Article  ADS  Google Scholar 

  27. Wang, H., Assawaworrarit, S. & Fan, S. Dynamics for encircling an exceptional point in a nonlinear non-Hermitian system. Opt. Lett. 44, 638–641 (2019).

    Article  ADS  Google Scholar 

  28. Alaee, R., Vaddi, Y. & Boyd, R. W. Dynamic coherent perfect absorption in nonlinear metasurfaces. Opt. Lett. 45, 6414–6417 (2020).

    Article  ADS  Google Scholar 

  29. Soriano, M. C., García-Ojalvo, J., Mirasso, C. R. & Fischer, I. Complex photonics: dynamics and applications of delay-coupled semiconductors lasers. Rev. Mod. Phys. 85, 421–470 (2013).

    Article  ADS  Google Scholar 

  30. Bender, N. et al. Depth-targeted energy delivery deep inside scattering media. Nat. Phys. 18, 309–315 (2022).

    Article  Google Scholar 

  31. Redding, B. et al. Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging. Proc. Natl Acad. Sci. USA 112, 1304–1309 (2015).

    Article  ADS  Google Scholar 

  32. VanWiggeren, G. D. & Roy, R. Communication with chaotic lasers. Science 279, 1198–1200 (1998).

    Article  ADS  Google Scholar 

  33. Argyris, A. et al. Chaos-based communications at high bit rates using commercial fibre-optic links. Nature 438, 343–346 (2005).

    Article  ADS  Google Scholar 

  34. Cao, H. & Wiersig, J. Dielectric microcavities: model systems for wave chaos and non-Hermitian physics. Rev. Mod. Phys. 87, 61–111 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  35. Jiang, X. et al. Chaos-assisted broadband momentum transformation in optical microresonators. Science 358, 344–347 (2017).

    Article  ADS  Google Scholar 

  36. Jiang, X., Qavi, A. J., Huang, S. H. & Yang, L. Whispering-gallery sensors. Matter 3, 371–392 (2020).

    Article  Google Scholar 

  37. Kullig, J., Jiang, X., Yang, L. & Wiersig, J. Microstar cavities: an alternative concept for the confinement of light. Phys. Rev. Res. 2, 012072 (2020).

    Article  Google Scholar 

  38. Shao, L. et al. Detection of single nanoparticles and lentiviruses using microcavity resonance broadening. Adv. Mater. 25, 5616–5620 (2013).

    Article  Google Scholar 

  39. Jiang, X. F. et al. Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities. Adv. Mater. 24, OP260–OP264 (2012).

    Google Scholar 

  40. Jiang, X.-F. et al. Free-space coupled, ultralow-threshold Raman lasing from a silica microcavity. Appl. Phys. Lett. 103, 101102 (2013).

    Article  ADS  Google Scholar 

  41. Jiang, X.-F., Zou, C.-L., Wang, L., Gong, Q. & Xiao, Y.-F. Whispering-gallery microcavities with unidirectional laser emission. Laser Photon. Rev. 10, 40–61 (2016).

    Article  ADS  Google Scholar 

  42. Yang, Q. F., Jiang, X. F., Cui, Y. L., Shao, L. & Xiao, Y. F. Dynamical tunneling-assisted coupling of high-Q deformed microcavities using a free-space beam. Phys. Rev. A 88, 023810 (2013).

    Article  ADS  Google Scholar 

  43. Türeci, H. E., Schwefel, H. G. L., Jacquod, P. & Stone, A. D. in Progress in Optics Vol. 47 (ed. Wolf, E.) 75–137 (Elsevier, 2005).

  44. Benzaouia, M., Joannopoulos, J. D., Johnson, S. G. & Karalis, A. Quasi-normal mode theory of the scattering matrix, enforcing fundamental constraints for truncated expansions. Phys. Rev. Res. 3, 033228 (2021).

    Article  Google Scholar 

  45. Sweeney, W. R., Hsu, C. W. & Stone, A. D. Theory of reflectionless scattering modes. Phys. Rev. A 102, 063511 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  46. Fyodorov, Y. V., Suwunnarat, S. & Kottos, T. Distribution of zeros of the S-matrix of chaotic cavities with localized losses and coherent perfect absorption: non-perturbative results. J. Phys. A 50, 30LT01 (2017).

    Article  MathSciNet  Google Scholar 

  47. Hentschel, M., Schomerus, H. & Schubert, R. Husimi functions at dielectric interfaces: inside-outside duality for optical systems and beyond. Europhys. Lett. 62, 636–642 (2003).

    Article  ADS  Google Scholar 

  48. Bittner, S. et al. Suppressing spatiotemporal lasing instabilities with wave-chaotic microcavities. Science 361, 1225–1231 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  49. Monifi, F. et al. Optomechanically induced stochastic resonance and chaos transfer between optical fields. Nat. Photon. 10, 399–405 (2016).

    Article  ADS  Google Scholar 

  50. Zhang, J. et al. Optomechanical dissipative solitons. Nature 600, 75–80 (2021).

    Article  ADS  Google Scholar 

  51. Horodynski, M., Kühmayer, M., Ferise, C., Rotter, S. & Davy, M. Anti-reflection structure for perfect transmission through complex media. Nature 607, 281–286 (2022).

    Article  ADS  Google Scholar 

  52. Türeci, H. E., Ge, L., Rotter, S. & Stone, A. D. Strong interactions in multimode random lasers. Science 320, 643–646 (2008).

    Article  ADS  Google Scholar 

  53. Redding, B., Choma, M. A. & Cao, H. Speckle-free laser imaging using random laser illumination. Nat. Photon. 6, 355–359 (2012).

    Article  ADS  Google Scholar 

  54. Almeida, V. R., Panepucci, R. R. & Lipson, M. Nanotaper for compact mode conversion. Opt. Lett. 28, 1302–1304 (2003).

    Article  ADS  Google Scholar 

  55. Balay, S. et al. PETSc Users Manual (Argonne National Laboratory, 2019).

  56. Vicente, H., Roman, J. E. & Vidal, V. SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31, 351–362 (2005).

    Article  MathSciNet  Google Scholar 

  57. Kucukcoban, S. & Kallivokas, L. F. A symmetric hybrid formulation for transient wave simulations in PML-truncated heterogeneous media. Wave Motion 50, 57–79 (2013).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

We thank Z. Li at Stevens Institute of Technology for polishing the edge couplers. This work was supported by the Air Force Office of Scientific Research and the Simons Foundation. Fabrication of samples for this work was performed at the Nanofabrication Facility at the Advanced Science Research Center at The Graduate Center of the City University of New York.

Author information

Author notes

  1. These authors contributed equally: Xuefeng Jiang, Shixiong Yin.

Authors and Affiliations

  1. Photonics Initiative, Advanced Science Research Center, The City University of New York, New York, NY, USA

    Xuefeng Jiang, Shixiong Yin, Huanan Li, Jiamin Quan, Heedong Goh, Michele Cotrufo & Andrea Alù

  2. Department of Electrical Engineering, City College, The City University of New York, New York, NY, USA

    Shixiong Yin & Andrea Alù

  3. MOE Key Laboratory of Weak-Light Nonlinear Photonics, School of Physics, Nankai University, Tianjin, China

    Huanan Li

  4. Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Julius Kullig & Jan Wiersig

  5. Physics Program, The Graduate Center, The City University of New York, New York, NY, USA

    Andrea Alù

Authors
  1. Xuefeng Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shixiong Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huanan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiamin Quan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Heedong Goh
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Michele Cotrufo
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Julius Kullig
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Jan Wiersig
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Andrea Alù
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

X.J., S.Y. and A.A. conceived the project. X.J. fabricated the device and designed the experiments. X.J. and S.Y. performed the experiments and analysed experimental data with help from J.Q., M.C. and A.A. Theoretical studies and full-wave simulations were performed by S.Y. with help from X.J., H.L., J.K., J.W. and A.A. Study of reflection zeros were performed by H.G. and S.Y. All authors discussed the results. A.A. supervised the project. X.J., S.Y. and A.A. wrote the paper with input from all co-authors.

Corresponding author

Correspondence to Andrea Alù.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks A. Stone 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 Figs. 1–9 and Discussion Sections I–VIII.

Source data

Source Data Fig. 1

b, Eigenfrequencies across Re(kR) = 25.0–29.2. c, Mode contributions from 47 notable quasi-normal modes. d, Magnitudes of the eigenvalues of the truncated scattering matrix. e, Complex reflection zeros across Re(kR) = 25.0–29.2.

Source Data Fig. 3

a, Reflectance across 1,520–1,545 nm for different relative phases. b–c, Reflectance at RSM(±) for different relative phases. d,g, Two-dimensional data of Husimi plots.

Source Data Fig. 4

Radiated power at different relative phases.

Source Data Fig. 5

a, Reflectance at RSM degeneracy for different relative phases. b, Radiated power at different relative phases at RSM degeneracy. d, Radiated power at different relative phases at different angles at RSM degeneracy.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, X., Yin, S., Li, H. et al. Coherent control of chaotic optical microcavity with reflectionless scattering modes. Nat. Phys. 20, 109–115 (2024). https://doi.org/10.1038/s41567-023-02242-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-023-02242-w

This article is cited by

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