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Output control of dissipative nonlinear multimode amplifiers using spacetime symmetry mapping

Nature Physics volume 21, pages 839–845 (2025)Cite this article

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Abstract

In many linear and nonlinear systems, time-reversal symmetry makes it possible to control the output waves by appropriately shaping the input waves. However, time-reversal symmetry is broken in systems with energy dissipation, necessitating a different approach for relating the input and output fields. We theoretically consider a saturated multimode fibre amplifier in which light generates a heat flow and suffers thermo-optical nonlinearity, thus breaking time-reversal symmetry. We identify a spacetime symmetry that maps the target output back to an input field. This spacetime symmetry mapping applies phase conjugation, gain and absorption substitution but not time reversal, and it holds in a steady state and for slowly varying inputs. Our approach enables coherent wavefront control of nonlinear dissipative systems.

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Fig. 1: Steady-state time-reversal of a multimode amplifier with thermo-optical nonlinearity and linear gain.
Fig. 2: Focusing through a nonlinear multimode amplifier with gain saturation.
Fig. 3: Spacetime symmetry mapping of a dynamic nonlinear amplifier.

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Data availability

The data are available via Zenodo at https://doi.org/10.5281/zenodo.14190653 (ref. 51).

Code availability

The codes are available at https://github.com/joe851642001/MWAT.

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Acknowledgements

We thank Y. Eliezer for assisting in establishing the time-domain simulation code. We also thank A. Yamilov, O. D. Miller and S. Fan for fruitful discussions. This work is supported by the Air Force Office of Scientific Research (Grant No. FA9550-24-1-0182 to H.C. and A.D.S.) and by the Simons Foundation (A.D.S. and M.F.). We acknowledge the computational resources provided by the Yale High Performance Computing Cluster.

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Author notes

  1. These authors contributed equally: Chun-Wei Chen, Kabish Wisal.

Authors and Affiliations

  1. Department of Applied Physics, Yale University, New Haven, CT, USA

    Chun-Wei Chen, A. Douglas Stone & Hui Cao

  2. Department of Physics, Yale University, New Haven, CT, USA

    Kabish Wisal

  3. Institut Langevin, ESPCI Paris, CNRS, PSL University, Paris, France

    Mathias Fink

Authors
  1. Chun-Wei Chen
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  2. Kabish Wisal
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  3. Mathias Fink
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Contributions

H.C. proposed the idea and initiated this project. C.-W.C. performed the numerical simulations under the supervision of H.C. K.W. performed the theoretical analysis under the supervision of A.D.S. M.F. provided key insights that shaped the scope of this study. C.-W.C., K.W., A.D.S. and H.C. wrote the paper with input from M.F.

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Correspondence to Hui Cao.

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Nature Physics thanks Mario Ferraro and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Sections I–VIII and Figs. 1–3.

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Chen, CW., Wisal, K., Fink, M. et al. Output control of dissipative nonlinear multimode amplifiers using spacetime symmetry mapping. Nat. Phys. 21, 839–845 (2025). https://doi.org/10.1038/s41567-025-02853-5

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