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# Random anti-lasing through coherent perfect absorption in a disordered medium

## Abstract

Non-Hermitian wave engineering is a recent and fast-moving field that examines both fundamental and application-oriented phenomena1,2,3,4,5,6,7. One such phenomenon is coherent perfect absorption8,9,10,11—an effect commonly referred to as ‘anti-lasing’ because it corresponds to the time-reversed process of coherent emission of radiation at the lasing threshold (where all radiation losses are exactly balanced by the optical gain). Coherent perfect absorbers (CPAs) have been experimentally realized in several setups10,11,12,13,14,15,16,17,18, with the notable exception of a CPA in a disordered medium (a medium without engineered structure). Such a ‘random CPA’ would be the time-reverse of a ‘random laser’19,20, in which light is resonantly enhanced by multiple scattering inside a disorder. Because of the complexity of this scattering process, the light field emitted by a random laser is also spatially complex and not focused like a regular laser beam. Realizing a random CPA (or ‘random anti-laser’) is therefore challenging because it requires the equivalent of time-reversing such a light field in all its degrees of freedom to create coherent radiation that is perfectly absorbed when impinging on a disordered medium. Here we use microwave technology to build a random anti-laser and demonstrate its ability to absorb suitably engineered incoming radiation fields with near-perfect efficiency. Because our approach to determining these field patterns is based solely on far-field measurements of the scattering properties of a disordered medium, it could be suitable for other applications in which waves need to be perfectly focused, routed or absorbed.

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## Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

K.P., M.K., A.B., P.A. and S.R. were supported by the Austrian Science Fund (FWF) through project I 1142- N27 (GePartWave). J.B. and U.K. were supported by the French Science Fund (ANR) through project GePartWave and by the European Union via the H2020 project OpenFet NEMF21. The computational results presented here were achieved in part using the Vienna Scientific Cluster (VSC).

### Reviewer information

Nature thanks Simon Horsley, Otto Muskens, Riccardo Sapienza and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

Authors

### Contributions

Measurements and data evaluation were carried out by K.P. under the supervision of U.K. J.B. and U.K. designed the experimental setup. S.R. proposed the project and supervised the theoretical and numerical tasks carried out by M.K., K.P., A.B. and P.A. K.P. and S.R. wrote the manuscript with input from all authors.

### Corresponding authors

Correspondence to Ulrich Kuhl or Stefan Rotter.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

## Extended data figures and tables

### Extended Data Fig. 1 Central antenna coupling.

The plot shows the reflection signal $${\left|R\right|}^{2}$$ measured for injection at the central antenna as a function of the signal frequency for different antenna lengths in the disordered configuration with 60 small scatterers shown in Fig. 1. One observes very clearly that at certain frequencies, pronounced minima of the reflection signal, and therefore maxima in the coupling efficiency of the antenna occur. For increasing antenna length these minima become lower until an optimal length is reached that is specific to each minimum (corresponding to ‘critical coupling’). By further increasing the antenna length, the coupling efficiency decreases again. For the minimum in the frequency range around 7.1 GHz (see also main text) the optimal antenna length is 7 mm, whereas in the range around 6.8 GHz a length of 7.5 mm provides the highest coupling efficiency.

### Extended Data Fig. 2 Simulated energy-flux distribution in the entire scattering region.

As a complement to Fig. 3, we provide here not only the simulated intensity (top panels) but also the Poynting vector (bottom panels) of the CPA states in the entire scattering region. In the top panels scatterers are displayed as white circles, with the white arrow indicating the position of the absorbing scatterer (that is, the central antenna), whereas in the bottom panels semi-transparent circles mark the scatterers and the filled circle represents the central antenna. For clarity, we plot the Poynting vectors on a different grid of points from that used in the insets in Fig. 3.

### Extended Data Fig. 3 Simulated intensity distribution in the presence and absence of the absorbing antenna.

To illustrate the effect of the absorbing scatterer (that is, the central antenna) on the microwave field, we compare the simulated intensity distributions of the CPA states discussed in the main text, injected here in the presence (top panels) and absence (bottom panels) of this absorber (all other parameters and the colour scale stay unchanged). The white arrow indicates the antenna position and white circles represent the scatterers. One can clearly observe that removing the absorbing scatterer causes considerably higher and differently distributed intensity maxima in the waveguide, stemming from additional interference contributions of the waves that are no longer absorbed by the antenna.

## Supplementary information

### Supplementary Information

This file contains 1) Additional measurement data, 2) Reports on performance checks, 3) More in-depth discussion of results presented in the main text. The file has 14 pages and contains 7 display items in colour.

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Pichler, K., Kühmayer, M., Böhm, J. et al. Random anti-lasing through coherent perfect absorption in a disordered medium. Nature 567, 351–355 (2019). https://doi.org/10.1038/s41586-019-0971-3

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• DOI: https://doi.org/10.1038/s41586-019-0971-3

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