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Polaritonic nonlocality in light–matter interaction


Subwavelength electromagnetic field localization has been central to photonic research in the last decade, allowing us to enhance sensing capabilities as well as increase the coupling between photons and material excitations. The strong and ultrastrong light–matter coupling regime in the terahertz range using split-ring resonators coupled to magnetoplasmons has been widely investigated, achieving successive world records for the largest light–matter coupling ever achieved. Ever shrinking resonators have allowed us to approach the regime of few-electron strong coupling, in which single-dipole properties can be modified by the vacuum field. Here, we demonstrate, theoretically and experimentally, the existence of a limit to the possibility of arbitrarily increasing electromagnetic confinement in polaritonic systems. Strongly subwavelength fields can excite a continuum of high-momenta propagative magnetoplasmons. This leads to peculiar nonlocal polaritonic effects, as certain polaritonic features disappear and the system enters the regime of discrete-to-continuum strong coupling.

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Fig. 1: Impact of nonlocality in nanoplasmonics.
Fig. 2: Cavity and electric-field parameters.
Fig. 3: Theory versus experiment.
Fig. 4: Finite-element simulation for a cSRR with 250-nm gap on 2DEG.

Data availability

The numerical simulation and measurement data that support the plots within this paper are available from the corresponding author upon reasonable request. Data that support the findings of this Article are also available in the ETH Research Collection43.

Code availability

The codes used in the theory part of this study are available from the corresponding author upon reasonable request.


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G.S., J.F. and S.R. thank J. Keller for help in the initial phase of the project. G.S. thanks M. Jeannin and R. Colombelli for discussions. S.R. thanks I.-C. Benea-Chelmus for fruitful discussions. G.S. and J.F. acknowledge financial support from ERC Advanced grant ‘Quantum Metamaterials in the Ultra Strong Coupling Regime’ (MUSiC) (ERC grant no. 340975). G.S. and J.F. also acknowledge financial support from the Swiss National Science Foundation (SNF) through the National Centre of Competence in Research Quantum Science and Technology (NCCR QSIT). S.D.L. is a Royal Society Research Fellow and was partly funded by the Philip Leverhulme Prize of the Leverhulme Trust. S.D.L. and E.C. acknowledge funding from the RGF\EA\181001 grant from the Royal Society.

Author information

Authors and Affiliations



G.S., J.F. and S.D.L. conceived the idea. S.R. designed and fabricated the devices, carried out all the optical measurements, analysed all experimental data and performed numerical simulations under the supervision of G.S. and J.F. E.C. and S.D.L. developed the theory. E.C. performed numerical simulations under the supervision of S.D.L. M.B. performed the epitaxial growth. S.R., S.D.L. and G.S. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Shima Rajabali, Simone De Liberato or Giacomo Scalari.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Photonics thanks Angela Demetriadou, Antonio Fernandez-Dominguez, Jacob Khurgin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Three sections (‘Supporting theory’, ‘Supporting experimental measurements’ and ‘Supporting numerical simulations’), Figs. 1–9 and eight references.

Supplementary Video 1

Animated electric-field distribution (the phase of the incident field is changing) for LP at 315 GHz to show the confined LP mode with a narrow spectral distribution (related to Fig. 4c).

Supplementary Video 2

Animated electric-field distribution (the phase of the incident field is changing) for UP at 655 GHz to show the excitation of plasmonic waves acting as a loss channel for the polaritonic mode (related to Fig. 4d).

Supplementary Video 3

Animated electric-field distribution (the phase of the incident field is changing) for LP at 177 GHz at a low magnetic field of B = 500 mT to show the excitation of plasmonic waves acting as a loss channel for the polaritonic mode (related to Supplementary Fig. 9b).

Supplementary Video 4

Animated electric-field distribution (the phase of the incident field is changing) for LP at 400 GHz at a high magnetic field of B = 1,500 mT to show the confined LP mode (related to Supplementary Fig. 9c).

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Rajabali, S., Cortese, E., Beck, M. et al. Polaritonic nonlocality in light–matter interaction. Nat. Photon. 15, 690–695 (2021).

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