Abstract
Metamaterials offer unprecedented control over wave propagation, but suffer from optical losses due to wave dissipation, particularly in optical imaging and sensing systems. Recent advances leveraging complex-frequency wave excitations with temporal attenuation offer promising solutions for optical loss compensation. However, this approach faces limitations in extreme loss scenarios. The complex-frequency wave requires sufficient temporal attenuation to offset material loss, inevitably triggering rapid signal decay to zero before reaching a quasi-static state. Here we engineer excitations with high-order temporal attenuation to slow down the decay rate. This allows the signal to persist for long enough to reach a quasi-static state and preserve the loss compensation efficiency. We experimentally demonstrate 20-fold noise suppression in plasmonic resonance systems compared with conventional complex-frequency excitations. This approach offers broad applicability across diverse fields, including imaging, biosensing and integrated photonic signal processing.
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Data availability
The experimental data are available via Figshare at https://doi.org/10.6084/m9.figshare.30858479.
Code availability
The codes are available via Figshare at https://doi.org/10.6084/m9.figshare.30866405.
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Acknowledgements
We are grateful to K. Zheng and S. Zhou for illuminating discussions. This work was supported by the New Cornerstone Science Foundation (S.Z.), National Natural Science Foundation of China (numbers 62325504 and 62288101; T.L.), the Research Grants Council of Hong Kong (AoE/P-502/20, STG3/E-704/23-N, 17309021; S.Z.) and Guangdong Provincial Quantum Science Strategic Initiative (GDZX2204004 and GDZX2304001; S.Z.).
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S.Z. and F.G. conceived the project and supervised the overall projects. Z.L. fabricated the PIT samples and carried out the Fourier transform infrared spectroscopy experiment. F.G. and S.C. performed the numerical simulations and analytical calculations. F.G. performed the microwave experiments. F.G., Z.L., S.C., X.W., T.L. and S.Z. participated in the analysis of the results. F.G. and S.Z. wrote the manuscript with input from all authors. All authors contributed to the discussion.
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Nature Physics thanks Seunghwi Kim, Yu-Gui Peng and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data
Extended Data Fig. 1 Recovering plasmonic resonances with HVG excitations in a weaker coupling case compared with Fig. 3.
(a) Polarizations (\(\widetilde{{\rm{p}}}\) and \({\widetilde{{\rm{p}}}}_{n}\)) and (b) transmittances \((\widetilde{T}\) and \({\widetilde{T}}_{n}\)) under excitation of real frequency and different orders of HVG. The virtual gains with different \(\beta\) are displayed in the inset. (c) The temporal evolutions of polarizations \({\widetilde{{\rm{p}}}}_{n}\left(\widetilde{\omega },t\right)\) for n = 1, 2, and 3. The spectra shown in (a) are selected at the moments indicated by the dashed lines in (c).
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Guan, F., Lin, Z., Chen, S. et al. High-order virtual gain for optical loss compensation in plasmonic metamaterials. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03171-0
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DOI: https://doi.org/10.1038/s41567-026-03171-0
