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Compensating losses in polariton propagation with synthesized complex frequency excitation

Nature Materials volume 23, pages 506–511 (2024)Cite this article

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Abstract

Surface plasmon polaritons and phonon polaritons offer a means of surpassing the diffraction limit of conventional optics and facilitate efficient energy storage, local field enhancement and highsensitivity sensing, benefiting from their subwavelength confinement of light. Unfortunately, losses severely limit the propagation decay length, thus restricting the practical use of polaritons. While optimizing the fabrication technique can help circumvent the scattering loss of imperfect structures, the intrinsic absorption channel leading to heat production cannot be eliminated. Here, we utilize synthetic optical excitation of complex frequency with virtual gain, synthesized by combining the measurements made at multiple real frequencies, to compensate losses in the propagations of phonon polaritons with dramatically enhanced propagation distance. The concept of synthetic complex frequency excitation represents a viable solution to the loss problem for various applications including photonic circuits, waveguiding and plasmonic/phononic structured illumination microscopy.

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Fig. 1: Concept of loss-compensation for polariton propagation using synthetic wave of complex frequency.
Fig. 2: AFM (top left panel) and s-SNOM (other panels) imaging in the vicinity of an antenna on an MoO3 film that supports hyperbolic PhPs.
Fig. 3: Synthetic s-SNOM imaging with a complex frequency of \({\tilde{\boldsymbol{f}}}={\mathbf{(}}{\mathbf{910-6.5i}}{\mathbf{)}}\) cm−1 in different transient snapshots and at different synthesized real frequencies.
Fig. 4: Investigation of interference of PhPs from two different circular antennas on MoO3 flake.

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Data availability

The data that support the findings of this study are available within this Article and the Supplementary Information.

Code availability

The code that supports the findings of this study is available from the corresponding author upon reasonable request.

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Acknowledgements

This work was supported by New Cornerstone Science Foundation and the Research Grants Council of Hong Kong, AoE/P-701/20, 17315522, A-HKU705/21 (to Shuang Zhang), the National Natural Science Foundation of China (51925203 to Q.D.; 52022025 to X.Y. and 52102160 to X.G.) and the Young Elite Scientists Sponsorship Program by CAST, 2022QNRC001 (to X.G.).

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Author notes

  1. These authors contributed equally: Fuxin Guan, Xiangdong Guo, Shu Zhang.

Authors and Affiliations

  1. New Cornerstone Science Laboratory, Department of Physics, University of Hong Kong, Hong Kong, China

    Fuxin Guan, Xiangdong Guo, Kebo Zeng, Yue Hu, Shaobo Zhou & Shuang Zhang

  2. CAS Key Laboratory of Nanophotonic Materials and Devices, CAS Key Laboratory of Standardization and Measurement for Nanotechnology, CAS Center for Excellence in Nanoscience, National Center for Nanoscience and Technology, Beijing, China

    Xiangdong Guo, Shu Zhang, Chenchen Wu, Xiaoxia Yang & Qing Dai

  3. School of Physics and Electronics, Hunan University, Changsha, China

    Yuanjiang Xiang

  4. Department of Electrical & Electronic Engineering, University of Hong Kong, Hong Kong, China

    Shuang Zhang

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Contributions

Shuang Zhang, F.G., Q.D. and X.G. conceived the project. F.G. and X.G. designed the experiments. X.G. and Shu Zhang prepared the experimental samples and performed the s-SNOM experiments with the help of C.W.; F.G. and X.G. analysed the experimental data and performed the simulation. F.G., X.G., Shu Zhang, K.Z., Y.H., Y.X., S. Zhou, X.Y., Q.D. and Shuang Zhang participated in the analysis of the results. F.G., X.G. and Shuang Zhang wrote the manuscript with input from all authors. Shuang Zhang and Q.D. supervised the overall projects. All authors contributed to the discussion.

Corresponding authors

Correspondence to Qing Dai or Shuang Zhang.

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Supplementary information

Supplementary Information

Supplementary Sections 1–4 and Figs. 1–11.

Supplementary Video 1

Wave propagation video.

Supplementary Video 2

Wave propagation video.

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Guan, F., Guo, X., Zhang, S. et al. Compensating losses in polariton propagation with synthesized complex frequency excitation. Nat. Mater. 23, 506–511 (2024). https://doi.org/10.1038/s41563-023-01787-8

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