Abstract
Metamaterials’ engineered internal structures enable customized material properties beyond those found in nature, such as the capability to guide, attenuate, and focus waves at will. Phononic metamaterials aim to manipulate mechanical waves, with broad applications in acoustics, elastodynamics and structural vibrations. A key bottleneck in the advancement of phononic metamaterials is their scalability beyond tens of unit cells per spatial dimension, which equally affects their design, simulation, and fabrication. Here, we present a framework for scalable inverse design of spatially graded phononic metamaterials for elastic wave guiding, together with a scalable microfabrication method. This framework enables the design and realization of complex waveguides including hundreds of thousands of unit cells, potentially extendable to millions with no change in protocol. Scalable designs are optimized with a ray tracing model for waves in spatially graded beam lattices and fabricated by photolithography and etching of silicon wafers, to create free-standing microarchitected films. Wave guiding is demonstrated experimentally by using pulsed laser excitation and interferometric displacement measurements. Broadband wave guiding is demonstrated, indicating the promise of our scalable design and fabrication methods for on-chip elastic wave manipulation.
Data availability
The experimental data generated in this study have been deposited in the ETH Zurich Research Collection database, which is publicly available at https://doi.org/10.3929/ethz-c-000785222.
Code availability
The codes for optimal tile design and assembly, and experimental data analysis generated in this study have been deposited in the ETH Zurich Research Collection database, which is publicly available at https://doi.org/10.3929/ethz-c-000785222.
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Acknowledgements
The authors thank Dr. Emil Bronstein for his assistance in setting up experimental scans. C.D. acknowledges partial support from an ETH Zurich Postdoctoral Fellowship. Mask writing and fabrication were performed in the cleanroom facility of the Binnig and Rohrer Nanotechnology Center of IBM Zurich.
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C.D., V.K. and D.M.K. designed the research. C.D. performed computational modeling and design. V.K. designed the microfabrication method and experiments. V.K. and C.D. performed the experiments and analysis. U.D. supported the microfabrication efforts. C.D., V.K. and D.M.K. wrote the manuscript.
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Dorn, C., Kannan, V., Drechsler, U. et al. Graded phononic metamaterials based on scalable microfabrication and design. Nat Commun (2026). https://doi.org/10.1038/s41467-026-69888-x
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DOI: https://doi.org/10.1038/s41467-026-69888-x
