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Deterministic inverse design of Tamm plasmon thermal emitters with multi-resonant control


Wavelength-selective thermal emitters (WS-EMs) are of interest due to the lack of cost-effective, narrow-band sources in the mid- to long-wave infrared. WS-EMs can be realized via Tamm plasmon polaritons (TPPs) supported by distributed Bragg reflectors on metals. However, the design of multiple resonances is challenging as numerous structural parameters must be optimized simultaneously. Here we use stochastic gradient descent to optimize TPP emitters (TPP-EMs) composed of an aperiodic distributed Bragg reflector deposited on doped cadmium oxide (CdO) film, where layer thicknesses and carrier density are inversely designed. The combination of the aperiodic distributed Bragg reflector with the designable plasma frequency of CdO enables multiple TPP-EM modes to be simultaneously designed with arbitrary spectral control not accessible with metal-based TPPs. Using this approach, we experimentally demonstrated and numerically proposed TPP-EMs exhibiting single or multiple emission bands with designable frequencies, line-widths and amplitudes. This thereby enables lithography-free, wafer-scale WS-EMs that are complementary metal–oxide–semiconductor compatible for applications such as free-space communications and gas sensing.

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Fig. 1: Flowchart of the design process.
Fig. 2: Experimental demonstration of TPP-EMs.
Fig. 3: Inversely designed TPP-EMs for various applications.
Fig. 4: Functionality enabled by the tunability of CdO plasma frequency.

Data availability

The authors declare that the data supporting the findings of this study are available within the paper and its supplementary information files. Additional data is available from the authors upon request.

Code availability

The algorithms used for this work are available within the paper as well as at our group website (


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M.H., J.R.N., J.-P.M., A.C. and J.D.C. gratefully acknowledge support for this work by Office of Naval Research grant N00014-18-1-2107. J.-P.M. and J.N. acknowledge support from the Army Research Office research grant W911NF-16-1-0406. J.N. gratefully acknowledges support from the Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program. Y.T. and B.A.L. thank the National Science Foundation for support (NSF 1452485). Funding for G.L. was provided through a Small Business Technology Transfer programme provided by the National Science Foundation, Division of Industrial Innovation and Partnerships (award no. 2014798). T.G.F. was supported by Vanderbilt University through J.D.C.’s start-up package. We thank the National Institute of Standards and Technology for providing the infrared absorption spectra of chemicals and N. Passler and A. Paarmann of the Fritz Haber Institute for their TMM code35,36 to validate our work.

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Authors and Affiliations



M.H., J.R.N., J.D.C. and J.-P.M. conceived the idea. M.H. developed the algorithm. J.R.N. and M.H. performed the infrared measurements. M.H. analysed the dependence of TPP-EM on CdO properties, and J.R.N. performed the analysis from a physics perspective. J.N. and A.C. fabricated the samples, and N.S.M. characterized the sample topography. M.H. and Y.T. completed the theoretical analysis regarding the algorithm. M.H. and G.L. performed the NDIR evaluation. All participated in the writing.

Corresponding authors

Correspondence to Mingze He or Joshua D. Caldwell.

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The authors declare no competing interests.

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Peer review information Nature Materials thanks Juerg Leuthold, Changying Zhao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–22, Tables 1 and 2, and Sections 1–22.

Supplementary Software

Algorithm used in the manuscript.

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He, M., Nolen, J.R., Nordlander, J. et al. Deterministic inverse design of Tamm plasmon thermal emitters with multi-resonant control. Nat. Mater. 20, 1663–1669 (2021).

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