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

Nature Materials volume 20, pages 1663–1669 (2021)Cite this article

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Abstract

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 (https://my.vanderbilt.edu/caldwellgroup/).

References

  1. Livingood, A. et al. Filterless nondispersive infrared sensing using narrowband infrared emitting metamaterials. ACS Photon. 8, 472–480 (2021).

  2. Lochbaum, A. et al. On-chip narrowband thermal emitter for mid-IR optical gas sensing. ACS Photon. 4, 1371–1380 (2017).

    Article  CAS  Google Scholar 

  3. Lochbaum, A. et al. Compact mid-infrared gas sensing enabled by an all-metamaterial design. Nano Lett. 20, 4169–4176 (2020).

    Article  CAS  Google Scholar 

  4. Baranov, D. G. et al. Nanophotonic engineering of far-field thermal emitters. Nat. Mater. 18, 920–930 (2019).

    Article  CAS  Google Scholar 

  5. Lu, G. et al. Narrowband polaritonic thermal emitters driven by waste heat. ACS Omega 5, 10900–10908 (2020).

    Article  CAS  Google Scholar 

  6. Howes, A., Nolen, J. R., Caldwell, J. D. & Valentine, J. Near-unity and narrowband thermal emissivity in balanced dielectric metasurfaces. Adv. Optical Mater. 8, 1901470 (2020).

    Article  CAS  Google Scholar 

  7. Kelley, K. P. et al. Multiple epsilon-near-zero resonances in multilayered cadmium oxide: designing metamaterial-like optical properties in monolithic materials. ACS Photon. 6, 1139–1145 (2019).

    Article  CAS  Google Scholar 

  8. Schuller, J. A., Taubner, T. & Brongersma, M. L. Optical antenna thermal emitters. Nat. Photon. 3, 658–661 (2009).

    Article  CAS  Google Scholar 

  9. Wang, T. et al. Phonon-polaritonic bowtie nanoantennas: controlling infrared thermal radiation at the nanoscale. ACS Photon. 4, 1753–1760 (2017).

    Article  CAS  Google Scholar 

  10. Arnold, C. et al. Coherent thermal infrared emission by two-dimensional silicon carbide gratings. Phys. Rev. B 86, 035316 (2012).

    Article  Google Scholar 

  11. Asano, T. et al. Near-infrared–to–visible highly selective thermal emitters based on an intrinsic semiconductor. Sci. Adv. 2, e1600499 (2016).

    Article  Google Scholar 

  12. Kaliteevski, M. et al. Tamm plasmon-polaritons: possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror. Phys. Rev. B 76, 165415 (2007).

    Article  Google Scholar 

  13. Sasin, M. E. et al. Tamm plasmon polaritons: slow and spatially compact light. Appl. Phys. Lett. 92, 251112 (2008).

    Article  Google Scholar 

  14. Sakurai, A. et al. Ultranarrow-band wavelength-selective thermal emission with aperiodic multilayered metamaterials designed by Bayesian optimization. ACS Cent. Sci. 5, 319–326 (2019).

    Article  CAS  Google Scholar 

  15. Wang, Z. et al. Ultra-narrow and wavelength-tunable thermal emission in a hybrid metal-optical Tamm state structure. ACS Photon. 7, 1569–1576 (2020).

    Article  CAS  Google Scholar 

  16. Wang, Z. et al. Narrowband thermal emission realized through the coupling of cavity and Tamm plasmon resonances. ACS Photon. 5, 2446–2452 (2018).

    Article  CAS  Google Scholar 

  17. Yang, Z.-Y. et al. Narrowband wavelength selective thermal emitters by confined tamm plasmon polaritons. ACS Photon. 4, 2212–2219 (2017).

    Article  CAS  Google Scholar 

  18. Botros, J., Ali, M. O., Tait, R. N., Amaya, R. E. & Gupta, S. Direct thermal emission testing of aperiodic dielectric stack for narrowband thermal emission at mid-IR. J. Appl. Phys. 127, 114502 (2020).

    Article  CAS  Google Scholar 

  19. Nolen, J. R. et al. Ultraviolet to far-infrared dielectric function of n-doped cadmium oxide thin films. Phys. Rev. Mater. 4, 025202 (2020).

    Article  CAS  Google Scholar 

  20. Liu, C. P. et al. Effects of free carriers on the optical properties of doped CdO for full-spectrum photovoltaics. Phys. Rev. Appl. 6, 064018 (2016).

    Article  Google Scholar 

  21. Runnerstrom, E. L., Kelley, K. P., Sachet, E., Shelton, C. T. & Maria, J.-P. Epsilon-near-zero modes and surface plasmon resonance in fluorine-doped cadmium oxide thin films. 4, 1885–1892 (2017).

  22. Sachet, E. et al. Dysprosium-doped cadmium oxide as a gateway material for mid-infrared plasmonics. Nat. Mater. 14, 414–420 (2015).

    Article  CAS  Google Scholar 

  23. Cleri, A. et al. Mid-wave to near-IR optoelectronic properties and epsilon-near-zero behavior in indium-doped cadmium oxide. Phys. Rev. Mater. 5, 035202 (2021).

    Article  CAS  Google Scholar 

  24. Xue, W. & Miller, O. D. High-NA optical edge detection via optimized multilayer films. Preprint at https://arxiv.org/abs/2101.03160 (2021).

  25. Jiang, J. & Fan, J. A. Multiobjective and categorical global optimization of photonic structures based on ResNet generative neural networks. Nanophotonics 10, 361–369 (2021).

    Article  Google Scholar 

  26. Bordes, A., Bottou, L. & Gallinari, P. SGD-QN: careful quasi-Newton stochastic gradient descent. J. Mach. Learn. Res. 10, 1737–1754 (2009).

    Google Scholar 

  27. Sohl-Dickstein, J., Poole, B. & Ganguli, S. Fast large-scale optimization by unifying stochastic gradient and quasi-Newton methods. Proc. Mach. Learn. Res. 32, 604–612 (2014).

  28. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. In 3rd International Conference on Learning Representations (eds Bengio, Y. & LeCun, Y.) ICLR (Poster) (dblp, 2015).

  29. Robbins, H. & Monro, S. A stochastic approximation method. Ann. Math. Stat. 22, 400–407 (1951).

    Article  Google Scholar 

  30. Zhang, W., Wang, B. & Zhao, C. Selective thermophotovoltaic emitter with aperiodic multilayer structures designed by machine learning. ACS Appl. Energy Mater. 4, 2004–2013 (2021).

    Article  CAS  Google Scholar 

  31. Brand, S., Kaliteevski, M. A. & Abram, R. A. Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface. Phys. Rev. B 79, 085416 (2009).

    Article  Google Scholar 

  32. Morozov, K. M. et al. Revising of the Purcell effect in periodic metal-dielectric structures: the role of absorption. Sci. Rep. 9, 9604 (2019).

    Article  Google Scholar 

  33. Kaliteevski, M. A. et al. Experimental demonstration of reduced light absorption by intracavity metallic layers in Tamm plasmon-based microcavity. Plasmonics 10, 281–284 (2015).

    Article  CAS  Google Scholar 

  34. Bikbaev, R. G., Vetrov, S. Y. & Timofeev, I. V. Transparent conductive oxides for the epsilon-near-zero Tamm plasmon polaritons. J. Opt. Soc. Am. B 36, 2817–2823 (2019).

    Article  CAS  Google Scholar 

  35. Passler, N. C. & Paarmann, A. Generalized 4 × 4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures. J. Opt. Soc. Am. B 34, 2128–2139 (2017).

    Article  CAS  Google Scholar 

  36. Passler, N. C., Jeannin, M. & Paarmann, A. Layer-resolved absorption of light in arbitrarily anisotropic heterostructures. Phys. Rev. B 101, 165425 (2020).

    Article  CAS  Google Scholar 

  37. Li, H. H. Refractive index of silicon and germanium and its wavelength and temperature derivatives. J. Phys. Chem. Ref. Data 9, 561–658 (1980).

    Article  CAS  Google Scholar 

  38. Burnett, J. H., Kaplan, S. G., Stover, E. & Phenis, A. Refractive index measurements of Ge. Proc. SPIE 9974, 99740X (2016).

    Article  Google Scholar 

  39. Gao, W. Spectroscopic ellipsometry studies on vacuum-evaporated zinc selenide thin film. Proc. SPIE 7283, 72832L (2009).

    Article  Google Scholar 

Download references

Acknowledgements

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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Author notes

  1. These authors contributed equally: Mingze He, J. Ryan Nolen.

Authors and Affiliations

  1. Department of Mechanical Engineering, Vanderbilt University, Nashville, TN, USA

    Mingze He, Guanyu Lu, Thomas G. Folland & Joshua D. Caldwell

  2. Interdisciplinary Materials Science Program, Vanderbilt University, Nashville, TN, USA

    J. Ryan Nolen

  3. Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA, USA

    Josh Nordlander, Angela Cleri, Nathaniel S. McIlwaine & Jon-Paul Maria

  4. Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN, USA

    Yucheng Tang, Bennett A. Landman & Joshua D. Caldwell

  5. Department of Physics and Astronomy, University of Iowa, Iowa City, IA, USA

    Thomas G. Folland

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Contributions

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.

Additional information

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). https://doi.org/10.1038/s41563-021-01094-0

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