Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Comment
  • Published:

Super-Planckian emission cannot really be ‘thermal’

A heat-powered emitter can sometimes exceed the Planck thermal-emission limit. We clarify when such super-Planckian emission is possible, arguing that far-field super-Planckian emission requires a distribution of energy that is not consistent with a unique temperature, and therefore the process should not be called ‘thermal emission’.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Thought experiment that explains Kirchhoff’s law of thermal radiation.
Fig. 2: Subwavelength thermal emitters.
Fig. 3: Non-equilibrium heat-powered emission.


  1. Planck, M. Ann. Phys. 309, 553–563 (1901).

    Article  Google Scholar 

  2. Kirchhoff, G. Lond. Edinb. Dubl. Phil. Mag. J. Sci. (1860).

    Article  Google Scholar 

  3. Baranov, D. G. et al. Nat. Mater. 18, 920–930 (2019).

    Article  ADS  Google Scholar 

  4. Liu, X. et al. Phys. Rev. Lett. 107, 045901 (2011).

    Article  ADS  Google Scholar 

  5. Greffet, J.-J. et al. Nature 416, 61–64 (2002).

    Article  ADS  Google Scholar 

  6. Inoue, T., De Zoysa, M., Asano, T. & Noda, S. Nat. Mater. 13, 928–931 (2014).

    Article  ADS  Google Scholar 

  7. Nefedov, I. S. & Melnikov, L. A. Appl. Phys. Lett. 105, 161902 (2014).

    Article  ADS  Google Scholar 

  8. Hsieh, M.-L., Lin, S.-Y., Bur, J. A. & Shenoi, R. Nanotechnology 26, 234002 (2015).

    Article  ADS  Google Scholar 

  9. Lin, S.-Y. et al. Sci Rep. 10, 5209 (2020).

    Article  ADS  Google Scholar 

  10. Yang, J. et al. Nat. Commun. 9, 4033 (2018).

    Article  ADS  Google Scholar 

  11. Raman, A. P., Anoma, M. A., Zhu, L., Rephaeli, E. & Fan, S. Nature 515, 540–544 (2014).

    Article  ADS  Google Scholar 

  12. Ilic, O. et al. Nat. Nanotechnol. 11, 320–324 (2016).

    Article  ADS  Google Scholar 

  13. Trupke, T. et al. Appl. Phys. Lett. 84, 1997 (2004).

    Article  ADS  Google Scholar 

  14. Luo, C., Narayanaswamy, A., Chen, G. & Joannopoulos, J. D. Phys. Rev. Lett. 93, 213905 (2004).

    Article  ADS  Google Scholar 

  15. Rousseau, E. et al. Nat. Photon. 3, 514–517 (2009).

    Article  ADS  Google Scholar 

  16. Kim, K. et al. Nature 528, 387–391 (2015).

    Article  ADS  Google Scholar 

  17. Yu, Z. et al. Nat. Commun. 4, 1730 (2013).

    Article  ADS  Google Scholar 

  18. Jain, P. K., Lee, K. S., El-Sayed, I. H. & El-Sayed, M. A. J. Phys. Chem. B 110, 7238–7248 (2006).

    Article  Google Scholar 

  19. Fernández-Hurtado, V., Fernández-Domínguez, A. I., Feist, J., García-Vidal, F. J. & Cuevas, J. C. Phys. Rev. B 97, 045408 (2018).

    Article  ADS  Google Scholar 

  20. Golyk, V. A., Krüger, M. & Kardar, M. Phys. Rev. E 85, 046603 (2012).

    Article  ADS  Google Scholar 

  21. Biehs, S.-A. & Ben-Abdallah, P. Phys. Rev. B 93, 165405 (2016).

    Article  ADS  Google Scholar 

  22. Ingvarsson, S., Klein, L., Au, Y.-Y., Lacey, J. A. & Hamann, H. F. Opt. Express 15, 11249 (2007).

    Article  ADS  Google Scholar 

  23. Thompson, D. et al. Nature 561, 216–221 (2018).

    Article  ADS  Google Scholar 

  24. Maslovski, S. I., Simovski, C. R. & Tretyakov, S. A. New J. Phys. 18, 013034 (2016).

    Article  ADS  Google Scholar 

  25. Fan, S. Joule 1, 264–273 (2017).

    Article  Google Scholar 

  26. Greffet, J.-J., Bouchon, P., Brucoli, G. & Marquier, F. Phys. Rev. X 8, 021008 (2018).

    Google Scholar 

  27. Khandekar, C., Yang, L., Rodriguez, A. W. & Jacob, Z. Opt. Express 28, 2045 (2020).

    Article  ADS  Google Scholar 

  28. Sakat, E. et al. Optica 5, 175 (2018).

    Article  ADS  Google Scholar 

  29. Xiao, Y., Wan, C., Shahsafi, A., Salman, J. & Kats, M. A. ACS Photonics 7, 853–860 (2020).

    Article  Google Scholar 

  30. Xiao, Y., Charipar, N. A., Salman, J., Piqué, A. & Kats, M. A. Light: Sci. Appl. 8, 51 (2019).

    Article  ADS  Google Scholar 

  31. Khandekar, C., Pick, A., Johnson, S. G. & Rodriguez, A. W. Phys. Rev. B 91, 115406 (2015).

    Article  ADS  Google Scholar 

  32. Khandekar, C., Lin, Z. & Rodriguez, A. W. Appl. Phys. Lett. 106, 151109 (2015).

    Article  ADS  Google Scholar 

  33. Zhu, L. & Fan, S. Phys. Rev. B 90, 220301 (2014).

    Article  ADS  Google Scholar 

  34. Hadad, Y., Soric, J. C. & Alu, A. Proc. Natl Acad. Sci. USA 113, 3471–3475 (2016).

    Article  ADS  Google Scholar 

  35. Yu, Z., Raman, A. & Fan, S. Proc. Natl Acad. Sci. USA 107, 17491–17496 (2010).

    Article  ADS  Google Scholar 

  36. Molesky, S., Jin, W., Venkataram, P. S. & Rodriguez, A. W. Phys. Rev. Lett. 123, 257401 (2019).

    Article  ADS  MathSciNet  Google Scholar 

Download references


M.A.K. and Y.X. acknowledge support from the National Science Foundation (NSF) (grant no. 1750341) and the Office of Naval Research (N00014-20-1-2297). M.S. acknowledges support from the NSF (grant no. 2108288) and the Welch Foundation (A-1886). We thank D. Seletskiy, whose live session at the SPIE Digital Forum helped us to crystallize some key questions, and J. Choy, for critical reading of the manuscript.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Mikhail A. Kats.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Takashi Asano, Jacob Khurgin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Supplementary information

Supplementary Information

Supplementary Figures 1-5, Supplementary Discussion

Source data

Source Data Fig. 1

Fig. 1b source data.

Source Data Fig. 2

Figs. 2b and 2d source data.

Source Data Fig. 3

Figs. 3d and 3e source data.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiao, Y., Sheldon, M. & Kats, M.A. Super-Planckian emission cannot really be ‘thermal’. Nat. Photon. 16, 397–401 (2022).

Download citation

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing