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Published July 26, 2023 | Supplemental Material
Journal Article Open

Direct observation of the violation of Kirchhoff's law of thermal radiation


Thermal emission—the process through which all objects with a finite temperature radiate electromagnetic energy—has generally been thought to obey reciprocity, where the absorbed and emitted radiation from a body are equal for a given wavelength and angular channel. This equality, formalized by Gustav Kirchhoff in 1860, is known as Kirchhoff's law of thermal radiation and has long guided designs to control the emitted radiation. Removing the constraint of Kirchhoff's law unlocks a multitude of applications and designs for thermal emitters. Decoupling the absorptivity and emissivity relationship can be leveraged to achieve novel functions, ranging from reducing re-emission losses to the Sun in the context of solar energy harvesting systems to radiative camouflage. Here we report the direct measurements of an inequality between the spectral directional emissivity and absorptivity for a photonic design that supports a guided-mode resonance coupled to a magneto-optic material. This inequality occurs under the application of an in-plane magnetic field that modifies the normally diagonal permittivity tensor to a non-diagonal tensor in magneto-optic InAs, resulting in an antisymmetric relationship where the magnetic tuning of enhanced emissivity for a given angle correlates with decreased absorptivity for the same angle.

Additional Information

© The Author(s), under exclusive licence to Springer Nature Limited 2023. We acknowledge discussions with A. Laucht and D. H. Drew. This work has been supported by DARPA NLM (grant no. HR00111820046). K.J.S. acknowledges support from the NSF for a graduate research fellowship. Contributions. H.A.A. and S.F. conceived the project. K.J.S. fabricated the samples and carried out the measurements, supported by S.B. K.J.S. led the data analysis and modelling, with support from S.B. and B.Z. H.A.A. supervised the project. K.J.S., S.B. and H.A.A. wrote the manuscript with input from all other authors. Data availability. The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. The authors declare no competing interests.

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Additional details

August 22, 2023
October 20, 2023