The promising structure to verify the Kirchhoff’s law for nonreciprocal materials


Radiation is the transmission of heat energy in the form of wave particles through a material medium. Since its invention, Kirchhoff’s law has been widely used to investigate thermal radiation in different materials, both reciprocal and nonreciprocal. Calculating radiative heat transfer between two or more mediums requires accurate determination of the individual materials’ emissivity, which may be challenging due to various reasons. For instance, emissivity measurements at moderate temperatures are challenging due to the extensive thermal background and relatively low signal-to-noise ratio effects.

Based on the existing literature, researchers have pointed out that the conventional Kirchoff’s laws hold only for reciprocal materials but not all nonreciprocal materials. Consequently, the experimental verification of Kirchoff’s laws for nonreciprocal materials has remained sparsely explored to date. This can be attributed to the challenges in accurately measuring the emissivity in the desired bands using the existing techniques because the proposed structures only realize strong nonreciprocal radiation at wavelengths exceeding 10 µm. Therefore, developing effective models for experimental verification of Kirchhoff’s’ laws is highly desirable.

To this account, Professor Xiaohu Wu from Shandong Institute of Advanced Technology proposed a planar structure for verification of Kirchoff’s laws for nonreciprocal materials. The author aimed to achieve strong nonreciprocal radiation at a wavelength of 10 µm and room temperature using the available absorptivity and emissivity measurement methods. The work is currently published in the research journal, ES Energy and Environment.

In his approach, the author adopted a simple planar design comprising a magneto-optical InAs material placed on top of a uniform silver layer exhibiting moderate magneto-optical effects. A diamond prism, with appropriate permittivity and refractive index, was chosen to provide a larger wavevector necessary to couple the incident light with guided modes inside the InAs. The relationship between the absorptivity, incidence angle, and wavelength in the presence and absence of magnetic fields was investigated.

Results showed that the proposed design could achieve strong nonreciprocal radiation at room temperature and near wavelength 10 µm with external magnetic field 3T via attenuated total reflection. This was attributed to the evanescent waves provided by the prism as well as the coupling between the guided modes inside the magneto-optical material InAs. In the absence of a magnetic field, the perfect absorptivity shifted toward a shorter wavelength because the absorptivity was symmetrical about the incidence angle. In contrast, when the external magnetic field was 3T, the perfect absorptivity shifted downwards and upwards when the incidence angle was negative and positive, respectively. Furthermore, the existing absorptivity and emissivity methods were accurately used to measure the thermal emissivity at room temperature to validate Kirchhoff’s laws for nonreciprocal materials. It was worth noting that the nonreciprocal radiation could be regulated by altering the prism’s permittivity or optimizing the thickness of the air gap and InAs.

In summary, Professor Wu proposed a simple planer design for achieving strong nonreciprocal radiation at moderate temperature and wavelength of 10 µm. Based on the results, the approach could be used together with the existing absorptivity and emissivity measurement technologies without serious difficulties. Therefore, the author, in a statement to Advances in Engineering, noted that the proposed structure is promising for practical verification of Kirchoff’s laws for nonreciprocal materials.

The promising structure to verify the Kirchhoff's law for nonreciprocal materials - Advances in Engineering
In this graphic, the left figure shows the structure to realize strong nonreciprocal radiation near wavelength 11 μm via attenuated total reflection, and the right figure shows the numerical results.

About the author

Dr. Xiaohu Wu received his B.S. degree in engineering mechanics from China University of Mining and Technology (Beijing) and Ph. D. degree from Peking University under the guidance of Prof. Ceji Fu. He was a visiting student at Georgia Institute of Technology from Sept. 2017 to Sept. 2018 under the guidance of Prof. Zhuomin Zhang. Currently, Dr. Wu is an associate researcher at Shandong Institute of Advanced Technology.

Dr. Wu’s main research interest is on thermal radiative properties of anisotropic materials and applications. He has published about 33 journal papers and give three conference presentations. Two of his papers were selected as cover articles by ES Energy & Environment. His Ph.D. thesis was published by Springer Nature and was recognized as outstanding doctoral research. Dr. Wu is the winner (along with his advisors) of the 2019 Hartnett-Irvine Award by the International Centre for Heat and Mass Transfer. Besides, his work was selected as “Optics in 2020” by the Optics & Photonics News of Optical Society of America (OSA). He is one of the early-career editorial board members of ES Energy & Environment. Dr. Wu’s website is


Wu, X. (2021). The promising structure to verify the Kirchhoff’s law for nonreciprocal materialsES Energy and Environment, 1-18. DOI: 10.30919/esee8c1047

Go To ES Energy and Environment

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