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.
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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.
The authors declare no competing interests.
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(a) Refractive index values (n and k, solid and dot-dashed lines respectively) of the InAs wafer for various temperatures. We observe shifts in n and k that correspond to a redshifting of the ENZ-wavelength of the wafer. (b) Temperature-dependent refractive index values of the deposited a-Si. The refractive index grows as a function of temperature. The extinction coefficient is negligible in the wavelength range. (c–e) Emissivity measurements taken at 50, 100, and 150 °C, respectively. The blue, green, and red curves are obtained by solving E E.D. 1 using the average measured refractive index of a-Si at each temperature. Both (a) and (b) were measured and fitted using a J.A. Woollam IR-VASE and the WVASE software.
(a) We begin with a bare InAs wafer for which we have already determined the temperature-dependent optical properties. (b) a 2-μm-thick a-Si layer is deposited on top of the InAs wafer via PECVD. (c) A 750-nm-thick layer of resist, ZEP520A, is spun onto the wafer and the grating pattern is written into the resist via EBPG. (d) The pattern is then developed, and remaining resist is baked. The resist left on the sample surface acts as a mask for the ICP-RIE process. (e) The resist mask is removed overnight and the a-Si GMR structure is cleaned and imaged with an optical microscope and SEM.
(a) Side-view SEM image of the 2-μm-thick a-Si layer on top of the InAs wafer. This sample was not used for the final grating structure, but rather for the optical characterization of the a-Si layer. (b) Top-view SEM of the fabricated grating structure.
(a) For emissivity measurements, the sample is mounted on a heater at the rotation axis of a goniometer, centered between the pole pieces of an electromagnet. The goniometer allows us to rotate the sample around the z-axis and probe the outgoing radiation at an angle θ. The sample emission is collected through a ZnSe lens and sent through an external port into an FTIR. We place a polarizer in front of the detector to resolve the TM and TE emission. (b) The absorptivity measurement system uses an FTIR source and detector mounted on a 2-θ rotation stage. Instead of an electromagnet, we use a Halbach array of permanent magnets to apply the magnetic field. The sample is still heated to the same temperatures as in the emissivity measurements so that we have a direct comparison of the absorptivity and emissivity as defined by the Kirchhoff’s Law.
Raw traces of the collected emission from a Carbon black reference (black) and the sample (red) at three different temperatures. The blue trace is the emission of Aluminum at 24 °C and represents the background emission contributions from the system. Traces taken at different temperatures are offset for clarity.
(a) Experimental data and fits for three different magnetic fields. (b) The extracted InAs contribution to the emissivity (amplitude) for varying magnetic field, modeled as a sigmoid. (c) Central wavelength of the InAs contribution (that is the sigmoid) for varying magnetic field. We observe a blueshift of the emission edge with increasing magnetic field. (d) The resonant emissivity contribution (amplitude) of the GMR structure is modified, but the spectral shift is dictated by the InAs magnetic field response (b and c). (e) Change in the resonant amplitude for all magnetic field values.
Extended Data Fig. 7 Experimental and simulated emissivity change for non-zero magnetic field exhibiting saturation effect as resonant sample emissivity approaches Blackbody limit.
(a) Experimental data (black points) with quadratic fit (solid red) for the full magnetic field range and linear fit (dot-dash blue) for the positive magnetic field range. (b) The same plot as in (a) for our simulated photonic structure. The magnitude of the change in emissivity as a function of magnetic field is larger, however we observe the same saturation behavior. Note that our resonant peak emissivity at θ = 65° is at a slightly longer wavelength (λ = 12.68 μm).
Extended Data Fig. 8 Experimental data comparing different regimes of the spectral and amplitude tuning of the peak emissivity for three angles.
(a) Emissivity for θ = −25° for three magnetic field values. At small angles, the spectral overlap of the InAs emissivity edge (∼13 μm) and the +1st order GMR (∼12.1 μm) is minimal, resulting in no tuning of the spectral position or magnitude of the emissivity peak of the overall structure. (b) At θ = 55°, the spectral position of the emissivity peak is tuned by the direction of the InAs emissivity edge shift (blueshift for +1.0 T and redshift for −1.0 T) relative to the +1st order GMR. We term this angular range where the InAs emissivity edge begins to change the spectral position of the emissivity peak as the ‘critical angle’ θC. (c) For large angles, we get strong emissivity amplitude tuning with little shift in the spectral position of the resonant emissivity.
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Shayegan, K.J., Biswas, S., Zhao, B. et al. Direct observation of the violation of Kirchhoff’s law of thermal radiation. Nat. Photon. 17, 891–896 (2023). https://doi.org/10.1038/s41566-023-01261-6