Abstract
The goal of this paper is to introduce a local form of Kirchhoff law to model light emission by nonequilibrium bodies. While absorption by a finite-size body is usually described using the absorption cross section, we introduce a local absorption rate per unit volume and also a local thermal emission rate per unit volume. Their equality is a local form of Kirchhoff law. We revisit the derivation of this equality and extend it to situations with subsystems in local thermodynamic equilibrium but not in equilibrium between them, such as hot electrons in a metal or electrons with different Fermi levels in the conduction band and in the valence band of a semiconductor. This form of Kirchhoff law can be used to model (i) thermal emission by nonisothermal finite-size bodies, (ii) thermal emission by bodies with carriers at different temperatures, and (iii) spontaneous emission by semiconductors under optical (photoluminescence) or electrical pumping (electroluminescence). Finally, we show that the reciprocity relation connecting light-emitting diodes and photovoltaic cells derived by Rau is a particular case of the local Kirchhoff law.
- Received 21 December 2017
DOI:https://doi.org/10.1103/PhysRevX.8.021008
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Hot objects such as the Sun or a tungsten filament emit radiation. This radiation can be described by a simple law—known as Kirchoff’s law—which states that the rate of thermal emission is proportional to the rate at which the object absorbs light. Despite reigning for about 160 years, Kirchoff’s law has its limits. It cannot be used in situations where parts of an object are at different temperatures, for example. We extend the law’s utility by deriving a form that works for bodies with different temperatures or different chemical potentials throughout, possibly paving the way for a new generation of radiation sources.
Antennas can concentrate electromagnetic radiation into a subwavelength volume, thereby enhancing the absorption of a subwavelength body by more than 2 orders of magnitude. Our results predict that by exciting only this volume, the emission will also be enhanced—the antenna extracts more radiation out of a given volume. The excitation can be a local increase in temperature or an optical or electrical pumping, either of which results in a local photon chemical potential (or a difference of quasi-Fermi levels). Furthermore, the antenna allows one to fine-tune the radiation properties such as polarization, spectrum, and direction to get a desired output.
Our formalism provides a new, practical tool for designing a diverse set of devices that rely on thermal emission, electroluminescence, and photoluminescence.
