Generalized Kirchhoff law

TL;DR

This paper extends Kirchhoff's law to non-isothermal, anisothermal media, establishing a link between local absorption and emission rates, enabling analysis of thermal radiation in non-equilibrium systems and guiding the design of advanced emitters.

Contribution

It introduces a generalized Kirchhoff law for anisothermal media, connecting local absorption and emission, with applications in non-equilibrium thermal radiation analysis and emitter design.

Findings

Local absorption rate equals local emissivity rate in anisothermal media

Framework applicable to microwave, X-UV radiation, and quantum electronic systems

Enables design of subwavelength hot emitters with controlled emission properties

Abstract

Thermal emission can be conveniently described using Kirchhoff law which states that the emissivity is equal to the absorptivity for isothermal bodies. For a finite size system, absorptivity is replaced by an absorption cross section. Here, we study the link between thermal emission and absorption by a finite size object which is not isothermal. We define a local absorption rate for a given incident plane wave and we prove that it is equal to the local emissivity rate. Hence, Kirchhoff law can be extended to anisothermal media. A practical consequence is the possibility of analysing thermal radiation by a variety of non-equilibrium systems such as microwave radiation in geophysical remote sensing or X-UV radiation by plasmas. This result provides a theoretical framework to analyse thermal emission by hot electrons in quantum wells, tunnel junctions or graphene. It paves the way to the design of a new generation of incandescent emitters made of subwavelength hot emitters coupled to cold antennas. The antennas control the emission spectrum, direction and polarization of the emitted radiation.