Adjoint Kirchhoff’s Law and General Symmetry Implications for All Thermal Emitters

Abstract

We study the relation between angular spectral absorptivity and emissivity for any thermal emitter, which consists of any linear media that can be dispersive, inhomogeneous, bianisotropic, or nonreciprocal. First, we establish an adjoint Kirchhoff’s law for mutually adjoint emitters. This law is based on generalized reciprocity and is a natural generalization of conventional Kirchhoff’s law for reciprocal emitters. Using this law, we derive all the relations between absorptivity and emissivity for an arbitrary thermal emitter We reveal that such relations are determined by the symmetries of the system, which are characterized by a Shubnikov point group. We classify all thermal emitters based on their symmetries using the known list of all three-dimensional Shubnikov point groups. Each class possesses its own set of laws that relates the absorptivity and emissivity. We numerically verify our theory for all three types of Shubnikov point groups: Gray groups, colorless groups, and black and white groups. We also verify the theory for both planar and nonplanar structures with single or multiple diffraction channels. Our theory provides a theoretical foundation for further exploration of thermal radiation in general media.