Validity of Kirchhoff's law for semitransparent films made of anisotropic materials

Abstract

Kirchhoff's law relates the emittance and absorptance of an object and has played an important role in radiative heat transfer calculations for many engineering applications. Along with the advancement of metamaterials, two-dimensional materials, and micro/nanoscale thermal radiation, Kirchhoff's law has been revisited by several groups. Some studies also questioned the derivations and applicability of the statement of Kirchhoff's law that appears in prevalent radiative heat transfer textbooks. The present study begins with a short review of Kirchhoff's law for isotropic objects and its validity for both hemispherical emittance and directional emittance. Then, this study formulates Kirchhoff's law for opaque anisotropic materials, considering both co-polarization and cross-polarization, and then for semitransparent films. It is shown that for macroscopic objects, as long as the Helmholtz reciprocity can be established, conventional expressions of Kirchhoff's law can be applied for engineering thermal analysis and design even with anisotropic media and metamaterials. Numerical examples and results are provided, based on a natural hyperbolic material and a magneto-optical material, to illustrate the reciprocity and applicability of Kirchhoff's law.