  Coherent thermal emission for a given polarization has been observed in many
metamaterials with micro/nanostructures. A complete description of the thermal
emission requires the full characterization of the spectral angular emissivity
for all polarization states. Emissivity is typically obtained based on the
equivalence between the absorptivity and emissivity according to Kirchhoff's
law; however, such relation may be invalid for nonreciprocal media. More
general approaches without the constrain of optical reciprocity are necessary
when dealing with magneto-optical materials and magnetic Weyl semimetals. Here,
a polarimetric analysis of thermal emission is carried out based on
fluctuational electrodynamics. The Stokes parameters are obtained using
coherency matrix for a multilayered system with anisotropic media, including
nonreciprocal materials. The results demonstrate that thermal emission may be
circularly or linearly polarized in different directions and frequencies. The
findings are consistent with the statements of the modified Kirchhoff's law
provided by several groups in recent years, and therefore, justify the
appropriateness of both the direct and indirect methods. This study will help
the design of desired thermal emitters for energy harvesting and thermal
control.
