Radiative heat transfer between two magnetodielectric metamaterial slabs with finite thickness in non-equilibrium situation

In this paper, we consider a system including two maghnetodielectric slabs with different temperature that are placed in vacuum at zero temperature and very short separation distances from each other. Based on the canonical quantization of the electromagnetic field in the presence of dissipative media, we investigate the radiative heat transfer arising from thermal and quantum fluctuations in out of thermal equilibrium but stationary situation. For this purpose, we calculate the ensemble average of Poynting vector by driving quantum correlation relations between noise polarization and magnetization operators and extracting the electromagnetic Green tensor of the system. Finally, we analyze the transferred radiation of aforementioned system by employing the numerical result of the Poynting vector