Abstract
In order to model the heat transfer dynamics in metamaterials (MMs), we develop a self-consistent theoretical formalism that combines the photonic mechanism, which involves the effects of the radiative heat transfer, with the phononic one, which comprises the effects of heat generation, heat storage, and heat conduction. The thermal conductivity tensor of the materials and the latent heat associated with material phase transitions are also considered in the formalism. As the first attempt in the construction of such a theory, here we study the propagation of fluctuating electromagnetic fields with slowly varying amplitudes (FEFSVA) through a dispersive and dissipative medium described by uniaxial effective permittivity and permeability tensors. Using the Poynting theorem for FEFSVA, we calculate the corresponding heat generation, accumulation, and release terms in a generalized heat transport equation. The dynamics of FEFSVA and its relation to the fluctuating source currents is described by constructing the matrix of dynamic dyadic Green's functions. In the framework of the fluctuation-dissipation theorem, we obtain correlation between the 6-vector fluctuating current densities with SVA through relating the power spectral density of these currents to the local temperature and the frequency-dependent constitutive parameters in a narrow band around the carrier frequency. With a motivation in the study of how the slowed down FEFSVA impacts on the heat conduction, we employ our formalism in order to obtain the group velocity of the FEFSVA propagating through a layered hyperbolic MM with the Drude type dispersion.