Radiative-conductive heat transfer dynamics in dissipative dispersive anisotropic media

Abstract We develop a self-consistent theoretical formalism to model the dynamics of heat transfer in
dissipative, dispersive, anisotropic nanoscale media, such as metamaterials. We employ our envelope
dyadic Green’s function method to solve Maxwell’s macroscopic equations for the propagation of
fluctuating electromagnetic fields in the media. We assume that the photonic radiative heat transfer
mechanism in the media is complemented by phononic mechanisms of heat storage and conduction,
accounting for effects of local heat generation and material phase transitions. By employing the Poynting
theorem and the fluctuation-dissipation theorem, we derive novel closed-form expressions for the coupling
term of photonic and phononic subsystems, which contains the heating rate and the radiative heat power
terms, as well as for the radiative heat flux. We apply our formalism to the paraxial heat transfer
in uniaxial media and present relevant closed-form expressions. By considering a Gaussian transverse
temperature profile, we also obtain and solve the integro-differential heat diffusion equations to model
the paraxial heat transfer in uniaxial reciprocal media.