Direct and Indirect Methods for Calculating Thermal Emission From Layered Structures With Nonuniform Temperatures

Abstract

The determination of emissivity of layered structures is critical in many applications, such as radiation thermometry, microelectronics, radiative cooling, and energy harvesting. Two different approaches, i.e., the “indirect” and “direct” methods, are commonly used for computing the emissivity of an object. For an opaque surface at a uniform temperature, the indirect method involves calculating the spectral directional-hemispherical reflectance to deduce the spectral directional emissivity based on Kirchhoff’s law. On the other hand, a few studies have used a combination of Maxwell’s equations with the fluctuation-dissipation theorem to directly calculate the emissivity. The present study aims at unifying the direct and indirect methods for calculating thermal emission from layered structures with a nonuniform temperature distribution. Formulations for both methods are given to illustrate the equivalence between the indirect and the direct methods. Thermal emission from an asymmetric Fabry-Perot resonance cavity with a nonuniform temperature distribution is taken as an example to show how to predict the intensity, emissivity, and the brightness temperature. The local density of states, however, can only be calculated using the direct method.

Spectral and total temperature-dependent emissivities of few-layer structures on a metallic substrate

“…We underline that in contrast to many works this method does not rely on Kirchhoff's law: we do not compute the reflectivity to determine the hemispherical emissivity. However, a previous work [18] emphasized the equivalence of the two methods: both of them allow considering temperature profiles in the emitting layers when the multilayer structure is not at equilibrium. In the following, we restrict ourselves to the equilibrium case.…”

Photo-induced thermal radiation within multilayers optics

“…Over a given period of time, we place ourselves in the situation of an optical filter where each layer has a different temperature. In this situation, the model of thermal radiation in an 1D multilayer structure can be found in [3], [4], or [5]. The major steps of the modelling are recalled here.…”

“…- To compute the thermal radiation of the medium, one needs to introduce this thermal current density in the Maxwell equations. Most of the literature [3], [4], [5], [17] make the use of the Dyadic Green function to solve this problem. We choose to use the results of the theory of bulk scattering [18] that enable to compute the power spectrum of a bulk distribution of current.…”

“…Thermal radiation in multilayers originates from both the ambient and the absorption-induced temperature, and has mostly been studied for opaque samples or for transparent samples supporting a constant temperature in time. Predictions can be found in the literature [2], [3], [4], [5] but often rely on approximations or assumptions, and are rarely connected to photo-induced effects in optical coatings.…”

Spectral emittance measurements of micro/nanostructures in energy conversion: a review

“…The study of emittance for micro/nanostructures encompasses both numerical calculations and experimental measurements [18]. Generally, both emittance measurements [19] and calculations [20] include the direct method and the indirect method. The latter uses the reflectance to calculated emittance based on Kirchhoff's law.…”