In this paper we revisit the absorption and thermal emission of electromagnetic radiation by a rough surface. We use a numerical simulation of the absorptivity of a grating to explore the validity of the ray tracing approach. We show that it often predicts correctly the absorptivity and emissivity of a surface with characteristic lengths on the order of a wavelength. Recent advances in the understanding of the microscopic mechanism of thermal emission in the near field are used to discuss the data and to explain this surprising result. We also identify three different regimes depending on the ratio of the period to the wavelength: the homogenization regime, the resonance regime, and the geometrical optics regime.

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Using two different methods, we study the radiative properties of rough surfaces, such as the bidirectional or the hemispheric directional reflectivity. The first method, which we call exact, is the integral method (MI). It is based on the electromagnetic theory and Green's theorem to describe the system through a system of equations for the field and its normal derivative (sources) at the surface. The method is computation expensive, requiring the inversion of possibly large complex matrices. The second method (MIR), which we will use and for which we extend the validity to include transverse polarization, reformulates the integral method to solve it by an iterative approach. It has the advantage that its first iteration corresponds to the Kirchoff approximation (AK). The following (higher order) terms bring corrections to AK, while reducing notably the computation load. Our main purpose is to study the stability of the MIR and to find the limits of its validity when compared with the (exact) MI. Our numerical results were carried out for perfectly conducting or dielectric surfaces with sinusoidal roughness for two polarizations, transverse electric and transverse magnetic. [Journal translation]

Geometric optics approximation for emissivity from triangular surfaces was compared with exact scattering predictions from electromagnetic theory. Rigorous electromagnetic scattering theory was numerically formulated based on the differential method. We have used a numerical simulation of the emissivity of gold and tungsten for a wavelength equal 0.55 micron to explore the validity of the geometric optics. Surface parameter domains for the regions of accuracy of the geometric optics approximation are quantified and presented as functions of surface slope and roughness. Influence on the validity of the approximate method of multiple scattering, the shadowing effect and the cavity effect of metallic surface have been investigated. For the latter, our interest was focused on the mechanism that enhances the emissivity of an interface when ruling a grating. It has been seen that the mechanism responsible for the enhancement of the emissivity depends very much on the period of the grating. For gratings with a period much smaller than the wavelength, the roughness essentially behaves as a transition layer with a gradient of the optical index. For different period / wavelength ratio, we have found a good agreement between the differential method and the homogenization regime when the period was smaller

Exact solutions for reflection and emission are compared to different approximations, the surface impedance boundary condition (SIBC) and the geometric optics approximation (GOA). The effects of the incidence angle, the material surfaces, the nature of polarization, and random roughness on the behavior of emissivity and reflectivity have been quantified. The contribution of the effects on the reflection and emission is used to investigate the domains of validity of approximation models.