Study of the emissivity of rough surfaces periodic using the method of coupled waves analysis (CWA) compared with method of geometrical optics approximation (GOA)

Taoufik Ghabara

doi:10.4236/ns.2011.31008

Abstract

We present in this paper a numerical study of the validity limit of the geometrical optics approximation compared with a differential method which is established according to rigorous formalisms based on the electromagnetic theory. The precedent studies show that this method is adapted to the study of diffraction by periodic rough surfaces. We determine by two methods the emissivity of gold and tungsten for surfaces with a rectangular or sinusoidal profile, for a wavelength equal to 0.55 microns. The monochromatic directional emissivity of these surfaces clearly depends on the angle of incidence, the surface profile, height, period and the nature of the material. We perform our calculations by a method of coupled wave analysis (CWA) and a geometric optics method (GOA). The latter method is theoretically valid only when the dimensions of the cavities are very large compared to the wavelength, while the CWA is theoretically correct whatever these dimensions. The main purpose of this work is to investigate the validity limit of GOA compared with CWA. The obtained results for a fixed height of the grating, allowed us to delimit the validity domain of the optic geometrical approximation for the treated cases. Finally, the agreement between the emissivity calculated by the differential method and that given on the basis of the homogenization theory is satisfactory when the period is much smaller than the wavelength.

Highlights

The theoretical or experimental determination of radiative properties of rough surfaces is the subject of several researches
While the integral methods are more effective to study the scattering of electromagnetic waves by rough surfaces [5,6], the differential methods seem best suited to solving the same problem with periodic rough surfaces
For an angle of incidence equal to 1 ̊, it follows an agreement between the differential method (CWA) and the geometric method (GOA) for gold and tungsten in the following cases: From the ratio d equal to 1.6 when the height h of the grating is equal 0.1 (Figures 3(a,b)), and ratio d above 3.2 when h is equal 1

Summary

Introduction

The theoretical or experimental determination of radiative properties of rough surfaces is the subject of several researches. The modelling of directional monochromatic emissivity of a rough surface remain a subject of theoretical, experimental and numerical researches [1,2] These parameters are involved in several application areas ranging from the calculation of energy exchange by radiation in the design of selective rough surfaces, in addition to current applications on the semiconductor industry [3] and the Solar energy [4]. In this context two methods are presented, one exact and based on electromagnetic theory, while the second is approximate and based on geometrical optics. While the integral methods are more effective to study the scattering of electromagnetic waves by rough surfaces [5,6], the differential methods seem best suited to solving the same problem with periodic rough surfaces

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