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

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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.

Keywords

Periodic Roughness; Differential Method (CWA); Geometric Optics Approximation (GOA); Homogenization Theory; Emissivity.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Carminati, R. and Greffet, J.J. (1998) A model for the radiative properties of opaque rough surfaces. Heat transfer, Proceedings of 11th IHTC, 7, Kyongyu, Koria, 23-28 August 1998.
[2]	Le, G., Olivier, J. and Greffet, J.J. (1997) Experimental and theoretical, porting a surface-phonon polariton. Physical Review B, 55, 10105-10114. doi:10.1103/PhysRevB.55.10105
[3]	Chinnok, C. (1994) Laser based systems easily find semiconductor defects. Laser Focus World, 30, 59-63.
[4]	He, X., Torranse, Sillon, F.X. and Greenberg, D. (1991) A comprehensive physical model for light reflection. Computer Graphics, Annual Conference Serie, 25, 175- 186.
[5]	Kakeun, T., Dimenna, R.A. and Buckius, R. (1997). Region of validity of the geometric optics approximation for angular scattering from very rough surfaces. International Journal of Heat and Mass Transfer, 40, 49-59.
[6]	Ranches. Gil, J.A. and Vesperinas, M.N. (1991) Light scattering from random rough dielectric surfaces. The Journal of the Optical Society of America, 8, 1270-1286.
[7]	Kong, J.A. (1977) Second-order coupled-mode equations for spatially periodic media. Journal Optical Society of America, 67, 825-829. doi.: 10.1364/JOSA.67.000825
[8]	Moharam, M.G. and Gaylord, T.K. (1980) Criteria for bragg regime diffraction by phase gratings. Optics Communications, 32, 14-22. doi:10.1016/0030-4018(80)90304-1
[9]	Moharam, M.G. and Gaylord, T.K. (1981) Coupled-wave analysis of reflection gratings. Applied Optics, 20, 240-244.
[10]	Moharam, M.G. and Gaylord, T.K. (1981) Rigorous coupled-wave analysis of planar grating diffraction. The Journal of the Optical Society of America, 71, 811-818. doi:10.1364/JOSA.71.000811
[11]	Moharam, M.G. and Gaylord, T.K. (1982) Chain-matrix analysis of arbitrary-thickness dielectric reflection gratings. Journal Optical Society of America, 72, 187-189. doi:10.1364/JOSA.72.000187
[12]	Moharam, M.G. and Gaylord, T.K. (1983) Rigorous coupled-wave analysis of grating diffraction-E-mode polarization and losses. Journal Optical Society of America, 73, 451-455. doi:10.1364/JOSA.73.000451
[13]	Moharam, M.G. and Gaylord, T.K. (1982). Diffraction analysis of dielectric surface-relief gratings. Journal Optical Society of America, 72, 1385-1392. doi:10.1364/JOSA.72.001385
[14]	Moharam, M.G. and Gaylord, T.K. (1986) Rigorous coupled-wave analysis of metallic surface-relief gratings. Journal Optical Society of America. A, 1, 1780-1787.
[15]	Chateau, N. (1994) Algorithm for the rigorous coupled-wave analysis of grating diffraction. Journal Optical Society of America. A, 11, 1321-1331.
[16]	Pai, D.M. and Awada, K.A. (1991) Analysis of dielectric gratings of arbitrary profiles and thicknesses. Journal Optical Society of America. A, 8, 755-762.
[17]	Li, L.F. and Haggans, C.W. (1993) Convergence of the coupled-wave method for metallic lamellar diffraction gratings. Journal Optical Society of America. A, 10, 1184-1189. doi:10.1364/JOSAA.10.001184
[18]	Ody Sacadura, J.F. (1972) Influence de la rugosité sur le rayonnement thermique émis par les surfaces opaques, Essai de modèle. Journal Int. Heat Mass Transfer, 15, 1451-1465.
[19]	Kanayama, K. (1972) Apparent directionnal emitances of V groove and circulair-groove rough surfaces. Journal Heat Transfer Japenese Research, 1, 11-32.
[20]	Druelle, P. (1978) Influence de macro-rugosités sur les caractéristiques radiatives de certaines surfaces. Application aux acier inoxydables, Thesis of Doctor Engineer. Central School of Arts and Manufactures.
[21]	Druelle, P. (1980) Caractéristiques radiatives des aciers inoxydables dans le domaine du visible, Schématisation de la rugosité à l’aide de calottes sphériques et étude d’un capteur solaire hémisphérique, Thesis of Doctor Engineer. Central School of Arts and Manufactures.
[22]	Ghamari, F. (1996) Contribution à l’étude de l’influence de la rugosité sur l’émissivité des surfaces opaques, PHD Thesis, Faculty of Sciences Tunis.
[23]	Bouchitté, R. and Petit, R. (1985) Homogeinization techniques as applied in the electromagnetic theory of gratings. Electromagnetics, 5, 17-36. doi:10.1080/02726348508908135
[24]	Southwell, W.H. (1991) Pyramid-array surface-relief structures proceducing antireflection index matching on optical surfaces. Journal Optical Society of America. A, 8, 549-553. doi:10.1364/JOSAA.8.000549
[25]	Petit, R. and Vincent, P. (1980) Electromagnetic theory of gratings. Springer-Verlag, Berlin, Heidelberg, New York.
[26]	Ghabara, T. (2003) Etude de l`emissivite des surfaces rugueuses periodiques a l`aide des methods d`analyse en ondes couplees. Comparaison avec la methode de l`optique geometrique. PHD Thesis, Faculty of Sciences Tunis.
[27]	Ghamari, F. and Ghabara, T. (2004) Influence of microroughness on emissivity. Journal of Applied Physics, 96, 2656-2664. doi:10.1063/1.1776634
[28]	Ghabara, T., Ghmari, F. and Sifaoui, S. (2007) Emissivity of triangular surfaces determined by differential method: From homogenization to validity limit of geometrical optics. American Journal of Applied Sciences, 4, 146-154. doi:10.3844/ajassp.2007.146.154
[29]	Ghamari, F., Sassi, I. and Sifaoui, M. (2005) Directional hemispherical radiative properties of random dielectric rough surfaces. Waves in Random and Complex Media, 15, 469. doi:10.1080/17455030500361838
[30]	Matchiane, M.B., Ghamari, F. and Sifaoui, (2004) Correction de L`approximation de Kirchhoff par la methode integrale reformulee, cas des reflectivites de surfaces sinusoidale. Canadian Journal of Physics, 82, 303. doi:10.1139/p04-008
[31]	Sassi, I. and Sifaoui, M.S. (2007) Comparison of geometric optics approximation and integral method for reflection and transmission from microgeometrical dielectric surfaces. American Journal of Applied Sciences, 4, 451-462.
[32]	Sassi, I. and Sifaoui, M.S. (2009) Effect of the material of rough surfaces and the incident light polarization on the validity of the surface impedance boundary condition and the geometric optics approximation for reflection and emission. American Journal of Applied Sciences, 4, 480- 488.