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

Imed Sassi; Faouzi Ghmari; Mohamed Salah Sifaoui

doi:10.1364/JOSAA.26.000480

Journal of the Optical Society of America A
Vol. 26,
Issue 3,
pp. 480-488
(2009)
•https://doi.org/10.1364/JOSAA.26.000480

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

Imed Sassi, Faouzi Ghmari, and Mohamed Salah Sifaoui

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Imed Sassi, Faouzi Ghmari, and Mohamed Salah Sifaoui, "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," J. Opt. Soc. Am. A 26, 480-488 (2009)

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Abstract

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.

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$θ_{0} = 0 °$ (1–3)	TM polarization		TE polarization
Values of $σ ∕ λ$	Applied Methods	Materials	Applied Methods	Materials
1. $0 < σ ∕ λ < 0.2$	SIBC and GOA	Al and W	SIBC and GOA	Al and W
2. $0.2 < σ ∕ λ < 0.3$	SIBC	Al	SIBC and GOA	Al and W
3. $0.3 < σ ∕ λ < 0.7$	Others Methods	Al and W	GOA	W
4. $σ ∕ λ < 0.1$	SIBC and GOA	Al and W	SIBC and GOA	Al and W
5. $0.1 < σ ∕ λ < 0.3$	SIBC	Al and W	GOA	W
6. $0.3 < σ ∕ λ < 0.7$	SIBC	Al	Others Methods	Al and W

$0 ° ∕ 30 °$	TM Polarization			TE Polarization
Material	$ε = 2.04$	$ε = 7.5$	Al	$ε = 2.04$	$ε = 7.5$	Al
${(σ ∕ λ)}_{\lim}$	0.02	0.1	0.2	0.04	0.2	0.7
$β_{\lim}$	1.62	8.05	15.79	3.23	15.8	44.71
${(ERR)}_{\lim}$	3.9%	3.7%	0.8%	0.1%	3.1%	0.6%
${(σ ∕ λ)}_{\lim}$		0.05	0.2		0.55	0.2
$β_{\lim}$		4.04	15.79		37.87	15.79
${(ERR)}_{\lim}$		4.9%	0.3%		4.1%	0.3%

$θ_{0} = 0 °$ (1–3)	TM polarization		TE polarization
Values of $σ ∕ λ$	Applied Methods	Materials	Applied Methods	Materials
1. $0 < σ ∕ λ < 0.2$	SIBC and GOA	Al and W	SIBC and GOA	Al and W
2. $0.2 < σ ∕ λ < 0.3$	SIBC	Al	SIBC and GOA	Al and W
3. $0.3 < σ ∕ λ < 0.7$	Others Methods	Al and W	GOA	W
4. $σ ∕ λ < 0.1$	SIBC and GOA	Al and W	SIBC and GOA	Al and W
5. $0.1 < σ ∕ λ < 0.3$	SIBC	Al and W	GOA	W
6. $0.3 < σ ∕ λ < 0.7$	SIBC	Al	Others Methods	Al and W

$0 ° ∕ 30 °$	TM Polarization			TE Polarization
Material	$ε = 2.04$	$ε = 7.5$	Al	$ε = 2.04$	$ε = 7.5$	Al
${(σ ∕ λ)}_{\lim}$	0.02	0.1	0.2	0.04	0.2	0.7
$β_{\lim}$	1.62	8.05	15.79	3.23	15.8	44.71
${(ERR)}_{\lim}$	3.9%	3.7%	0.8%	0.1%	3.1%	0.6%
${(σ ∕ λ)}_{\lim}$		0.05	0.2		0.55	0.2
$β_{\lim}$		4.04	15.79		37.87	15.79
${(ERR)}_{\lim}$		4.9%	0.3%		4.1%	0.3%

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Journal of the Optical Society of America A