Numerical Analysis of Mueller Matrix for Random Rough Surfaces

Fig. 3. Variation curve of scattering Mueller matrix on random rough surface with incident angle ( $δ = 0.2 λ, l = 4 λ$ ). (a) $m_{00} / m_{00}$ ; (b) $m_{01} / m_{00}$ ; (c) $m_{10} / m_{00}$ ; (d) $m_{11} / m_{00}$ ; (e) $m_{22} / m_{00}$ ; (f) $m_{23} / m_{00}$ ; (g) $m_{32} / m_{00}$ ; (h) $m_{33} / m_{00}$

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Fig. 4. Variation curve of scattering Mueller matrix on random rough surface with incident angle( $δ = 0.2 λ, l = 2 λ$ ). (a) $m_{00} / m_{00}$ ; (b) $m_{01} / m_{00}$ ; (c) $m_{10} / m_{00}$ ; (d) $m_{11} / m_{00}$ ; (e) $m_{22} / m_{00}$ ; (f) $m_{23} / m_{00}$ ; (g) $m_{32} / m_{00}$ ; (h) $m_{33} / m_{00}$

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Fig. 5. Variation curve of scattering Mueller matrix on random rough surface with incident angle ( $δ = 0.3 λ, l = 2 λ$ ). (a) $m_{00} / m_{00}$ ; (b) $m_{01} / m_{00}$ ; (c) $m_{10} / m_{00}$ ; (d) $m_{11} / m_{00}$ ; (e) $m_{22} / m_{00}$ ; (f) $m_{23} / m_{00}$ ; (g) $m_{32} / m_{00}$ ; (h) $m_{33} / m_{00}$

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Fig. 6. Variation curve of scattering Mueller matrix on random rough surface with relative roughness. (a) $m_{00}$ ; (b) $m_{01}$ ; (c) $m_{10}$ ; (d) $m_{11}$ ; (e) $m_{22}$ ; (f) $m_{23}$ ; (g) $m_{32}$ ; (h) $m_{33}$

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Fig. 7. Fitting to the relationship curve of $m_{22}$ and relative roughness for copper

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Table 1. Refractive index of the material at a wavelength of 0.905 μm
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Table 1. Refractive index of the material at a wavelength of 0.905 μm
Target material Copper Iron Nickel Glass Lithium niobate
n 0.3+5.768i 3.12+3.87i 2.65+4.63i 1.5 $n_{o} = 2.23, n_{e} = 2.16$

Table 2. Fitted $δ / l$ by three methods

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Table 2. Fitted $δ / l$ by three methods

Method	Linear fitting	Nonlinear fitting	Fourier fitting
Expression	$\frac{δ}{l} = \frac{1}{b} (m_{22} - a)$	$\frac{δ}{l} = - \frac{B + (B^{2} + 4 C \cdot m_{22} {- 4 A \cdot C)}^{\frac{1}{2}}}{2 C}$	$\begin{array}{l} \frac{δ}{l} = a_{0} + a_{1} c o s (w \cdot m_{22}) + b_{1} s i n (w \cdot m_{22}) + \\ a_{2} c o s (2 w \cdot m_{22}) + b_{2} s i n (2 w \cdot m_{22}) + \\ a_{3} c o s (3 w \cdot m_{22}) + b_{3} s i n (3 w \cdot m_{22}) \end{array}$
Coefficient	$\begin{array}{l} a = - 1.25466, \\ b = 42.24163 \end{array}$	$\begin{array}{l} A = - 2.54789, B = 42.24163, \\ C = - 174.09065 \end{array}$	$\begin{array}{l} w = 2.496, a_{0} = 4.097, a_{1} = - 3.26, \\ b_{1} = 5.449, a_{2} = - 1.36, b_{2} = - 2.638 \\ a_{3} = 0.6467, b_{3} = 0.06506 \end{array}$

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Lu Yang, Qian Tong, Zhiyin Zhou, Siyuan He, Zhe Song. Numerical Analysis of Mueller Matrix for Random Rough Surfaces[J]. Laser & Optoelectronics Progress, 2023, 60(5): 0529002

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