Correlation of Optical Constants and Morphologies with Mueller Matrix for Micro-Rough Surfaces
This paper focuses on the coupling relationships between the optical constants (<i>n</i>: refractive index; <i>k</i>: extinction coefficient) and Mueller matrix elements, as well as between the morphological parameters (<i>σ</i>: root mean square roughness; <i&...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Applied Sciences |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2076-3417/15/11/6149 |
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| Summary: | This paper focuses on the coupling relationships between the optical constants (<i>n</i>: refractive index; <i>k</i>: extinction coefficient) and Mueller matrix elements, as well as between the morphological parameters (<i>σ</i>: root mean square roughness; <i>τ</i>: correlation length) and Mueller matrix elements, of randomly micro-rough surfaces. The electromagnetic response of randomly micro-rough surfaces was simulated by the finite-difference time-domain method, so that the rough surfaces’ reflection coefficients of incident light in the p and s directions could be obtained. According to the formula for the Jones-to-Mueller matrix conversion, we obtained a 4 × 4 Mueller matrix of rough surfaces. The simulation method was validated with experimental results measured by Mueller matrix spectroscopic ellipsometry. It was found that the Mueller matrix element <i>m</i><sub>12</sub> has great potential to invert the optical constants of the rough surfaces, whose refractive indices, <i>n</i>, and extinction coefficients, <i>k</i>, are in the ranges of 0 ≤ <i>n</i> ≤ 4 and 0 ≤ <i>k</i> ≤ 10, respectively. The Mueller matrix element <i>m</i><sub>34</sub> is proportional to the morphological parameters <i>σ</i>/<i>λ</i> (<i>λ</i>: incident wavelength) or <i>σ</i>/<i>τ</i>. Moreover, the expressions (<i>S</i> + <i>β</i><sub>2</sub>) ∝ <i>σ</i>/<i>λ</i> and (<i>S</i> + <i>β</i><sub>2</sub>) ∝ <i>σ</i>/<i>τ</i> can be applied to predict the morphologies of rough surfaces within morphological parameter ranges of 0.003 ≤ <i>σ</i>/<i>λ</i> ≤ 0.015 and 0.125 ≤ <i>σ</i>/<i>τ</i> ≤ 0.75. This research signifies a key step toward the ability to invert the morphological parameters or optical constants of micro-rough surfaces through a Mueller matrix. |
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| ISSN: | 2076-3417 |