Correlation of Optical Constants and Morphologies with Mueller Matrix for Micro-Rough Surfaces

This paper focuses on the coupling relationships between the optical constants (n: refractive index; k: extinction coefficient) and Mueller matrix elements, as well as between the morphological parameters (σ: root mean square roughness; τ: 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 m₁₂ has great potential to invert the optical constants of the rough surfaces, whose refractive indices, n, and extinction coefficients, k, are in the ranges of 0 ≤ n ≤ 4 and 0 ≤ k ≤ 10, respectively. The Mueller matrix element m₃₄ is proportional to the morphological parameters σ/λ (λ: incident wavelength) or σ/τ. Moreover, the expressions (S + β₂) ∝ σ/λ and (S + β₂) ∝ σ/τ can be applied to predict the morphologies of rough surfaces within morphological parameter ranges of 0.003 ≤ σ/λ ≤ 0.015 and 0.125 ≤ σ/τ ≤ 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.