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.