研究目的
To develop an efficient and numerically stable method for calculating the optical quantities of multi-layer systems with randomly rough boundaries using the second order Rayleigh–Rice theory.
研究成果
An efficient method for calculating optical quantities in multi-layer systems with rough boundaries was developed using second-order RRT. The method handles arbitrary PSDF and includes polarization mixing. For Gaussian PSDF, integrals simplify to single numerical evaluations. The approach is suitable for optical characterization and synthesis of thin films with roughness, offering improved numerical stability and efficiency over previous methods.
研究不足
The Rayleigh–Rice theory is limited to roughness with small slopes and heights much smaller than the wavelength of light. The method may involve numerical challenges such as simple poles in integrands for non-absorbing media and potential overflows in exponential factors for thick absorbing layers. It assumes isotropic media and parallel mean planes of boundaries.
1：Experimental Design and Method Selection:
The method is based on the Rayleigh–Rice theory (RRT) for electromagnetic wave reflection from rough surfaces, extended to multi-layer systems. It uses a perturbation approach with a four-dimensional matrix formalism inspired by Yeh's method, but optimized to a two-dimensional formalism for numerical efficiency. The theory assumes small roughness heights and slopes compared to the wavelength of light.
2：Sample Selection and Data Sources:
The system consists of N+1 isotropic, homogeneous, nonmagnetic media separated by N slightly rough boundaries with parallel mean planes. The roughness is described by functions fq(r) with statistical properties given by power spectral density functions (PSDF).
3：List of Experimental Equipment and Materials:
No specific experimental equipment is mentioned as the paper is theoretical; it involves mathematical modeling and numerical calculations.
4：Experimental Procedures and Operational Workflow:
The process involves formulating boundary conditions in Fourier space, solving perturbatively up to second order, and deriving Fresnel coefficients. Numerical integration is required for general PSDF, but analytical simplifications are possible for Gaussian PSDF.
5：Data Analysis Methods:
Data analysis involves evaluating integrals numerically or analytically, using statistical averaging over roughness realizations, and computing optical quantities like reflection and transmission coefficients.
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