Efficient angle-resolved transfer-matrix method incorporating Gaussian roughness for THz multilayers

We present the efficient angle-resolved rough-surface transfer-matrix method (RS-TMM). This compact formulation involves Gaussian roughness statistics and k z -dependent attenuation factors explicitly in the (2 × 2) interface matrices. The entire multilayer stack can subsequently be solved in a single matrix product, and the formulation analytically recovers the smooth-surface limit as σ r → 0. The formulation preserves the algebraic clarity, numerical stability, and O ( N ) computational complexity of classical matrix optics, while eliminating the need for per-layer parameter tracking, meshing, and iterative solvers. The method’s analytical consistency is validated by proving its algebraic equivalence to the recursive Green-function formulation within the Rayleigh domain. For frequencies 0.1-1 THz and root-mean-square surface roughness σ r ≤60μm, the model agrees closely with recursive-method benchmarks. Running in milliseconds on a laptop, RS–TMM enables frequency-, angle-, and material-parameter sweeps for real-time indoor THz links and imaging.