Physics-constrained, Kramers–Kronig-consistent retrieval of the refractive index and thickness of porous silicon thin films from multi-angle reflectance

The retrieval of the optical constants of a thin film from its reflectance becomes demanding when the film is not a homogeneous, flat-interface material, as in porous silicon. There the standard approach, postulating a dielectric model and fitting its parameters, grows less reliable, the residual error increases, and the fit can become time consuming. For such complex materials we propose a change of point of view, representing the refractive index n(λ) directly on a set of nodes constrained only by simple, physics-founded rules rather than by an assumed dielectric model. The method is implemented in a Python code, Ophira (OPtical tHIn-film Reflectance Analyzer), which retrieves n(λ) and the thickness d from spectra measured at several incidence angles. The retrieval is constrained only by smoothness, monotonicity in the transparent region and optical-thickness anchoring, and is verified a posteriori through Kramers-Kronig consistency and geometric triangulation. Applied to porous silicon across a range of porosities, including the high-porosity regime where effective-medium and oscillator models struggle, it yields reflectance fits and thicknesses consistent with electron-microscopy cross sections and with an established oscillator-based analysis. Ophira is proposed as a complement to model-based tools, not a replacement.