Using Narrow Line-Width Laser to Measure the Thickness and Refractive Index of the Film

We demonstrate applications of a novel setup which is used for measuring the relative phase difference between S and P polarization at an oblique incidence point in optically denser medium by analyzing the relative frequency shift of adjacent axial modes of S and P resonances of a monolithic folded Fabry-Perot cavity (MFC). The relative phase difference at a reflection point A in an optically denser medium is inferred to be around -167.4° for a confocal cavity and -201.1° for a parallel cavity. Given the n1, n3, φ1, φ3, λ, and Δ, the elliptic formula tan(ψ)exp(iΔ) = Rp/Rs is used to find a solution for thickness d and refractive index n2 of the thin film coated on point A, where Rs and Rp are total refractive index of s and p component of light related to two unknown values. Since it is hard to deduce an analytical solution for thickness and refractive index of the film, we firstly used exhaustion method to find the set of solution about thickness and refractive index when assumed there is no light absorption by the film and then Particle Swarm Optimization (PSO) to find a set of solution of thickness and complex refractive index which accounts the light absorption by the film.