Transformation of Fresnel’s interface reflection and transmission coefficients between normal and oblique incidence

Abstract

If w denotes an interface Fresnel reflection or transmission coefficient for s - or p -polarized light at an oblique angle of incidence ϕ, and z denotes the same coefficient at normal incidence, we find that w is an analytic function of z, w = f(z), that depends on ϕ but not on the specific optical properties of the two media on both sides of the interface. All four functions that correspond to the four distinct Fresnel coefficients and their inverses are determined. We single out for detailed examination, as an example, the relationship between the reflection of s -polarized light at 45° angle of incidence and at normal incidence for any transparent medium/absorbing medium interface by considering the mapping properties of the associated transformation and its inverse between the z and w planes. A useful byproduct of this investigation is a technique for the determination of the optical properties of isotropic and uniaxially and biaxially anisotropic absorbing media from measurement of reflectance at normal and oblique incidence.