Fresnel's interface reflection coefficients for the parallel and perpendicular polarizations: global properties and facts not found in your textbook

Abstract

This paper reviews recently obtained results related to Fresnel's reflection coefficients which play a central role in the optics of light reflection by surfaces and thin films. Topics include conjugate and reciprocal interfaces between transparent media, reflectance matching between normal and oblique incidence, and reflectance switching. For light reflection at interfaces between transparent and absorbing media, contours of constant pseudo-Brewster angle and of constant principal angle are presented in the complex plane, along with a discussion of a condition of maximum minimum parallel reflectance at oblique incidence. Conformal mappings that describe the transformation of the Fresnel coefficients between normal and oblique incidence, and between the s and p polarizations at the same angle, are included. Reflectance for incident light of arbitrary polarization is also considered. Finally, trajectories that describe the evolution of the Fresnel coefficients with angle of incidence are presented.