Critical-Angle Differential Refractometry of Lossy Media: A Theoretical Study and Practical Design Issues

At a critical angle of incidence, Fresnel reflectance at an interface between a fronttransparent and a rear lossy medium exhibits sensitive dependencies on the complex refractiveindex of the latter. This effect facilitates the design of optical sensors exploiting single (or multiple)reflections inside a prism (or a parallel plate). We determine an empirical framework that capturesperformance specifications of this sensing scheme, including sensitivity, detection limit, range oflinearity and—what we define here as—angular acceptance bandwidth. Subsequently, we developan optimization protocol that accounts for all relevant optical or geometrical variables and that canbe utilized in any application.