Abstract
At a critical angle of incidence, Fresnel reflectance at an interface between a front transparent and a rear lossy medium exhibits sensitive dependencies on the complex refractive index 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 captures performance specifications of this sensing scheme, including sensitivity, detection limit, range of linearity and—what we define here as—angular acceptance bandwidth. Subsequently, we develop an optimization protocol that accounts for all relevant optical or geometrical variables and that can be utilized in any application.
Highlights
Refractive index sensors are intensely investigated for numerous biomedical [1,2,3], chemical [4,5]and industrial [6,7] applications
Associated with Fresnel reflectance properties at planar interfaces, differential refractometry offers an alternative path to sensing refractive index changes, by exploitation of interference [28], deflection [29] or critical-angle [30,31,32,33,34,35] effects
The underlying principle of operation is simple: provided that the front medium is optically denser than the sample, there exists a sharp transition from total internal reflection (TIR) to partial internal reflection, taking place at a critical angle which corresponds to the location of an abrupt discontinuity in the derivative of reflectance with respect to incidence angle
Summary
Refractive index sensors are intensely investigated for numerous biomedical [1,2,3], chemical [4,5]. The reflectance derivative with respect to incidence angle, peaking to a finite value, is no longer the proper quantity to conceptualize the sensing principle; this purpose is better served by reflectance derivatives with respect to the real and imaginary index of the sample These are negative quantities exhibiting local extrema at the vicinity of the transition from ATIR to partial internal reflection, albeit at slightly different “critical” angles. We attempt a theoretical study of CADR with lossy media, accounting for (i) the standard prism configuration, (ii) an alternative geometry that exploits multiple reflections inside a parallel plate Both schemes are, in principle, compatible with optofluidic technologies and static or real-time monitoring applications. Our results provide a universal roadmap for rapid performance evaluation and optimization of CADR devices, which might be essential for pushing the technique’s detection limit from the current standard (∼ 100 μRIU) down to the current state-of-the-art (∼ 1 μRIU for CADR [31], as well as for all noninterferometric methods), or even lower
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