Measuring and sensing a complex refractive index by laser reflection near the critical angle

Abstract

We analyze the use of laser reflection near the critical angle for different refractometric measurements. We consider using dynamic reflectometry to obtain direct measurements of the angle differential of the reflectivity. From the angular profile of the differential reflectivity it is possible to obtain measurements of the absolute values of the real and imaginary parts of the refractive index (RI). For sensing purposes we consider monitoring the reflectance and/or its angular derivative near the critical angle for high-resolution sensing. We give simple and general formulas to estimate the resolution of the different measurements and give some estimates based on our experimental system. We show that a single instrument may be able to measure the real and imaginary parts of the RI with an uncertainty in the order of 10 26 . In sensing variations of the RI, the same instrument may yield a resolution of the order of 10 27 for slow variations. However, if the RI is modulated harmonically in time, the same instrument might detect an amplitude of modulation as low as ;10 210 . In addition, we study the applicability of the technique to turbid media consisting of particles in suspension. We illustrate the potential of the technique for that application with a few experiments on liquid milk and on water suspensions of polystyrene particles. We give experimen- tal evidence showing it is possible to sense the physical state of particles in solution even when the particles have a diameter as large as the wavelength. We also show that the RI of a liquid sample can be moni- tored through a physical or chemical process even if the liquid is vigor- ously stirred. © 2002 Society of Photo-Optical Instrumentation Engineers.