Reflectivity of a gaussian beam near the critical angle with external optically absorbing media

One can use the angle-modulated reflectance of a gaussian beam near the critical angle to sense with high resolution the index of refraction of the external medium. We analyze in detail the reflectivity of a gaussian beam near the critical angle and its dependence on the optical absorption of the external medium. The given formulation is relatively simple and is useful in discerning the effects of the various parameters involved on the reflectivity and its differentials with respect to the angle of incidence. The results presented can be readily used for the quantitative design of novel sensors based on modulated reflectance near the critical angle. We provide a simple algebraic expression for the loss of sensitivity of modulated reflectance near the critical angle as the sample's absorption coefficient increases. We find that, in a typical case, the sensitivity has decreased to approximately half its value for transparent samples when the absorption coefficient has increased to 25 cm(-1). We conclude that modulated reflectance near the critical angle remains a competitive technique for monitoring the index of refraction of an external medium with an absorption coefficient of as much as 120 cm(-1). We compared experimentally obtained curves of the first differential of the reflectivity with respect to the angle of incidence with theory and found good agreement.