Detecting and analysing wavelength-scale optical gradients at an interface by their effects on the internal reflectance near the critical angle

TL;DR

This paper investigates how a refractive-index gradient at an interface affects internal reflectivity near the critical angle, providing theoretical insights useful for biological and medical applications involving surface phenomena.

Contribution

It offers a theoretical analysis of reflectivity near the critical angle with a depth-dependent refractive index, highlighting how to detect and characterize surface gradients.

Findings

Reflectivity curves are sensitive to refractive-index gradients.

The analysis helps identify the presence of surface gradients.

Insights into the viability of characterizing surface gradients.

Abstract

Light's internal reflectivity near a critical angle is very sensitive to the angle of incidence and the optical properties of the external medium near the interface. Novel applications in biology and medicine of subcritical internal reflection are being pursued. In many practical situations the refractive index of the external medium may vary with respect to its bulk value due to different physical phenomena at surfaces. Thus, there is a pressing need to understand the effects of a refractive-index gradient at a surface for near-critical-angle reflection. In this work we investigate theoretically the reflectivity near the critical angle at an interface with glass assuming the external medium has a continuous depth-dependent refractive index. We present graphs of the internal reflectivity as a function of the angle of incidence, which exhibit the effects of a refractive-index gradient at the interface. We analyse the behaviour of the reflectivity curves before total internal reflection is achieved. Our results provide insight into how one can recognise the existence of a refractive-index gradient at the interface and shed light on the viability of characterising it.