Remote photoluminescence effects mediated by asymmetric semi-transparent mirrors and their potential application for non-invasive biosensing

Diabetes is a growing problem worldwide and is expected to become worse without proper management or awareness. Current estimates predict that the number of those suffering with diabetes mellitus will rise from 463 million worldwide in 2021 to roughly 700 million by 2045. Currently, for many sufferers the only available means of measuring and treating their diabetes is through invasive single-use tests that measure glucose levels in the blood. While accurate, these flash measurements give only snapshots of current glucose levels and often cause pain, discomfort and embarrassment, discouraging regular testing and results in poor glycaemic control which can lead to complications such as cardiovascular disease, limb amputations, neuropathy and retinopathy. Additionally, the use of disposable tests not only contributes to the growing global waste crisis but also adds extra financial burden to sufferers in that would be exacerbated for those poorer or deprived regions. To resolve these issues, many attempts at constructing non-invasive glucose sensors have been made. However, these often face challenges when differentiating the molar absorptivity of many other compounds and proteins within the blood from that of glucose as well as account for the skins opacity and its ability to scatter light which limits the accuracy and applicability of these devices. In this work we propose a new method to non-invasively measure glucose concentrations using near-infrared light. At these wavelengths, light can freely pass through the skin, allowing us to exploit the photoluminescent behaviour of Er3+ ions positioned outside the body. By measuring the change in the photoluminescent behaviour of these Er3+ ions, the concentration of glucose molecules in the skin’s interstitial fluid can be non-invasively determined. To achieve this, we introduce medium space coordinates that allows us to preserve our concept of a free space photon in a dielectric medium and extend the quantisation scheme developed by Bennett, et al. (Bennett, et al., Eur. J. Phys. 37(1), p.014001) across different media. Then, by introducing the quantum mirror image method we can quantise the electromagnetic field in the presence of a semi-transparent mirror system with light incident from both sides. We then utilise medium space coordinates to expand upon the work by Furtak-Wells, et al. (Furtak-Wells, et al., Phys Rev A, 97(4), p.043827) to include the more realistic scenario where the semi-transparent mirror has absorption and is positioned at the interface between two media with different refractive indices. In this scenario, the forward-reverse reflectance of the mirror no longer needs to be the same and the phase changes experienced by light interacting with the mirror can now take a much wider array of allowable values. When this tunable asymmetric semitransparent mirror is placed between two distant atoms (atom a and b), quantum interference effects between the possible paths of photons emitted from atom a and those emitted from the projected mirror-image of atom b allows an interaction to occur between these atoms over a distance larger than is possible with conventional dipole-dipole interactions. Using spin coating and vapour deposition methods, samples are constructed that allow us to control the properties of the semi-transparent mirror and the atom/mirror-image atom distance. Then, with these techniques photoluminescent erbium doped nanoparticles and glass substrates are fixed on opposite sides of a tunable semi-transparent mirror a distance 2.2mm apart. The photoluminescent behaviour of the system was analysed using the Laplace transform, the photoluminescent lifetime and the shape of the photoluminescent decay curve for different mirror properties and atom/mirror-image atom distances. From this we were able to find evidence that indicates the presence of a remote mirror-mediated effect on the photoluminescent system that depends on both the properties of the mirror and the atom/mirror-image atom distance. We conclude by proposing further experiments to determine the feasibility of the remote mirror-mediated effect for the in-vitro sensing of glucose concentrations in solution. Potential improvements to the experimental setup and considerations of the differences between the in-vitro model of the skin are discussed. Finally, potential avenues for further theoretical and experimental research into this effect are proposed.