Computational Modelling of Nanoscale Interactions for Nanophotonics and Biosensing

Abstract

In the pursuit of understanding molecular behaviour, advanced sensing techniques have been developed to detect things that would otherwise not be visible to the naked human eye. A subclass of these techniques relies on the resonant properties of optical whispering gallery modes (WGMs) to detect single molecules and to probe their conformational changes. Whilst WGM-based biosensors have extraordinary sensitivity, it remains a challenge to extract information about the target molecules from the biosensor signals due to the multivariate nature of the problem. The spectral signals encode information about the species, charge, and conformation of the target molecule, as well as the location of the molecule within the biosensing field.

This thesis explores the relationship between these variables and the magnitude of the biosensor signals using advanced multi-scale computational methods in photonics and molecular modelling. In the first section, we investigate biosensor signals from the catalytic cycle of Adenylate Kinase (AdK); a large protein with more than 3000 atoms. We assume that the AdK molecule is situated in a region of high field intensity (plasmonic hot spot) to ensure that the molecule can be detected above the noise threshold of the WGM biosensor. The plasmonic field is typically non-uniform over the length scale of the AdK molecule. We demonstrate that an atomistic model is required to decode the kinetics of enzymes from the biosensor signals.

In the second section, we develop a model to investigate solvent effects on the polarizability of Ångstrom-sized amino acids. Molecular polarizability serves as a molecular fingerprint that is encoded in the biosensor signals. Our model builds on existing methods in density functional theory to calculate molecular polarizability, including solute-solvent interactions using an implicit solvent model. We combine elements from electronic structure theory and classical electromagnetism to account for changes in the local biosensing fields due to the solvent environment. The hybrid polarizability model captures the variation of molecular polarizability as a function of protonation state and performs approximately 7 times faster than the Onsager self-consistent reaction field model.

In the third section, we investigate a different problem, concerning dispersion effects in matter-wave lithography. Fabricating patterned nanostructures with matter-waves can help to realise new nanophotonic devices. However, it is challenging to design patterns with nanoscale features due to dispersion effects. We consider the propagation of a helium matter-wave through different holes in hexagonal boron nitride and use a quantum-mechanical model to calculate the van der Waals dispersion coefficients of edge atoms surrounding the holes. We find that the resulting diffraction patterns are affected by the shape and size of the holes, where the smallest holes have a radius of just 6 Å. These results can be used to predict the resolution limits of nano-hole patterns on nanophotonic materials.