Numerical modelling of optical biosensors

Resonant optical biosensors have recently become an important tool for bioscience research and drug discovery.

This project aims to develop an efficient modelling technique for quantitative description, analysis, and optimisation of advanced biosensors beyond the state of the art, based on optical resonances of dielectric micro- and metal nano-particles. This technique will employ a novel theoretical method in electrodynamics, the resonant state expansion (RSE), which we have recently invented and verified. The RSE uses the resonances of a system. These are a fundamental and powerful concept in physics, dealing with a countable number of states and thus offering a natural discretisation of the properties of the system. This is in contrast to the artificial grid used in other methods in order to discretise the material continuously distributed in space.

In optical systems, resonant states (RSs) are eigen-solutions of the Maxwell equation having outgoing wave boundary conditions. Their energies are generally complex, reflecting the fact that the excitations of the system decay in time, leaking to the environment. As a consequence of this leakage, RSs are characterised by exponentially growing tails outside the system that requires a modified normalisation.

Activities

We have applied the RSE to calculate the RSs in finite 1D and 2D systems, such as perturbed planar and cylindrical resonators. The method was shown to be particularly suited for the calculation of sharp resonances, such as WGMs in microcylinders and microspheres, where popular computational techniques, such as FDTD or finite element method (FEM) fail or need excessively large computational resources. An example of the RSE calculation of the WGMs in a dielectric microcylinder with a scattering wire inside is shown in Fig. 1, demonstrating the quality of the RSE versus exact solution and the best available calculation using COMSOL.

We have recently extended this application to 3D systems with arbitrary perturbations, taking into account the mixing of TE and TM polarisations of light, and demonstrated the accuracy and convergence. We have also demonstrated that the RSE method is suited to calculate accurately and efficiently changes of the frequency and the linewidths of the resonances due to a small perturbation, such as the analyte of a biosensor. The novel technique based on the RSE will be able to overcome limitations of presently available numerical tools.