The resonant state expansion (RSE) is a new powerful theoretical method in electrodynamics and wave optics, recently invented in Cardiff. Being applicable to a very broad variety of electromagnetic problems, it is particularly suitable for treating modes in open optical resonators, such as semiconductor microcavities and micropillars, dielectic microcylinders and microspheres, which have ultra-high quality modes in their spectra, often called whispering gallery modes (WGMs). Some novel applications of WGMs include photonic cavity microlasers and resonant optical biosensors - both will be in the focus of this research project. One of the aims of the project is to apply the RSE to cylindrical and spherical optical resonators (working as biosensors) with attached nanoparticles/molecules (analytes) perturbing their WGMs and modifying their spectral properties. The scattering amplitudes of ideal and perturbed microcylinders and microspheres will be calculated using the Green’s function of the open system and its spectral representation. Then, more complicated systems with perturbations, close to realistic biosensors in use, will be considered. Another task of the project is to use the RSE as a double-step perturbation theory in order to calculate optical modes in resonators with defects. This will include rather complicated resonators, such as micropillars, in which the modes cannot be calculated exactly by any known computational methods, even without defects. The idea of the double-step RSE is to use an analytically treatable and relatively simple ideal spherical resonator as a starting point for the RSE and calculate the modes in an ideal micropillar first. Then, introducing a defect in the ideal pillar, treat this defect as a perturbation in the second step. Such defects fabricated in resonators are very important for their microlaser applications, as they provide a tool to control the emission properties of particular modes. Finally, the project may include application of the RSE to fibre optic cables and photonic crystal structures for which the theory requires certain modifications and further generalisation.
This project is available for self-funded or sponsored students only.