The resonant-state expansion (RSE) is generalised to open optical systems with an arbitrary dispersion of the dielectric constant. In the non-dispersive case we use frequency independent refractive index, moving onto to cases which display dispersion. The RSE converts the Maxwell wave equation into a linear matrix eigenvalue problem in the basis of unperturbed resonant states, in this way numerically exactly finding all relevant eigenmodes of the optical system. The present generalisation is verified by applying it to the analytically solvable system of a spherical metallic nano-particle in vacuum, with the dispersion of the dielectric constant described by the Drude model and extended with the addition of Lorentz poles. Approximating the frequency dispersion of the permittivity of materials with simple analytical functions is of fundamental importance for understanding and modeling the optical response of materials and resulting structures. In the generalised Drude-Lorentz model, the permittivity is described in the complex frequency plane by a number of simple poles having complex weights, which is a physically relevant and mathematically simple approach: By construction, it respects causality and represents physical resonances of the material, and can be implemented easily in numerical simulations. We report here an efficient method of optimising the fit of measured data with the Drude-Lorentz model having an arbitrary number of poles. We show examples of such optimisations for metals and semiconductors, for different frequency ranges. We use this to produce accurate parameters for us to realistically simulate large perturbations starting from dielectric materials such as sand, to dispersive materials such as gold and gallium arsenide. We also analyse the evolution of surface plasmons in gold and use the RSE to perturb gallium arsenide into the gain threshold.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:768108 |
| Date | January 2019 |
| Creators | Sehmi, Hame |
| Publisher | Cardiff University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://orca.cf.ac.uk/119884/ |
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