Madelung formalism approach for non-local nanoplamonics

• Main Author: Azinheira Alves, Rúben
• Format: Dissertation
• Language: English
• Published: University of Birmingham 2022
• Subjects: QC Physics

The main focus of this thesis is to provide an insight on modelling plasmonic systems. The recent advent of new fabrication techniques have pushed plasmonic systems further and further into the nanoscale. However, on one hand, the extreme confinement of plasmons can force them to exhibit some quantum properties that classical and macroscopic modelling of such systems simply fails to capture. On the other, plasmonic system are typically of the size that quantum models such as density functional theory, to give an example, are impractical due to the large number of interactions that need to be addressed. The more practical solutions is then the development of semi-classical models that keep the simplicity of the macroscale while addressing some of the quantum behaviour of plasmons. In this thesis, I start by describing a classical, but valuable, tool to obtain the response of plasmonic systems analytically, called transformation optics. Then, I present a variation of the popular hydrodynamic Drude model, where I replace the fluid equations and their need for additional boundary conditions with a non-linear Schrödinger equation using the Madelung formalism. In order to prove that this new interpretation is valid, I push the non-local, non-linear Schrödinger equation into its linear and local limit and compare the results with full wave simulations and transformation optics. Then, I introduce a super-Gaussian potential into my equation in order to introduce heuristically electron spill-out non-locality and compare the results with a popular non-local model readily available in the literature. With this comparison I am able to devise a fitting parameter and show that it is invariant on small changes of the geometry. With this proposed methodology, I was able to include the electron spill-out heuristically in a simple and modular method.