PhD Comprehensive Exam | Kamran Akbari, Energy Losses and Radiation in Interaction of Relativistic Charged Particles with Layered Nano-structures

MC 6460

Candidate

Kamran Akbari , Applied Mathematics, University of Waterloo

Title

Energy Losses and Radiation in Interaction of Relativistic Charged Particles with Layered Nano-structures

Abstract

The study of the interaction of relativistic charged particles with matter at the nano-scale is important since it is at the core of many problems in Electromagnetic Theory, Condensed Matter Physics, Nano-science and Technology, Mathematical Physics, Electrical Engineering, and Material Science. One of the most import configurations for such interactions arises in the context of electron-energy-loss spectroscopy (EELS) of nano-meter sized specimens within transmission electron microscope.

Investigation of the optical characteristics of two-dimensional (2D) electron systems, such as excitation of surface plasmons in graphene by swift electrons, has been performed in recent years by means of the EELS. In my study, I aim to theoretically model and analyze such interactions in layered nano-structures containing 2D materials, such as graphene, phosphorene, and other materials. Particularly, I focus on the optical characteristics of those interactions and draw conclusions for their applications in Nano-Photonics.

I present a fully relativistic formulation of the energy loss of a charged particle traversing a number of graphene layers. In particular, a decomposition of the energy loss into transition radiation and plasmon excitation is shown to uphold the energy conservation. I further improve the model to consider a more general case in which the 2D material under study has tensor conductivity and is probed by an electron with an arbitrary angle incidence. In order to consider the presence of dielectric regions and the resulting effects, like Cherenkov radiation and transition radiation coming from the inhomogeneity of the medium, I improve the mathematical formulation by introducing a dyadic Green’s function (DGF) for layered media. Having formulated the DGF problem, I delve into the problem of a rough boundary between dielectric regions. Finally, I propose several short and long term goals for future research.