One of the fundamental charge distributions for which an analytical expression of the electric field can be found is that of a line charge of finite length. Nevertheless, the result we will encounter is hard to follow. Two limiting cases will help us understand the basic features of the result.

Research article by: Surendra B. Anantharaman, Kiyoung Jo, and Deep Jariwala

Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, 19104, USA

Abstract: Semiconductors in all dimensionalities ranging from 0D quantum dots and molecules to 3D bulk crystals support bound electron-hole pair quasiparticles termed as excitons. Over the past two decades, the emergence of a variety of low-dimensional semiconductors that support excitons combined with advances in nano-optics and photonics has burgeoned a new area of research that focuses on engineering, imaging, and modulating coupling between excitons and photons, resulting in the formation of hybrid-quasiparticles termed exciton-polaritons. This new area has the potential to bring about a paradigm shift in quantum optics, as well as classical optoelectronic devices. Here, we present a review on the coupling of light in excitonic semiconductors and investigation of the unique properties of these hybrid quasiparticles via both far-field and near-field imaging and spectroscopy techniques. Special emphasis is laid on recent advances with critical evaluation of the bottlenecks that plague various materials towards practical device implementations including quantum light sources. Our review highlights a growing need for excitonic materials development together with optical engineering and imaging techniques to harness the utility of excitons and their host materials for a variety of applications.

To have a certain solution at hand is often useful construct another one out of it. This is the case for the electrostatic potential and field of the charged ring that can be generalized to the homogeneously charged disk and cylinder. Find out how to calculate the solutions on the axis of symmetry.