The Dispersion Relations And Application Of Plasmons In Solid

The collective description is the essential way to analysis the properties of this electrons system, and the corresponded plasmon collective excitation is the keystone in physics. One important aspect is the response of electrons system, which can exist in solid, to external electromagnetic wave. Evidently, the longitudinal component corresponds to the rearrangement of electronic charge, whereas the transverse component is related to the induced electrical currents based on the group of Maxwell's. Longitudinal plasmon is the quantum of the collective excitations of free electrons, and also is the central object of this text. Experimental and theoretical studies of plasmons have mainly focused on the excitation energies and dispersion relations. In this thesis, we start with self-consistent field approximation, combined the second quantum suppose, then derive the expression of lindhard function in different dimensions and calculate the dispersion relation of the longitudinal plasmons detailedly.There are many means to study the dispersion relation of plasmons, which can be found in the first chapter. However, two and one dimensional systems have unique properties , which is different from three dimensional systems, because the effect of dimension is very different. In the second chapter of this thesis, we discuss the oscillation of electron density induced by external electromagnetic wave in different systems, and calculate the dispersion relation of the longitudinal plasmons with the Lindhard dielectric function in the long-wavelength and high-frequency limits, and analysis the physics significance and comparing to the result with hydrodynamical description.Some application and development of plasmon that can be find in the third chapter, emphasize particularly surface plasmon (quasi-two dimensional electron system),including basic properties and application. According to our following work, we introduce negative index materials briefly and current status. Pendry et al designed the periodic metal wires and split-ring-resonators structure using effective dielectric constant and permeability, producing negative dielectric and permeability, which make negative materials to be a hotspot. Meanwhile, plasmonic is gradually to be an absolute subject and it's future prospects in various applications including plasmonic chips, light generation, and nanolithography.