The Interaction Of The Electromagnetic Wave And The Surface Plasmons In The Low Dimensional Solid

Along with the development of the electromagnetic metamaterials, the surface plas-mons retrieve much more attention due to their potential applications, especially for the study of the surface plasmons associated with the metamaterials in recent years. Started with the fundamental principles and the properties of the surface plasmons, we investigate the responses of the eigen modes to the incident waves in detail. Furthermore, the interac-tion between the surface plasmon and the incident wave has been analyzed by the attenuated total reflectivity (ATR) technique. We present the physics factor and the mechanism influ-encing the reflectivity. Beside, we discuss the impacts of the temperature on the dispersion relations based on the analysis forms at the absolute zero.In the first part of this thesis, we demonstrate the eigen modes on the interfaces of the electromagnetic metamaterials and calculate the ATR spectra. The contents and the conclusions are presented as follows:Firstly, the eigen modes on the semi-infinite metamaterial are studied. All the results show that the interfaces associated with metamaterial can support the surface plasmon po-laritons, which are excited by p- or s-polarized incident waves (i.e.TM or TE modes). The propagating properties are dependent on the coefficients of the metamaterial. Moreover, the surface plasmon polaritons not only propagate in the frequency regions of the stop-bands, but also propagate in the pass-bands of the metamaterial, which is different from metal. The dispersion relations may become two branches with lower and higher frequency, respec-tively. After that, using the ATR spectra, the coupling between the incident waves and the surface plasmons are detail discussed. Then, several factors contributed to the coupling are calculated and analyzed. When the matching conditions are satisfied, the incident waves couple with the surface plasmons and the coupling strengths are influenced by the thickness of the middle layer or the damping of metamaterial. However, the incident angle and the fractional ratio of the unit cell occupied by the interior of the split ring in metamaterial will affect the coupling frequency and the coupling strengths.Secondly, we calculate the eigen modes on the upper and lower interface of the mate-material slab with finite thickness. The coupling of the eigen modes for the symmetry and antisymmetry case are given successfully. We point that the interactions decrease with the increasing thickness of the slab, which will evolve into the case of the semi-infinite when the thickness is large enough. Similarly, the ATR spectra dependent on the thicknesses of the air and the slab are presented. We conclude that the thickness of the air influences the cou- pling strength without changing the coupling frequency, whereas the slab thickness effects the coupling strength and frequency simultaneously.In the second part of this thesis, based on the free electrons system, we discuss the influence of temperature on the Lindhard function and the dispersion relations. Firstly, at the absolute zero, the analysis forms of Lindhard function are derived for different dimensions (three dimension two dimension,one dimension). Secondly, we calculate the change of Lindhard and the dispersion numerically. At the same time, the explanations are presented. We find that the influence of temperature is correspond to the Fermi wavevector (or the Fermi Temperature), which does not change the relation between frequency and wavevector. At the limit of small wavevector, the dispersion relations near the room temperature are close to the zero one with the increasing temperature when the Fermi wavevector is larger. However, the tendency is contrary when the Fermi wavevector is smaller.