Analysis Of Mesoscopic And Microcosmic Physics Based On FDTD Method

FDTD algorithm has always been an important subject in the field of computational electromagnetics research. Studies done previously were mostly focused on improving the algorithm itself, and achievements made have been demonstrated as guidance both in the actual production and engineering applications. However, with the further development of electromagnetics, new phenomena cannot be described just using Maxwell equations. FDTD algorithm needs to be used in a broader area. The trend is consistent with the prosperity of interdisciplinary sciences as well. Bases on the above description, several new attempts to expand the application of FDTD algorithm have been made, which can solve typical problems in the macroscopic, microscopic and microcosmic areas.The main contributions of this thesis are described as follow:1. The research background, evolution, principles and key technologies of the FDTD scheme are presented.2. Electromagnetics scattering computations are reproduced correctly. RCS, which is considered an important physical value, is obtained by using the FDTD method. The numerical results prove the effectiveness of the method.3. Semi-classical theory, which is regarded as theoretical foundation of the laser physics,is a combination of macroscopic electromagnetic theory and microscopic particle the-ory. The model and concept of the laser physics is based on the above theory. Using the advanced numerical algorithm to simulate the laser process is considered as a new attempt in the electromagnetic field beyond microwave band. We use Four-energy-level atomic system to model the gain media, which is the subject in our experiments. The FDTD method is applied to solve three groups of coupled Maxwell’s equations, the rate equations and electric polarization equation. Meanwhile, three pump mech-anisms, i.e, gaussian pump, homogenerous pump and optical pump, are presented for a thorough analysis. The results show good agreement with lasing theories and our numerical model can be used as an efficient tool for follow-up studies. 4. Random is a fantasy concept. After the fundamental research on gain media, model of the two-dimensional random laser is formed. The polarization property, threshold feature and saturation characteristic are investigated. Finally, atomic spontaneous emission of the one dimensional laser is simulated.5. Problems in the microscopic field involving the solution of the schrodinger equation and the simulation of the nano-scale structure are studied. We start from the FDTD method, combine the critical technique used in the electromagnetic computations, and do research on the classical problem in quantum mechanics. Then a high order and sympletic scheme are applied to quantum simulations. It is found that the FDTD method is an effective tool for microscopic simulations.