The Time Domain Finite Difference Method Of Maxwell-Schrodinger Coupled System Based On Potentials Equations

Recent advances in technology have shrunk the length scales of electronic devices down to nanometers which are much smaller compared to optical wavelengths.Due to this miniaturization,the quantum effects are becoming more and more important in the simulation of the entire system.If only the classic Maxwell equation is considered in the simulation of electronic devices,it will bring great error.The simulation of system which contains charged particles and classical electromagnetic fields needs to consider the effects of quantum property.Hence,it is imperative to model the quantum effect of particles by solving the Schrodinger equation.In this paper,the Time Domain Finite Difference(FDTD)simulation of Maxwell-Schrodinger coupled system is deeply studied.The system is an effective tool for simulating and studying the interaction of electromagnetic radiation with charged particles in semi-classical systems.The traditional Maxwell equation is susceptible to low frequency collapse by solving the electric field and magnetic field,so this method is not suitable when the device size is much smaller than the electromagnetic wave wavelength.Based on this,a new method of applying vector magnetic position and scalar potential is proposed to replace the traditional Maxwell equation.This new method is more suitable for this system because it is stable in the low frequency range.The main research work of this paper is as follows:1.Introduced the FDTD method system of some basic theoretical knowledge.The formula of the potentials equations which are equivalent to the traditional Maxwell equation are derived to solve the electromagnetic problem,we call them A-? equations.And the A-0 equations are discretized and differentiated.2.The Perfectly Matched Layers(PML)technique and the Total Field and Scattered Field(TF/SF)technique of the A-? equations are discussed.And compared with the traditional Maxwell equation.3.The Schrodinger equation is studied based on the FDTD method.Two different discrete forms of the Schrodinger equation are discussed.The simulation of the open problem of Schrodinger equation is realized.4.The equations of the Maxwell-Schrodinger coupled system which are based on potentials equations are derived.And the equations are discretized and differentiated.The Sch;rodinger equation was modified with electromagnetic radiation in mind.The particle current term which couples the two equations is explained.The stability conditions of the coupled system are analyzed and derived.Finally,an artificial quantum dot is added for simulation.