Improvement Of Finite-Difference Time-Domain Algorithm And Its Application In Modeling Quantum-Electromagnetic Multiple Physical Fields

In recent years,with the rapid development of modern electronic technology,the characteristic size of integrated circuits and components has been reduced to nanometer level,and the capacity of storing and processing information per unit volume has been improved by a million times,which greatly improves the performance of the miniaturized and intelligent computers.However,the quantum effect in high integrated system and electromagnetic structure are gradually prominent,and the modeling scheme based on the classical electromagnetic theory has been unable to meet the design and simulation requirements of nano electronic equipment.Therefore,the multi physical field modeling and simulation of micro-quantum and macro-electromagnetic system has become an urgent scientific problem,particularly for developing the high-frequency,high-speed,broadband and multi-functional integrated electromagnetic components and chips miniaturization,which is also the core technical problem to be solved in nano electronics and information technology.The early theoretical research and commercial software are mostly based on the classical electromagnetic theory to simulate the nano electromagnetic system,in which the active,nonlinear and quantum properties of the quantum are simply replaced by the classical Hertz dipole.At present,some researchers have proposed to couple the Schrodinger equation or optical Bloch equation(describing the micro-quantum system)with the Maxwell equation or potential function equation(describing the macro-electromagnetic system)and study the multi physical field problems existing in the nano electromagnetic system.However,these coupled models are usually non-symplectic and using dipole approximation.The numerical results are not in good agreement with the experimental results.In addition,the electromagnetic equations based on potential function containing the higher-order partial derivatives in temporal and spatial domain simultaneously,which is difficult in numerical implementations.In addition to the modeling of quantum-electromagnetic coupling systems,the numerically solving the coupled equations is also the hot topics for the researchers.As a simple and universal numerical algorithm,the finite-difference time-domain(FDTD)algorithm,especially with the benefit of the rapidly developed computer performance,has been widely used in many engineering fields.For example,the design of circ uit,antenna,electronic device,the calculation of radar cross section of military targets such as shipboard aircraft and ships,medical electromagnetic imaging,biological tissue simulation and son on.The advantages of FDTD method are obvious,however this explicit algorithm discretized Maxwell equations by the second-order central difference,has low calculation accuracy and restricted time stability condition.This drawback has greatly limited the applications of the FDTD algorithm,especially for simulating the dispersive medium and the electromagnetic problem including the fine structure that needs fine mesh subdivision.In addition,if the calculation area contains multi-media areas(such as dispersion media area,perfectly matched layer area,etc.),different numerical iteration formula should be used to simulate different computation regions,which limits the flexibilities of the electromagnetic modeling method.In view of the limited application scope,complex formula,difficulties in numerical realization and disadvantages of traditional FDTD method,this thesis mainly focuses on the improvement of FDTD numerical algorithm,the construction of quantum electromagnetic multi physical field numerical model and the efficient and accurate numerical solution.The main innovations are listed as following:1.Based on the recursive integration(RI)method,a unified FDTD model for dispersion media and perfectly matched layer(PML)is proposed,which makes the iterative formula of electromagnetic field components in different calculation areas(including dispersion area and PML area)represented by the same discrete equation.In addition,the method has good compatibility with traditional FDTD code.This is because the electromagnetic component of the whole calculation area can be solved by the traditional formula,and then the electric field component in the dispersive media area can be modified by adding auxiliary variables directly.2.A high-order explicit spatial filtering symplectic FDTD(SF-SFDTD)method with controllable stability condition is proposed.The traditional SFDTD method can be extended by using the spatial filtering method.The CFL limitation of the SFDTD method can be released by discarding the unstable spatial harmonics at each field updated cycle.This approach provides an explicit SF-SFDTD method with controllable stability,which is much more easily to be implemented in the practical application compared with other implicit FDTD methods.Because it has the same updatin g formulas of the field components resembling the conventional SFDTD and only requires to execute the spatial filtering operation in each iteration.3.The potential function based electromagnetic equation and Schrodinger equation are combined to solve the multi-physical field problem.The symplectic framework of the coupled equation is constructed.The symplectic structure properties of the two subsystems are also proved,and the corresponding numerical solution method of SFDTD is also offered.The numerical simulation of the coupled equation is accurate,stable,efficient.4.A hybrid electromagnetic potential function equation with simple form,highly coupled field components(E,B,A,(37))and self-consistent solution are proposed.Then the equations are coupled with optical Bloch to solve the quantum electromagnetic multi-physical field problems.The particle in cell(PIC)method is developed to solve the spatial scale mismatch between the macro-electromagnetic system and the microquantum system.