Finite Difference Time Domain Method For Complex Materials And Its Implementation

With the high-speed development of the computer performance, the finite difference time domain(FDTD) method whose numerical simulation is the most complete and the most essence for electromagnetic field problems has increasingly received attention. Based on the analysis of the principle of finite difference time domain method and MIT open source software MEEP, we study how to modify source code to add the function of simulation magneto-optical medium, active material and Raman nonlinear dispersive media.By studying the error of using difference instead derivative in chapter two, we find that the central difference is more precise. We discuss the Maxwell’s equations with magnetic charge and magnetic current. Then, this thesis introduces the Yee difference grid, describing the position of electric field and magnetic field in the grid, and the updating step in time. Finally, we derive the update formula of magnetic field intensity and electric field strength by disceting the Maxwell’s equations.Study the unidirectional boundary mode along magnetic domain-wall in magneto-optical medium under reversed external magnetic field in chapter three. Then according to the off-diag elements of magneto-optic material’s permeability or permittivity is imaginary number, we discuss how to modify the code to add the simulation of magneto-optical materials. Finally, we verify the unidirectional boundary mode along magnetic domain-wall in magneto-optical, and analyze the impact of parameters to unidirectional boundary mode.The active material relates to energy level transition. This thesis describes the rate equation theory of atomic energy level transition in chapter four. And then analyse the method of combining the auxiliary differential equations(ADE) with the rate equations to update the polarization. Finally we discuss how to add interface of the new class in the CTL file, and use an example to test the modification.Finally we discuss the Raman nonlinear dispersive media in chapter five. The thesis introduces spontaneous Raman scattering and stimulated Raman scattering. We discuss the Lorentz dispersion model as a reference. Then, we combine the auxiliary differential equations(ADE) with FDTD method to deduce the update formula of polarization. Based on the results, we discuss how to add a new class including the storage of variables and update function, and use an example to verify the modification.