Investigation Of FDTD Methods For Chiral Medium

The interaction of electromagnetic waves with different materials has been an active area of research for many years, and chiral material is one of the research objects. There are magnetoelectric coupling terms in the constitutive equations of chira media. Because of these terms, the polarize plane of linear polarized wave propagated in it will rotate, which leads to the application of chiral media in many important aspects in the microwave field. However, with these coupling terms, the traditional FDTD method can no longer be used to model chiral media unless approximation schemes or some other methods are used to deal with them. Fortunately, this problem is skillfully solved recently by using the Double-gird scheme proposed for bi-isotropic media. Based on this scheme, the dissertation studies FDTD methods for nondispersive chiral meida. The main contents are as follows:1. Introduction of the basic knowledge about FDTD method. In this section, the research history and the basic knowledge of FDTD are reviewed. Three kinds of unconditionally stable FDTD methods, which are the ADI-FDTD based on the alternating direction implicit algorithm, the CN-FDTD based on the Crank-Nicolson algorithm and the LOD-FDTD based on the locally one-dimensional algorithm, are introduced in detail. In addition, an introduction of the programming technique of Mur absorbing boundary condition is also given in the unconditionally stable method.2. The study of single frequency FDTD methods for one dimensional chiral media. In this section, three kinds of method for modeling chiral media are proposed. They are simple leapfrog FDTD algorithm based on traditional Yee grid, an unconditionally stable method similar to alternating direction implicit (ADI) FDTD, and a similar locally one dimension (LOD) FDTD method characterized by analytical solution based on Double-grid scheme. The unconditionally stable FDTD methods proposed in this dissertation are different from those in isotropic media. These algorithms are characteristic of regarding the two sections on the right side of the resulting equations as two directions, thereby a one dimensional problem in actual is equivalent to a two dimensional problem, and then we implement unconditionally stable algorithm to this effective two dimension problem. This is the reason why we call these methods "similar unconditionally". One time step of the LOD-like method characterized by analytical solution is divided into two sub time steps. One step is iteratived according to FDTD, and the other step is iteratived by analytical solution. These methods are verified numerically through the computation of the rotation angles of the polarization when a linear polarized wave propagates in a homogeneous chiral media and through a chiral slab respectively. As to the unconditionally stable methods, we also present the theoretical demonstration of unconditional stability.3. The study of multiple frequency FDTD methods for one dimensional chiral media. In this part, we propose a simple leapfrog algorithm and a LOD-like method, based on the Double-grid scheme. The ADI-like method reported in literature is also introduced. Apart from the demonstration of the unconditional stability of LOD-like method and ADI-like method, we still validate these methods by simulating the transmission and reflection coefficients of a chiral slab, a PEC backed chiral slab, and multiple chiral condition. Compared with the ADI-like approach, the LOD-like approach is characterized by lighter calculation burden and higher accuracy. Additionally, the issue of applying the dispersion Mur absorbing boundary condition to terminate chiral media is also proposed and validated in this section.4. The study of multiple frequency FDTD methods for two and three dimensional chiral media. In this part, a simple leapfrog algorithm and a LOD-like method based on the Double-grid scheme are proposed, and the leapfrog method is validated by simulating the reflection coefficient of waveguides partially filled with chiral media. We also propose and validate the method of implementing the PEC boundary by adding a mirror layer in the condition of Double-gird.