The finite difference time domain method for computational electromagnetics

Three computer programs are presented in this dissertation. The first one is a onedimensional (1D) program, simulating a sinusoidal signal propagating along the xaxis. The second one is a two-dimensional (2D) program, simulating radiation from a narrow slit. The third one is also a 2D program, which is a simulation of a Time Domain Reflectometer (TDR) probe. A graphical user interface (GUI) is included in the 1D program, which makes the computer program user-friendly. A flowchart with details is included in the appendices. When applying FDTD to problems where solution regions are unbounded, difficulty arises. Since no computers can store unlimited amount of data, it is necessary to somehow, limit the solution regions. Mur’s first-order absorbing boundary condition (ABC) is a method to achieve this. The derivation of Mur’s ABC is given in details in Chapter Four, and implemented in the 1D program. This program serves as an introduction to FDTD. The 2D program simulating radiation from a narrow slit has two interesting aspects. The perfectly matched layer (PML) is expected to absorb all electromagnetic (EM) waves. No EM waves are supposed to pass through a perfect electric conductor (PEC). Surprisingly, EM waves do penerate through the connecting points between PEC and PML. The reason and solution for this ‘leakage’ are given in this dissertation. Also one might find it a bit confusing to observe that in this program, the x-component of electric field seems to be propagating along the y-direction. The clarification is given in this dissertation. TDR can be used to measure the amount of moisture in soil. In the TDR program, it is required to simulate a 2D model of a TDR probe of given geometry, and to specify the time constant of a raised cosine function. A plane wave using the raised cosine function is then introduced into the TDR probe