Electromagnetic Simulation Using the FDTD Method

Preface ix Guide to the Book xi 1 One-Dimensional Simulation with the FDTD Method 1 1.1 One-Dimensional Free Space Simulation, 1 1.2 Stability and the FDTD Method, 5 1.3 The Absorbing Boundary Condition in One Dimension, 5 1.4 Propagation in a Dielectric Medium, 7 1.5 Simulating Different Sources, 8 1.6 Determining Cell Size, 10 1.7 Propagation in a Lossy Dielectric Medium, 10 1.A Appendix, 13 References, 14 2 More on One-Dimensional Simulation 21 2.1 Reformulation Using the Flux Density, 21 2.2 Calculating the Frequency Domain Output, 24 2.3 Frequency-Dependent Media, 27 2.3.1 Auxiliary Differential Equation Method, 30 2.4 Formulation Using Z Transforms, 32 2.4.1 Simulation of Unmagnetized Plasma, 33 2.5 Formulating a Lorentz Medium, 36 2.5.1 Simulation of Human Muscle Tissue, 39 References, 41 3 Two-Dimensional Simulation 53 3.1 FDTD in Two Dimensions, 53 3.2 The Perfectly Matched Layer (PML), 56 3.3 Total/Scattered Field Formulation, 65 3.3.1 A Plane Wave Impinging on a Dielectric Cylinder, 67 3.3.2 Fourier Analysis, 70 References, 71 4 Three-Dimensional Simulation 85 4.1 Free Space Simulation, 85 4.2 The PML in Three Dimensions, 89 4.3 Total/Scattered Field Formulation in Three Dimensions, 92 4.3.1 A Plane Wave Impinging on a Dielectric Sphere, 92 References, 96 5 Examples of Electromagnetic Simulation Using FDTD 113 5.1 Nonlinear Optical Pulse Simulation, 113 5.2 Finding the Eigenfunctions of a Two-Dimensional EM Cavity, 120 5.3 Simulation of RF Coils, 127 References, 136 6 Quantum Simulation 151 6.1 Simulation of the One-Dimensional, Time-Dependent Schrodinger Equation, 151 6.2 Tunneling, 156 6.3 Why Semiconductors Have Energy Bands, 157 References, 160 Appendix A The Z Transform 169 A.1 The Sampled Time Domain and the Z Transform, 169 A.1.1 Delay Property, 172 A.1.2 Convolution Property, 172 A.2 Examples, 174 A.3 Approximations in Going from the Fourier to the Z Domain, 176 References, 178 Index 179