Electromagnetic Simulation Using the FDTD Method (eBook)

DENNIS M. SULLIVAN is Professor of Electrical andComputer Engineering at the University of Idaho, Moscow. Anaward-winning author and researcher, he has done extensive work inseveral areas of simulation, including EM dosimetry, hyperthermiacancer treatment, nonlinear optics, and quantum semiconductors. In1997, Dr. Sullivan won the R. P. W. King Award from the IEEEAntennas and Propagation Society for the "Best Paper by a YoungInvestigator" for his paper "Z Transform Theory and FDTD Method."He is an IEEE Fellow, and is also the author of QuantumMechanics for Electrical Engineers, published by Wiley-IEEEPress.

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