EM diffraction modeling with numerical methods

Electromagnetic scattering theory is crucial to understand interaction of electromagnetic waves with objects and medium in which it propagates. Scattering fields are formed primarily by reflected, refracted and diffracted fields. There are also other wave phenomenon such as creeping waves, whispering-galley waves, etc. but all these phenomenon are formed by the interaction of reflected, refracted and diffracted fields. Each scattering phenomenon should be considered carefully in the design of electronic devices. For example, warplane designer should minimize radar cross section (RCS) by avoiding reflective surfaces that may direct incoming radar wave towards radar receiver. Another example is that, today's electronic circuits contain so many components and conductive traces. Unwanted incoming radiation can reach critical components by being subjected to various scattering mechanisms. Therefore, EMC engineers should protect important parts of the devices by applying shielding techniques. As a final example, mobile phone designers should control the electromagnetic energy radiated towards human head to reduce specific absorption rate (SAR) value. This is accomplished by covering the back side of mobile phone with specific materials e.g. perfect electric conductor (PEC) materials. All these applications require extensive knowledge on scattering theory. Reflection and refraction phenomenon has long been analyzed via well-known Snell's law. On the other hand, diffraction is much more difficult to analyze. There is no simple formulation to analyze diffraction. Exact solutions of diffracted fields are only known for a limited number of geometries such as wedge, sphere, and cylinder. In addition, these solutions are generally in the form of infinite series that are slowly convergent at high frequencies (i.e. when the wavelength is very small compare to the object size). Hence their applicability is limited. High frequency asymptotic (HFA) methods such as geometric theory of diffraction (GTD) and physical theory of diffraction (PTD) are developed to overcome this difficulty. These methods are derived from the exact solution of the problem and can be used to analyze diffraction mechanism at high frequencies. With today's high speed modern computers, it is also possible to analyze diffraction phenomena numerically. Numerical methods such as finite difference time domain (FDTD), method of moments (MoM) and finite element method (FEM) can be used for this purpose. These methods are used in broad range of frequencies and the upper frequency limit depend on the computer's resources. In this dissertation, we advanced the numerical diffraction theory by proposing three novel time domain based diffraction models: double tip diffraction model (Chapter 3), soft-hard strip diffraction model (Chapter 4) and time domain fringe current model (Chapter 5). In double tip diffraction model study, we obtained diffracted fields around 2D rectangular object for various incidence angles and rectangle thicknesses with FDTD method. The verification is performed with MoM model. In soft-hard strip diffraction model study, diffracted fields around a 2D canonical strip geometry with one face hard and the other face soft boundary condition (BC) is obtained with FDTD method. The model is verified with existing MoM solution. Finally in time domain fringe current model, we obtain fringe currents that are induced on 2D wedge geometry that is illuminated by a line source. We then calculate fringe waves radiated by fringe currents and verified proposed model with existing PTD and MoM solutions.