A selective review of high-frequency techniques in computational electromagnetics

Solution to high-frequency electromagnetic problems require increased computational resources if ldquoexactrdquo numerical techniques such as finite difference time domain (FDTD), finite element methods (FEM), or, the method of moments (MoM) with free-space Greenpsilas function, are used. These approaches require discretization of the entire structure into cubic cells of sizes between lambda/10 and lambda/20 , with still finer gridding near source and material interface regions. This process yields accurate results, but consumes computational resources directly proportional to the electrical size of the problem. An alternative to such exact approaches is the access to, and application of, analytical techniques that have the potential to generate better-than-acceptable answers in these high frequency regions. These special class of techniques, developed from the principles of quasi- or ray-optics and their sophisticated extensions, have found extensive applications for a wide variety of problems. Notable amongst a class of ray-optic analysis methods are: uniform theory of diffraction (UTD), physical theory of diffraction (PTD) and the spectral theory of diffraction (STD). A common interesting feature is that the computation time is inversely proportional to the electrical size of the problem and thus serves to complement the exact approaches. Additionally, due to the nature of these quasi- or ray-optic methods, the dominant contributors to the complete solution can be realized in terms of ldquoraysrdquo that provide deeper physical insight into the various electromagnetic interaction mechanisms. In this exposition, the early experimental work on light scattering by perfectly conducting circular cylinders, and mathematical foundations of the state-of-art ray-optic methodologies are comprehensively reviewed. The versatility of the high-frequency, ray-optic techniques will be exemplified through some select numerical examples from the NEC-BSC version 4.2 (numerical electromagnetics code - basic scattering code), that employs the UTD formulations. Recent research topics associated with the present high-frequency methods, such as the Stokes phenomenon, complex rays, hybrid ray-mode methods are discussed, followed by an extensive list of references.