Semi-analytical FDTD modeling of axisymmetrical and periodic structures

A finite-difference time-domain method (FDTD) has become an essential tool in the modern engineering and scientific research from RF through THz technology up to optical spectrum. Among many other reasons, it follows from great flexibility as well as competitive computational requirements of the FDTD method when compared to other numerical modeling methods. Nevertheless, market demands are always well ahead of the current computational horizons of the classic FDTD method, prompting development of semi-analytical numerical methods that enable modeling of the most challenging electromagnetic (EM) applications. As an example of those continuing trends, we will recall semi-analytical FDTD solutions for axisymmetrical and periodic structures, both widely addressed in the literature and solvable by the commercial EM simulation tools. It will be shown that a tremendous cut of required computational resources is achievable when the FDTD method is supported by appropriate analytical solutions. Several application examples, like cylindrical corrugated horn antenna, Cassegrain reflectors, photonic crystals and micro-structured telecommunications fibers, will be presented.