Faster and More Accurate Time Domain Electromagnetic Simulation Using Space Transformation

Abstract

A novel finite difference time domain (FDTD) method based on space transformations is developed that overcomes the inherent obstacles of the conventional FDTD algorithm in a spatially complex domain. Our method leads to an adaptive mesh for the investigated structure based on its geometrical shape without adding additional numerical problems such as late-time instability. In this method, mesh boundaries can follow arbitrary geometrical shapes precisely meaning that discretization errors are minimized. Such errors can be considerable when dealing with large material differences or boundary conditions within the simulation domain. Different meshing and transformation techniques for a variety of different scenarios are presented. We show how boundaries discontinuity can be handled using our method without resulting artificial singularities or zeros. Unlike previous works no dispersive medium has been used so the simulation speed is similar to the standard FDTD method. The usability and superiority of this method in terms of simulation run time and accuracy are shown through a couple of scattering and plasmonic problems. Also, the result of any simulations are validated using finite element method.

Keywords

• Transformation optics
• plasmonic
• waveguide
• FDTD
• SERS