Difficulties faced by Yee’s scheme in photonics problems

Abstract

Abstract Popular Yee’s scheme for the FDTD method faces a number of difficulties for problems in layered media: if dielectric permittivity is discontinuous, the accuracy strongly deteriorates, if magnetic permeability is also discontinuous at the same points, the scheme does not allow to perform computation. We provide rigorous mathematical explanation of these difficulties and show them to have fundamental nature. For problems involving dielectric media interfaces, we propose technique allowing to improve the accuracy.