Hybrid Method of combined difference and spectrum for time-domain maxwell’s equations

Abstract

For the finite-difference time domain (FDTD) method, the electromagnetic scattering problem, which requires the characteristic structure size to be much smaller than the wavelength of the exciting source, is still a challenge. To circumvent this difficulty, this paper presents a novel hybrid numerical technique of combined difference and spectrum for time-domain Maxwell s equations. With periodical continuation of each time-dependent quantity in Maxwell s equations, the solutions before and after the continuation remain consistent in the first period, which results in the conversion of the continuous spectrum problem to a discrete one. The discrete spectrum of the field after continuation is obtained from difference methods for Maxwell s curl equations in frequency-domain, and the time domain solution of the original problem is derived from their inverse Fourier transform. Due to its unconditional stability, the proposed scheme excels FDTD in resolving the aforementioned problems. In addition, this method can simulate dispersive media whose electric susceptibility cannot be expressed with Debye or Lorentz types of models. In dealing with boundary conditions, it can utilize the perfectly matched layer (PML) without extra codes. Numerical experiments demonstrate its effectiveness, easy implementation and high precision.