An improved unconditionally-stable six-stages split-step FDTD method with low numerical dispersion

An improved unconditionally-stable six-stages split-step finite-difference time-domain (FDTD) method based on the split-step scheme and Crank-Nicolson scheme is presented, which provides low numerical dispersion. Firstly, along the positive and negative of the x, y, and z coordinate directions, the matrix derived from the classical Maxwell´s equations is split into six sub-matrices. Simultaneously, three controlling parameters are introduced to decrease the numerical dispersion error. Accordingly, the time step is divided into six sub-steps. Secondly, the analysis shows that the proposed method is unconditionally stable. Thirdly, the process of obtaining the controlling parameters is shown. Furthermore, the error of the numerical dispersion can be decreased significantly. Finally, numerical experiments are presented to substantiate the efficiency of the proposed method.