An improved unconditionally-stable FDTD method based on the split-step scheme with low dispersion

An improved unconditionally-stable finite-difference time-domain (FDTD) method based on the split-step scheme is presented, which provides low numerical dispersion. Firstly, symmetric operator and uniform splitting are adopted to split the matrix derived from the classical Maxwell´s equations into four sub-matrices. Simultaneously, two controlling parameters are introduced to decrease the numerical dispersion error. Accordingly, the time step is divided into four sub-steps. Secondly, theoretical proof of the unconditional stability is given. Thirdly, the process of obtaining the controlling parameters is shown. In addition, the error of the numerical dispersion can be decreased significantly. Finally, numerical experiments are presented to substantiate the proposed method.