Within the framework of the finite-difference time-domain (FDTD) and the weighted Laguerre polynomials (WLPs), we derive an effective update equation of the electromagnetic in the dispersive media by introducing the factorization-splitting (FS) schemes and auxiliary differential equation (ADE). As two examples, we employ a 2-D parallel plate waveguide loaded with two dispersive medium columns and a thin grapheme sheet to calculate the plane wave propagation by using the FS-ADE-WLP-FDTD method. Compared with the ADE-FDTD and the ADE-WLP-FDTD methods, the results from our proposed method show its accuracy and efficiency for dispersive media simulation.
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