In this paper, we propose a new technique for the transient scattering problem of periodically arrayed dispersion media for the TE case by using a combination of the Fourier series expansion method (FSEM) and the fast inversion Laplace transform (FILT) method, and analyze the pulse response for various widths of the dispersion media. As a result, we clarified the influence of the dispersion media with an air region on the resulting waveform.